Exercises in GCSE Mathematics Intermediate level. Robert Joinson. Sumbooks

Eercises in GCSE Mathematics Robert Joinson Sumbooks

Sumbooks Chester CH 8BB Eercises in GCSE Mathematics- First Published 997 Reprinted 998 Updated 00 Amended 00 Copyright R Joinson and Sumbooks This package of worksheets is sold subject to the condition that it is photocopied for educational purposes only on the premises of the purchaser ISBN 0 980

Preface This book covers the GCSE syllabi to be eamined for the first time in 00. It was written with year pupils in mind but can be used in year 0 for those pupils intending to do the higher papers at the end of year. Some areas have more questions than are needed for some pupils. Eercises on pages,,,,,, 6, 7, 8 and 0 contain lots of questions and are aimed at pupils requiring a great deal of practice. However the questions are graded and it might only be necessary for some students to do the first column and then each row when they begin to have problems. In general questions in the same row tend to be of the same difficulty, whereas the difficulty increases down the page. All graphs can be accommodated on A size graph paper used in 'portrait' mode. The answers to the questions on reflections, rotations, translations and enlargements can be drawn within the size of graph paper indicated in the question. I would like to thank my wife Jenny and my daughters Abigail and Hannah for all the help and encouragement they have given me in writing this. R Joinson August 00 Chester

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Contents Multiplication and Division Negative Numbers Use of the Calculator Estimation Fractions, Decimals and Percentages 6 Fractions, Decimals and Percentages 7 Interest 8 Scale Drawings and Ratio 9 Standard Form 0 Prime Factors Number Patterns and Sequences Number Patterns and Sequences Distance Time Diagrams Distance Time Diagrams Conversion Graphs 6 Conversion Graphs 7 Sketching and Recognising Graphs 8 Sketching and Recognising Graphs 9 Plotting Graphs 0 Plotting Graphs Substitution Simplifying Epressions Indices Multiplying Brackets Factorising 6 Equations 7 More Equations 8 Straight Line Graphs and Simultaneous Equations 9 Trial and Improvement 0 Inequalities Inequalities - Graphs Rearranging Formulae Bearings Parallel Lines Nets and Isometric Drawing 6 Triangles 7 Regular Polygons 8 Irregular Polygons 9 Pythagoras' Theorem 0 Trigonometry Trigonometry Trigonometry Trigonometry Reflections, Rotations and Translations Reflections, Rotations and Translations 6 Reflections, Rotations and Translations 7 Reflections, Rotations and Translations

8 Enlargements 9 Enlargements 0 Similar Shapes Locus Problems Locus Problems Degree of Accuracy Circumference of a Circle. Area and Perimeter 6 Volume 7 Compound Measure - Speed and Density 8 Compound Measure - Best Buy and a Mied Eercise 9 Formulae for Area, Volume and Perimeter 60 Formulae for Area, Volume and Perimeter 6 Questionnaires 6 Pie Charts 6 Frequency Polygons 6 Frequency Polygons 6 Mean, Median, Mode and Range 66 Mean 67 Mean 68 Mean - diagrams 69 Mean - Frequency distributions with class intervals 70 Mean - Histograms 7 Cumulative Frequency 7 Cumulative Frequency 7 Scatter Diagrams 7 Scatter Diagrams 7 Probability 76 Probability 77 Probability 78 Tree diagrams 79 Relative Frequency 80 Relative Frequency 8 Constructions 8 Simultaneous Equations 8 Using Simple Equations 8 Using Quadratic Equation 8 Surds 86 Recognising Graphs 87 Plans and Elevations () 88 Plans and Elevations () 89 Moving Averages 90 Recurring Decimals 9 Stem and Leaf Diagrams 9 Bo Plots

Sumbooks 00 Eercise Short division with or without remainders Multiplication and Division Do not use a calculator ) 7 7 ) 8 6 ) 9 8 ) 06 ) 8 9 6) 0 6 7) 7 8) 86 7 9) 97 0) 6 8 ) 9 ) 76 6 Eercise Long division with or without remainders ) 87 7 ) 96 ) 8 ) ) 76 6 6) 67 7) 8) 8 9) 96 6 0) 8 ) 6 ) 8 7 ) 8 ) 97 ) 67 6) 67 7) 8 8) 6 7 9) 8 0) 96 Eercise Division without remainders (answer in decimal form) ).0 ).0 ) 8 8 ) ) 0 6) 9 6 7) 88 8 8) 90 8 9) 8 0) 7 6 ) 7.6 ) 0 8 ) ) 8 8 ) 6) 6 8 7).7 8) 0. 9) 8.8 7 0) 8 Eercise Long multiplication ) 7 ) 8 9 ) 6 7 ) ) 86 6) 7 7) 6 7 8) 9) 6 7 0) ) 7 6 ) 7 ) 86 ) 8 6 ) 7 7 6) 86 7 7) 9 9 8) 76 9) 9 69 0) 9 7

Sumbooks 00 Negative Numbers Do not use a calculator Eercise Calculate the final temperature. ) ºC increases by 9ºC ) ºC falls by ºC ) ºC falls by ºC ) ºC increases by ºC ) ºC falls by 8ºC 6) 9ºC ºC 7) 8ºC ºC 8) ºC + ºC 9) 8ºC ºC 0) 6ºC ºC ) 7ºC + ºC ) ºC + ºC ) 0ºC 6ºC ) ºC ºC ) 6ºC + 6ºC 6) 7ºC 6ºC 7) ºC + 6ºC 8) 7ºC + 6ºC 9) 7ºC 9ºC 0) ºC + 7ºC Eercise What is the change in temperature between each of the following? ) ºC and 7ºC ) 7ºC and ºC ) ºC and ºC ) 7ºC and ºC ) 6ºC and ºC 6) 7ºC and 0ºC 7) ºC and ºC 8) 7ºC and ºC 9) ºC and ºC 0) ºC and 7ºC ) 8ºC and ºC ) 0ºC and ºC ) 7ºC and ºC ) 8ºC and 6ºC ) 9ºC and ºC 6) ºC and ºC 7) ºC and ºC 8) 6ºC and 8ºC 9) 6ºC and 0ºC 0) ºC and 0ºC Eercise In each of the following, write down the number represented by the? )? = )? = )? = ) 7? = 9 ) +? = 6) +? = 7)? = 7 8) +? = 9)? + = 0)? = )? = )? = )? + = 7 ) +? = 9 )? = 6) 7 +? = 0 7) 8 +? = 8) 0? = 6 9) +? = 6 0)? = Eercise ) Two numbers are multiplied together to make 0. One of the numbers is 6. What is the other? ) Two numbers are multiplied together to make 8. One of the numbers is 6. What is the other? ) Two numbers are multiplied together to make 60. The sum of the two numbers is. What are they? ) Two numbers are multiplied together to make. The sum of the numbers is 0. What are the numbers?

Sumbooks 00 Use of the Calculator Eercise Calculate each of the following pairs of problems. Predict the answers before you do them. ) + 8 and ( + 8) ) + and ( + ) ) 8 and (8 ) ) 0 6 and (0 6) ) 6 + and 6 ( + ) 6) 0 8 + and 0 (8 + ) 7) 6 + and 6 ( + ) Eercise ( give your answer correct to significant figures wherever necessary ) 6.9 8..7. ) ).8.6. ).7 +.6. )...8 6..8 ) 6).. 7 +.6..7 +.6. 7). (.6.) 8) (. +.6) (.7.6) 9) 9.7 7 0).. ( ).6.8. 6..8 7 + ) ) 7.8 (. 6.) 8 ) 7. 9.8 +.7 ) ) 9.8.. 8 6. 6) 7) 8. (.8 +.6) 6. (.87 +.6) 8) 9) (6..6).6 0).7.8 7. +.7 9.8 9.8.. 8.67 +. 6...87 7.6 9...6.7 (.6 +.67) ) 6cos0 )..cos0 ) ( 6 + tan) ) 6 + sin0 ) tan + sin 6) (. + tan0 ) + (.6).6 +. sin 7) ------------------------------------------------------- 8).8 + 0. 8.9. + tan7 -----------------------------------------------------..86

Sumbooks 00 Estimation Do not use a calculator In each of the following questions a) write down a calculation that could be done mentally to check the answer to each of the following and b) write down your answer Eercise ) 7 6 ) 67 ) 8 ) 78 6 ) 8 6) 6 7) 7 89 8) 0 9) 96 6 0) 87 6 ) 67 09 ) 0 7 ) 87 ) 6 8 ) 6 6) 8 7) 6 87 8) 77 9) 6 88 0) 6 Eercise ) 6..876 ).9. ) 7.68 7.8 ) 9. 0.076 )..00 6) 0.00 0.07 7) 7.6 9. 8) 7.7.6 9)..98 0) 8.6 0.7 ) 0.6 0. )..6 --------------------------. ).6.78 7.6 +.87 ----------------------------- ) --------------------------.7.6 ). +.6 7..8 -------------------------- 6) --------------------------.7.68.6.7 7) 0..6 6. +.9 ----------------------------- 8) --------------------------. 0. 9). 0.8.. ----------------------------- 0) --------------------------.6.6 ) 7. (.) ( 6.8) 7. --------------------------------- ) ------------------------------------ 0 + 7 8.97. ).(.8 +.9) (.78).79 ------------------------------------------ ) --------------------------------- 8.. 0.6 0.7 ) If v = 9.8 7. estimate the value of v. 6) If c =..6..6 estimate c.. 7. 7) t = -------------------------- estimate the value of t. 9.8.( 6.8 +.) 8) D = ------------------------------------------ estimate the value of D. 6.8. 9) Estimate the value of 8 8 0.

Sumbooks 00 Fractions, Decimals and Percentages Eercise Change into decimals (correct to decimal places where necessary) 7 ) -- ) -- ) -- ) -- ) ----- 6) ----- 8 8 0 8 7 8 7) ----- 8) ----- 9) ----- 0) ----- ) ----- ) ----- 7 0 7 8 9 ) ----- ) -- ) -- 6) ----- 7) ----- 8) ----- 0 7 9 6 6 Eercise Change these decimals into percentages ) 0.6 ) 0. ) 0.7 ) 0.87 ) 0.6 6) 0. 7) 0. 8) 0.96 9) 0. 0) 0.6 ) 0.8 ) 0.86 ) 0.9 ) 0. ) 0.6 6).9 7).8 8) 6. Eercise Change into percentages correct to significant figures 8 7 9 ) -- ) ----- ) ----- ) ----- ) ----- 6) ----- 0 0 6 0 7) ----- 8) 8 ----- 9) ----- 0) ----- ) ----- ) ----- 0 7 0 8 7 8 8 7 ) ----- ) ----- ) ----- 6) ----- 7) -------- 8) ----- 6 9 6 6 96 Eercise Compare each of the following sets of numbers by first changing them into percentages and then writing them down in order of size, smallest to largest. ) -- 0. % ) -- 8 0. 6% 7 ) -- 0.8 87% ) ----- 8 6 0. % 7 ) ----- 0. 0% 6) ----- 0 6 0.7.7% 8 9 7) ----- 0. 0% 8) ----- 7 0.7 7.% 6 8 9) ----- 0. % 0) ----- 8 0..6% Eercise Calculate 7 ) -- of 0 ) -- of 0 ) -- of 90 ) -- of.68 8 8 7 ) -- of 0 metres 6) -- of -- metres 7) ----- of 7 8) ----- of 8 metres 8 6 7 9 7 9) ----- of 66 0) ----- of. metres ) -- of ) ----- of 7.7 metres 0 6 8 0

Sumbooks 00 6 Fractions, Decimals and Percentages Eercise ) 7% of 600 ) % of 0 ) 6% of 90 ) % of00 ) % of 6 6) 0% of.0 7) 60% of 9 8) 7% of 8 metres 9) % of 9 0) 7% of.0 ) % of 6.0 ) 9% of 00 Eercise Change these marks into percentages. (Give your answer correct to the nearest whole number) ) out of 0 ) 8 out of 60 ) 7 out of 0 ) 7 out of 80 ) 6 out of 90 6) 97 out of 0 7) out of 00 8) 6 out of 70 9) 8 out of 0 0) 6 out of 0 ) 7 out of 0 ) 76 out of 0 ) out of 76 ) 8 out of 9 ) 6 out of 68 6) 7 out of Eercise Find the percentage profit on each of the following, correct to the nearest whole number. ) ) ) ) ) 6) 7) 8) 9) 0) Buying Price Selling Price 00 0 0 80 60 80.0.80.80.0,00,700,000 7,000.0.00 900 90 00 00 Eercise Find the selling price for each of these. ) ) ) ) ) 6) 7) 8) 9) 0) Buying Price Profit 00 7% 00 % 0 0% 000 % 00 % 00 7.% 70 % 9,000 % 80 7% 0 %

Sumbooks 00 7 Interest Eercise Find the simple and compound interest (without using the compound interest formula) on each of the following. Wherever necessary give your answer correct to the nearest penny. ) 00 invested for years at % interest per annum. ) 0 invested for years at % interest per annum. ) 00 invested for years at 9% interest per annum. ) 000 invested for years at 0% interest per annum. ) 00 invested for years at 7% interest per annum. 6) 000 invested for years at % interest per annum. 7) 00 invested for years at % interest per annum. 8) 0 invested for years at 7% interest per annum. 9) 0 invested for years at 8% interest per annum. 0) 00 invested for years at 6% interest per annum. Eercise The Compound Interest Formula is R = P + -------- n 00 Where represents the amount in the bank after n years with a rate of R% on a principle of P. ) Use the compound interest formula to calculate the amount of money in a bank account when a) 00 Euros is invested for years at a rate of.% b) 00 Euros is invested for 7 years at a rate of.7% c),00 Euros is invested for years at a rate of.6% ) 6,000 Euros is invested in an account that pays interest at a compound rate of.7% R a) Calculate the value of = + -------- 00 b) By using the key on your calculator, make a list of the amounts of money in the y account at the end of each of the 0 years the money is left in the account. ) Calculate the interest gained when 0,000 Euros is invested for years in a bond which pays an interest of.7% per annum. ) What is the difference between the simple and compound interest earned on an investment of,000 Euros over a period of years at a rate of.86%?

Sumbooks 00 8 Scale Drawings and Ratio Do not use a calculator Eercise Fill in the missing values for each of the following Scale Dimensions on Drawing Actual Dimensions : : 0cm :0 6.cm 0cm :0 0cm :0 0cm :8.8cm 0cm 6 metres cm metres :0. metres :00.cm.cm metres 7cm 7.cm :00 7.m :7 6cm cm.m : 8cm :0.6cm.cm.cm :7 600cm :0.6cm Eercise Divide each of the following into the ratios given. ) 900 into the ratio : ) 000 into the ratio :7 ) 00 into the ratio : ) 600 into the ratio 7:8 ) 800 into the ratio : 6) 700 into the ratio :9 7) 60 into the ratio 7: 8) 6 into the ratio 9: 9) 0 into the ratio 8: 0) 00 into the ratio :: ) 0 into the ratio :6:7 ) into the ratio :: ) 008 into the ratio 7:8:9 ) into the ratio 7:9: ) 0 into the ratio :8:9 6) 78.0 into the ratio ::7 7) 0 into the ratio 6:8: 8).86 into the ratio :7: 9) 86 into the ratio :7: 0) into the ratio ::7 Eercise Three people, A, B and C, share an amount of money in the ratios shown below. In each case calculate the total amount of money shared out and the amount C gets. ) Ratio ::. A gets 8 ) Ratio ::. B gets ) Ratio :8:0. B gets ) Ratio ::7. A gets ) Ratio 7::. B gets 99 6) Ratio ::. A gets.6 7) Ratio ::8. B gets. 8) Ratio :6:. B gets 6.7 9) Ratio :7:9. A gets. 0) Ratio ::. B gets 6.0

Sumbooks 00 9 Standard Form Eercise Write down these numbers in standard form ) 6 ) 6 ) 800 ) 9 000 ) 6 000 6) 0. 7) 0.0 8) 0.00 9) 0.000 0) 0.0000 ) 0.00 ) 7. Change these numbers from standard form. ). 0 ). 0 ).8 0 6). 0 7 7). 0 8). 0 6 9).80 0 0) 9.6 0 ). 0 ).97 0 ).6 0 6 ).8 0 Eercise Calculate each of the following, leaving your answer in standard form. Round off to significant figures where necessary. ) (. 0 ) (.0 0 ) ) (. 0 ). 0 ) (.6 0 ) (. 0 ) 7) (. 0 0 ) (.7 0 ) 9) ( 8. 0 6 ).6 0 ( ) ( ) ( ) ) (.6 0 ).8 0 ) ( 6. 0 ) (.7 0 8 ) 6) (.8 0 ) (.8 0 7 ) 8) ( 7.6 0 6 ) (. 0 ) 0) (. 0 ).6 0 ( ).7 0 7 8.6 0 ) 7 ),000,000 (. 7 0 6 ) (. 0 ) (.8 0 7 ) (.6 0 ) ) ).7 0 6. 0 Eercise ) If = 0 and y = 0 write down the value of a) y and b) + y leaving your answer in standard form. ) If = 0 and y = 0 write down the value of a) y and b) + y leaving your answer in standard form. ) If = 0 and y = 7 0 write down the value of y leaving your answer in standard form. ) The mass of the earth is.976 0 kilograms and the mass of the moon is 7. 0 kilograms. Write down the ratio of the mass of the moon to that of the earth in the form : n. ) The distance of the moon from the earth is 8 00 kilometres. The speed of light is approimately.0 0 kilometres per second. How long does it take light to travel from the moon to the earth? 6) A neutron has a mass of.67 0 7 kilograms and an electron 9.09 0 kilograms. Calculate the ratio of the mass of a neutron to the mass of an electron in the form : n. 7) Light travels at a speed of approimately.0 0 kilometres per second. a) How far will it travel in year (6 days)? b) If the distance from the earth to a star is 7.86 0 kilometres, how long will its light take to reach earth?

