# Practice Book. Practice. Practice Book

Size: px
Start display at page:

Transcription

2 Grade 10 MATHEMATICS PRACTICE TEST ONE Marks: Fred reads at 300 words per minute. The book he is reading has an average of 450 words per page. 1.1 Find an expression for the number of pages that Fred has read after x hours. (4) 1. How many pages would Fred have read after 3 hours? (1). The next two questions are based on the expression 6 37xxy Factorise the expression. (). Find the value of y if x =. (1).3 For what value/s of x will y = 0? () 3. The sum of two numbers is 5. Their product is 3. Find the sum of the squares of the two numbers by answering the following questions. 3.1 Expand to complete the following: yx )( (1) 3. If the two numbers mentioned above are x and y, then write down the equations for the sum and the product of the two numbers. (1) 3.3 Substitute the information given above into your answer for 3.1 and hence determine the sum of the squares of the two numbers. (Hint: make sure to include both sides of the identity.) (3) 4. Factorise the following expressions: 4.1 x xy y 463 (3) xx 6 () xx () 6 1 p (3)

3 5. Solve for x: 5.1 x 4 x 3 3 (3) 5. (1 )(1 ) 3 5xxxx (4) 5.3 x 1 1 x (3) 6. Study the graph of xfbelow )( and answer the questions that follow. 6.1 What is the range of xf?)( (1) 6. If )( tan kxf, find the value of k. () 6.3 For what value/s of x is xfincreasing? )( ()

4 7. Study the graph below and answer the questions that follow. 7.1 What is the period of xf?)( (1) 7. Write down the equation of (xf ). () 7.3 What is the maximum value of xf?)( (1) 7.4 Which one of the following statements is correct? (Write down only the correct letter.) a) xfis )( not symmetrical about any line. b) xfis )( symmetrical about the x-axis. c) xfis )( symmetrical about the y-axis. d) xfis )( symmetrical about the line y = x. (1) 8. Find the missing term of each of the following sequences: 8.1 3;;?;; 7;; 9 (1) 8. 6;;?;; 4;; 48 (1) 8.3 1;; ;; 4;; 7;;?;; 16 (1) 8.4 1;; 3;; 7;;?;; 1 (1) p?;; ;; 3 q pq (1) [TOTAL: 50 marks] 3

5 Grade 10 MATHEMATICS PRACTICE TEST TWO Marks: Consider a function of the form f x ax b.) ( 1.1 Determine the coordinates of the turning point of xfin )( terms of a or b. () 1. Depending on the values of a and b, the turning point could be either a maximum or a minimum. If the turning point is a minimum, write down the possible values of a and b. (3) 8. Consider the functions xf )( 4 and xxg )(.4 x.1 Sketch ( and ) xgxfon )( the same set of axes. Label all intercepts with the axes, asymptotes and turning points. (4). There is one value that xgcan )( take on that xfcannot. )( Write down this value. (1) 3. Refer to the graph below and answer the questions that follow. The functions drawn 6 below are: xf )( k and xxg )(. x 3.1 Find the value of k. () 3. Find the coordinates of point A. (3) 3.3 Write down the domain of (xf ). () 4

6 3.4 Find the coordinates of point B. (1) 3.5 Find the y coordinate of point C (which is directly above point B). () 4. The function xx ) is given. f ( 4.1 Sketch the graph of xfshowing )( all intercepts with the axes and other important points. (5) 4. What is the range of xf?)( () 4.3 For what value/s of x is xf?0)( () 4.4 What will the equation of xfbecome )( if the graph is shifted down by 3 units? (1) 5. Use your knowledge of quadrilaterals to answer the following questions. 5.1 Below are pairs of parallelograms. If you are only given information about their diagonals, in which pair(s) can you distinguish between the two parallelograms? a) a rhombus and a rectangle b) a square and a rhombus c) a kite and a trapezium d) a rectangle and a square () 5. Match each definition with the correct figure. If a definition applies to more than one figure, then choose the figure that it describes the best. You may only use each definition once. (Write the number of the figure and the letter of the definition you do not have to rewrite the whole definition.) Figure Definition (i) square A a quadrilateral with diagonals that bisect at 90 (ii) rhombus B a quadrilateral with one pair of parallel sides (iii) kite C a quadrilateral with a 90 corner angle and four equal sides (iv) trapezium D a quadrilateral with equal adjacent sides (8) 5

7 6. For each of the following, determine whether the statement is true or false. If false, correct the statement. 6.1 Both pairs of opposite sides of a kite are parallel. () 6. The diagonals of a rectangle bisect at 90. () 6.3 The adjacent sides of a rhombus are equal. () 6.4 A trapezium has two pairs of parallel sides. () 6.5 A square is a rhombus with a 90 corner angle. () [TOTAL: 50 marks] 6

8 Grade 10 MATHEMATICS PRACTICE TEST THREE Marks: Which of the following accounts would the best investment? Assume that you have R1 000 to invest for 3 years. a) Zebra Bank offers 8% per annum compounded monthly. b) Giraffe Savings offers 8,% per annum compounded yearly. c) Rhino Investments offers 8,4% per annum simple interest. (5). The points A(x;;1), B( 1;;4), C and D are shown on the Cartesian plane below..1 If the gradient of AB is 3, show that x =. (3) 1. If the gradient of AD is, show that D is the point (0;;). (3).3 If D is the midpoint of AC, find the coordinates of C. (4).4 Determine whether ABC is equilateral, isosceles or scalene. Show all of your working. (5) 7

