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

Transcription

1 Write your name here Surname Other names Edexcel GCSE Centre Number Mathematics A Paper 1 (Non-Calculator) Tuesday 11 June 2013 Morning Time: 1 hour 45 minutes Candidate Number Higher Tier Paper Reference 1MA0/1H You must have: Ruler graduated in centimetres and millimetres, protractor, pair of compasses, pen, HB pencil, eraser. Tracing paper may be used. Total Marks 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 there may be more space than you need. Calculators must not be used. Information The total mark for this paper is 100 The marks for each question are shown in brackets use this as a guide as to how much time to spend on each question. Questions labelled with an asterisk (*) are ones where the quality of your written communication will be assessed. Advice Read each question carefully before you start to answer it. Keep an eye on the time. Try to answer every question. Check your answers if you have time at the end. Turn over P43598A 2013 Pearson Education Ltd. 6/5/5/ *P43598A0128*

2 GCSE Mathematics 1MA0 Formulae: Higher Tier You must not write on this formulae page. Anything you write on this formulae page will gain NO credit. Volume of prism = area of cross section length Area of trapezium = 1 2 (a + b)h cross section h a length b Volume of sphere = Surface area of sphere = 4 2 Volume of cone = h Curved surface area of cone = r l h r In any triangle ABC A b c C a B The Quadratic Equation The solutions of ax 2 + bx + c = 0 where 0, are given by b b ac x = ± ( 4 ) 2a 2 Sine Rule a b c = = sin A sin B sinc Cosine Rule a 2 = b 2 + c 2 2bc cos A Area of triangle = 1 2 ab sin C 2 *P43598A0228*

3 Answer ALL questions. Write your answers in the spaces provided. You must write down all stages in your working. You must NOT use a calculator. 1 Given that = write down the value of (a) (b) (Total for Question 1 is 2 marks) 2 Mr Mason asks 240 Year 11 students what they want to do next year. 15% of the students want to go to college. 3 of the students want to stay at school. 4 The rest of the students do not know. Work out the number of students who do not know.... (Total for Question 2 is 4 marks) *P43598A0328* 3 Turn over

4 3 Sixteen babies are born in a hospital. Here are the weights of the babies in kilograms Show this information in an ordered stem and leaf diagram. Key: (Total for Question 3 is 3 marks) 4 (a) Expand 3(2 + t) (b) Expand 3x(2x + 5)... (1) (c) Expand and simplify (m + 3)(m + 10)... (2)... (2) (Total for Question 4 is 5 marks) 4 *P43598A0428*

5 5 Write 525 as a product of its prime factors.... (Total for Question 5 is 3 marks) 6 Ed has 4 cards. There is a number on each card ? The mean of the 4 numbers on Ed s cards is 10 Work out the number on the 4th card.... (Total for Question 6 is 3 marks) *P43598A0528* 5 Turn over

6 7 y P O x (a) Translate shape P by the vector 5 2 (2) 6 *P43598A0628*

7 y B O A 2 x 3 4 (b) Describe fully the single transformation that maps shape A onto shape B (3) (Total for Question 7 is 5 marks) *P43598A0728* 7 Turn over

8 8 Margaret has some goats. The goats produce an average total of 21.7 litres of milk per day for 280 days. Margaret sells the milk in 1 litre bottles. 2 Work out an estimate for the total number of bottles that Margaret will be able to fill with the milk. You must show clearly how you got your estimate.... (Total for Question 8 is 3 marks) 9 Matt and Dan cycle around a cycle track. Each lap Matt cycles takes him 50 seconds. Each lap Dan cycles takes him 80 seconds. Dan and Matt start cycling at the same time at the start line. Work out how many laps they will each have cycled when they are next at the start line together. Matt... laps Dan... laps (Total for Question 9 is 3 marks) 8 *P43598A0828*

9 10 The diagram shows a garden in the shape of a rectangle x Diagram NOT accurately drawn x + 6 All measurements are in metres. The perimeter of the garden is 32 metres. Work out the value of x... (Total for Question 10 is 4 marks) *P43598A0928* 9 Turn over

10 *11 Debbie drove from Junction 12 to Junction 13 on a motorway. The travel graph shows Debbie s journey Distance from Junction 12 (kilometres) Time (minutes) Ian also drove from Junction 12 to Junction 13 on the same motorway. He drove at an average speed of 66 km/hour. Who had the faster average speed, Debbie or Ian? You must explain your answer. (Total for Question 11 is 4 marks) 10 *P43598A01028*

11 12 On the grid, draw the graph of y = 1 x + 5 for values of x from 2 to 4 2 y O x 1 (Total for Question 12 is 3 marks) *P43598A01128* 11 Turn over