Sumbooks 00 0 Prime Factors Do not use a calculator Eercise The prime factors of a number can be found by using a tree diagram. The eample below shows how to find the prime factors of 6. In the same way find the prime factors of the other numbers. 6 68 90 0 Eercise Write down all the factors of the following numbers. ) ) 0 ) ) 0 ) 6) 0 7) 8) 60 9) 7 0) 8 ) 90 ) 00 ) 0 ) 0 ) 0 Eercise Epress the following numbers as products of their prime factors. ) 0 ) 60 ) 00 ) 0 ) 60 6) 67 7) 9 8) 7 9) 0)0 ) 680 ) 0 ) 60 ) 76 ) 0 Eercise Epress the following numbers as products of their prime factors. In each case state the smallest whole number it has to be multiplied by to produce a perfect square. ) ) 8 ) 80 ) 80 ) 6 6) 7) 8) 68 9) 608 0) 980 ) 600 ) 60 ) 00 ) 9 ) 80 Eercise Calculate the largest odd number that is a factor of each of the following. ) 08 ) 80 ) 00 ) 7 ) 9 6) 0 7) 88 8) 70 9) 780 0) 68 ) 8 ) 00 ) 60 ) 0 ) 90

Sumbooks 00 Number Patterns and Sequences Eercise In each of the following patterns write down the net two numbers ),, 6, 8, 0... ), 7, 9,,... ) 7, 0,, 6, 9... ), 9,, 7,... ), 8,, 8,... 6),,, 0, 9... 7),, 6, 9,... 8),, 6, 8,... 9), 7,, 7,... 0),,, 8,... ) 0,,, 6, 0... ),, 8,, 7... ),,, 9, 7... ) 0, 0, 9, 7,... ), 9, 6,, 0... 6),, 0, 6,... 7) 7,,,,... 8) 8, 8, 7,,... 9),,, 7,... 0),,, 7,... ),,, 7, 0... ),, 7,,... ),,, 8, 6... ),, 7,,... Eercise In each of the following patterns (a) write down the net two numbers, (b) write down in words the rule for finding the net number and (c) write down the rule for finding the nth number in the pattern in terms of n. ),,, 7, 9... ),, 8,,... ), 9,, 7,... ) 6,, 8,, 0... ) 7,, 9,,... 6), 7,, 7,... 7) 0, 8, 6,,... 8) 7,,, 8,... 9), 6, 0,, 8... 0) 7,,,,... ), 0,, 0,... ), 8,,, 0... ),,,,... ), 9, 6,, 0... ),,, 7, 9... Eercise ) The diagrams below show square 'holes' surrounded by centimetre squares. Length of side Number of squares 8 6 Find the number of squares needed for holes of side a) cm b) cm c) n cm d) Calculate the number of squares needed for a hole of side 0cm. ) A child places blocks on a floor making the pattern shown below. The first row contains block, the second blocks, the third and so on. Row st nd rd th How many blocks will be in a) row b) row 6 c) row n d) Calculate how many will be in row 0.

Sumbooks 00 Number Patterns and Sequences ) The diagram shows a number of rectangles where the length is unit longer than the width. Rectangle number Find the areas of a) Rectangle b) Rectangle c) rectangle n d) Calculate also the area of rectangle 0 ) A library shelving system is made from uprights and shelves as shown below. upright uprights uprights no shelves shelves 0 shelves How many shelves can be made from a) uprights b) uprights c) n uprights. d) How many shelves are needed for 0 uprights. ) Shapes are made from matchsticks as shown below. layer layers layers 7 matches matches 7 matches Write down the number of matches needed for shapes with a) layers b) layers c) n layers Calculate how many matches are needed for a shape having layers. ) Pens, in which animals are kept are made from posts and cross bars. One pen requires posts and 8 cross bars, bars along each side. pen 8 cross bars posts pens cross bars 6 posts pens 0 cross bars 8 posts If more pens are made in this way, write down the number of posts and cross bars needed for a) pens b) pens c) n pens. Calculate the number of posts needed if there are cross bars.

Sumbooks 00 Distance Time Diagrams ) D 00 Distance (miles) ) Distance (miles) 0 H 0 G 0 00 F 8.00 ) Town B Distance from town A 00 80 60 0 0 H 0 Town A.00 Time taken (hours) 8.0 9.00 Time (Hrs and mins).00.00 Time The diagram shows the journey of a lorry from home H to destination D. a) What is the distance between H and D? b) For how long did the driver stop? c) What was his average speed when travelling slowest? d) What was the average speed for the whole journey? The diagram shows a distance time graph for two buses A and B, travelling between towns F, G and H. Bus A travels from F to H and bus B from H to F. Find a) the average speed of bus A between F and G in miles per hour. b) the length of time bus A stops at G c) the time at which bus B leaves H d) the average speed of bus B in m.p.h e) the approimate time at which the buses pass each other f) the approimate distance from G at which the buses pass g) the time at which bus B arrives at F. Two towns are 0 miles apart. The graph shows the journeys of two trains. The first goes from A to B. The second goes from B to A. From the graph find a) the speed of the first train over the first part of its journey. b) the time at which the first train stopped and for how long. c) the speed of the first train during the second part of its journey. d) the average speed of the second train. e) the time and distance from town A of the two trains when they passed each other.

Sumbooks 00 ) 0 Distance Time Diagrams B Distance travelled from home (km) 0 0 A 0:00 :00 :00 :00 :00 :00 6:00 7:00 8:00 Time The diagram shows a distance-time graph for two journeys. One journey is by bicycle, the other is jogging. a) Which journey do you think is by bicycle and why, A or B? b) What is the average speed of the cyclist on her outward journey? c) Who travelled furthest? d) What is the average speed of the jogger on his homeward journey? e) For how long did the jogger stop? f) If both journeys were made along the same road, at what approimate times did they meet? g) At what time did the cyclist arrive home? ) Two cars, A and B travel between two towns X and Y Y. The distance time graph shows the distance from town X. 0 Dist. (miles) 80 Half the journey is along a motorway and half is not. a) How far apart are the two towns? b) Calculate the speeds of car A over the two sections. c) Calculate the speeds of car B over the two sections. 0 X 0:00 Car B Car A 0:00 0:00 0:00 06:00 07:00 08:00 Time d) For how long did car B stop? e) At what time, and how far from town X, are the two cars when they pass each other? f) Approimately how far apart are the two cars at 06:00? g) At what times will the cars be 0 miles apart?

Sumbooks 00 Conversion Graphs ) The graph can be used to convert pounds ( ) into Euros. Use it to convert; a).0 into Euros b).00 Euros into pounds and pence. 6 Pounds ( ) 6 7 8 Euros ) The graph can be used to convert pounds ( ) into US dollars ($). Use it to convert; a) 70 into dollars b) $60 into pounds. 0 Dollars ($) 00 0 0 0 0 0 0 0 0 60 70 80 Pounds ( )

Sumbooks 00 6 Conversion Graphs ) kg is approimately.lbs. Calculate what 0 kg is in pounds. From this information draw a conversion graph to convert kg into pounds. Use a horizontal scale of cm to 0kg and a vertical scale of cm to 0lbs. From your graph convert; a) kg into pounds b) 7 pounds into kg. ) It is known that gallon is approimately equal to. litres. Use this information to change 0 gallons into litres. Plot a graph to convert gallons into litres using a scale of cm to represent gallons on the horizontal ais and cm to represent litres on the vertical ais. From your graph; a) convert gallons into litres b) convert litres into gallons In each case give your answer correct to decimal place. ) The table below shows the cost of gas. There is a fied charge of 0.00. Cost 0.00.00 8.00 60.00 Units Used 0,000,000 0,000 Use this information to plot a conversion graph with a scale of cm to represent 000 units on the horizontal ais and cm to represent 0 on the vertical ais. From your graph find; a) the cost of,00 units b) the number of units that can be bought for.00. ) Water is run from a tap into a container which has a large base and narrower neck. The height of the water in the container is measured every 0 seconds. The following table gives the results; Height of water (cm) 0 8 8 0 Time (secs) 0 0 60 90 0 0 Using a vertical scale of cm to represent 0cm for the height of the water and a horizontal scale of cm to represent 0 secs for the time, plot the above information to produce a conversion chart. From your graph find; a) the time it takes to reach a height of cm b) the height of water after the tap has been running for -- minutes. ) David has to make pastry but his scales measure in ounces and the recipe uses grammes. He has a tin of beans which say on the label that -- ounces is equivalent to 0 grammes. Using a scale of cm to represent oz on the horizontal ais and cm to represent 0 grammes on the vertical ais, draw a line to show the relationship between ounces and grammes. From the graph convert the following to the nearest half ounce, so that David can use his scales; a) 8g of butter b) 00 g of flour When he has mied all the ingredients together he weighs out -- ounces of pastry. c) What is this weight in grammes?

Sumbooks 00 7 Sketching and Recognising Graphs ) Sammi walks to school, keeping at the same speed all the way. Which of these graphs represents her journey. a) b) c) Distance travelled Distance travelled Distance travelled Time taken Time taken Time taken ) The Swimming Pool Corporation makes round swimming pools. The table below shows their prices. Diameter 8 metres 0 metres metres metres 6 metres Cost 90,000,0,880 7,680 Which of these graphs represents the prices of the pools. a) b) c) Price Price Price Diameter Diameter Diameter ) A train travels from Dorcaster to Newchester. Its speed increases from 0 to 60mph. It then travels at a constant 60mph and finally it slows down from 60mph to 0mph. Which of these diagrams shows that journey. a) b) c) d) Speed Speed Speed Speed Time Time Time Time ) A shop sells stamps which cost p each. In order to help calculate their cost, the assistant uses the following list of prices to help him. Number of stamps Cost 0 0 0 00 p..0.0 Sketch the graph which represents their price plotted against the number sold.

Sumbooks 00 8 Sketching and Recognising Graphs ) A water tank with straight sides is full. A tap at the bottom is turned on and the water drained out at a constant rate. Which of these diagrams shows this. a) b) c) d) Height Height Height Height of water of water of water of water Time Time Time Time ) A car is bought for 000. During each year it loses 0% of its value at the beginning of that year. (compound depreciation). Which of these diagrams represents its value? a) b) c) d) Value Value Value Value Time Time Time Time ) Niki travels to her gran's house. The first part of her journey she travels by bike, the second part she walks, and the last part she goes by bus. Which of these diagrams represents her journey? a) b) c) Distance Distance Distance Time Time Time ) The table below shows the volume of some cubes. Sketch a graph of the length of their side against their volume. Length of side (cm) 0 0 Volume of cube (cm ) 8 000 8,000

Sumbooks 00 9 Plotting Graphs ) a) Complete the table below which gives the values of y = + for values of ranging from to +. y b) On graph paper, draw the graph of y = +. Use the scale of cm to unit on the ais and cm to units on the y ais. c) From your graph determine, correct to decimal place, the values of when y=6 d) Draw the line y =7 on the same graph and write down the co-ordinates of the points where they cross. ) a) Complete the table below which gives the values of y = + for values of ranging from to +. y 0 7 0 b) On graph paper, draw the graph of y = +. Use the scale of cm to unit on the ais and cm to units on the y ais. c) Draw the line y =+ on the same graph and write down the co-ordinates of the points where they cross. d) Show that the solution to the equation + = 0 can be found at these points. Write down the solution to this equation ) a) Complete the table below which gives the values of y = +6 for values of ranging from. to +.. y. 0. 0 0.. 6 7 b) On graph paper, draw the graph of y = +6. Use the scale of cm to unit on the ais and cm to unit on the y ais. c) Draw the line y = + 6 on the same graph and write down the co-ordinates of the points where they cross. d) Show that the solution to the equation = 0 can be found at these points. Write down the solution to this equation ) a) Complete the table below which gives the values of y = 6 for values of ranging from to +. y 0 6 b) On graph paper, draw the graph of y = 6. Use the scale of cm to unit on the ais and cm to units on the y ais. c) Draw the line y =0 on the same graph and write down the co-ordinates of the points where they cross, correct to decimal place. d) Show that the solution to the equation 6= 0 can be found at these points. Write down the solution to this equation

Sumbooks 00 0 Plotting Graphs ) a) Complete the table below which gives the values of y = + -- for values of ranging from 0. to 8. y 0. 8 7.. b) On graph paper, draw the graph of y = + --. Use the scale of cm to unit on the ais and cm to unit on the y ais. c) From your graph determine, correct to decimal place, the value of when y=6.. d) Draw the line y = 8 -- on the same graph and write down the co-ordinates of the points where they cross, correct to decimal place. e) Show that the solution to the equation -- + -- = 0 can be found at these points. Write down the solution to this equation. ) a) Complete the table below which gives the values of y = ++ for values of ranging from to +. y 0 8 b) On graph paper draw the graph of y = + +. Use the scale of cm to unit on the ais and cm to units on the y ais. c) By drawing a suitable straight line on the grid, solve the equation ++= 7 ) a) Complete the table below which gives the values of y = for values of ranging from. to +. y. 0. 0 0...7.7.7 b) On graph paper, draw the graph of y =. Use the scale of cm to unit on the ais and cm to units on the y ais. c) By drawing a suitable straight line on the grid, solve the equation = 0 ) a) Complete the table below which gives the values of y = -- for values of ranging from 0. to 8. 0. 8 y b) On graph paper, draw the graph of y = --. Use the scale of cm to unit on the ais and cm to unit on the y ais. c) By drawing a suitable straight line on the grid, solve the equation 7 + -- = 0

Sumbooks 00 Substitution Calculate the following values given that a =, b = and c = ) a + b ) a b ) a b c ) a + b c ) c 7a 6) a b + 6 Calculate the values of the epressions in questions 7 to given that a =, b = and c = 7) a + b c 8) a + b c 9) 6a 7b 0) a + b c ) a b c ) a b c ) If v = u + at, find v when u =, a = 0. and t = 6 ) Find the area of a circle of radius.cm if A = πr and π =. ) Find the circumference of a circle of diameter 6.cm if C = πd 6) If y = m + c find the value of y when m = 6, = and c = 7) The volume of a cone is given by V = -- πr h. Find its volume when π =., r = cm, and h =.cm. 8) The temperature F ( o Fahrenheit) is connected to the temperature C ( o Celsius) by the formula C = -- (F ). Find, to the nearest degree, the value of C when F = 8 o 9 9) Find the simple interest paid if the principal (P) is 0, the time (T) is years and the rate PTR of interest (R) is 9.% using the formula I = ---------- 00 0) If v = u + as find v when u = 7., a =. and s = 0. ) If v = gh find v when g = 9.8 and h =. ) If S = -- (u + v)t find S when u = 0, v = 7. and t =.. + y ) If A = -------------- find A when = 6 and y = 9 R ) If P = -------- find P when (a) R = 6, = 7 and y =, (b) R =, =, and y = y bc ) If = ---------- find when b = and c = 9. b c 6) If y = + find y when is (a) (b) 7) If y = + find y when is (a) (b) 8) If y = ( + )( ) find y when is (a) (b) 9) If y = ( )( + ) find y when is (a) 7 (b) 0) If y = + -- find y when = ) If v = u + at, calculate v when u = 0, a = 9.8 and t = 6. ) If v = u + as, calculate the value of v when u = 0, a = 9.8 and s = 0

Sumbooks 00 Simplifying Epressions Eercise Simplify ) 7 + ) ) 6 9 7) + 8 9) + 0 ) 7 ) + ) 9 + 7) + 6 9) 8 + ) + + 8 ) 8 6 + ) 6 + 8 7) 9 + 8 9) 8 + 6 Eercise Simplify ) y + 8y ) 9y 6y ) 6y 8y 7) y + y 9) 6a 7a ) b + b + a + a ) b + a + b + a ) 6a a + b + b 7) a + b a b 9) 6 + 8y 0 9y ) 6 + y 8 6y ) y + y 6y ) 7ab + 6b ab b ab 7) ab + bc ab + bc 6ab bc 9) 9y + y + y ) + ) + y + + y ) y + + y 7) 6 y + y + y + y 9) + ) 0 ) 8 9 6) 7 0 8) 6 + 9 0) ) 9 6 ) 6 7 + 6) 6 0 8) 7 + + 0) + 9 ) 6 + 9 ) 8 0 6 + 6) 9 6 + 8) 7 + + 9 0) 6 + 8 ) y + y ) 6) 7 9 8) + 7 0) w w ) 9 + 7y + + 6y ) + 6y + y + 6) p p + q + 7q 8) + 7y y 0) a + b 7a b ) a + 9b 6a b ) y + y + y 6) y + 7 y y 8) 7y + 9yz y yz + 7y yz 0) ab a ab + a + 9ab ) 7y + 6y ) 7 + y y 6) 9 + 8) 7 y y y + y 0) y y

Sumbooks 00 Indices Eercise Write down the values of the following. ) ) ) ) ) 0 6) 0 7) 0 8) 0 Eercise Use a calculator to write down the values of the following. ) 6 ) 6 ) 7 ) 7 6 ) 9 6) 7) 6 8) 7 9 Eercise Write down the answers to these both in inde form and, where necessary, numerical form. ) ) ) ) 0 0 ) 7 7 6) 8 8 8 7) 8) a a 0 9) b b b 0) y 0 y Eercise Write down the answers to each of the following in inde form. ) 8 ) 9 ) 7 7 7 ) 0 0 0 7 ) 7 0 6) 0 7) 9 7 8) 6 9) 8 0 0) 0 7 ) a a ) y y ) 7 9 8 0 Eercise Write down the answers to each of the following in inde form. ) ) ) ) ) 6) ( ) ( ) ( 7 ) ( ) ( ) ( ) ( ) 8 ( 7 ) ( ) ( ) ( ) ( y ) 7) 8) 9) 0) ) ) Eercise 6 Calculate the answers to each of these in numerical form. ) ( ) ) ( ) ) ( 7 ) ) ) 6) ( ) 7) ( ) 8) ( 7 ) 9) 0) ( ) ( ) ( ) ( ) Eercise 7 Simplify each of the following ) a) b) 6 c) a a 8 d) y y ) a) a a b) a a c) d) 0 ) a) ( a 6 ) b) ( ) 6 c) ( y ) d) ( b ) 6 ) a) ( y) b) ( ab) a c) ( y) y d) ( ab) b ) a) ( ) b) ( ) c) ( ) d) ( a) 0b 00 7 6) a) a a b) 7 c) d) 0b 0 7) a) b) 9a a c) 6y y 8) a) b) c) 8

Sumbooks 00 Eercise Calculate ) 8 ) 6 ( ) ( ) 7) 0) 6 Multiplying Brackets ) 7 ) 8) 6 ( ) ) ( ) ) ( 6) 6) 8 9) 7 ( ) ( ) ) 8 7 Eercise Epand and simplify ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )+ 6 ( 7y) ( ) ( y) ( ) ( + ) ( ) ( + ) ( ) ( ) ) + y ) ) + 7) 9) ) y + y ) 7 y + y ) y + y 7) + y 9) 7 y ) ) 6 + ) + ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )+ ( + y) ( ) ( + y) ( ) ( ) ( )+ ( ) ( ) ( ) ( ) ( + ) ) 6 + ) + 6) 7 8) + 0) 7 + 8y + + y ) + 8y 66 y ) + y y 6) + y 8) y 0) + ) + ) 6) 6 Eercise Epand and simplify ( )( + ) ( )( + ) ( )( ) ( )( 6) ( )( + ) ( )( + ) ( )( 7 ) ( )( 9 ) ) + ) + ) + 7) 6 + 9) ) 6 ) 6 ) 8 6 7) ( + ) 9) ( ) ( )( + ) ( )( 6 + 7) ( )( ) ( )( ) ( )( + ) ( )( 8) ( )( ) ( )( ) ) + ) + 6) + 8) + 0) ) 7 ) 6 6) + 7 8) ( 6 ) 0) ( 9)

Sumbooks 00 Factorising Eercise Factorise ) + 6 ) z + 7) 6 0 0) + 6y ) 8 8z 6) a + 9) 6a b + 8c ) ) 8y + 0 8) 6 ) + 6y ) 8y + 7z 7) 6 + 6 0) a + 0b c ) 6 6) 8y 6 9) a 6 ) a + b ) p 0q 8) ) 9a + b Eercise Factorise ) a a ) 7) y + y 0) 6 9 ) 0a a ) 6y y ) a + 6a 8) 0 ) 6y + 0y ) 8 ) 9 6) b b 9) z z ) z 6z ) 7a 8a Eercise Factorise ) ab + a ) a + 6a 7) ab a + a 0) 0y + y ) 6p q pq ) y ) 9 6 8) 7a ab ) 6y 8yz ) 9ab a b ) 6a ab 6) y + 6 9) πr 6πrh ) 8pq p q ) 6 y y Eercise (mied) Factorise ) a + b ) y + y 7) y 0) 6a + 0 ) 8a + 6a ab ) ah a ) abc bc 8) 7 y + ) 9ab 7b ) 8 + y 6z ) a + b + 0c 6) 6y y 9) πd 7πd ) 6a + 8a ) + + y