10 Grade 10 MATHEMATICS PRACTICE TEST FOUR Marks: Simplify the following expressions as far as possible: xx () 1. 1 x xx (3) 3 7. Bernard inherited a flat in England that belonged to his grandmother. He decided to sell it and use the money to buy a house in South Africa. Below are the exchange rates at the time of the sale: Cross rates Rand (R) Pound ( ) 1 Rand (R) = 1 R14,46 1 Pound ( ) = 0, The flat was sold for How many Rands is this? (). Would Bernard want a strong Rand or a weak Rand? Give a reason for your answer. ().3 Refer to the table of cross rates. Describe the mathematical relationship between the two numbers 14,46 and 0,069. (1) 3. The diagram below shows squares of increasing sizes. With each extra layer of small squares we add, we build a bigger square. In the second layer, we add 3 small squares. In the third layer, we add 5 small squares. 3.1 How many tiles will there be in total if we have n layers of small squares? () 9

11 3. How many small squares will be added on in layer 5? (1) 3.3 Write down an expression for the number of tiles added on in layer n. (3) 3.4 Study the pattern carefully and use the relationship between the layers and the whole area to find the value of the following sum to terms: () 3.5 Use your answer to 3.4 to find the value of the following sum to terms: () 4. Use the figure below to answer the questions that follow. 4.1 Find the midpoint of AC. () 4. Use midpoints to prove that ABCD is a parallelogram. (3) 4.3 Prove that ABCD is NOT a rhombus in two different ways: a) using sides (3) b) using diagonals (3) 4.4 Prove that ABCD is not a rectangle. (4) 10

12 5. Your friend Nandi is working on a homework exercise. She is getting very frustrated because her answers do not seem to make any sense. In the two triangles below, she is trying to solve for x. Explain why her answers do not make sense in each case. (5) 6. Your favourite soccer team is changing its kit. The new kit will be a striped shirt and plain shorts. The team colours are blue and white. The stripes and the background colour of the shirt must be different (i.e. white with blue stripes or blue with white stripes). 6.1 Write down the different possible colour combinations for the team kit. () 6. What is the probability that the stripes on the shirt and the shorts will be the same colour? (3) 7. For two events, A and B, the probability of both occurring is 0, and the probability of neither occurring is 0, If P(A) = 0,6, use a Venn diagram to find P(B). (3) 7. Find P(A or B). () [TOTAL: 50 marks] 11

13 Grade 10 MATHEMATICS PRACTICE TEST ONE MEMORANDUM hour = 60 minutes in one hour, Fred reads = words. Pages per hour = = 40 pages after x hours = 40x (4) 1. Pages read = 40(3) = 10 (1).1 RHS = 6 37 xx 35 = ( 6 5)( xx 7) (). y = 6 37 xxsubstitute 35 x = = 6() 37() 35 = 85 (1).3 0 = ( 6 5)( xx 7) x = 5 or x 7 () 6 1

14 3.1 yx )( = xy y (1) 3. yx = 5 xy = 3 (1) 3.3 yx )( = xy y 5 = x )3(y yx = 19 (3) 4.1 x xy y 463 = x ( yy 3()3 ) = ( 3 )( xy ) (3) xx= 6 ( 5 )( xx 3) () 4.3 xx = xx ) ( () p = (1 )(1 pp ) = (1 )(1 )(1 )(1 ppp ) (3) 13

15 x x 4 1 = = x 3 x 3 3x 1 = 4x 7 x = 1 x = 1 (3) 7 5. ( 1 )(1 = xx ) xx 53 x = 1 x = xx 53 0 = xx = ( 4 1)( xx 1) 1 or x = 1 (4) x = 1 x 7 x 1 = 13 x )7( 7 x 1 x33 = 7 x 1 = 3 3x 4x = 4 x = 1 (3) 14

16 6.1 Ry (1) 6. The tangent graph has been shifted up by units. k = k = () x 90 or x 70 In other words, all values of x between 90 and 70, except for 90, 90 and 70. () (1) 7. y = 3cos x 1 () (1) 7.4 c) (1) (add on each time) (1) 8. 1 (multiply by each time) (1) (add 1, add, add 3, add 4...) (1) (add, add 4, add 6...) (1) 8.5 p q 1 (multiply by each time) (1) pq [TOTAL: 50 marks] 15

17 Grade 10 MATHEMATICS PRACTICE TEST TWO MEMORANDUM 1.1 Turning point occurs at x = 0, and when x = 0, y = b. Thus, the turning point is (0;;b). () 1. If the turning point is a minimum, then the parabola must be U shaped. This means that the coefficient of x must be positive. There is no restriction on the value of b. a > 0 Rb (3).1 (4). 4 (1) 16

18 3.1 Point D = (0;;) (y-intercept of the line y = x + ) The hyperbola has been shifted up by units because y = is now its asymptote. k = () 3. A is the x-intercept of the hyperbola where y = 0. 6 y = x 0 = 6 x 6 x = 6 = x x = 3 Thus, A is the point (3;;0). (3) 3.3 Domain: xrx 0, () 3.4 At B, y = 0, so substitute into y = x +. 0 = x + x = Thus B is the point ( ;;0). (1) 3.5 Point C will have the same x-value as point B because it is directly above it. Since we know the x-value, we can substitute into the equation of the hyperbola to find y. 6 y = x 6 = = 5 () 17