Sumbooks 00 6 Equations Find the value of the letter in each of the following equations Eercise ) + = 6 ) = 7) 6 y = 0) a = 6 ) 7b = 6) a + = 0 9) 7 = 8 ) y + = ) + 7 = 7 ) y 7 = 8) = ) 6 = ) y = 7) 9a + 6 = 0) 7 = 7 ) b + = ) 7 + y = 9 6) a 9 = 8 9) 9 = ) 8y = 6 ) b = 0 8) + 6 = 0 ) 6 7 = ) 6y = Eercise ) + = ) + = 7) = 0) + 6 = ) + = 6) + 7 = 9) + 9 = + ) 6 = ) + = 8) 6 = ) 8 + = 0 ) + = 7) 6 = + 0) + 7 = ) 7 6 = 6 6) + = 9) 7 = ) 7 + 7 = 9 ) = + 6 8) = + ) + = Eercise ) ( + ) = 8 ) ( + ) = 6 7) ( ) = 7 0) ( + ) = ) ( + ) = 0 6) ( + ) = 8 9) ( + ) = ( ) ) ( + ) + = ) ( ) = 9 ) 7( ) = 8) ( + ) = 8 ) ( ) = ) ( ) = 7) 6( 6) = + 0) ( + ) = ( 9) ) ( ) + = 9 ) ( + ) = 6) ( + ) = 6 9) ( 7) = ) ( + 6) = ) 6( + 7) = 8) ( + ) = + 8 ) ( ) = ( ) ) ( + ) = 87

Sumbooks 00 7 More Equations Find the value of the letter in each of the following Eercise ) = 6 ) = 6 7) 7 9 = 0) + = ) + = 6) 7 9 6 = + 9) = ) + = 6 ) 8) + = + + = ) = ) 7 0 = 8) 7 = ) + 7 = ) = 6 7) 6 + = 7 0) + = 7 + ) = 7 6) + = 9) + = ) -- ( + ) + -- ( ) = ) ) -- ( + ) + -- ( + ) = 7 ) ) -- ( ) + -- ( ) = 6) ) 6 = 8 6) = 9) = 9 ) 6 = ) + = 9 8) 6 7 + = ) = ) 7 = 6 7) 0) 7 = ( + ) = 6 -- ( 0 ) + -- ( + 7) = -- ( 8 + ) -- ( ) = 8 -- ( + ) -- ( 7 ) = Eercise ) ( )( ) = 0 ) ( + )( ) = 0 7) + + 6 = 0 0) + = 0 ) 7 + 0 = 0 6) 0 = 0 9) + = 0 ) 6 + 9 = 0 ) ( + )( ) = 0 ) ( + 6)( ) = 0 8) + 6 = 0 ) + + 8 = 0 ) + 9 + 0 = 0 7) + 6 = 0 0) 8 0 = 0 ) 0 + = 0 ) ( + )( + ) = 0 6) ( + 0)( + ) = 0 9) + + = 0 ) + 8 = 0 ) + 7 + = 0 8) 9 0 = 0 ) = 0 ) = 0

Sumbooks 00 8 Straight Line Graphs and Simultaneous Equations Eercise Draw the graph of each of the following equations ) y = + ) y = 7) y = + 0) y = + ) y = + 6) y = + 9) y = ) y = + ) y = + ) y = 6 8) y = + ) y = ) y = 7) y = + 0) y = + ) y = ) y = + 6) y = 9) y = ) y = 6 ) y = 7 8) y = ) y = + 7 ) y = + ) y = 8) + y = 6 ) y = 0 ) + y = 0 7) + y = 0 6) y = + 9) + y = 0 ) 6 y = 0 ) y = 0 8) y + + = 0 7) y = 7 0) 6 + y = ) y = 0 6) + y = 0 9) + y = 0 Eercise Solve each of the following pairs of simultaneous equations by drawing them. All diagrams can be drawn on aes where lies between and 6, and y lies between and 6. ) y = and + y = 9 ) + y = and y = + ) y = and y = 7) y = and y = + 9) y = + and + y = ) + y + = 0 and y = ) y = and y = + ) y = and + y = 6 ) y = + and + y = 6 6) y = + and + y = 8) + y = and y = + 0) y = 0 and y = 0 ) y = + and + y = 6 ) y = + and + y =

Sumbooks 00 9 Trial and Improvement Eercise Calculate the value of, correct to decimal place for each of the following, using a trial and improvement method. Show all your attempts. ) = ) = 7 ) = 86 ) = 97 ) = 6) = 77 7) = 60 8) = 7 9) = Eercise By using a suitable trial and improvement method find the value of, correct to one decimal place, which satisfies each of the following equations. Show all your attempts. ) + = ) + = 7 ) = ) = 9 ) + = 6) + = 7) = 8) = 7 9) + = 67 0) + = ) = 67 ) = 00 ) If = 0, find the value of correct to decimal place. ) If + = 7, what is the value of correct to decimal place? ) Calculate the value of in the equation + = 6, correct to one decimal place. 6) Solve the equation = 0, correct to decimal place. 7) A square has an area of cm. Use a trial and improvement method to calculate the length of one side. 8) The longer side of a rectangle is cm greater than the shorter side. If its area is cm use a trial and improvement method to calculate the size of the shorter side? 9) The perpendicular height of a right angled triangle is cm more than its base. If its area is 9cm, what is the length of its base. 0) A cuboid has a height and length which are each 6cm greater than its width. If its volume is 600cm, calculate its width correct to one decimal place.

Sumbooks 00 0 Inequalities Solve these inequalities in the form a number, a number, > a number or < a number. ) + > ) + < ) 7 < + ) + < 8 ) > 7 6) > 7 7) 8) 9) 0) + 7 ) 6 < 6 ) < 6 + 9 ) 6 6 0 ) + 0 ) + 7 < 0 6) 6 > 7) < + 0 8) > + 7 9) + 8 0) 8 + < 60 ) + ) + > 8 ) > + ) 7 < ) + 7 6) 6 + 9 7) + 9 + 8) 7 < 9) > + 0) + < + ) -- 7 ) -- ) ) -- + > ) -- 6> 0 6) -- + 7 8 -- + > 0 6 7) 7 -- -- 8) 9 -- > -- + 9) -- 8 > -- + 7 8 0) ( + ) > ) ( + 8) > ) ( + 7) > 0 ) ( + ) 6 ) ( + ) 6 ) ( + ) 6) > ( + ) 7) + > ( + ) 8) 9 > ( + ) 9) ( + ) + 0 0) ( 7) + ) 6( 7) + 8

Sumbooks 00 Inequalities - Graphs ) 6 The diagram shows the graphs of y = --, y = and =. From the diagram write down the co-ordinates of a point (,y) which satisfies the inequalities y > --, y < and >. ) 0 0 6 7 8 6 The diagram shows the graphs of y = +, 7y + = and =. From the diagram write down a point (,y) which satisfies the inequalities y +, 7y + > and. 0 0 6 7 8 ) Using a scale of 0 to 8 on the ais and 0 to 0 on the y ais, plot the following graphs; y =, y = 7 and y =. Shade in the region which satisfies all the inequalities y<, < 7 and y >. ) Using a scale of 0 to 9 on the ais and 0 to 9 on the y ais, plot the following graphs; y =, y = 6 and 8 + 8y = 6. Shade in the region which satisfies all the inequalities y>, y < 6 and 8 + 8y > 6. ) Using a scale of 0 to 8 on the ais and 0 to 0 on the y ais, plot the following graphs; y = --, = and 8 + y = 0. Shade in the region which satisfies all the inequalities y > --, and 8 + y < 0. 6) Using a scale of 0 to 8 on the ais and 6 to 6 on the y ais, plot the following graphs; y =, = 6 and y =. Shade in the region which satisfies all the inequalities y<, < 6 and y>. Which of the following points lie within this region? (,), (, ), (,), (,) 7) Using a scale of 0 to 8 on the ais and 0 to 8 on the y ais, plot the following graphs; y = -- +, = and 7 + 6y =. Shade in the region which satisfies all the inequalities y -- +, > and 7 + 6y <. Which of the following points lie within this region? (,), (,), (,), (,).

Sumbooks 00 Rearranging Formulae Rearrange each of the following formulae to make its subject the letter indicated in the brackets. ) C = πd (D) ) C = πr (r) ) F = ma (m) ) V = lbh (h) ) A = --bh (h) 6) = --πr h (h) 7) y = m + c (c) 8) y = m + c (m) 9) v = πr h (h) 0) v = πr h (r) ) C = -- ( F ) (F) ) y = -- ( a+ b) (b) 9 ) = gh (h) ) v = u + as (s) v ) ut + --at = (a) 6) s = -- ( u+ v)t (v) 7) N = π l (l) 8) X = lr (r) 9) A = + y ( y) -------------- () 0) p = ----------------- 6 () ) p = R D ------- () ) C = -------- y zy (y) ) I = PTR -- w (w) ) I = ---------- y 00 (R) ) C = d + t () 6) A = π( R r ) (R) 7) A = π( R r ) (r) 8) = a+ b (b) C( c) a 9) a = -------------------- (b) 0) = ----------- (b) b a+ b

Sumbooks 00 Bearings Eercise Draw diagrams to show the following bearings. ) A is 00 from B ) C is from D ) G is from H ) J is from K ) L is 7 from M 6) P is 08 from Q 7) R is 098 from T 8) U is 076 from V Eercise By measuring these angles, write down the bearing of point P from point A in each case. ) P A ) P N N ) P A ) A ) N S A P P S A Eercise ) If the bearing of A from B is what is the bearing of B from A? ) If the bearing of C from D is what is the bearing of D from C? ) A ship sails from port P on a bearing of 0 for 6km until it reaches point X. It then changes course onto a bearing of for a distance of 8km until it reaches point Y. Draw the ship s path accurately using a scale of cm to km. What is the bearing and distance of point Y from the port P? ) An aeroplane flies from airport A on a bearing of 0 for 7km until it reaches point B. It then changes course onto a bearing of for a distance of 80km until it reaches point C. Draw the aircraft s path accurately using a scale of cm to 0km. What is the bearing and distance of point C from the airport A?

Sumbooks 00 Parallel Lines In each of the following diagrams find the sizes of the marked angles. ) ) 6 7 a b c ) ) d e g f ) 6) h 87 i j 7 80 l k n m 7) 8) p 8 q u v 8 t 68 r w s 9) 0) y z β α δ

Sumbooks 00 Nets and Isometric Drawing ) Draw the net of a cube whose sides are cm. ) Draw the net of this cuboid. Also draw, on triangular dotty paper or isometric paper, a cuboid whose volume is the same as this one. cm 6cm cm ) This diagram shows part of the net of a triangular prism. Copy and complete the diagram. On triangular dotty paper or isometric paper, draw a diagram of the shape. 6cm cm cm ) Draw the net of this triangular prism cm cm 6cm ) The diagram on the right shows part of the net of a square based pyramid. Copy and complete the diagram. On triangular dotty or isometric paper, sketch a diagram of the shape. cm cm 6) The diagram shows a square based pyramid. Its base edges measure cm and its sloping edges are 6cm. Draw the net of its shape. 7) The diagram shows part of the net of a rectangular based pyramid. Copy and complete the diagram. On triangular dotty or isometric paper, sketch a diagram of the shape. cm cm cm cm 8) The diagram shows a rectangular based pyramid. Its base edges measure.cm and cm and its sloping edges are each cm. Draw the net of the shape.

Sumbooks 00 6 Triangles Calculate the sizes of each of the marked angles. ) º 0º ) 0º 0º y ) y 0º ) 0º ) y y 0º 0º 6) y º z 7º º z y 7) y z 8) 9) y º 6º z 0) ) º 7º º z y y z ) y 0º ) A BC=AC º B 70º y C

Sumbooks 00 7 Regular Polygons Calculate the interior and eterior angles in each of the regular shapes in questions to. ) A Heagon ) A Nonagon (9 sides) ) A sided figure ) A 0 sided figure ) 6) A E A B z F B y D C ABCDE is a regular pentagon. Line BF is a line of symmetry. a) What is the size of angle? b) Calculate the sizes of angles y and z. H G r s q C D ABCDEFGH is a regular octagon. CG is a line of symmetry. Calculate the sizes of angles p, q, r, s and t. F p t E 7) A G w B F y E z D v C ABCDEFG is a regular heptagon. Three lines of symmetry are shown. What are the sizes of angles v, w,, y and z? 8) What is the order of rotational symmetry of a regular octagon? 9) Eplain why a regular pentagon will not tessellate and a regular heagon will. 0) How many lines of symmetry has a regular nonagon? ) ABCDEFGHIJ is a regular 0 sided polygon (decagon) with centre O (where the lines of symmetry cross). Calculate the sizes of the angles ABC and AOC.

Sumbooks 00 8 Irregular Polygons ) A quadrilateral has internal angles of 90º, 00º and 0º. What is the size of the fourth angle? ) A heagon has angles of 00º, 0º, º, 0º and 0º. What is the size of the sith angle? ) An octagon has si angles of º. If the remaining two angles are equal, what is the size of them? ) A heptagon has si angles each of 0º. What is the size of the other angle? ) A decagon has two angles of the same size and a further eight angles of twice the size. What are the sizes of the angles? 6) What is the size of the angle? 60º 7) This heagon is symmetrical about the line AD. The angles at A and B are 0º and 0º. If the side BC is parallel to FE and the angle at C is twice the angle at D, what are the sizes of the other angles? A B F C E D A 8) The pentagon ABCDE has three angles of 90º. If the other two angles are equal, what are their size? E B D C 9) In the diagram, the octagon has two lines of symmetry. There are two different sizes of angle in the shape. If one of them is 0º, what is the other? A 0) The diagram shows the cross section of a steel bar. It is symmetrical about the line AB. If it has si interior angles of 90º and another of 60º, what are the sizes of the other interior angles? B

Sumbooks 00 9 Pythagoras' Theorem ) Calculate the length of the hypotenuse in each of the following triangles a) b) c) 6cm cm 8cm cm 9cm 6cm ) Calculate the length of the side marked in each of the following right angled triangles. a) 7cm b) cm.cm c) cm 6cm 6cm ) ) A 6 cm 6 cm cm Calculate the height of this isosceles triangle O cm B cm Find the distance of point T from the centre of the circle T ) Calculate the base 6) 0cm radius R of this cone cm 7cm of height cm and slant height of 7 cm 0cm R A kite has sides measuring 0cm and 0cm with the small diagonal measuring 8cm. Find the length of the longer diagonal 7) Calculate the length of the diagonal of a rectangle measuring 9cm by cm. 8) A rhombus has diagonals of 7cm and cm. Find the length of its sides. 9) A square has a side of 7cm. Find the length of its diagonals. 0) How far from the centre of a circle of radius 7cm is a chord of length 7cm ) A ladder rests against a wall. The ladder is metres long. The base of the ladder is m from the foot of the wall. How far up the wall will the ladder rest? ) A ladder, 6 metres long, rests against the side of a house. The ladder reaches metres up the side of the house. How far, to the nearest centimetre, is the bottom of the ladder from the base of the house? ) Calculate the length of the side of a square whose diagonal is cm.

Sumbooks 00 0 Trigonometry Use the sine ratio ) Calculate the length of the unknown side () in each of the following triangles. a) 8.cm 7 o b) 6 o cm c) 7 o.7cm d) 7 o 9.7cm e) cm 79 o ) Calculate the sizes of the unknown angles in each of the following triangles. a) b) 8.cm c) 7.cm cm 7cm cm cm d) cm 9cm e) 8.cm cm ) Calculate the length of the unknown side () in each of the following triangles a).cm b) 8.cm 80 o c) 7 o 67 o.6cm d).cm o e) o 7.cm

Sumbooks 00 Trigonometry Use the cosine ratio ) Calculate the length of the unknown side () in each of the following triangles. a) cm b) c) 70 o 6 o o 7.cm.6cm d) e) o cm 6 o 6.cm ) Calculate the sizes of the unknown angles in each of the following triangles. a) b) 7cm c) cm.6cm 0cm 7.cm 6.cm d) 8.6cm e) 9.7cm cm 7.cm ) Calculate the length of the unknown side () in each of the following triangles a) o cm b) 7cm 6 o c).6cm 7 o d) 6 o.cm e).cm 9 o

Sumbooks 00 Trigonometry Use the tangent ratio ) Calculate the length of the unknown side () in each of the following triangles. a) b) 9.cm 9 o 7 o 6.8cm c).cm 7 o d) e).cm 7 o 7cm 9 o ) Calculate the sizes of the unknown angles in each of the following triangles. a) b) c) cm 7cm cm cm 0cm d) cm 6cm e) cm.cm cm ) Calculate the length of the unknown side () in each of the following triangles. a) cm b) c) cm o d) 7 o 6cm cm 6 o e) 7 o 8 o 6.7cm

Sumbooks 00 Trigonometry Use the sine, cosine or tangent ratios. a) b).6cm Calculate the length of side 67 7cm Calculate the length of side c) d) e) f) g).6cm.6cm.cm Calculate the sizes of the two unknown angles 7.9cm Calculate the sizes of the two unknown angles.6cm 7.cm 6.cm Calculate the length of side Calculate the sizes of the two unknown angles A ladder rests against a wall. If the ladder is metres long and its base is. metres from the bottom of the wall, what angle does it make with the wall? h) m 6m A boat B is 6 metres from the bottom of a cliff of height metres. Calculate the angle of depression,, of the boat from the top B of the cliff. i) A ladder,. metres long, rests against a wall at an angle of to the wall. How far up the wall does the ladder reach and how far is its base from the wall? j) The angle between the diagonal and longest side of a rectangle is. If the longest side measures 6cm, what is the length of the shortest side? k) A swimming pool is metres long. If its depth varies from metre to. metres, at what angle to the horizontal is its base?