19 4.1 (5) 4. y, Ry () 4.3 x 11, Rx () 4.4 y = x 3 = x 1 (1) 5.1 (a) and (d) () 5. (i) C (ii) (iii) A D (iv) B (8) 18

20 6.1 False, both pairs of adjacent sides of a kite are equal. () 6. False, the diagonals of a rectangle bisect each other, but not necessarily at 90. () 6.3 True () 6.4 False, a trapezium has one pair of parallel sides. () 6.5 True () [TOTAL: 50 marks] 19

21 Grade 10 MATHEMATICS PRACTICE TEST THREE MEMORANDUM 1. The best investment will be the one that has the highest value after three years. Zebra Bank: A = 0, (1 ) = R1 70,4 Giraffe Savings: A = 1 000(1 + 0,08) 3 = R1 66,7 Rhino Investments: A = 1 000(1 + (0,084 3)) = R1 5 Zebra Bank is the best investment. (5) 0

22 .1 m AB = x 41 )1( 3 = 3 x 1 3x + 3 = 3 3x = 6 x = (3). Equation of AD: y = 1 cx Substitute in point A( ;;1). 1 1 = c = c Since D is the y-intercept of AD, D must be the point (0;;). Or answer by inspection. (3).3 Let C be (x;;y). x = 0 x = y 1 = y = 3 C is the point (;;3). Or answer by inspection. (4) 1

23 .4 AB = ( 4 1) ( 1 ( )) = 10 BC = 4( )3 1( ) = 10 AC = ( 3 1) ( ( )) = 0 ABC is an isosceles triangle because it has two equal sides. (5)

24 3.1 a) b) AB tan BD (1) BC tan BD (1) 3. AB = BD.tan and BC = BD.tan (from 3.1) AB BD.tan = BC BD. tan = tan tan (3) 3.3 AC = AB + BC BC = AC AB = 6 AB AB tan = BC tan AB 6 AB = tan,76 tan 39,97 AB 6 AB = 0,5 AB = 6 AB 3AB = 6 AB = units (4) 3.4 0,0 (1) 3

25 4.1 No, an average is not guaranteed to persist. If he were to take his yearly average and apply that to a given week it might be more reliable, but to use a single week s average to try to predict future performance is not wise. In the short run almost anything can happen one could have a good or bad week. It does not make sense to base statistics on a few short-term observations. (3) 4. No, the results are not completely reliable. Firstly, testing the product while the women are at a spa is misleading. The results of the spa treatment can not easily be separated from the results of the face cream. Secondly, there are too few people in the test group to make any deductions. What seems true for six people may not apply on a larger scale. The women might also have responded positively for emotional and psychological reasons. (5) 4.3 No, some people die very young and some people die very old. The highs and the lows balance out. An average does not describe every value in the range. () 4

26 5.1 False. Diagonals can be equal if opposite sides are equal. See below. () 5. True () 5.3 False, a kite and a square also have adjacent sides that are equal. () 5.4 False, diagonals do not necessarily bisect see below. () 5.5 True () [TOTAL: 50 marks] 5

27 Grade 10 MATHEMATICS PRACTICE TEST FOUR MEMORANDUM 1.1 ( 3)(3 = ) 39 xx () 1. 1 xx 1 7( ) 3(xxx 1) x = = = x 3 x 1 x 3 1 (3) = R ,46 = R (). Bernard would want a weak Rand relative to the Pound. This would mean that he would receive more Rands for each Pound that he earned on the sale. ().3 An inverse or reciprocal relationship ( ) exists between the two rates. Mathematically: 1 14,46 1 0,069 and 14, 46 ( ) (either description will earn 1 mark) (1) 0,069 6

28 3.1 n () 3. 9 (1) 3.3 Tiles added = n 1 (3) 3.4 With each layer we add on, we make a bigger square. This means that the sum of n layers (odd numbers) is n. This tells us that the sum of n odd numbers is n. Sum of odd numbers = = () 3.5 This is almost the same as the sequence in 3.4, except each term is 1 larger. This means that the whole sum will be a total of larger. Sum to = = Note: A general term for the sum of this sequence would be S n = n + n, or S n = n(n + 1). () 7

29 Midpoint AC = ;; = 1;; () Midpoint BD = ;; = 1;; AC and BD share a midpoint and therefore they bisect each other. This means that ABCD is a parallelogram (diagonals bisect). (3) 4.3 a) Using sides, simply prove that adjacent sides are not equal. (ABCD is a gm) AB = 3( = )1 1( )4 9 AD = ( 3 ( 3)) ( 1 ( 3)) = 40 Adjacent sides are not equal and therefore parallelogram ABCD is not a rhombus. (3) b) Diagonals of a rhombus bisect at 90. Using gradients: m AC = )5(3 8 = 1 3 m BD = )3(1 4 = )3(4 7 m BD m AC 1, so diagonals are not perpendicular. Parallelogram ABCD is therefore not a rhombus. (3) 8

30 4.4 m AD = )3(3 6 = )3(1 = 3 m DC = )5(3 = 3 5 Since m DC m AD 1, there is no right angle between AD and DC. Since ABCD does not have four right angles, it cannot be a rectangle. (4) 5. Triangle 1 The longest side in a right-angled triangle is always the hypotenuse. In this triangle, the hypotenuse is not the longest side, which is impossible. If we try to solve for x using Pythagoras, we will not be able to find a solution because the triangle does not make sense. Triangle In this triangle, the sum of the angles is not 180 ( = 18 ). This triangle also does not make sense. If we try to use trig ratios to solve for x, we will get a slightly different answer depending on which angle we use. This is because a right-angled triangle can not have a 9 angle and a 63 angle these angles would belong to different triangles, hence the two different answers. (5) 6.1 Blue shirt, white stripes;; blue shorts Blue shirt, white stripes;; white shorts White shirt, blue stripes;; blue shorts White shirt, blue stripes, white shorts () 6. 1 = (3) 4 9