Sumbooks 00 Reflections, Rotations and Translations ) The diagram shows a triangle A,B,C. Copy this diagram and show the reflections; a) A',B',C' about the ais b) A'', B'', C'' about the y ais. y A B C 6 0 6 ) The diagram shows a rectangle A,B,C,D. Copy this diagram and show the reflections; a) A',B',C',D' about the line = b) A'',B'',C'',D'' about the line y =. y A D B C 6 0 6 ) The diagram shows a shape A,B,C,D,E. Copy this diagram and show; a) the reflection A,B,C,D,E about the line = b) the reflection y A,B,C,D,E about the line y = 0. c) The translation to A,B,C,D,E. 6 6 A E 0 B D C 6

Sumbooks 00 Reflections, Rotations and Translations y ) The diagram shows a square A, B, C, D. Copy this diagram and show the reflections A B a) A', B', C', D' about the line y = b) A'', B'', C'', D'' about 6 D 0 C 6 the line y = y ) The diagram shows a rectangle A, B, C, D. Copy this diagram and show the reflections A a) A', B', C', D' about D the ais b) A'', B'', C'', D'' about the y ais 6 0 B 6 C y ) The diagram shows a triangle A, B, C. Copy this diagram and show the reflections B a) A', B', C' about the line y = b) A'', B'', C'' about 6 A 0 6 the line y = C

Sumbooks 00 6 Reflections, Rotations and Translations ) The diagram below shows the triangle A, B, C. Copy this diagram and show the rotation a) to A, B, C of 90º clockwise about (0,0) b) to A, B, C of 90º anticlockwise about (0,0) Also show the translation 6 to A, B, C. 6 y B A C 6 0 6 ) The diagram below shows the rectangle A, B, C, D. Copy this diagram and show the rotation a) to A', B', C', D' of 90º clockwise about (,) b) to A", B", C", D" of 80º about (,) y A B D C 6 0 6

Sumbooks 00 7 Reflections, Rotations and Translations ) The diagram below shows the heagon A, B, C, D, E, F. Copy this diagram and show: a) the rotation to A', B', C', D', E', F' of 90º clockwise about (0,0) b) the translation to A", B", C", D", E", F", y A B 6 F 0 C 6 E D ) The diagram below shows the parallelogram A, B, C, D. Copy this diagram and show a) the rotation to A', B', C', D' of 90º clockwise about (0,0) b) the translation to A", B", C", D". y A B 6 0 6 D C

Sumbooks 00 8 Enlargements ) The diagram shows a rectangle A, B, C, D. Copy this diagram and enlarge it by a scale factor of through the point (0,0) y 0 8 6 A B D C 0 0 6 8 0 ) The diagram shows a triangle A, B, C. Copy this diagram and enlarge it by a scale factor of through the point (0,0 y 0 8 6 A C B 0 0 6 8 0

Sumbooks 00 9 Enlargements ) The diagram shows a rectangle A, B, C, D. Copy this diagram and enlarge it by a scale factor of -- through the point (, ) y 6 0 A B 6 D C ) The diagram shows a triangle A, B, C. Copy this diagram and enlarge it by a scale factor of -- through the point (, ) A y C B 6 0 6

Sumbooks 00 0 Similar Shapes ) The two triangles below, ABC and DEF are similar. a) Which angle is equal to angle CAB? b) What is the scale factor between triangles ABC and DEF? c) Calculate the size of side DE. d) Calculate the size of side AC. A 7.cm.cm D C.cm B F 7.6cm E ) The diagrams below show the fronts of two similar garden sheds. a) What is the ratio of the lengths of the smaller shed to the larger one? b) What is the width of the larger shed? c) What is the total height of the smaller shed?.8m.m.m.m ) In the diagram, AE is parallel to BD. a) Which angle is equal to angle EAC? b) Calculate the length of BD. c) Calculate the length of AB..7cm A B.8cm E.7cm D.cm C ) In the diagram AB is parallel to DE a) Which angle is equal to angle ACB? b) What is the ratio of the lengths of triangle ABC to CDE? c) Calculate the length of CE. d) Calculate the length of BC. D.8cm A.8cm C 9cm.º cm B E

Sumbooks 00 Locus Problems ) Plot the centre of this circle, with a diameter of cm, as it rolls along the line to the right. ) Plot the locus of the centre of the circle, diameter cm, as it rolls around the outside corner. ) Plot the locus of the centre of the circle, diameter cm, as it rolls around the inside corner. ) Plot the locus of the centre of the circle, diameter cm, as it rolls around the two corners. ) A bo, cm square, is turned about corner C until it moves from position to position. Plot the locus of corner D. A Position B Position cm D C A B 6) Plot the path of corner D as the bo is pushed over onto its side CB. 6cm D cm C 7) Bo ABCD, dimensions cm by cm, is rolled over from position to position then position. a) Which side is now on the bottom? b) Plot the path of corner C. A D Position B Position Position C

Sumbooks 00 Locus Problems ) A house has eternal dimensions of 6 metres by 0 metres. It has security lights on each corner with detectors which can recognise movement up to a distance of 8 metres. Using a scale of cm to represent metres, shade in the area in which it will detect movement. 6 metres 0m ) The entrance to a yachting marina is though a gap in the breakwater. The breakwater is 0 metres wide and the gap is 0 metres. Yachts cannot go within 6 metres of the breakwater. Using a scale of cm to represent metres, shade in the area around the breakwater within which yachts are not allowed. Breakwater Breakwater ) A field is watered through a nozzle which moves along a fied rail 0 metres long. Water can reach up to a distance of 0 metres from the nozzle. Using a scale of cm to represent metres, draw a diagram to show the area which can be covered by the water. Track. Nozzle 0 metres ) The diagram shows the plan of a house and garden. A tree is to be planted which must be at least 0 metres from the house and metres from each of the fences. It also has to be at least 6 metres from the apple tree, located in the corner of the garden, metres from each of the two fences. Using a scale of cm to represent 0 metres, copy this diagram and shade in the area in which the tree can be planted. Fence 6m House Fence 0m Garden m Fence. Apple tree Fence 0m ) An aeroplane s course is determined by three radar stations, A, B and C. C is km north of B and A is km west of B. An aeroplane must always be the same distance from A and B until it is 0km from C when it turns due west. By construction, show the course of the aeroplane with respect to the three stations. Use a scale of cm to represent km. How far from B is the aeroplane when it alters course? North. A km C. km. B

Sumbooks 00 Degree of Accuracy Eercise. ) Round off each of the following numbers to the accuracy stated. a) to the nearest thousand. b) 6 to the nearest hundred. c) 7 to the nearest ten. d) 78 to the nearest hundred. e) 60 to the nearest thousand. f) 7 to the nearest thousand. ) Round off the number 97. a) to the nearest ten. b) to the nearest hundred. c) to the nearest thousand. d) to the nearest ten thousand. ) Which of these numbers can be rounded off to 000? a) b) 9 c) 6 d) 7 e) 00 f) 99 g) 00 h) 99 ) State the limits between which the following whole numbers lie. Each has been rounded off in the way shown in the brackets. a) 00 (to the nearest 00) b) 00 (to the nearest 00) c) 00 (to the nearest 00) d) 000 (to the nearest 000) e) 70000 (to the nearest 0000) f) 7000 (to the nearest 000) g) 0000 (to the nearest 000) h) 0 (to the nearest 0) i) 70 (to the nearest 0) j) 0 (to the nearest 0) Eercise. Copy these diagrams into your book and fill in the blanks with either a number, < or. ) ) ) ) ) 0 0.? A length of cms to the nearest centimetre 0. Length <... 9 9. 0 0. A length of 0 cms to the nearest centimetre 9.... Length... 0.? 9. 9. 9. A time of 9. seconds, to the nearest 0. second.... time... 9. 7.8? 7.8? 7.8 A mass of 7.8 Kg to decimal places... Mass <....6.60.6.6.6 A capacity of.6 litres correct to d.p..60... capacity....6 Eercise. Each of these values has been rounded to the last figure shown.write down their limits. ) 9. seconds ) 6. mm ) 9. kg ) 7.6 kilometres ) 9.6 metres 6).6 seconds 7) 6 mg 8) 7. litres 9) 7. centimetres 0) 6.8 tonnes ) 9. ml ). seconds

Sumbooks 00 Circumference of a Circle. In each of the following questions use π =. or use the π button on your calculator. Eercise Calculate the circumference of each of the following circles ) Radius cm ) Radius 6cm ) Radius 0cm ) Radius 8 metres ) Radius 8 metres 6) Radius 7 metres 7) Diameter cm 8) Diameter 6cm 9) Diameter cm 0) Diameter.m ) Diameter 7m ) Diameter m Eercise Calculate the diameters of circles with the following circumferences (correct to significant figures) ) 0cms ) 0 cms ).metres ) metres ) 6cms 6) 76metres Eercise ) A car wheel has a diameter of 0cm. How far will the car travel if the wheel turns times? ) If the same car wheel turns 00 times, find the distance travelled correct to the nearest metre. ) A hose pipe is stored by winding it around a drum of diameter 70cms. If it makes turns, how long is the hose correct to the nearest metre? ) A car has a wheel diameter of cms. How many revolutions does it make while travelling a distance of kilometre? (give your answer correct to the nearest whole number) ) A length of cotton measuring metres is wound around a cotton reel of diameter cms. How many turns does it make? (correct to the nearest turn) 6) A bicycle wheel has a diameter of 6cms. How many turns will it make while travelling a distance of km? 7) Another bicycle travels km and its wheels each turn 7 times. Calculate the diameter of its wheels, correct to the nearest cm. 8) A pulley wheel, of diameter. metres, raises a lift in a hotel from the ground floor to the 9th floor. In doing so it makes 9 complete turns. What is the distance, correct to the nearest centimetre, between each floor?. 9) An artificial lake is in the shape of a circle of diameter 00 metres and has a path running around it. It is planned to hold a 0 kilometre race around the lake. How far apart, to the nearest metre, must the start and finish be?

Sumbooks 00 Area and Perimeter ) Calculate the areas and perimeters of rectangles measuring; a) cm by cm b) 6cm by 8cm c) 9cm by.cm d) 8.cm by 9.cm e). metres by 80cm f) 60cm by 0.9 metres. ) Calculate the areas of the following shapes; a) b) 8cm.8cm c) cm d) 7cm.cm 8cm 9cm 0cm cm ) Calculate the areas of the following circles. Use π=. or the π button on your calculator. Give your answer correct to decimal place. a) Radius cm b) Radius 7.cm c) Radius 9cm d) Diameter 7cm e) Diameter.6cm f) Diameter 7.cm ) Calculate the areas of the shaded parts of each of the following shapes. a) b) c) 6cm 8cm cm cm cm cm 7cm 8cm 6cm d) e) f) 0cm 6cm 7cm 8cm 0cm cm 0cm 7cm 6cm cm cm cm ) How many 0cm square tiles are needed to cover the floor of a room measuring metres by -- metres? 6) A lawn is in the shape of a quarter circle. If its radius is 8 metres, calculate its area and perimeter.

Sumbooks 00 6 Volume Eercise Without using a calculator, change; ) cm into mm ) 0.00cm into mm ).m into cm ) 0.0m into cm ) 0,000 mm into cm 6),00,000 cm into m 7) 0.m into litres 8),000 ml into litres 9) 8 litres into ml 0) 0.00 litres into ml. Eercise ) A cardboard bo is in the shape of a cuboid measuring 6cm by cm by cm. Calculate its volume. ) A large cardboard bo has internal base dimensions of 80cm by 0cm and a height of 60cm. It is to be packed with smaller boes measuring 0cm by cm by 6cm. How many boes can be put on the bottom layer and how many of these layers can be put in altogether? ) A trench 0.7m wide by.m deep and 0 metres long is dug on a building site. Calculate the amount of earth removed. ) A cylindrical drinks can has a base of 7cm and a height of 0cm. Calculate; a) its volume in cm and b) its capacity correct to the nearest ml. ) A water tank, in the shape of an open cuboid, has a base measuring 0cm by 60cm and a height of 0cm. How many litres of water will it hold? 6) A circular pond of m diameter and cm depth is filled with water. How many litres are needed? 7) A rolling pin is made from pieces of wood as shown below. The thicker piece is cm in diameter and cm long. The two end pieces are each.cm in diameter and 0cm long. If cm of this wood weighs 0.7g, find its total weight. 8) A beaker is in the shape of a cylinder with a base diameter of cm and a height of 9cm. How many times can the beaker be completely filled from a jug holding litres? 9) A metal tube has an outside diameter of.cm and a thickness of mm. If its length is m, calculate the volume of metal it contains to the nearest cm. 0) An open tank, in the form of a cuboid, can hold 00 litres of water. If its base has dimensions of 0cm by 80cm, what is its height? ) A water tank, in the shape of an open cuboid, has a base measuring 0cm by 70cm and a height of 0cm. It has water in it to a depth of 0cm. A metal cube of sides cm is lowered into the water. By how much will the water rise? ) A swimming pool is 0.8m deep at the shallow end and m deep at the other end. If its length is m and its width is 0m, calculate its capacity in litres. m 0.8m m 0m

Sumbooks 00 7 Compound Measure - Speed and Density Eercise. Speed ) A car travels at the following speeds (a) 0 mph (b) 0 mph (c) 60 mph. In each case say how far the car travels in (i) -- hour (ii) hours (iii) -- hour ) A train goes from Chester to London, a distance of 00 miles. It travels at a speed of 80 mph. (a) How far does it travel in hours? (b) How far will it travel in hour (c) How long will it take to travel from Chester to London? ) (a) A train travels between two towns, A and B. Its average speed is 60mph. The train takes -- hours. How far apart are the towns? (b) Another train makes the same journey. This train takes hours. What is its average speed? ) Jane travels to London down the motorway. She travels the first 7 miles at an average speed of 0 mph. She then travels the remaining 0 miles at an average speed of 0 mph. How long did her journey take? ) A car travels at an average speed of 60 miles per hour down the motorway. How far will the car travel in (a) minutes (b) hour 0 minutes Eercise. Density ) These cubes measure cm by cm by cm. -- Their volumes are each cm. The weight of each black cube in g. The weight of each white cube is g. Calculate the average weight of (a) black and white cubes (b) black and white cubes ) Red centimetre cubes weigh g and blue centimetre cubes weigh g. Find an arrangement of cubes which give an average density of.g per cm. ) Using red and blue cubes find an arrangement with an average density of.g per cm. ) Can you list other arrangements of blue and red cubes which give an average density of.g per cm? ) Black cubes weigh 6 gram and white cubes weigh grams. (a) A black cube and a white cube are put together. What is their average density? (b) If one black cube and white cubes are put together, what is their average density?

Sumbooks 00 8 Compound Measure - Best Buy and a Mied Eercise Eercise. Finding the best buy Calculate which of the following sizes give the best buy. ) Toothpaste costing 8p for a 7ml tube,. for a ml tube.90 for a 00ml tube ) Shampoo costing 0p for a 0ml bottle 9p for a 00ml bottle 0p for a 800ml bottle ) Baked beans costing 8p for a 0g tin p for a 0g tin 6p for a 700g tin ) Paint costing.0 for a litre tin. for a -- litre tin 7.9 for a litre tin ) Oil paint is sold in different sizes. A 7ml tube costs.0. A 0ml tube costs.0. A 00ml tube costs.0. Eercise. Mied ) Decide which one of the following pairs of cars is the most economical. (a) Car A travels 80 miles and uses litres of petrol. Car B travels 0 miles and uses 7 litres of petrol. (b) Car C travels 60 miles and uses 9 litres of petrol. Car D travels 96 miles and uses litres of petrol. ) Sally has to paint the ceilings of her house. She needs to give each two coats and the total area of the 8 ceilings is 0 square metres. litre of paint will cover m. If she can buy the paint in litre and -- litre tins, how much paint will she buy? ) David plans to spread "lawn care" over his lawn. The instructions say that it has to be used at the rate of -- ounces per square yard. His lawn is in the shape of a rectangle measuring 0 yards by 8 yards. How much "lawn care" will he have to buy if it is sold in lb packets? (Note 6 ounces (oz) = pound (lb)) ) Jane needs to paint the walls in her bedroom. The room measures m by m and is -- metres high. However m is taken up by the door and a window. Paint is sold in litre and litre cans and it will cover the walls at a rate of m per litre. She gives the walls coats of paint. How many cans of paint will she have to buy?

Sumbooks 00 9 Formulae for Area, Volume and Perimeter With each of the following shapes a number of formulae are given. Decide which formula best satisfies the situation given. ) Which formula could be used to find (a) the area (b) the perimeter? w (i) w + y + z (ii) wy + yz (iii) w + wz yz (iv) w ( y) + z y z (v) w + + z (vi) w+ + y+ z ) Which formula could be used to find (a) the area (b) the perimeter? y r (i) (iii) (v) --πr + + --y --πr + + y+ --y --πr +.y (ii) (iv) -- ( πr + + y) (vi) --πr + + y --πr + + y ) Which formula could be used to find (a) the volume (b) the surface area? (i) --h w (ii) --h + w h w (iii) (v) --h+ w --h + hw (iv) (vi) --h + hw --h+ hw + w ) Which formula could be used to find (a) the area (b) the perimeter? h w (i) 6( h+ w) hw (iii) h + w (ii) (iv) --h --π h + w ( + w) (v) --π ( h + w ) h (vi) -- ( h + w ) ) In this bottle shape, which formula could be used to find (a) the volume (b) the surface area? y (i) (iii) (v) 7 --πy 7y 6 --π y -----π y (ii) (iv) (vi) --πy --π 6y 8 -- y y

Sumbooks 00 60 Formulae for Area, Volume and Perimeter ) An electrician installs the electrical wiring in new houses. She estimates the amount of cable needed for a house by using one of the formulae shown below, where L is the length of the front of the house, H is the height of the house and W is the distance from the front to the back of the house. H W L a) L + W + 7H + 0 b) L(W + 9H) c) LW + LH + HW d) LWH (i) Eplain why you think that formula d is not the one she uses. (ii) Which formula do you think she uses? Eplain how you come to this conclusion. ) Which of the following formulae could represent (a) area, (b) volume and (c) perimeter? The letters a, b, c, d, and y are dimensions measured in centimetres. ) ab + cd ) a+ b + cd ) a+ + y ) ab + y ) πa + b 6) + ab + c 7) ay + bac 8) a + πa + c 9) ( + y) 0) -- ( 7 + y a ) ) 7y + πab ) y πy ) ( y + ) ) π( a b ) ( a + b ) ( a + b ) ) -------------------------- 6) ----------------------- 6 7) + 7y --ab 8) 7 + b 7 a a y 9) -------------------------------------------- 0) --------------------------- 7 --a

Sumbooks 00 6 Questionnaires ) A large company want to build a supermarket in the town. Paul designs a questionnaire to find out whether local residents want it and if so whether they will use it. Write down two questions he might use, each question having a choice of responses. ) Bill is keen to have a wine bar in the high street. He wants to find out what local residents think. In order to get an unbiased response, he chooses two of the following groups of people to ask. (a) the youth club (b) the old peoples home (c) the local supermarket (d) the residents of the high street (e) the residents of a local housing estate Which groups do you think he should choose and why? ) The local council decide to pedestrianise the centre of town (i.e. stop all vehicles using it). They decide to ask the traders in the town centre their opinion and no one else. Is this a good idea? Eplain your answer. ) The school committee decide that the tuck shop is to sell vegetarian snacks. The snacks they want are a) fruit b) yoghurt c) oatmeal biscuits d) nuts and e) wholemeal sandwiches. Devise a questionnaire in which they can determine the snacks pupils like best. ) A new burger restaurant is to be opened near to Claire's school. Lots of the local people have said that they don't want it. Claire thinks that most people do want it to be opened so she writes a questionnaire to get the necessary evidence. She decides to give out the questionnaire to members of year. (a) Why is this not a good idea? (b) Which of the following groups of people would give the least biased replies? Say why. (i) Members of the youth club (ii) Customers leaving the local supermarket (iii) Members of the local golf club (iv) The people living net to the school 6) The manager of a D.I.Y. store wants her staff to wear a new uniform. She thinks that they should all wear green tops and either a black skirt or trousers. The deputy manager thinks that they would prefer a red top and jeans. The manager designs this questionnaire for the staff I think that it is a good idea to have green tops and either a black skirt or trousers as our school uniform. Please indicate whether you agree with me by ticking the appropriate bo below Agree Disagree Do you think that this is a good questionnaire? Make comments

Sumbooks 00 6 Pie Charts ) A class of 6 pupils were asked how they normally came to school. said they came by bus, 0 walked, 8 came by car and by bicycle. Draw a pie chart to show this information by first calculating a) the number of degrees representing pupil and hence b) the number of degrees representing each of the groups. ) The number of people, correct to the nearest 00, who voted at the local election were Conservative 600 Labour 00 Liberal Democrat 700 Independent 00 Green party 00 Draw a pie chart to show this. ) A town council wants to make its transport system more efficient. As a first step they interviewed a sample of 900 people. They were asked how they got into town. Their results were as follows. Train 0 Bus 0 Car 00 Bicycle 0 Walked 0 Show this information on a pie chart. ) The United Kingdom is made up of the following approimate areas, measured in millions of hectares England. Wales Scotland 8 Northern Ireland. Show this information on a pie chart. ) David earns 90 a week. His epenses each week are as follows Lodging/Food 0 Clothes 0 Entertainment Bus fares Savings Other 8 Show this information on a pie chart 6) 0º º Oak Ash Horse Birch Chestnut º 0º 60º Beech 90º Sycamore The pie chart shows the composition of a mied woodland area. Altogether there are,60 trees. Calculate a) how many trees are represented by º b) how many trees there are of each type 7) The table below shows the number of visitors to Dibchester castle in 996. Spring Summer Autumn Winter 700 00 800 00 Construct a pie chart to show this information. Write down a) the number of degrees representing 00 people b) the number of degrees representing each season.