31 7.1 P(B) = 0,3 (3) 7. P(A or B) = 0,4 + 0, + 0,3 = 0,9 (or, use 1 0,1 = 0,9) () [TOTAL: 60 marks] 30

32 Maskew Miller Longman (Pty) Ltd Forest Drive, Pinelands, Cape Town Maskew Miller Longman (Pty) Ltd 011

### Geometry of 2D Shapes

Name: Geometry of 2D Shapes Answer these questions in your class workbook: 1. Give the definitions of each of the following shapes and draw an example of each one: a) equilateral triangle b) isosceles

### Biggar High School Mathematics Department. National 5 Learning Intentions & Success Criteria: Assessing My Progress

Biggar High School Mathematics Department National 5 Learning Intentions & Success Criteria: Assessing My Progress Expressions & Formulae Topic Learning Intention Success Criteria I understand this Approximation

### http://www.castlelearning.com/review/teacher/assignmentprinting.aspx 5. 2 6. 2 1. 10 3. 70 2. 55 4. 180 7. 2 8. 4

of 9 1/28/2013 8:32 PM Teacher: Mr. Sime Name: 2 What is the slope of the graph of the equation y = 2x? 5. 2 If the ratio of the measures of corresponding sides of two similar triangles is 4:9, then the

### Target To know the properties of a rectangle

Target To know the properties of a rectangle (1) A rectangle is a 3-D shape. (2) A rectangle is the same as an oblong. (3) A rectangle is a quadrilateral. (4) Rectangles have four equal sides. (5) Rectangles

### Geometry Module 4 Unit 2 Practice Exam

Name: Class: Date: ID: A Geometry Module 4 Unit 2 Practice Exam Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Which diagram shows the most useful positioning

### /27 Intro to Geometry Review

/27 Intro to Geometry Review 1. An acute has a measure of. 2. A right has a measure of. 3. An obtuse has a measure of. 13. Two supplementary angles are in ratio 11:7. Find the measure of each. 14. In the

### SAT Subject Math Level 2 Facts & Formulas

Numbers, Sequences, Factors Integers:..., -3, -2, -1, 0, 1, 2, 3,... Reals: integers plus fractions, decimals, and irrationals ( 2, 3, π, etc.) Order Of Operations: Arithmetic Sequences: PEMDAS (Parentheses

### You must have: Ruler graduated in centimetres and millimetres, protractor, compasses, pen, HB pencil, eraser, calculator. Tracing paper may be used.

Write your name here Surname Other names Edexcel IGCSE Centre Number Mathematics A Paper 3H Monday 6 June 2011 Afternoon Time: 2 hours Candidate Number Higher Tier Paper Reference 4MA0/3H You must have:

### The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Student Name:

GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Wednesday, August 18, 2010 8:30 to 11:30 a.m., only Student Name: School Name: Print your name and the name of

### CAMI Education linked to CAPS: Mathematics

- 1 - TOPIC 1.1 Whole numbers _CAPS curriculum TERM 1 CONTENT Mental calculations Revise: Multiplication of whole numbers to at least 12 12 Ordering and comparing whole numbers Revise prime numbers to

### Conjunction is true when both parts of the statement are true. (p is true, q is true. p^q is true)

Mathematical Sentence - a sentence that states a fact or complete idea Open sentence contains a variable Closed sentence can be judged either true or false Truth value true/false Negation not (~) * Statement

### Definitions, Postulates and Theorems

Definitions, s and s Name: Definitions Complementary Angles Two angles whose measures have a sum of 90 o Supplementary Angles Two angles whose measures have a sum of 180 o A statement that can be proven

GRADE 10 TUTORIALS LO Topic Page 1 Number patterns and sequences 3 Functions and graphs 6 Algebra and equations 8 1 Finance 1 3 Analytical Geometry 14 3 Transformation 16 3 Trig / Mensuration 1 4 Data

### SGS4.3 Stage 4 Space & Geometry Part A Activity 2-4

SGS4.3 Stage 4 Space & Geometry Part A Activity 2-4 Exploring triangles Resources required: Each pair students will need: 1 container (eg. a rectangular plastic takeaway container) 5 long pipe cleaners

### 4. How many integers between 2004 and 4002 are perfect squares?

5 is 0% of what number? What is the value of + 3 4 + 99 00? (alternating signs) 3 A frog is at the bottom of a well 0 feet deep It climbs up 3 feet every day, but slides back feet each night If it started

### Co-ordinate Geometry THE EQUATION OF STRAIGHT LINES

Co-ordinate Geometry THE EQUATION OF STRAIGHT LINES This section refers to the properties of straight lines and curves using rules found by the use of cartesian co-ordinates. The Gradient of a Line. As

### The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Thursday, August 13, 2009 8:30 to 11:30 a.m., only.

GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Thursday, August 13, 2009 8:30 to 11:30 a.m., only Student Name: School Name: Print your name and the name of your

### CSU Fresno Problem Solving Session. Geometry, 17 March 2012

CSU Fresno Problem Solving Session Problem Solving Sessions website: http://zimmer.csufresno.edu/ mnogin/mfd-prep.html Math Field Day date: Saturday, April 21, 2012 Math Field Day website: http://www.csufresno.edu/math/news

### Intermediate Math Circles October 10, 2012 Geometry I: Angles

Intermediate Math Circles October 10, 2012 Geometry I: Angles Over the next four weeks, we will look at several geometry topics. Some of the topics may be familiar to you while others, for most of you,

### MATHEMATICS: PAPER I. 5. You may use an approved non-programmable and non-graphical calculator, unless otherwise stated.

NATIONAL SENIOR CERTIFICATE EXAMINATION NOVEMBER 015 MATHEMATICS: PAPER I Time: 3 hours 150 marks PLEASE READ THE FOLLOWING INSTRUCTIONS CAREFULLY 1. This question paper consists of 1 pages and an Information

### Parallel and Perpendicular. We show a small box in one of the angles to show that the lines are perpendicular.

CONDENSED L E S S O N. Parallel and Perpendicular In this lesson you will learn the meaning of parallel and perpendicular discover how the slopes of parallel and perpendicular lines are related use slopes

### Algebra III. Lesson 33. Quadrilaterals Properties of Parallelograms Types of Parallelograms Conditions for Parallelograms - Trapezoids

Algebra III Lesson 33 Quadrilaterals Properties of Parallelograms Types of Parallelograms Conditions for Parallelograms - Trapezoids Quadrilaterals What is a quadrilateral? Quad means? 4 Lateral means?

### The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Student Name:

GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Thursday, June 17, 2010 1:15 to 4:15 p.m., only Student Name: School Name: Print your name and the name of your

### www.sakshieducation.com

LENGTH OF THE PERPENDICULAR FROM A POINT TO A STRAIGHT LINE AND DISTANCE BETWEEN TWO PAPALLEL LINES THEOREM The perpendicular distance from a point P(x 1, y 1 ) to the line ax + by + c 0 is ax1+ by1+ c

### The Triangle and its Properties

THE TRINGLE ND ITS PROPERTIES 113 The Triangle and its Properties Chapter 6 6.1 INTRODUCTION triangle, you have seen, is a simple closed curve made of three line segments. It has three vertices, three

### Geometry Regents Review

Name: Class: Date: Geometry Regents Review Multiple Choice Identify the choice that best completes the statement or answers the question. 1. If MNP VWX and PM is the shortest side of MNP, what is the shortest

### Geometry 1. Unit 3: Perpendicular and Parallel Lines

Geometry 1 Unit 3: Perpendicular and Parallel Lines Geometry 1 Unit 3 3.1 Lines and Angles Lines and Angles Parallel Lines Parallel lines are lines that are coplanar and do not intersect. Some examples

### QUADRILATERALS CHAPTER 8. (A) Main Concepts and Results

CHAPTER 8 QUADRILATERALS (A) Main Concepts and Results Sides, Angles and diagonals of a quadrilateral; Different types of quadrilaterals: Trapezium, parallelogram, rectangle, rhombus and square. Sum of

### The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Thursday, January 24, 2013 9:15 a.m. to 12:15 p.m.

GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Thursday, January 24, 2013 9:15 a.m. to 12:15 p.m., only Student Name: School Name: The possession or use of any

### Selected practice exam solutions (part 5, item 2) (MAT 360)

Selected practice exam solutions (part 5, item ) (MAT 360) Harder 8,91,9,94(smaller should be replaced by greater )95,103,109,140,160,(178,179,180,181 this is really one problem),188,193,194,195 8. On

### 37 Basic Geometric Shapes and Figures

37 Basic Geometric Shapes and Figures In this section we discuss basic geometric shapes and figures such as points, lines, line segments, planes, angles, triangles, and quadrilaterals. The three pillars

### 11.3 Curves, Polygons and Symmetry

11.3 Curves, Polygons and Symmetry Polygons Simple Definition A shape is simple if it doesn t cross itself, except maybe at the endpoints. Closed Definition A shape is closed if the endpoints meet. Polygon

### Right Triangles 4 A = 144 A = 16 12 5 A = 64

Right Triangles If I looked at enough right triangles and experimented a little, I might eventually begin to notice a relationship developing if I were to construct squares formed by the legs of a right

### The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Wednesday, January 28, 2015 9:15 a.m. to 12:15 p.m.

GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Wednesday, January 28, 2015 9:15 a.m. to 12:15 p.m., only Student Name: School Name: The possession or use of any

### Equation of a Line. Chapter H2. The Gradient of a Line. m AB = Exercise H2 1

Chapter H2 Equation of a Line The Gradient of a Line The gradient of a line is simpl a measure of how steep the line is. It is defined as follows :- gradient = vertical horizontal horizontal A B vertical

### The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Tuesday, August 13, 2013 8:30 to 11:30 a.m., only.

GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Tuesday, August 13, 2013 8:30 to 11:30 a.m., only Student Name: School Name: The possession or use of any communications

### SOLVING TRIGONOMETRIC EQUATIONS

Mathematics Revision Guides Solving Trigonometric Equations Page 1 of 17 M.K. HOME TUITION Mathematics Revision Guides Level: AS / A Level AQA : C2 Edexcel: C2 OCR: C2 OCR MEI: C2 SOLVING TRIGONOMETRIC