Sumbooks 00 6 Frequency Polygons Eercise Construct a frequency polygon from each of the following sets of data ) This table shows the heights of 0 tomato plants. Height of tomato plant 89cm 90cm 9cm 9cm 9cm Frequency 6 ) This table shows the number of goals scored per game in the English football league during one particular week. Number of goals scored Frequency 0 6 7 8 0 7 7 ) A milkman delivers milk to 00 houses on his morning round. The table shows the number of bottles the households take. Number of bottles 6 Frequency 7 9 0 70 0 8 7 0 ) A firm makes egg timers, which are supposed to run for eactly minutes. A sample of 00 were tested and the times they gave were as follows. Time (secs) 6 7 8 9 0 Frequency 8 8 0 0 Eercise Construct a frequency polygon from each of the following sets of grouped data. In each case make a list of the mid value of each group first (as in question ). ) The scores of 00 students in an eamination were as follows. Mark Frequency Mid mark 0- - - 0 0 0 - - - 6-7- 8-9- 0 0 60 70 80 90 00 7 9 67 8 6..... 6. 7. 8. 9. ) This table shows the marks gained by 00 students in an eamination. Mark Frequency 0- - - 0 0 0 - - - 6-7- 8-9- 0 0 60 70 80 90 00 0 6 8 7 0 ) This table shows the heights of 00 college students in a class (to the nearest cm). Height (cm) - 6-0 - 6-6- 66-7- 76-8- 60 6 70 7 80 8 Frequency 7 0 6 0 8 8 Why do you think that this polygon has two peaks? ) This table shows the times at which 600 pupils arrived at school. Time Number 8.0-8.0-8.0 8.0 8.0-8.0-8.0-8.0 8.0 9.00 9.00-9.0-9.0 9.0 0 6 0 9 7 0 From the polygon decide at which time you think that school starts.

Sumbooks 00 6 Frequency Polygons ) These tables show the average monthly rainfall and temperature at two holiday destinations. Destination A Month Temp ºC Rainfall cm Destination B Month Temp ºC Rainfall cm J F M A M J J A S O N D 9 0 7 0 8..0.6.9.8.7.0..9. 8. 6. J F M A M J J A S O N D 7 0 6 7 7 0...7 6. 7. 8.0 6. 6..0... a) Draw a frequency polygon showing the temperatures at both destinations. Show both polygons on the same diagram. (i) Which destination is in Australia and which is in Europe? (ii) Give reasons for your choice. (iii) In which months of the year are the temperatures about the same? b) Draw a frequency polygon to show the rainfall at both destinations. Choose the best month to go on holiday, for each destination. Eplain why you made your choices. ) The following table shows the amount of profit made by a company during 99 and 99 (in millions of pounds) Year J F M A M J J A S O N D 99...9...0...9..0.9 99.7..0.7.8.7..0..9.7. a) Draw a frequency polygon showing the profits for both years. Show them both on the same diagram. Plot the profit vertically and the twelve months of the year horizontally. b) From the diagram, make comments on (i) The profit in 99 compared with 99. (ii) The trend at the end of 99 (i.e. are profits still going down or are they picking up?) Eplain your answer. (iii) Predict what the profits will be for the first three months of 99. ) Devonham High School are allowed to enter one person for each event in the annual county games. The three best athletes in the 00 metres are Brian, Mike and John. At the last ten races in which they ran against each other, their times (in seconds) were Brian.......... Mike..7.9..0.7.9.8..7 John.9.9.8.7.6..... Draw the three frequency polygons on one diagram, using a different colour for each. Use a scale of cm between each of the races on the horizontal ais and cm to represent 0.sec on the vertical ais. Begin your vertical scale at secs. From the diagram decide who is to represent the school. Eplain why you chose that person. ) The table below shows the profits made by two companies during 99. Month J F M A M J J A S O N D Company A...6..8...9..0.7.9 Company B.....7...7.8.9.9. Draw a frequency polygon showing the profits for both companies. Show both polygons on the same diagram. Compare the two graphs and make comments

Sumbooks 00 6 Mean, Median, Mode and Range Eercise In each of the following, put the data into a frequency table and write down the mode and range..,,,,,, 6,,,,,,,,,,,,,,,,,,,,,,,,, 7, 6.,, 7,,, 8, 0, 0,, 8,, 9,, 6, 0, 8, 0, 6,, 8,, 9, 0,, 7,, 0, 7,,, 9 8,,, 6,, 6, 0,,,, 8, 7,, 0,,.,, 7,,,, 7,, 6,,, 6, 7,,, 6, 7 7, 6,,,, 7,, 6, 6,,,,,,,,, 6,,,, 6,, 7, Eercise. Find the median and range of each of the following sets of data.. 8, 7,, 0,,, 6, 6,,,,, 8, 7 0,, 9,,,, 7. 9, 9, 7, 6, 7,,,,, 7, 7, 6,, 7,, 8. 70, 7, 0, 7, 80, 8, 6, 0, 8, 8 9, 0, 70, 68, 7, 8, 77, 7, 60, 7, 7, 8, 6,,, 6,,, 7 Eercise. Calculate the mean of each of the following sets of data, giving your answer correct to four significant figures wherever necessary.. cm, 7cm, 8cm, cm, cm, cm, cm, 9cm, 8cm, 6cm. grams, 0 grams, 8 grams, 7 grams, 68 grams. 6 metres, m, m, 8m, m, 6m, m, 7m, m, m., 6, 0,, 7, 9,.,,,, 0, 8 6..6,.9,.7,.,.,.0 7. --, 7 --, 9 --, -- 8. 79,,,,, 9., 6, 7, 6, 7, 6, 8, 0,, 0., 8, 7, 7,, 6,,, 0 Eercise. In each of the following give the answer correct to four significant figures wherever necessary.. The mean of si numbers is. and the mean of a further seven numbers is. What is the mean of all thirteen numbers combined?. The mean weight of si people is 8kg. If three more people, weighing 9kg, 07kg and 78kg join them, what is their new mean weight?. The mean weight of si people in a lift is 90kg. If the maimum total weight allowable in the lift is tonne, approimately how many more people will be allowed in?

Sumbooks 00 66 Mean. Find the average speed of a car which travels 9 miles in hours, then 8 miles in hours and finally 87 miles in hours.. The car in question returns home in 6 hours. What is the average speed for the complete journey?. A batsman scores 7, 7,, 8,, 9 and 7 in 7 innings. What is his batting average?. The cricketer in question scored 0 (zero) in his eighth innings. What was his new batting average?. A car makes the following journeys. miles in city traffic using -- gallons of petrol, 86 miles on the motorway using gallons of petrol and 9 miles on country roads using gallons of petrol. Calculate the average fuel consumption of the car in miles per gallon. 6. A cricketer has a batting average of 7 runs per innings over 7 innings. During his net three innings he scores 6, 7 and 0. What is his new batting average? 7. A certain type of vegetable is classed as grade, grade or grade. Grade have an average weight of less than 0 grams, Grade from 0 grams to 00 grams and Grade more than 00 grams. What grade are the following (a) A bag weighing kg containing vegetables. (b) A bag weighing kg containing vegetables. (c) A bag weighing -- kg containing 6 vegetables. If the three bags are mied together, what grade would they be sold as? 8. Sarah keeps records of how much petrol her car uses. She finds that after servicing the car she gets a better fuel consumption. These are her figures for last year. Month Speedometer reading Petrol used (miles) Beginning End Litres January 7 07 February 07 77 6 March 77 7 6 April 7 90 May 90 09 8 June 09 July 6 9 August 6 690 9 September 690 6 October 6 668 November 668 68 6 December 68 70 Calculate her average fuel consumption for each month (in miles per litre) Use these figures to determine in which month she had the car serviced

Sumbooks 00 67 Mean Find the mean value for each of the following sets of frequencies, correct to significant figures.. The number of children in the families of pupils in a class. No. of children frequency in a family 7 7. The number of absentees from a class during a period of 60 days. No. of absentees frequency (days absent) 0 9 6 6 7. The number of broken glasses found when 00 boes, each containing 6 glasses were opened. No. of broken glasses frequency 0 7 76 9 0 6 6 ) Packets of sweets each contain sweets. The number of red sweets were counted in a sample of 00 packets. Number of red sweets frequency (number of packets) 6 7 8 8 9

Sumbooks 00 68 Mean - Diagrams ) The goals scored by 0 teams on a Saturday are shown below in the diagram. Calculate the mean number of goals scored. Frequency 8 0 6 8 0 6 8 0 0 6 7 Goals scored per match ) The diagram shows the marks obtained by year 0 in an eamination. Calculate the mean mark. Frequency 0 8 6 0 8 6 0 0 6 7 8 9 0 Number of students ) Jane carries out a survey to find the number of brothers and sisters year 8 pupils have. The results are shown in the diagram. Calculate the mean number they have. Frequency 0 0 0 0 0 6 7 Numbers of brothers and sisters

Sumbooks 00 69 Mean - Frequency distributions with class intervals By first finding the mid value of each class interval, calculate an approimate mean for each of the tables of values shown below. State also the modal class in each case.. This table shows the heights of a sample of pupils in a school. Height of child(cm) Frequency 0 < h 0 0 < h 0 0 < h 0 0 < h 60 60 < h 70 7 Give your answer correct 70 < h 80 to the nearest millimetre.. This table shows the weights, in grammes, of kg bags of potatoes. Weight of bag Frequency 000 < w 00 76 00 < w 00 00 < w 00 8 00 < w 00 00 < w 00 7 Give your answer correct 00 < w 060 to the nearest gramme..this table shows the weekly wage for employees in a factory. Wage Frequency 0 < 80 7 80 < 0 6 0 < 60 60 < 00 7 00 < 0 0 < 80 80 < 0 Give your answer correct 0 < 60 to the nearest penny.. The life, in hours, of batteries tested by a manufacturer. Life (hours) Frequency 0 < h < h 0 9 0 < h 7 < h 0 0 < h < h 0 9 Give your answer correct 0 < h 6 to the nearest minute.. This table shows the heights of tomato plants ranging from 9 cms to 6 cms. Height of plant Frequency 9 < h 0 0 < h 0 < h < h 7 < h 0 < h Give your answer correct < h 6 to the nearest millimetre.

Sumbooks 00 70 Mean - Histograms ) The frequency table below shows the heights of 86 plants. (a) Draw a histogram of the information. (b) By using the mid-value for each class interval, calculate an approimate value for the mean height of the plants. Height of plant Frequency (centimetres) 0 h < h < 7 h < h < h < h < 6 6 ) This histogram shows the weights of 8 students within the range 0 to 0kg. Calculate the mean weight. ) This histogram shows the percentage marks scored by a group of students in an eamination. Calculate the mean mark. ) Bill does a survey of 00 school children in year 7. He measures their height and plots them as a histogram. Calculate an approimate value for their mean height Frequency Frequency Frequency 8 6 0 8 6 0 0 0 60 70 80 90 00 0 0 0 Weight in kg 0 6 8 0 0 0 0 0 0 0 60 70 80 90 00 Percentage mark 8 0 6 8 0 0 0 0 0 Height (cm)

Sumbooks 00 7 Cumulative Frequency ) The table below shows the frequency distribution of the weekly wages for employees in a factory. Wages ( w) Frequency 0 < w 80 7 80 < w 00 00 < w 0 0 < w 0 0 < w 80 0 7 a) Complete this cumulative frequency table. Wage Cumulative frequency 80 00 0 7 b) Draw the cumulative frequency graph c) From the graph estimate (i) the median wage (ii) the interquartile range (iii) the approimate number of employees who earn more than 0 per week. ) Frequency 0 0 0 0 0 60 6 70 7 80 8 90 This diagram shows the heights of 0 plants. a) Use the diagram to complete the table below. Height of plants(cm) 60 cm < height 6 cm 6 cm < height 70 cm 70 cm < height 7 cm 7 cm < height 80 cm 80 cm < height 8 cm 8 cm < height < 90 cm Frequency Cumulative frequency 6 6 b) From the table above, draw the cumulative frequency diagram. c) From the cumulative frequency diagram estimate (i) the median (ii) the number of plants whose height is less than 8 cms.

Sumbooks 00 7 Cumulative Frequency ) Nina carries out a survey of the speeds of vehicles passing a certain point on a motorway. Her results are shown in the table below. Speed (mph) 0 < speed 0 0 < speed 0 0 < speed 0 0 < speed 60 60 < speed 70 70 < speed 80 80 < speed 90 Frequency 6 8 7 6 Cumulative frequency a) Copy and complete the table for the cumulative frequency. b) Draw the cumulative frequency graph. c) From the graph estimate (i) the median speed (ii) the approimate number of cars whose speed is below 7mph ) Batteries are tested by using them in an electric toy and recording the length of time the toy operates before the battery fails. The results of 0 batteries are shown below Time (t hours) Frequency 9 < t < t < t < t 7 7 < t 9 0 9 a) From the data draw a cumulative frequency graph. b) From the graph, estimate (i) the median life of a battery (ii) the interquartile range. If the battery company guarantee that their batteries last longer than hours, approimately what percentage of their batteries don't meet this criteria? ) The table below shows the runs scored by batsmen in a cricket team. Runs scored Frequency - 0-0 - 60 6-80 8-00 0 6 a) Complete this cumulative frequency table Runs Cumulative frequency 0 0 60 0 b) Draw the cumulative frequency graph c) From the graph estimate (i) the median number of runs scored (ii) the number of times more than 70 was scored

Sumbooks 00 7 Scatter Diagrams Draw a scatter diagram for each of the following results. Draw a line of best fit and use it to answer each of the questions. You must show clearly on your diagram how you get your answer. ) A class of pupils sat an eamination in mathematics. The eamination consisted of two papers. The following table shows the marks scored by a sample of 0 of the pupils. Paper Paper 6 77 8 9 7 67 7 9 7 6 6 6 7 7 7 a) A pupil missed paper but got on paper. What was her estimated mark for paper? b) Another pupil missed paper but got 8 on paper. What was her estimated mark for paper? ) A garden centre raises plants from seed. The gardener puts the seeds into trays of different sizes. When they have germinated he takes one tray of each size and checks how many plants have germinated. No of seeds in tray No of plants germinated 0 0 6 0 00 8 7 79 He finds that he has forgotten to check a tray which holds 70 seeds. How many plants would he epect from it? ) The heights and weights of 7 ladies are shown in the table below. Height (cm) Weight (kg) 0 60 6 68 70 7 60 6 6 6 Estimate the weight of a woman whose height is 8cm. ) A survey is carried out into the sizes of 0 apple trees in a garden. The height is measured (using trigonometry) and the circumference of its trunk is measured one metre from the ground. This is a table of the results obtained. Circumference cm Height metres 8.9 7. 9. 0..6.8.7.. 8.0 0.8 What is the approimate circumference of a tree whose height is.m? ) The table shows the number of hours of rainfall per day at Northend-on-sea and the number of deck chairs hired out each day over a period of one week. Hours of rainfall 0 7 0 No of deck chairs hired out 0 00 60 90 0 From your graph predict how many deck chairs would be hired out if there were 8 hours of rainfall.

Sumbooks 00 7 Scatter Diagrams Draw a scatter diagram for each of the following results. Draw a line of best fit and use it to answer each of the questions. You must show clearly on your diagram how you get your answer. ) A vertical spring, fied at its upper end, was stretched by a weight at its lower end. The length of the spring for different loads was measured and the results recorded, as follows. Load (g) 0 0 0 0 0 0 60 Length (cm)...7. 6. 7.7 8.6 From your diagram, estimate a) The load when the length of the spring is cm. b) The length of the spring for a load of g. 70 9. 80 0.6 ) David travels to work each day by car. Most of his journey is down a ten mile stretch of motorway. Over a ten day period, he records the time taken to get to work and the speed he travels down the motorway. Speed (mph) Time taken (min) 6 9 0 6 0 70 7 60 70 9 70 8 8 From your diagram, estimate how fast he would have to travel down the motorway in order to get to work in 0 mins. ) At the end of each week, Jenny saves whatever pocket money she has left from that week. She finds that the more times she goes out each week, the less money she has left. Here is a table showing the number of times she went out over a period of 8 weeks, together with the amount of money she saved. Number of times out Money saved (pence) 0 90 0 0 80 80 90 80 Jenny wants to save.0 every week for her holidays. From your graph decide on the maimum number of times she can go out each week. ) In an eperiment twelve pupils were weighed and their heights measured. Here are their results. Weight (kg) Height (cm) 9 8. 6 6 7 60. 8 66 66 8 66. 7 6 76. 9 7 79. It is known that another pupil weights 7kg. Approimately how tall is he?