### 39 Symmetry of Plane Figures

39 Symmetry of Plane Figures In this section, we are interested in the symmetric properties of plane figures. By a symmetry of a plane figure we mean a motion of the plane that moves the figure so that

### CHAPTER 8 QUADRILATERALS. 8.1 Introduction

CHAPTER 8 QUADRILATERALS 8.1 Introduction You have studied many properties of a triangle in Chapters 6 and 7 and you know that on joining three non-collinear points in pairs, the figure so obtained is

### Mathematics (Project Maths Phase 1)

2011. S133S Coimisiún na Scrúduithe Stáit State Examinations Commission Junior Certificate Examination Sample Paper Mathematics (Project Maths Phase 1) Paper 2 Ordinary Level Time: 2 hours 300 marks Running

### Estimating Angle Measures

1 Estimating Angle Measures Compare and estimate angle measures. You will need a protractor. 1. Estimate the size of each angle. a) c) You can estimate the size of an angle by comparing it to an angle

### Pythagorean Theorem: 9. x 2 2

Geometry Chapter 8 - Right Triangles.7 Notes on Right s Given: any 3 sides of a Prove: the is acute, obtuse, or right (hint: use the converse of Pythagorean Theorem) If the (longest side) 2 > (side) 2

### SAT Subject Math Level 1 Facts & Formulas

Numbers, Sequences, Factors Integers:..., -3, -2, -1, 0, 1, 2, 3,... Reals: integers plus fractions, decimals, and irrationals ( 2, 3, π, etc.) Order Of Operations: Aritmetic Sequences: PEMDAS (Parenteses

### Math 531, Exam 1 Information.

Math 531, Exam 1 Information. 9/21/11, LC 310, 9:05-9:55. Exam 1 will be based on: Sections 1A - 1F. The corresponding assigned homework problems (see http://www.math.sc.edu/ boylan/sccourses/531fa11/531.html)

### 43 Perimeter and Area

43 Perimeter and Area Perimeters of figures are encountered in real life situations. For example, one might want to know what length of fence will enclose a rectangular field. In this section we will study

### High School Geometry Test Sampler Math Common Core Sampler Test

High School Geometry Test Sampler Math Common Core Sampler Test Our High School Geometry sampler covers the twenty most common questions that we see targeted for this level. For complete tests and break

### Paper 1. Calculator not allowed. Mathematics test. First name. Last name. School. Remember KEY STAGE 3 TIER 5 7

Ma KEY STAGE 3 Mathematics test TIER 5 7 Paper 1 Calculator not allowed First name Last name School 2009 Remember The test is 1 hour long. You must not use a calculator for any question in this test. You

### The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Wednesday, January 29, 2014 9:15 a.m. to 12:15 p.m.

GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Wednesday, January 29, 2014 9:15 a.m. to 12:15 p.m., only Student Name: School Name: The possession or use of any

### UNIT H1 Angles and Symmetry Activities

UNIT H1 Angles and Symmetry Activities Activities H1.1 Lines of Symmetry H1.2 Rotational and Line Symmetry H1.3 Symmetry of Regular Polygons H1.4 Interior Angles in Polygons Notes and Solutions (1 page)

### Vocabulary Words and Definitions for Algebra

Name: Period: Vocabulary Words and s for Algebra Absolute Value Additive Inverse Algebraic Expression Ascending Order Associative Property Axis of Symmetry Base Binomial Coefficient Combine Like Terms

### CIRCLE COORDINATE GEOMETRY

CIRCLE COORDINATE GEOMETRY (EXAM QUESTIONS) Question 1 (**) A circle has equation x + y = 2x + 8 Determine the radius and the coordinates of the centre of the circle. r = 3, ( 1,0 ) Question 2 (**) A circle

### The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Thursday, August 16, 2012 8:30 to 11:30 a.m.

GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Thursday, August 16, 2012 8:30 to 11:30 a.m., only Student Name: School Name: Print your name and the name of your

### Teacher Development Workshop

Teacher Development Workshop Senior Phase Mathematics 6009701866735 CONTENTS PAGE CONTENTS PAGE... 2 ACTIVITY A:... 3 MATHEMATICS INTRODUCTION TO CAPS... 5 ACTIVITY B: MATHEMATICS TEXTBOOKS... 5 ACTIVITY

### Paper 1. Calculator not allowed. Mathematics test. First name. Last name. School. Remember KEY STAGE 3 TIER 6 8

Ma KEY STAGE 3 Mathematics test TIER 6 8 Paper 1 Calculator not allowed First name Last name School 2009 Remember The test is 1 hour long. You must not use a calculator for any question in this test. You

### Mathematics (Project Maths Phase 3)

2014. M329 Coimisiún na Scrúduithe Stáit State Examinations Commission Leaving Certificate Examination 2014 Mathematics (Project Maths Phase 3) Paper 1 Higher Level Friday 6 June Afternoon 2:00 4:30 300

### SAT Math Facts & Formulas Review Quiz

Test your knowledge of SAT math facts, formulas, and vocabulary with the following quiz. Some questions are more challenging, just like a few of the questions that you ll encounter on the SAT; these questions

### Mathematics A *P44587A0128* Pearson Edexcel GCSE P44587A. Paper 2 (Calculator) Higher Tier. Friday 7 November 2014 Morning Time: 1 hour 45 minutes

Write your name here Surname Other names Pearson Edexcel GCSE Centre Number Mathematics A Paper 2 (Calculator) Friday 7 November 2014 Morning Time: 1 hour 45 minutes Candidate Number Higher Tier Paper