Sumbooks 00 7 Probability Find the probability of the events in questions to 6 happening ) Throwing a number on a dice numbered to 6 ) Drawing a king from a pack of playing cards (there are kings in a pack) ) Selecting a girl at random from a class of 0 boys and girls. ) Winning first prize in a raffle if you hold 0 tickets and 00 have been sold. ) Picking an even number from the numbers to 0 inclusive. 6) Throwing an odd number on a dice numbered to 6. 7) Find the probability of an event not happening if the probability of it happening is 0.. 8) The order of play in a badminton competition in decided by drawing names from a hat. Si names, Jane, Andrew, Stephen, Claire, Jenny and Jonathan are put into the hat and drawn at random. Find the probabilities of a) drawing Claire's name first b) drawing a boy's name first c) not getting Stephen's name first. 9) A bag contains discs, red, green and blue. A disc is taken out at random. What is the probability of drawing a) a green disc b) a red disc c) a disc which is not a blue disc. 0) In a raffle, 000 tickets are sold. Emily buys tickets. What is her chance of winning? If the chance of David winning is 0.0, how many tickets did he buy? What is the probability of him not winning? ) A biased spinner has the numbers,, and on it. The probability of getting a is 0., a is 0., and a is 0.. a) What is the probability of getting a? b) What number are you most likely to get? c) If it is spun 00 times, how many 's would you epect to get? d) What is the probability of scoring a or a? e) What is the probability of scoring a 6? ) A fair dice is numbered to 6 and a fair spinner is numbered to. The dice and spinner are played at the same time. What is the probability of getting a) a on the dice and a on the spinner? b) a total of? c) a and a (any way around)? d) a total score of 0? ) 0 cards have the numbers to 0 on them. The cards are shuffled and placed face down on the table. A card is drawn at random. Calculate the probability of each of the following a) The card drawn will have the number 6 on it b) The number on the card will be greater than 6 After the card has been taken it is returned to the pack and another taken. What is the probability that c) The number 6 will be chosen both times d) A number greater than 6 will be chosen both times e) A number greater than 6 is chosen the first time and one less than 6 the second time. ) The probability of drawing a red ball from a bag is 0. and the probability of a black is 0.. a) What is the probability of drawing a red or a black? b) If there are 0 black balls in the bag, how many red balls are there?

Sumbooks 00 76 Probability ) Two dice are thrown together and their values added. Copy and complete the table below to show their sums and find the probability that their sum is 8. First Dice 6 ) Two dice bearing the numbers,,,,, are thrown together and the numbers shown are added. Copy and complete the table below which shows the possible outcomes. First Dice What is the probability of getting a total of a) 6 b) more than c) less than Second Dice 6 Second Dice ) Five cards have the numbers,,,, on them. Two cards are taken at random and their sum recorded in this table. Copy and complete the table. Use the table to find the probability of obtaining a sum a) of 8 b) greater than 9

Sumbooks 00 77 Probability ) The diagram shows two spinners, one numbered to, the other to. The outcome += is shown a) Make a list of all the possible outcomes. b) What is the probability of getting numbers adding up to? c) What is the probability of getting a sum of more than? ) ) Red discs Blue discs Three red discs are numbered to, and two blue discs are numbered and. A red disc is chosen at random followed by a blue disc. List all the possible outcomes. What is the probability of getting a) a followed by a? b) a and a in any order? c) a and a in any order? Three black cards are numbered to and red cards are numbered to. A black card is chosen at random followed by a red card. a) List all the possible outcomes. b) In how many ways can the cards add up to 6? c) What is the probability of the two cards adding up to 6? ) A bag contains red discs with the numbers to on them. A second bag holds 6 discs, white, black, one green and one yellow. A disc is taken at random from both bags. Copy and complete this table of possible results. First bag Second bag W W B B G Y Use the table to find the probability of choosing a) a followed by a black disc b) a black disc c) a black or white disc. W B G

Sumbooks 00 78 Tree diagrams ) A bag contains red counters and two blue counters. A counter is taken from the bag, its colour noted and replaced. This is done a second time. The tree diagram shows what happens. a) Copy and complete the diagram. b) What is the probability of getting a red followed by a blue counter? c) What is the probability of drawing two red counters? Second Counter ) The probability that Dave will win the long jump final is 0. and the probability that he will win the 00 metres is 0.. Draw a tree diagram to show this. From the diagram find a) the probability of him winning both b) the probability of him winning neither c) the probability of him winning one only. ) A bag contains blue and white discs. A second bag contains blue and white discs. Complete the tree diagram and use it to find the probability of getting a) a blue followed by a white disc. b) two blue discs. c) two discs of the same colour. ) In form C there are girls and 0 boys. In D there are 8 boys and girls. Two people are to be chosen at random, one from each group. Show this on a tree diagram. From the diagram find the probability of choosing a) a boy and a girl b) two boys c) two girls ) A bag contains red sweets and green sweets. A second bag contains red sweets and green sweets. A sweet is chosen at random from each bag in turn. Draw a tree diagram to represent this. From the diagram find the probability of taking a) a red followed by a green sweet b) two sweets of the same colour c) at least one red sweet R B First counter B W ( ) R B R 8 ( ) ( ) B B W ( ) ( ) ( ) ( )

Sumbooks 00 79 Relative Frequency ) Two dice are thrown together and their values added. Copy and complete the table below to show their sums and find the probability that their sum is 6. Second Dice 6 First Dice 6 If the dice are thrown 80 times, approimately how many times would you epect to get a total of 6? ) A bag contains discs with the numbers to on them. A second bag holds 6 discs, red, white and one green. A disc is taken at random from both bags, and then returned. Copy and complete this table of possible results. First bag Second bag R R R W W W G G a) Use the table to find the probability of choosing (i) a followed by a white disc (ii) a red disc b) If this procedure is carried out 00 times, how many times would you epect to choose (i) a red disc? (ii) a disc with a number on it? ) A drawing pin is thrown in the air and allowed to fall to the ground. It can either land point upwards or point down. The table shows the number of times it lands each way. Number of throws 0 0 0 0 0 Number of times point up 8 9 6 Number of times point down 7 6 From the results (a) suggest what you think the probability is of it landing point up? (b) eplain why you would not make any assumptions after 0 throws. (c) calculate how many times you think it will fall point up when thrown 00 times. ) Jenny does a survey of the people using her local newsagents over a period of 0 minutes. She counts 0 men and 0 women leaving the shop. a) What is the probability that the net person to leave the shop will be a man? b) During the day 000 people use the shop. Approimately how many will be women? R

Sumbooks 00 80 Relative Frequency ) Over a period of 0 minutes, buses, 0 cars, 0 lorries and vans travel down the high street. a) What is the probability that the net vehicle will be a van? b) Over the net hour approimately how many vehicles would you epect to travel down the street? c) How many of those vehicles would you epect to be buses? d) During another period, 0 lorries are observed. Approimately how many vans would you epect? ) A fair dice having the numbers to 6 is thrown 60 times. a) How many times would you epect the number 6 to occur? b) How many times would you epect the number to be greater than? ) A bag contains red, white and yellow coloured discs. A disc is taken from the bag, its colour noted and then replaced. This is carried out 00 times. Red is chosen times, white 9 times and yellow 9 times. a) If there are 0 discs in the bag, how many of each colour would you epect there to be? b) If the eperiment is carried out 00 times, how many times would you epect to get a white disc? ) A machine makes plastic cups. An inspector checks 00 cups and finds that 90 are acceptable and 0 are not. a) What is the probability that the net cup will be acceptable? During the day 00,000 cups are made. b) Approimately how many are likely to be unacceptable? c) If,000 cups are unacceptable the net day, approimately how many have been made altogether? ) Raffle tickets are sold in aid of the local church. 00 are blue, 00 white and 0 pink. They are all put into a bo and taken out at random. a) What is the probability that the first ticket is blue? b) If there are prizes to be won, about how many prize-winners would you epect to have a blue ticket? 6) David has a biased coin. He tosses the coin 60 times and fills in the table shown below as he is doing it. Number of tosses Number of heads Number of tails Probability of a head Probability of a tail 0 7 0 0 0 0.7 0. 0. 0. 0 8 0.6 a) Copy and complete the table b) Plot a graph of 'Number of tosses' against 'Probability of a head'. Use the scale of cm to represent 0 tosses on the horizontal ais and cm to represent 0. on the vertical ais. From your graph estimate the probability of getting a head. 0 8 0 9 60

Sumbooks 00 8 Constructions Using ruler and compass only, construct each of the following. Do not use a protractor. a) an angle of 60 b) an angle of 90 c) an angle of 0 d) an angle of e) an angle of 0 f) g) h) 90 90 60 60 6cm 90 90 6cm 60 60 7cm 0 90 cm i) j) k) This shape is made up from equilateral triangles 0 0 0 cm 90 l) m) 0 60 cm 60 8cm 0 0 cm? n) The diagram on the right shows a sketch of an 8cm square metal plate with a hole at the centre. The shape is symmetric about the lines AB and CD. Draw an accurate drawing of the hole. What is the length of dimension A cm C B 6cm dia D

Sumbooks 00 8 Simultaneous Equations ) + y = 0 ) + y = 8 ) + y = ) + y = 8 + y = 6 + y = + y = 0 + y = 6 ) + y = y = 6) + y = 9 y = 7 7) y = 0 + y = 8) + y = 8 y = 6 9) + y = 0) + y = ) 6 + y = 0 ) y = y = + y = 7 + y = + y = 7 ) + y = 8 ) + y = ) + y = 6) + y = y = 9 y = 6 6 y = + y = 7) A family of adults and children go to the cinema. Their tickets cost a total of.00. Another family of adult and children go to the same cinema and their bill is.60. a) Letting represent the cost of an adult s ticket and y the cost of a child s ticket, write down two equations connecting and y. b) Solve for and y. c) What are the prices of an adult s and a child s ticket? 8) The sum of two numbers is 9 and their difference is 9. a) Letting and y be the two numbers write down two equations. b) Solve the equations. 9) A rectangle has a perimeter of cm. Another rectangle has a length double that of the first and a width one third of that of the first. The perimeter of the second is 7cm. Letting and y represent the dimensions of the first rectangle, write down two equations containing and y. Solve the equations and write down the dimensions of the second rectangle. 0) oranges and apples weigh 70 grams. oranges and apples weigh 70 grams. Let and y represent their weights. Write down two equations containing and y. Calculate the weights of each piece of fruit. ) Three mugs and two plates cost 7.0, but four mugs and one plate cost 7.90. Let represent the cost of a mug and y the cost of a plate. Write down two equations involving and y. Solve these equations and calculate the cost of seven mugs and 6 plates. ) Sandra withdrew 00 from the bank. She was given 0 and 0 notes, a total of notes altogether. Let represent the number of 0 notes and y the number of 0 notes. Write down two equations and solve them. ) A quiz game has two types of question, hard (h) and easy (e). Team A answers 7 hard questions and easy questions. Team B answers hard questions and easy questions. If they both score 7 points, find how many points were given for each of the two types of question. ) A man stays at a hotel. He has bed and breakfast (b) for three nights and two dinners (d). A second man has four nights bed and breakfast and three dinners. If the first man s bill is 90 and the second man s bill is, calculate the cost of a dinner. ) Four large buckets and two small buckets hold 8 litres. Three large buckets and five small buckets hold 68 litres. How much does each bucket hold?

Sumbooks 00 8 Using Simple Equations ) A bus costs 00 to hire for a day. A social club charges 0 for each non member (n) and 6 for each member (m) to go on an outing. a) Write down an equation linking m and n and the cost of hiring the bus if the club is not to lose money. b) If twenty members go on the outing, how many non-members need to go? ) Annabel has two bank accounts, both containing the same amount of money. She transfers 00 from the first account to the second. She now has twice as much money in the second account. a) If she originally had in each account, how much does she have in each after the transfer? b) Write down an equation linking the money in her two accounts after the money has been moved. c) How much money has she altogether? ) Lucy buys 00 tiles for her bathroom. Patterned tiles cost p each and plain white tiles cost 8p each. She spends eactly 00 on patterned tiles and white tiles. a) Write down, in terms of, the number of white tiles she buys. b) Write down an equation for the total cost of the tiles. Calculate the value of. c) How many white tiles did she buy?. ) The length of a rectangle is cm and its width is ( )cm. If its perimeter is numerically the same as its area, calculate the value of and hence its area cm ) Three consecutive numbers are added together and their sum is 69. a) If the first number is, write down epressions for the nd and rd numbers. b) Use these epressions to calculate the value of and hence the three numbers. ( )cm 6) The distance between two towns, A and B is 00 miles. A car travels between the two towns on motorways and ordinary roads. Its average speed on the motorways is 60mph and 0mph on the ordinary roads. a) If is the distance travelled on the motorways, write down, in terms of the distance travelled on ordinary roads. b) Write down, in terms of, the time taken to travel the two parts of the journey. c) If the total time taken was 6 hours, write down an equation in terms of and solve it. What distance was travelled on ordinary roads? 7) Sarah drives her car from her home to the railway station, a distance of kilometres. She then gets the train and travels to London, 8 times the distance she travelled in her car. If her total journey is 6 kilometres, calculate the length of the car journey. 8) Calculate the sizes of the angles in each of these diagrams a) b) +0 + + + +

Sumbooks 00 8 Using Quadratic Equation ) A rectangle has a length of ( + ) centimetres and a width of ( ) centimetres. a) If the perimeter is cm, what is the value of? b) If the area is 8 cm, show that 0 = 0 and calculate the value of when the area is 8cm ( + ) cm ( ) cm ) people go to the cinema. The cost of one ticket is ( ). If the total cost of the tickets is, calculate the number of people who went to the cinema. ) The mean of numbers is. If the total of all the numbers is 70: a) show that 70 = 0. b) Hence calculate. c) What is the mean of the numbers? ) The square and the rectangle have the same areas. a) Show that = 0 b) calculate and hence the area of the square. + ) Shirts cost ( 6) each. If (+) shirts are bought for a total of 80. a) Show that 0 = 0 b) Solve this equation c) (i) What is the cost of one shirt? (ii) How many shirts were bought? 6) A right angled triangle has the dimensions, measured in centimetres, shown in the diagram. a) By using Pythagoras theorem, show that 0 = 0 b) Solve this equation and write down the length of the sides of the triangle. ( + ) ( ) ( + ) 7) A company manufacture thousand boes of chocolates each week. The number of chocolates in each bo is (+) chocolates. During one particular week, the chocolate making machine breaks down and they only make ( 9) thousand boes. At the end of the week they find that they have produced 0 thousand chocolates. a) Show that 6 = 0. b) Solve this equation and calculate the number of boes produced.

Sumbooks 00 8 Surds Do not use a calculator Eercise Simplify each of the following by writing as products of whole numbers and surds. The first one has been done for you. ) = = = ) ) 7 ) ) 6) 6 7) 8 8) 0 9) 7 0) 7 ) 80 ) ) 7 Eercise Simplify each of the following by rationalising the denominator. The first one has been done for you. 0 0 0 0 0 ) ------ = ------ ------ = --------------- = ------------ = ------------ = ) ------ ) ------ ) ------ ) --------- 7 6 6 6) ------ 7) ------ 8) ------ 9) ------ 9 7 0 0) ------ ) ------ ) ------ ) ------ 7 0 ) ------ ) ------ 6) ------ 7) ------ 7 Eercise Simplify each of the following, the first one has been done for you. ) 8 = = = = = 6 ) 0 ) 6 ) ) 6) 0 7) 8) 6 9) 8 0) 0 ) 0 ) ) 0 ) ) 8 6) 0 Eercise In each of the following right angled triangles, write down the length of the unknown side as a surd. a) b) c) d) e) cm cm cm cm cm cm cm cm cm 6cm

Sumbooks 00 86 Recognising Graphs Below there are sketches of graphs and functions representing them. Write down the letter of the function which goes with its graph. (i) y (ii) y (iii) y (iv) y (v) y (vi) y (vii) y (viii) y (i) y () y (i) y (ii) y a) y = b) y = c) y = + d) y = e) = f) y = + g) y = h) y = + i) y = + j) y = -- k) y = l) y = 6

Sumbooks 00 87 Plans and Elevations The diagram below shows an engineering component. In the grid below it three views of the component have been started, two elevations in directions S(side) and F(front), and a plan P. Finish off these three elevations. P 6 0 S F S F P

Sumbooks 00 88 Plans and Elevations Below are shown two engineering components. Draw diagrams of each shape when viewed from the directions A, B and C. ) A C B ) A B C

Sumbooks 00 Intermediate 89 Moving Averages The table below shows the value of sales in a shop over a period of 0 days. The proprietor wants to keep track of the trend in her sales over a period of time so she calculates a simple 7 day moving average. Day Value of Sales 0 00.00 6 7 8 9 0 6 7 8 9 0 0.00 0.00 0.00 0.00 0.00 7.00 0.00 0.00.00.00 9.00 0.00 9.00.00 7.00.00 6.00 0.00 7 day moving average 68.7 a) If sales on a Sunday are usually lower than other days, what day of the week is day? b) Eplain why there can be no moving average for day. c) When can the first moving average be calculated? d) Complete the table of moving averages. e) By looking at the moving averages, what do you think the trend in sales is?

Sumbooks 00 Intermediate 90 Recurring Decimals ) Without using a calculator, change the following fractions into recurring decimals. 8 7 a) -- b) -- c) -- d) -- 9 9 9 9 7 6 e) ----- f) ----- g) ----- h) ----- 99 99 99 99 Use a calculator to change these fractions into recurring decimals. 8 7 i) -------- j) -------- k) -------- l) -------- 999 999 999 999 ) Which of the following fractions are equivalent to recurring decimals? 7 a) ----- b) ----- c) ----- d) -- 99 8 e) 97 f) -------- g) ----- h) ----- i) -- 88 6 j) 6 6 k) ----- l) ----- m) -------- n) ----- 6 80 660 o) ----- 6 7 ----- 6 -------- ) It is said that fractions with denominators that have prime factors of only and will represent terminating decimals. For eample 0 = so ----- = 0.0 6 = so ----- = 0.97 0 6 Other fractions are represented by recurring decimals. For eample = so ----- = 0.06 6 = so ----- = 0. 0 7 6 9 6 Write down five fractions representing terminating decimals and five fractions representing recurring decimals. In each case write down both the fraction and the decimal. ) Consider the number 0.. Call this a) Write down the value of 0. 0. Call this 0. b) Write down the value of 0. 00. Call this 00. c) What is the value of 000? d) Subtract from 000 to get 999. Write down the value of 999? e) What is 0. as a fraction? ) Change each of the following recurring decimals into fractions in their lowest terms. a) 0. b) 0.0 c) 0. 0 d) 0.8 e) 0.0 f) 0. 0 g) 0.6 h) 0.0 i) 0. 8 j) 0.0 0 9

Sumbooks 00 9 Stem and Leaf Diagrams ) Below is shown a stem and leaf diagram for the number of DVD s sold by a shop over a period of one month., 0,,, 6, 8, 7,, 6, 9, 6, 8,, 7 6,,, 0,,, 6 7,, 8, 8, 6 7 0, 7 6 a) What does the 0 represent in the th row? b) What does the represent in the th row? c) How many days are in the month? d) What are the greatest and least number of DVD s sold? e) What is the range for the sales? ) The times taken for marathon runners to complete a race (to the nearest minute) are shown in the table below. 70, 7, 0, 0, 86, 6, 9, 79, 9, 87 6, 8, 0, 7, 86, 0, 9, 8, 79, 68 8 9 79 9 Draw a stem and leaf diagram to show this data. ) The table below shows the amount of rainfall (to the nearest 0.mm) each day over a period of one month for a town on the east coast of England..,.0,.,.,.,.8,.,.,.9,.6,.6, 0.0,.,., 0. 6, 0.7, 0., 0.0,.,.,.6,..8,.7,.0,.9,.,.,.,. a) Draw a stem and leaf diagram for the data with each row representing 0.mm of rain. The table below shows the amount of rainfall (to the nearest 0.mm) each day over the same period for a town on the west coast of Ireland..6,.0,.,.,.6,.,.,.,.,.,.6,.9,.,,0,,,.,.,., 0.0, 0.0,.7,.,.9,.7,.9,.,.7,.,.0,. b) Draw a stem and leaf diagram for the data with each row representing 0.mm of rain. c) Use your diagrams to comment on the differences between the two sets of data.

Sumbooks 00 9 Bo Plots ) The diagram below shows a vertical bo plot representing the marks obtained in a science eamination by year 0 pupils. 00 0 Use the diagram to estimate the following. a) What was the highest score? b) What was the lowest score? c) What was the median score? d) What was the lower quartile? e) What was the upper quartile? f) If there are 0 pupils in the year, how many scored between the lower and upper quartiles? g) How many pupils scored less than the median? ) At a factory there are 600 full time employees who are paid at the end of each month. The following figures relate to their pay for January. Highest wage,00 Lowest wage,00 Lower quartile,00 Upper quartile,00 Median,800 Represent this information on a horizontal bo plot. 0 ) The bo plot below represents the ages of male members of a fitness club. 0 0 0 0 60 70 80 90 Age The following values represent the female members. Lowest age 9 Highest age 8 Lower quartile 7 Upper quartile Median age 6 Copy the bo plot for the male members and on the same diagram show the values for the female members. Comment on the differences between the male and female results.

Answers. Multiplication and division Eercise ) 8r ) r ) r6 ) 6r ) 0r 6) 66r 7) 8) 9) 9r 0) 7r6 ) 7r8 ) 96 Eercise ) r ) r ) 7r7 ) r7 ) 6r0 6) 8r 7) 7r 8) r 9) r 0) r7 ) r ) 0r ) r ) 6r ) 6r 6) 9r7 7) 0r 8) 6r 9) 0r 0) 8r8 Eercise ) 7. ) 6. ) 7. ) 6.8 ) 7. 6). 7). 8). 9) 0. 0). ). ) 6. ) 6. ) 9.7 ). 6) 9. 7).9 8) 0.08 9) 8. 0).7 Eercise ) 86 ) 96 ) ) ) 6 6) 07 7) 8 8) 86 9) 0 0) 06 ) 6 ) 966 ) 7066 ) 9 ) 9 6) 696 7) 66 8) 690 9) 60 0) 808. Negative numbers Eercise ) ) ) ) ) 6) 7) 0 8) 9) 0) ) ) ) 6 ) 0 ) 0 6) 7) 7 8) 9 9) 6 0) Eercise ) ) 6 ) 9 ) 9 ) 6) 7 7) 8) 9 9) 8 0) ) ) ) ) ) 6 6) 7) 6 8) 8 9) 6 0) Eercise ) ) 0 ) 6 ) 6 ) 6) 6 7) 8) 7 9) 0) 7 ) 7 ) 8 ) 9 ) ) 0 6) 7 7) 7 8) 6 9) 0 0) 0 Eercise ) ) ) 0 and 6 ) and. Use of the Calculator Eercise ) 6, ), ),8 ) 7, ) 8, 6) 7, 7) 6,6 Eercise ).9 ).68 ) 7. ).668 ) 0.9 6) 0.980 7). 8) 8. 9) 0.77 0).960 ) 6. ).7 ) 0. ).0 ).0 6).890 7).8 8). 9).0 0).8 ) 0.68 ).0 ).70 ) 9. ).9 6) 8.98 7).80 8).99. Estimation Page 9 Eercise ) 800 ) 00 ) 00 ) 000 ) 00 6) 000 7) 600 8) 000 9) 6000 0)8000 ) 0000 ) 0000 ) 0000 ) 0000 ) 60000 6) 00000 7) 0000 8) 0000 9) 60000 0) 0000 Eercise ) 8 ) 600 ) 00 ) 0.8 ) 0.06 6) 0.0000 7) 9 8) 9) 0) 8. ) 0. ) ) 0 ) ) 6) 7) 0. 8) 0 9) 0. 0) 0. ) 0. ) 00 ) ) 00 ) 00 6) 90 7) 8) 9) 00,000. Fractions, Decimals and Percentages Eercise ) 0.7 ) 0.6 ) 0. ) 0.7 ) 0.67 6) 0. 7) 0. 8) 0.8 9) 0.08 0) 0.8 ) 0.6 ) 0.667 ) 0. ) 0.86 ) 0.6 6) 0.7 7) 0.78 8) 0.6 Eercise ) 6% ) % ) 7% ) 87% ) 6% 6) % 7) % 8) 96.% 9).% 0) 6.% ) 8.% ) 8.6% ) 9.% ) 0% ) 60% 6) 90% 7) 8% 8) 6% Eercise ) 80% ) 80% ) 6.67% ) % ) 6.% 6).7% 7).8% 8) 8% 9).% 0).% ) 6.% ) 6.88% ) 69.% ) 79.% ) 86.7% 6) 7.% 7).9% 8) 9.8% Eercise ) 0., %, ) 6%, 8, 0. ) 0.8, 87%, 7 8 ) 0., %, 6 ) 0%, 0., 0 6).7%, 6, 7 0.7 7) 0%,, 8 0. 8) 0.7, 7.%, 9 7 9) 0., %, 6 8 0) 0.,.6%, 8 Eercise ) ) ) 78.7 ).0 ).m 6) 9.7m 7). 8) 6.7m 9).0 0).7m ) 8.0 ).m

Page 9 6. Fractions, Decimals and Percentages Eercise ) ) ) ) 0 ) 90p 6) 60p 7).0 8).6m 9).6 0). ) 8.8 ) 6 Eercise ) 8% ) 6% ) 68% ) 6% ) 6% 6) 6% 7) % 8) 90% 9) 70% 0) 6% ) 8% ) 69% ) 7% ) 6% ) 9% 6) 60% Eercise ) 0% ) 60% ) % ) 0% ) % 6) % 7) % 8) 6% 9) 6% 0) % Eercise ) 7 ) ) 80 ) 00 ) 6) 7) 87.0 8) 60 9) 0.60 0) 9 7. Interest Eercise ),.0 ) 6, 8.6 ), 7. ) 00, 6.0 ), 7.6 6) 0, 9.7 7) 00, 0.6 8) 6.80, 7.9 9),.8 0) 0,.0 Eercise ) a) 9. b) 6.79 c) 07. ) a).07 b) 68, 677., 6886.8, 70.0, 78.9, 790.7, 87.9, 866., 907., 997.69 ) 7.77 ) 90.66 Eercise ) 6, 6 ) 6,, ) 6, 0 ) 6, 77 ) 88, 6 6) 0., 6.0 7) 0.0,.6 8).6,.6 9) 8., 0.79 0).80, 66.0 9. Standard Form Eercise ).6 0 ).6 0 )8. 0 )9. 0 ).6 0 6). 0 7). 0 8). 0 9). 0 0). 0 ). 0 ).7 0 )00 ) 000 )8000 6) 000000 7) 00 8) 0000 9) 8000 0) 0. 0096 ) 0. 0000 ) 0. 00097 ) 0. 000006 ) 0. 00008 Eercise ) 7. 0 6 ).88 0 9 ).7 0 6 ).68 0 ). 0 6).88 0 7).0 0 8).766 0 8 9).906 0 0)6.60 0 0 ).67 0 ).09 0 ). 0 7 ).9 0 Eercise ) 6 0 0, 0 ) 9 0 8,6 0 ). 0 7 ) :8. ).8secs 6) :0.0008 7) a. 9.6 0 km b. 8. years 8. Scale Drawing and Ratio Eercise ) 0cm ) 8cm ) 6cm ) 7cm ) 00cm 6) 6cm 7) :0 8) :0 9) cm 0).m ) :00 ) :. ).cm ) 0cm ) :0 6).cm 7) 9m 8) : 9) 8cm 0) 0cm Eercise ) 00, 00 ) 00, 700 ) 7, ) 80, 0 ) 0, 0 6) 0, 0 7), 8 8) 9, 770 9) 80, 6 0) 00, 00, 00 ), 0, 7 ) 70, 0, 0 ) 9, 6, 78 ), 0, 9 ), 00, 6) 6.80,.0, 9.0 7) 6, 8, 66 8).98,.6, 7.6 9),, 68 0) 7.0, 98, 7.0 0. Prime Factors Eercise 90 68 7 0 0 7

Page 9 Eercise ),,, ),,,,0,0 ),,,,6,8,, ),,,,6,0,,0 ),,,8,6, 6),,,,8,0,0,0 7),,,9,, 8),,,,,6,0,,,0,0,60 9),7 0),,,,6,7,,,,8,,8 ),,,,6,9,0,,8,0,,90 ),,,,0,0,,0,00 ),,,,, 6, 8, 0,,, 0,, 0, 0, 60, 0 ),,, 0,, 6, 6, 0 ),,,, 6, 0,,, 0, 0, 7, 0 Eercise ) ) ) ) 7 ) 6) 7) 7 8) 7 9) 7 0) ) 7 ) ) 7 ) ) 7 Eercise ), ), ), ), ), 6) 7, 7 7)7, 7 8), 9) 9, 8 0) 7, ), 6 ), 0 ), ) 6, ) 7, Eercise ) 7 ) ) ) 7 ) 7 6) 6 7) 7 8) 9) 9 0) 7 ) 9 ) 7 ) ) ) Eercise ) a. 0 b. c. n+ d. 8 ) a. 9 b. c. n d. 79. Number Patterns and Sequences ) a. 0 b. 0 c. n( n+) d. 0 ) a. b. 0 c. ( n ) d. ) a. b. 7 c. n+ d. 6 ) a. 0,6 b., c. n+, 6 n+ d.. Distance Time Diagrams ) a. 0 miles b. 0 mins c. 0mph d. mph ) a. mph b. mins c. 8:0 d..mph e. 8:7 f.. miles g. 8:8. Distance Time Diagrams ) a. 60mph b. :0; mins c) 80mph d. 7 mph e. :0, 68 miles ) a. Journey B. It goes further in a shorter time. b. kph c. B d. 7.kph e. hours 8 mins f. : and : g. 7: ) a. miles b. 8 mph and 7 mph c. 60 mph and. mph d. 6 mins e. 0:, 0 miles f. 0 miles g. 0:00 and 06:. Number Patterns and Sequences Eercise ), ),7 ), ),9 ) 8, 6) 8,7 7) 8, 8),0 9),7 0) 7, ), ),0 ), ) 0, ) 7, 6), 7), 8), 7 9) 0, 8 0) 6, ),6 ), ),6 ) 6,7 Eercise ),; Add ; n- ) 7,0; Add ; n ),9; Add ; n+ ) 6,; Add 6; 6 n ) 7,; Add 6; 6 n+ 6) 7,;Add ; n+7 7) 0,8; Subtract ; n 8), ; Subtract ; 0 n 9),6; Subtract 6; 8 6 n 0),; Add ; n 9 ) 0,; Add ; n 0 ) 6,; Add 6; 6 n 0 ), 7; Subtract ; 7 n ), 6; Subtract ; n ), ; Subtract ; n. Conversion Graphs ) a. 6.0 b..0 (appro0 ) a. $ b. 7 6. Conversion Graphs ) a. b. ) a. 9. b. 7. ) a. 88 b. 9000 ) a. 0 secs b. cms ) a. b. 7 c. 8 7. Sketching and recognising Graphs ) b ) b ) c )

Page 96 8. Sketching and recognising Graphs ) d ) b ) b ) 9. Plotting Graphs ) a. 7,, c..7,.7 d. (,7) (,7) ) a. 8,, c. (,) (,) d. = or = ) a..6,.87, 6., 9.7 c. (0,6) (,7) (,) d. =, 0 or ) a. 6,, 6, c. (.,0) (.,0) d. =. or. Eercise ) y ) 8y ) y ) 8 ) y 6) 8 7) 9y 8) 6 9) a 0) 9w ) b + a ) + y ) 7b + 8a ) + 7y ) a + 7b 6) 8p + 0q 7) 8a + b 8) + 6y 9) 6 y 0) a + b ) y ) 6a b )y y 0)8ab + a ) )y ) + 7y ) )6y + 6)6 + 7)y y 8) y 9y 9) 0) y. Indices Eercise ) 9 ) 7 ) 8 ) ) 00 6) 000 7) 0,000 8) 00,000 0. Plotting Graphs ) a. 9,6,. c.. d. (0.8,7.6) (.,.) e. =0.8 or. ) a.,8, c. Line is +7, solution is = or ) a. 7,., c. Line is, Solution is =., 0. or. ) a. 6,.,.7 c. Line is, Solution is =0.8 or =6.. Substitution ) ) ) 6 ) ) 6) 7 7) 8) 9) 0 0) ) 6 ) ). ) 0.7 ) 0. 6) 7).7 8)8 o C 9) 7. 0) 9.8 ). ) 96.88 ) 0. ) a. 6.7 b.. ) 9. 6) a. b. 8 7) a. 66 b. 6 8) a. 6 b. 0 9) a. b. 0) 7. ) 8.8 ) 8.7. Symplifying Epressions Eercise ) ) ) 9 ) ) 6) 7) 8) 9) 6 0) 8 ) ) ) ) 0 ) 6) 6 7) 8) 9) 0) 0 ) ) ) ) ) 6) 6 7) 9 8) 9) 0) Eercise ) 7,776 ),6 ) 6,8 ) 7,69 ) 9,09 6) 6,0 7),86,809 8) 0,,607 Eercise ) 7, 8 ) 9, 968 ) 6, 096 )0 7, 0, 000, 000 ) 7 8,, 76,80 6)8, 768 7) 7 8)a 9)b 9 0) y Eercise ) ) ) 7 )0 ) 6)0 7)9 8) 9)8 6 0)0 )a ) y ) Eercise ) 8 ) 0 ) 7 9 ) ) 6 6) 7) 6 8)7 8 9) 0 0) 8 ) 0 ) y 9 Eercise 6 ) 96 ) 88 ) 7 ) ) 7 6) 00000 7) 9898 8) 98 9) 7776 0) 60000 Eercise 7 ) a. b. c. a d. y )a. a b. c. d. 6 )a. a b. 8 c. y 8 d. b 8 )a. y b. a b c. y 6 d. a b 6 )a. 9 b. 8 c. 7 d.a 6)a. a b. c. b d. 7)a. b. 08a 7 c. 0y 9 8)a. 6 b. c.

Page 97. Multiplying Brackets Eercise ) ) ) ) ) 6 6) 0 7) 0 8) 0 9) 0) 0 ) ) 6 Eercise ) + y )8 + ) + ) ) 8 0 6) + 8 7) 8)0 9)9 + 6 0) + 0y ) y )0y ) y ) 8 + y )0 6) + y 7)8 9y 8) 6y 9) y 0)6 + 7 ) )7 ) 7 + ) 6 )6 + 7 6)6 Eercise ) + + 6 ) + + ) + + 8 )0 + 7 + )6 6) 7) 8 8) + 6 9)8 0) + 8 ) )6 8 + 6 ) 8 + 0 ) 9 + 0 ) 7 70 + 6) + 9 7) + 0 + 9 8)6 + 9)6 0 + 0)6 + 7 + 8. Factorising Eercise )( + ) )( ) )( ) )(z + ) ) (y + ) 6)6(y ) 7)( ) 8)8( ) 9)(7a 8) 0)( + y) )8( + y) ) 7(a + b) )( 9z) )9(y + z) )8(p q) 6)(a + ) 7) 6( + ) 8)( ) 9)(a b + c) 0)(a + b c) ) ( a + b) Eercise ) a( a) ) y(6 y) ) (9 ) ) ( ) )a( + a) 6) b( b) 7) y( + y) 8) ( ) 9)z(z ) 0) ( ) ) y(y + ) ) 6z( z) ) a( 7a) ) (6 ) )9a(a ) Eercise ) a(b + ) ) ( y) )a( b) )a( + a) )( ) 6) (y + 6 ) 8)7a(a b) 7)a(b + a) 9)πr(r h) 0)y( + y) )8y( z) ) pq( p) )pq(p q) ) ab(9b a) )y( y) Eercise ) (a + b) )a(h a) )(a + b + c) )y(y + 7) )bc(a c) 6)y( 7y) 7)(7 6y) 8)7(y + ) 9)πd( 7d) 0)(8a + ) )9b(a b) )6a( + a) )a( + a b) )( + y z) ) ( + + y) 6. Equations Eercise ) = ) = 0 ) y = ) = 6 ) y = 8 6) a = 7 7) y = 8) = 0 9) = 0) a = ) = 7 )y =. ) b = ) y = 6 ) b =. 6) a = 7) a = 8) = 9) = 0) = ) = 7 )y =. ) b = ) y = Eercise ) = ) = ) = 6 ) = ) = 6) = 7) = 6 8) = 9) =. 0) = ) =. ) =. ) = ) = ) = 6) = 9 7) = 8 8) = 9) = 0) = 8 ) = Eercise ) = ) = ) = ) = 7 ) = 6) = 6 7) = 8) = 9) = 0) = ) = 8 ) = ) = ) = ) = 6) = 7) = 0 8) = 0 9) = 0) = 7 ) = 8 ) = ) = ) = 7 7. More Equations Eercise ) = ) = ) = 8 ) = 8 ) = 0 6) = 8 7) = 8 8) = 9) = 0) = 6 ) = ) = 90 ) = ) = ) = 6) = 9 7) = 8 8) = 9) = 6 0) = ) = 6 ) = 7 ) = ) = ) = 6) = 0 7) = 6 8) = 0 9) = 0) = 8 ) = ) = ) = 7 ) = ) = 6) = Eercise ) = or ) = or ) = or ) = or ) = 6 or 6) = or 7) = or 8) = or 9) = or 0) = or ) = 9 or ) = 9or ) = or ) = or ) = or 6) = or 7) = 6 or 8) = 0 or 9) = or 7 0) = or0 ) = or 7 ) = = =

8. Straight Line Graphs and Simultaneous Equations ) ) ) ) ) 6 8) 7) 9) 0) ) ) ) ) 7 6) ) 6 6) 7) 8) 9) 0) ) 0) 6 ) 6) 7) 7 8) 9) ) 6) 7) ) 9) ) ) ) 8) ) 7 ) ) Page 98