### Lecture 8 : Coordinate Geometry. The coordinate plane The points on a line can be referenced if we choose an origin and a unit of 20

Lecture 8 : Coordinate Geometry The coordinate plane The points on a line can be referenced if we choose an origin and a unit of 0 distance on the axis and give each point an identity on the corresponding

Quadrilaterals / Mathematics Unit: 11 Lesson: 01 Duration: 7 days Lesson Synopsis: In this lesson students explore properties of quadrilaterals in a variety of ways including concrete modeling, patty paper

### of surface, 569-571, 576-577, 578-581 of triangle, 548 Associative Property of addition, 12, 331 of multiplication, 18, 433

Absolute Value and arithmetic, 730-733 defined, 730 Acute angle, 477 Acute triangle, 497 Addend, 12 Addition associative property of, (see Commutative Property) carrying in, 11, 92 commutative property

### Situation: Proving Quadrilaterals in the Coordinate Plane

Situation: Proving Quadrilaterals in the Coordinate Plane 1 Prepared at the University of Georgia EMAT 6500 Date Last Revised: 07/31/013 Michael Ferra Prompt A teacher in a high school Coordinate Algebra

### FACTORING QUADRATICS 8.1.1 and 8.1.2

FACTORING QUADRATICS 8.1.1 and 8.1.2 Chapter 8 introduces students to quadratic equations. These equations can be written in the form of y = ax 2 + bx + c and, when graphed, produce a curve called a parabola.

### In mathematics, there are four attainment targets: using and applying mathematics; number and algebra; shape, space and measures, and handling data.

MATHEMATICS: THE LEVEL DESCRIPTIONS In mathematics, there are four attainment targets: using and applying mathematics; number and algebra; shape, space and measures, and handling data. Attainment target

### Mathematics Second Practice Test 1 Levels 4-6 Calculator not allowed

Instructions Use black ink or ball-point pen. Fill in the boxes at the top of this page with your name, centre number and candidate number. Answer all questions. Answer the questions in the spaces provided

### a. all of the above b. none of the above c. B, C, D, and F d. C, D, F e. C only f. C and F

FINAL REVIEW WORKSHEET COLLEGE ALGEBRA Chapter 1. 1. Given the following equations, which are functions? (A) y 2 = 1 x 2 (B) y = 9 (C) y = x 3 5x (D) 5x + 2y = 10 (E) y = ± 1 2x (F) y = 3 x + 5 a. all

### 2004 Solutions Ga lois Contest (Grade 10)

Canadian Mathematics Competition An activity of The Centre for Education in Ma thematics and Computing, University of W aterloo, Wa terloo, Ontario 2004 Solutions Ga lois Contest (Grade 10) 2004 Waterloo

Geometry Progress Ladder Maths Makes Sense Foundation End-of-year objectives page 2 Maths Makes Sense 1 2 End-of-block objectives page 3 Maths Makes Sense 3 4 End-of-block objectives page 4 Maths Makes

### The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION MATHEMATICS A. Thursday, January 29, 2009 1:15 to 4:15 p.m.

MATHEMATICS A The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION MATHEMATICS A Thursday, January 29, 2009 1:15 to 4:15 p.m., only Print Your Name: Print Your School s Name: Print your

### MATH 60 NOTEBOOK CERTIFICATIONS

MATH 60 NOTEBOOK CERTIFICATIONS Chapter #1: Integers and Real Numbers 1.1a 1.1b 1.2 1.3 1.4 1.8 Chapter #2: Algebraic Expressions, Linear Equations, and Applications 2.1a 2.1b 2.1c 2.2 2.3a 2.3b 2.4 2.5

### Hiker. A hiker sets off at 10am and walks at a steady speed for 2 hours due north, then turns and walks for a further 5 hours due west.

Hiker A hiker sets off at 10am and walks at a steady speed for hours due north, then turns and walks for a further 5 hours due west. If he continues at the same speed, what s the earliest time he could

### The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY

GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Wednesday, June 20, 2012 9:15 a.m. to 12:15 p.m., only Student Name: School Name: Print your name and the name

### Stage 1 Higher Revision Sheet

Stage 1 Higher Revision Sheet This document attempts to sum up the contents of the Higher Tier Stage 1 Module. There are two exams, each 25 minutes long. One allows use of a calculator and the other doesn

### DEFINITIONS. Perpendicular Two lines are called perpendicular if they form a right angle.

DEFINITIONS Degree A degree is the 1 th part of a straight angle. 180 Right Angle A 90 angle is called a right angle. Perpendicular Two lines are called perpendicular if they form a right angle. Congruent

### 6 EXTENDING ALGEBRA. 6.0 Introduction. 6.1 The cubic equation. Objectives

6 EXTENDING ALGEBRA Chapter 6 Extending Algebra Objectives After studying this chapter you should understand techniques whereby equations of cubic degree and higher can be solved; be able to factorise

### You must have: Ruler graduated in centimetres and millimetres, protractor, compasses, pen, HB pencil, eraser, calculator. Tracing paper may be used.