Page 99 Eercise ) =. y =. ) = y = ) = y = ) = y = ) = y = 6) = 0. y = 7) = y = 8) = y = 9) =. y = 0) = y = ) = y = ) =. y = ) = y = ) = y = 9. Trial and Improvement Eercise ). ).8 ). ).6 ). 6). 7).9 8).9 9). Eercise ). ).6 ) 7. ) 9. ). 6).7 7) 7. 8) 9.8 9).0 0).6 ). ).9 ). ).7 ).7 6).7 7).7 8).6 9). ins 0).0 cm 0. Inequalities ) > ) < ) > ) < 6 ) > 0 6) < 0 7) 8) 9) 0) ) < ) > 6 ) 6 ) 7 ) < 6) < 9 7) > 8 8) < 8 9) 8 0) ) 0 ) < 6 ) < ) > ) 0 6) 7). 8) <. 9) > 8. 0) < 7 ) ) ) 0 ) > ) > 80 6) > 7) 0 8) < 9) < 0) > ) > ) > ). ) ) 6) > 7 7) > 9 8) > 6 9) 6 0) ) 0. Inequalities Graphs ) (,) (,) (.,.) etc ) (,) (,) (,) (.,.) etc ) Area bounded by (,) (7,) (7,7) ) Area bounded by (,) (6,6) (,6) ) Area bounded by (,) (,.8) (.8,.9) 6) (, ) and (,) 7) (,) (,) and (,). Rearranging Formulae ) D = C π ) r = π C ) h = lb V ) h = A b 7) c = y m 8) m = y c 9) h = v πr 0) r = v πh ) m = F a 6) h = V πr ) F = 9 C + ) b = y a ) h = v ) s = v u g a (s ut) ) a = t 6) v = s u t N 7) π 8) X 9) A y l py D 0) 6 p + y ) ) R Cz ) Iy ) 00I PT ) 6) A + r 7) R A π π C( c) 8) a 9) a a 0) a. Bearings Eercise ) A B ) H ) o 0 o 7 L G o ) ) J 6) C o K o Q o 8 C d t M 7) P T 8) o U 8 R o 76 V Eercise ) N 9 o E or 09 o ) S 8 o W or 8 o ) N 8 o W or o ) S 6 o W or o ) N 7 o E or 07 o Eercise ) S 6 o E or o ) N o E or 0 o ) 9. km S 88 o E or 09 o ) km S o W or o. Parallel Lines ) o, 6 o, o ) o, 7 o ) 8 o ) 7 o ) 7 o, o, 0 o 6) 7 o, 9 o, o, 9 o 7) o, o, o D

Page 00 8) 6 o, 6 o, 6 o, 60 o, 0 o 9) o, 6 o, 6 o 0) 8 o, o, 6 o. Nets and Isometric Drawing (Diagrams are not to scale- use as a guide only) ) ) ) An eample would be or etc 6. Triangles ) 0 o ) 70 o and 60 o ) 0 o, 60 o ) 70 o, 60 o ) o, 0 o, 09 o 6) 9 o, 7 o, o 7) o, 9 o, 7 o 8) 7 o, 7 o, 6 o 9) 60 o, 0 o 0) 09 o, 7 o, 09 o ) 90 o, o, o ) 0 o, 6 o ) 0 o, 0 o 7. Regular Polygons ) 0 o, 60 o ) 0 o, 0 o ) 0 o, 0 o ) 6 o, 8 o ) 90 o, 7 o, o 6) o, 67. o,. o, o, o 7). o, 6. o,. o, 8.6 o, 90 o 8) 8 9) The interior angle of a regular pentagon is not a factor of 60 o but in a regular heagon it is. 0) 9 ) o, 7 o ) 8. Irregular Polygons ) 6 o ) o ) 0 o ) 0 o ) 80 o, 60 o 6) 0 o 7) 7 o and o 8) o 9) 0 o 0) 90 o ) 6 9. Pythagoras Theorem ) a. cm b. 0cm c..cm ) a..606cm b. 8.9cm c..cm ).67cm ).7cm ).899cm 6) 0.8cm 7) cm 8).0cm 9) 9.899cm 0) 6.06cm ).8cm ) m cm ) 8.8cm 6) 7) 6 6 6 6 6 6 6 6 0. Trigonometry ) a. 6. b. 9.80 c..08 d..0 e..76 ) a..90 o and.0 o b. 9.79 o and 0. o c. 8.68 o and. o d. 6.9 o and 6.6 o e. 6.87 o and. o ) a..866 b. 8.8 c.. d..8 e..7 8). Trigonometry ) a..0 b. 6. c..9 d..89 e..6 ) a..8 o and 6.6 o b..7 o and. o c..86 o and 8. o d. 8.7 o and. o e. 9.6 o and 0.6 o ) a. 6.6cm b..cm c..6cm d..cm e. 6.cm

Page 0. Trigonometry ) a.. b.. c..68 d..60 e. 8. ) a. 9. o and 0.7 o b..97 o and 6.0 o c.. o and 7.9 o d. 6.9 o and 8.6 o e. 6. o and.7 o ) a. 6.66 b. 0.70 c..09 d..0 e.70. Trigonometry a. =.9 b. =.6 c. 9.8 o and 0.9 o d. =.890 e. 7.09 o and 6.9 o f..7 o and 7.6 o g. 7.6 o h. 8.7 o i..0m,.6m j..07cm k..7 o 7. Reflections, Rotations and Translations ) a. (,) (, ) (0, ) (, ) (,) (0,) b. (, ) (, ) (0, ) (, ) (, ) ( 6, ) ) a. (,) (,0) (, ) (,0) b. ( 6,0) (,0) (, ) (, ) 8. Enlargements ) (,8) (,8) (,) (,) ) (,9) (,) (,) 9. Enlargements ) (,) (.,) (., ) (, ) ) (,) (0, ) (, ). Reflections, Rotations and Translations ) a. (, ) (,.) (, ) b. (,) (,.) (,) ) a. (0,) (,) (,) (0,) b. (, ) (, ) (,0) (,0) ) a. (, ) (0, ) (0, ) (, ) (, ) b. (,) (,) (,) (,) (,) c. (,) (,) (,0) (,0) (,) 0. Similar Shapes ) a. FDE b. : or.: c..8cm d. 6.6cm ) a. : or :. b. m c..6m ) a. DBC b..8cm c..cm ) a. DCE b. :. or : c. 7cm d..6. Locus Problems ) ). Reflections, Rotations and Translations ) a. (, ) (,) (,) (, ) b. (,) (, ) (, ) (,) ) a. (, ) (,) (,) (, ) b. (,) (, ) (, ) (,) ) a. (0, ) (, ) (, ) b. (0,) (,) (,) ) ) ) 6) 6. Reflections, Rotations and Translations ) a. (, ) (., ) (, ) b. (,) (.,) (,) c. (, ) (,.6) (, ) ) a. (.6, ) (.6, ) (, ) (, ) b. (, 0.6) ( 6, 0.6) ( 6,) (,) 7) a) AB b)

Page 0. Locus Problems ) ) ). Circumference of a Circle Eercise ).6cm ) 7.70cm ) 6.8cm ).m ) 0.7m 6).988m 7) 7.70cm 8) 0.7cm 9) 7.08cm 0) 7.66m ).m ) 7.66m Eercise ) 6.6cm ).cm ) 7.0cm ).77m ) 8.8cm 6) 6.0m Eercise ) 78.cm ) 786m ) 6m ) 79 turns ) turns 6) 979 turns 7) cm 8) m 8cm 9) m ) ) 9.km. Degree of Accuracy Eercise ) a. 000 b. 00 c. 60 d. 800 e. 000 f. 000 ) a. 00 b. 00 c. 000 d. 0000 ) a,b,f,g. ) a. 0 9 b. 0 9 c.,0,9 d.,00,99 e. 6,000, 7,999 f. 600 799 g. 0,00 0,99 h. i. 7 7 j. Eercise ).cm ),< ) 9., < ) 7.8, 7.8 ), < Eercise ) 9., 9. ) 6., 6. ) 9., 9. ) 7., 7.6 ) 9.6, 9.6 6).6,.6 7)., 6. 8) 7., 7. 9) 7., 7. 0) 6.7, 6.8 ) 9., 9. ).,.. Area and Perimeter ) a. 9cm and cm b. 8cm and 8cm c. 0.6cm and.8cm d. 78.cm and.cm e. 0.96m and m f..m and m ) a. 96cm b..9cm c. 68cm d. 67.cm ) a. 8.cm b. 76.7cm c..cm d. 8.cm e. 0.cm f. 7.8cm ) a. 8cm b. cm c..99cm d. 0cm e. 7.cm f. 0cm ) 0 6) 0.7cm, 8.68cm 6. Volume Eercise ) 000 ) ),00,000 ) 000 ) 0 6).m 7) 00 8) 9) 8,000 0) Eercise ) 080cm ), ) 6.8m ) a. 8.89cm b. 8ml ) 90 6) litres 7) 77.8g 8) times 9) 69cm 0) 00cm ).9mm ) 0, 000 litres

Page 0 7. Compound Measure - Speed and Density Eercise ) a. 0, 80, 0 b., 60, 7. c. 0, 0, ) a. 60 miles b. 0 miles c. hours ) a. 90 miles b. mph ) hours ) a. miles b. 70 miles Eercise ) a. g b..7g ) red blue etc. ) red blue etc. ) multiples of red and blue. ) a. g per cm b. g per cm 8. Compound Measure - Best Buy and Mied Eercise ) ml ) 800ml ) 700g ) litre ) 0ml Eercise ) a. B b. D ) tins of litres ) packets ) tin of litres and tin of litres 9. Formulae for Area, Volume and Perimeter Eercise ) a, (iii) b. (v) ) a. (v) b. (iv) ) a. (i) b. (iv) ) a. (vi) b. (iii) ) a. (v) b. (ii) 60 Formulae for Area, Volume and Perimeter ) (i) She is trying to get a length of cable. Multiplying L, W and H togethergives a cubic measurement (ii) 'a' because all the dimensions are in length. All the others give either area or volume measurements. ) Area.,,,, 6 Volume. 7, 0 Perimeter, 9, 8 6. Questionaires These answers are eamples only, there are many other acceptable answers ) a How often do you use a supermarket (i) Once a week (ii) Less than once a week (iii) Never? b Do you think there is a need for a supermarket in the town? (i) Yes (ii) No (iii) Don't know ) The local supermarket good cross-section of ages- potential customers. Residents of the high street- they will be most affected, so probably biased. Residents of the local housing estate-crosssection of ages- potential customers ) No- they will probably get a one-sided view of the problem (biased). ) Would you be prepared to buy vegetarian food from the tuck shop? yes/no. Which two of the following would you prefer to eat? a) Fruit b) Yoghurt c) Oatmeal biscuits d) Nuts e) Wholemeal sandwiches. ) a. Biased- needs a group more representative of people in general. b. (i) Biased- same age group (ii) Probably the least biased group as they are more representative of people in general (iii) Biased- no young people. (iv) It is important to ask these people as they will be most affected but they will be biased. 6) Not a good questionairre because a) it only gives one choice, b) it puts pressure on the staff to agree by saying the manager thinks it is a good idea. It would be better to give the two choices with no comment about whether the manager likes it. A third choice such as 'None of these' or a space for their own comment would make it less biased. 6. Pie Charts ) 0 o, 0 o, 00 o, 80 o and 0 o ) Angles of the pie chart are: 90 o, 60 o, 0 o, 7 o and 0 o ) Angles are: 0 o, 00 o, 60 o, 0 o and 60 o ) 87. o, 0 o, 0 o,. o ) 60 o, 0 o, 60 o, 8 o, 0 o and o 6) a. 6 b. 70, 0, 60, 70, 80, 90. 7) a. o b. 8 o, 6 o, 96 o, o

6. Frequency Polygons Eercise 6 0 89 90 9 9 9 Eercise ) Page 0 70 60 0 0 0 0 0 0..... 6. 7. 8. 9. ) 0 9 8 7 6 0 0 6 7 ) 00 80 60 ) 0 0 0 6 7 0 0 0 0 6 7 8 9 0 ) 0 0 0 0..... 6. 7. 8. 9. ) 0 8 6 0 8 6 0. 6 7 8 ) 00 0 00 0 00 0 0 8. 8. 8. 8. 8. 9.0 9.

Page 0 6. Frequency Polygons ) a) 0 0 0 0 J F M A M J J A S O N D (i) A-Europe, B- Australia (ii) Temperatures are high in August in Europe and high in February in Australia. (iii) May and October. b) 9 8 7 6 0 J F M A M J J A S O N D Personal choices with references made to a) the temperatures b) the rainfall. a) 6 0 J F M A M J J A S O N D b) (i) Profits in 99 were generally higher than in 99. (ii) Profits are picking up as the graph is generally rising, but it did the same in 99 and then fell in the new year. (iii) Just over million per month ).8.6.. 6 7 8 9 0 Choose from a)brian is most consistant b)john is getting worse c) Mike is not consistant but has best times. )... J F M A M J J A S O N D Company A's profits are steadily rising but company B's profits went down substantially during the first half of the year, but rose again during the second half.

Page 06 6. Mean, Median, Mode and Range. Eercise ) 6 7 8 7 7 Mode=, Range =6 ) 0 6 7 8 9 8 6 9 6 Mode=, Range=9 ) 6 7 7 0 8 7 Mode=, Range= Eercise ) 6 7 8 9 0 Median=, Range=9 ) 6 7 8 9 Median=6., Range=7 ) Median=6., Range=78 Eercise ).6cm ) ).0 ). ) 8.7 6).8 7). 8) 90 9) 06. 0). Eercise ). ) 86.kg ) 66. Mean ).mph ) 6.77mph ).7 ) 8. ).08mpg 6) 0. 7) a. Grade b. Grade c. Grade. Grade 8) 0.7, 0.6, 0., 0., 0., 0., 0., 0., 0., 0.8, 0.7, 0.6 October 67. Mean ). ). ) 0.087 ).6 68. Mean ).68 ).6 ).0 69. Mean ) Mean 6.cm Modal Class 0 60 ) Mean 06 Modal Class 000 00 ) Mean.9 Modal Class 80 0 ) Mean 8 hours mins Modal Class 0 ) Mean.cm Modal Class 70. Mean ) Mean.7 ) Mean 78.6 ) Mean.06 ) Mean 8.6 7. Cumulative Frequency ) a. 80 00 0 0 80 7 6 8 90 c. (i) 7 (ii) (iii) ) a. 6 70 7 80 8 90 77 9 0 0 c. (i) 7 (ii) 97 7. Cumulative Frequency ) a. 0 0 0 60 70 80 90 9 70 8 8 86 c. (i) mph (ii) 68 ) a. 7 9 7 0 b. (i). hours (ii).9 hours. 7.6% ) a. 0 0 60 80 00 0 68 8 8 c. (i) 6 (ii) 9

7. Scatter Diagrams Answers are approimate ) a. 6 b. 79 ) 8 ) 7kg ).8cm ) 0 7. Scatter Diagrams Answers are approimate ) a. 9g b. 8.cm ) 6mph ) ) cm 78. Tree Diagrams ) a. ( ),( ), 6 ( ) b. ) a. 0.06 b. 0.6 c. 0.8 ), 8, 8, 8 ) a. ) a. 8 a. 8 6 b. b. b. 9 0 c. 6 c. 8 c. 9 c. 9 0 Page 07 7. Probability ) 6 ) 9) a. ) 6) ) or ) 7 0 7) 0.7 8) a. b. c. 6 6 b. or c. 9 or b. 0 c. 0.98 0) a. or 00 00 ) a.0. b. c. 0 d. 0. e. 0 ) a. 8 ) a. 0 ) a. 0.8 b. 6 b. or 8 6 b. 0 or 76. Probability ) 6 ) a. or 6 9 ) a. or 0 0 77. Probability ) b. or c. b. or 6 b. 6 or 0 or c. 8 or 9 c. 00 ) ) a. b. or 6 6 6) ) a.,,,,,,,,,,,, b. c. 6 7) ) a. 0 b. 0 0 c. 6 d. c. 6 or c. d. 0 e. 79. Relative Frequency ) ) a. (i) (ii) b. (i) 0 (ii) 0 ) a. b. Too few throws c. 0 ) a. 8 b. 6 80. Relative Frequency ) a. b. 0 c. 0 d. 7 6) a. 0 b. 0 7) a., and b. 0 9 8) a. 0 b. 0,000 c. 0,000 9) a. b. 8 0) b. 0.7 8. Simultaneous Equations ), ), ), ), ), 6), 7), 8), 9), 0), ), ), ),6 ) 9, )., 6), 7).0,.80 8), 9).8,6. 0) 0,90 ) 8.6 ) 7,6 ), ) ),7 8. Using Simple equations )a)0n + 6m = 00 b) 8 ) a) 00, +00 b) +00=( 00) c) 800 ) a) 00 b) 7 c) ) 8.8 ),, 6) 0 7) 8) a) 0, 7, b) 70, 9, 7, 0 8. Using Quadratic Equations ) a) 8 b) ) 6 ) b) 0, c) 7 ) b),00 ) b) c) 9, 0 6) 9,, 7) b) 6000

Page 08 8. Surds Eercise ) ) 6 ) ) ) 6) 7 7) 8) 9) 6 0) ) ) ) 7 88. Plans and Elevations ) A B Eercise 7 ) ) ------ ) ------ ) ------ ) --------- 7 6) 7) 8) 9) 0) C 7 ) --------- ) ) 7 ) 7 ) ------------ 6) 7 7) Eercise ) 6 ) 0 ) ) 6 ) 7 6) 7) 6 8) 9) 6 0) ) 6 ) 7 ) ) 6 6 ) 6 6 6) ) A C B Eercise a) b) 0 c) d) e) 86. Recognising Graphs (i) f (ii) e (iii) k (iv) c (v) d (vi) j (vii) b (viii) l (i) i () a (i) h (ii) g 87. Plans and Elevations F S P 89 Moving Averages a) Saturday b) There has to be at least 7 days for this moving average to be calculated. c) Day 7 d) Day Value of Sales 0 00.00 6 7 8 9 0 6 7 8 9 0 0.00 0.00 0.00 0.00 0.00 7.00 0.00 0.00.00.00 9.00 0.00 9.00.00 7.00.00 6.00 0.00 e) The sales are increasing. 7 day moving average 6..7 7.86 69.9 68.7 67.86 7.9 80.00 8.86 8. 9. 9.86 97. 98.7

Page 09 90 Recurring Decimals ) a) 0. b) 0.8 c) 0. d) 0.7 e) 0. f) 0. 7 g) 0. 6 h) 0. i) 0. j) 0. k) 0. 8 l) 0.0 7 ) a, b, c, f, g, h, i, m, n ) - Five fractions of each type - ) a) 0 =. b) 00 =. c) 000 =. d) 999 = e) 6 = -------- or -------- 999 0 9 0 ) a) ----- b) ----- c) ----- d) ----- e) ----- f) ----- 99 99 99 99 6 g) ----- h) -------- i) ----- j) -------- 99 999 7 9. Stem and Leaf Diagrams ) a) 70 b) 6 c) 0 d) 76 and 0 e) 6 ). 6,, 8 7 0, 9,, 9, 9 8 6, 7,, 6,, 9,,,, 0,, 7, 0 ) a) 0 0,, 0 0 6, 7,, 8, 9, 6,, 8 0,,,,,, 6, 7, 9,,,, 0, 6 b). 0 0, 0 0,,, 6, 9, 9, 7 0,,,, 0 6, 6,,, 9,,,, 0,,, 7, 7 c) The rainfall in England averages about mm per day whereas the rainfall in Ireland averages about.mm per day. In England the rainfall is spread between 0 and.6mm. In Ireland it is generally spread between. and.7mm although there are two days when it is zero. On days when it rains in Ireland it rains more than in England. ) ) 000 000 000 000 Wages in Male 0 0 0 0 60 70 80 90 Age Female In all areas the female values are higher than those of the male. This may not be significant in the highest and lowest values as they may be rogue but the lower and higher quartiles do show that the average ages of the female members are higher than those of the males. 9. Bo Plots ) a) 96 b) 8 c) d) e) 68 f) appro 7 g) appro 7