Write your name here Surname Other names Edexcel IGCSE Mathematics B Paper 1 Centre Number Candidate Number Monday 6 June 2011 Afternoon Time: 1 hour 30 minutes Paper Reference 4MB0/01 You must have: Ruler

### Conjectures. Chapter 2. Chapter 3

Conjectures Chapter 2 C-1 Linear Pair Conjecture If two angles form a linear pair, then the measures of the angles add up to 180. (Lesson 2.5) C-2 Vertical Angles Conjecture If two angles are vertical

### Extra Credit Assignment Lesson plan. The following assignment is optional and can be completed to receive up to 5 points on a previously taken exam.

Extra Credit Assignment Lesson plan The following assignment is optional and can be completed to receive up to 5 points on a previously taken exam. The extra credit assignment is to create a typed up lesson

### Solutions Manual for How to Read and Do Proofs

Solutions Manual for How to Read and Do Proofs An Introduction to Mathematical Thought Processes Sixth Edition Daniel Solow Department of Operations Weatherhead School of Management Case Western Reserve

### Chapter 8 Geometry We will discuss following concepts in this chapter.

Mat College Mathematics Updated on Nov 5, 009 Chapter 8 Geometry We will discuss following concepts in this chapter. Two Dimensional Geometry: Straight lines (parallel and perpendicular), Rays, Angles

### 4.4 Transforming Circles

Specific Curriculum Outcomes. Transforming Circles E13 E1 E11 E3 E1 E E15 analyze and translate between symbolic, graphic, and written representation of circles and ellipses translate between different

### Paper Reference. Edexcel GCSE Mathematics (Linear) 1380 Paper 4 (Calculator) Monday 5 March 2012 Afternoon Time: 1 hour 45 minutes

Centre No. Candidate No. Paper Reference 1 3 8 0 4 H Paper Reference(s) 1380/4H Edexcel GCSE Mathematics (Linear) 1380 Paper 4 (Calculator) Higher Tier Monday 5 March 2012 Afternoon Time: 1 hour 45 minutes

### Section 9-1. Basic Terms: Tangents, Arcs and Chords Homework Pages 330-331: 1-18

Chapter 9 Circles Objectives A. Recognize and apply terms relating to circles. B. Properly use and interpret the symbols for the terms and concepts in this chapter. C. Appropriately apply the postulates,

### 1.4. Arithmetic of Algebraic Fractions. Introduction. Prerequisites. Learning Outcomes

Arithmetic of Algebraic Fractions 1.4 Introduction Just as one whole number divided by another is called a numerical fraction, so one algebraic expression divided by another is known as an algebraic fraction.

### Understanding Basic Calculus

Understanding Basic Calculus S.K. Chung Dedicated to all the people who have helped me in my life. i Preface This book is a revised and expanded version of the lecture notes for Basic Calculus and other

### http://jsuniltutorial.weebly.com/ Page 1

Parallelogram solved Worksheet/ Questions Paper 1.Q. Name each of the following parallelograms. (i) The diagonals are equal and the adjacent sides are unequal. (ii) The diagonals are equal and the adjacent

### 2015 Chapter Competition Solutions

05 Chapter Competition Solutions Are you wondering how we could have possibly thought that a Mathlete would be able to answer a particular Sprint Round problem without a calculator? Are you wondering how

### 9 Area, Perimeter and Volume

9 Area, Perimeter and Volume 9.1 2-D Shapes The following table gives the names of some 2-D shapes. In this section we will consider the properties of some of these shapes. Rectangle All angles are right

### Unit 8 Angles, 2D and 3D shapes, perimeter and area

Unit 8 Angles, 2D and 3D shapes, perimeter and area Five daily lessons Year 6 Spring term Recognise and estimate angles. Use a protractor to measure and draw acute and obtuse angles to Page 111 the nearest

### Chapter 9. Systems of Linear Equations

Chapter 9. Systems of Linear Equations 9.1. Solve Systems of Linear Equations by Graphing KYOTE Standards: CR 21; CA 13 In this section we discuss how to solve systems of two linear equations in two variables

### Mathematics standards

Mathematics standards Grade 6 Summary of students performance by the end of Grade 6 Reasoning and problem solving Students represent and interpret routine and non-routine mathematical problems in a range

### Algebra Geometry Glossary. 90 angle

lgebra Geometry Glossary 1) acute angle an angle less than 90 acute angle 90 angle 2) acute triangle a triangle where all angles are less than 90 3) adjacent angles angles that share a common leg Example:

### www.mathsbox.org.uk ab = c a If the coefficients a,b and c are real then either α and β are real or α and β are complex conjugates

Further Pure Summary Notes. Roots of Quadratic Equations For a quadratic equation ax + bx + c = 0 with roots α and β Sum of the roots Product of roots a + b = b a ab = c a If the coefficients a,b and c

1.2 GRAPHS OF EQUATIONS Copyright Cengage Learning. All rights reserved. What You Should Learn Sketch graphs of equations. Find x- and y-intercepts of graphs of equations. Use symmetry to sketch graphs

### Geometry: Classifying, Identifying, and Constructing Triangles

Geometry: Classifying, Identifying, and Constructing Triangles Lesson Objectives Teacher's Notes Lesson Notes 1) Identify acute, right, and obtuse triangles. 2) Identify scalene, isosceles, equilateral

### Paper Reference. Ruler graduated in centimetres and millimetres, protractor, compasses, pen, HB pencil, eraser. Tracing paper may be used.

Centre No. Candidate No. Paper Reference 1 3 8 0 3 H Paper Reference(s) 1380/3H Edexcel GCSE Mathematics (Linear) 1380 Paper 3 (Non-Calculator) Higher Tier Monday 18 May 2009 Afternoon Time: 1 hour 45