12 *13 Here is a map. The position of a ship, S, is marked on the map. N C S Scale 1 cm represents 100 m Point C is on the coast. Ships must not sail closer than 500 m to point C. The ship sails on a bearing of 037 Will the ship sail closer than 500 m to point C? You must explain your answer. (Total for Question 13 is 3 marks) 12 *P43598A01228*

13 14 2 < n 3 (a) Represent this inequality on the number line n (2) (b) Solve the inequality 8x 3 6x (2) (Total for Question 14 is 4 marks) *15 One sheet of paper is cm thick. Mark wants to put 500 sheets of paper into the paper tray of his printer. The paper tray is 4 cm deep. Is the paper tray deep enough for 500 sheets of paper? You must explain your answer. (Total for Question 15 is 3 marks) *P43598A01328* 13 Turn over

14 16 The normal price of a television is reduced by 30% in a sale. The sale price of the television is 350 Work out the normal price of the television.... (Total for Question 16 is 3 marks) 14 *P43598A01428*

15 17 Sumeet has a pond in the shape of a prism. 1 m 2 m 0.5 m 1.3 m Diagram NOT accurately drawn The pond is completely full of water. Sumeet wants to empty the pond so he can clean it. Sumeet uses a pump to empty the pond. The volume of water in the pond decreases at a constant rate. The level of the water in the pond goes down by 20 cm in the first 30 minutes. Work out how much more time Sumeet has to wait for the pump to empty the pond completely.... (Total for Question 17 is 6 marks) *P43598A01528* 15 Turn over

16 18 Solve the simultaneous equations 4x + 7y = 1 3x + 10y = 15 x =... y =... (Total for Question 18 is 4 marks) 19 Write these numbers in order of size. Start with the smallest number (Total for Question 19 is 2 marks) 16 *P43598A01628*

17 20 A N x D Diagram NOT accurately drawn 4x M B C ABCD is a square with a side length of 4x M is the midpoint of DC. N is the point on AD where ND = x BMN is a right-angled triangle. Find an expression, in terms of x, for the area of triangle BMN. Give your expression in its simplest form.... (Total for Question 20 is 4 marks) *P43598A01728* 17 Turn over

18 21 The table below shows information about the heights of 60 students. Height (x cm) Number of students 140 < x < x < x < x < x < x (a) On the grid opposite, draw a cumulative frequency graph for the information in the table. (3) 18 *P43598A01828*

19 60 50 Cumulative frequency Height (cm) (b) Find an estimate (i) for the median, (ii) for the interquartile range.... cm... cm (3) (Total for Question 21 is 6 marks) *P43598A01928* 19 Turn over

20 22 P and Q are two triangular prisms that are mathematically similar. B E A 10 cm 2 6 cm C 15 cm D 12 cm F Diagram NOT accurately drawn Prism P Prism Q Prism P has triangle ABC as its cross section. Prism Q has triangle DEF as its cross section. AC = 6 cm DF = 12 cm The area of the cross section of prism P is 10 cm 2. The length of prism P is 15 cm. Work out the volume of prism Q.... (Total for Question 22 is 4 marks) 20 *P43598A02028*

21 23 Simplify 4( x + 5) 2 x + 2x (Total for Question 23 is 2 marks) *P43598A02128* 21 Turn over

22 24 Bill works for a computer service centre. The table shows some information about the length of time, t minutes, of the phone calls Bill had. Time (t minutes) 0 < t < t < t < t < t 45 Number of calls On the grid, draw a histogram to show this information. Frequency density Time (t minutes) (Total for Question 24 is 3 marks) 22 *P43598A02228*

23 25 The expression x 2 8x + 21 can be written in the form (x a) 2 + b for all values of x. (a) Find the value of a and the value of b. a =... The equation of a curve is y = f(x) where f(x) = x 2 8x + 21 The diagram shows part of a sketch of the graph of y = f(x). b =... (3) y y = f(x) M O x The minimum point of the curve is M. (b) Write down the coordinates of M. (...,...) (1) (Total for Question 25 is 4 marks) *P43598A02328* 23 Turn over

24 26 Fiza has 10 coins in a bag. There are three 1 coins and seven 50 pence coins. Fiza takes at random, 3 coins from the bag. Work out the probability that she takes exactly (Total for Question 26 is 4 marks) 24 *P43598A02428*

25 27 b S N R Diagram NOT accurately drawn P a Q PQRS is a parallelogram. N is the point on SQ such that SN : NQ = 3 : 2 PQ = a PS = b (a) Write down, in terms of a and b, an expression for SQ. SQ =... (1) (b) Express NR in terms of a and b. NR =... (3) (Total for Question 27 is 4 marks) *P43598A02528* 25 Turn over

26 28 The diagram shows a sketch of the graph of y = cos x y 1 O A x 1 (a) Write down the coordinates of the point A. (...,...) (1) (b) On the same diagram, draw a sketch of the graph of y = 2 cos x (1) (Total for Question 28 is 2 marks) TOTAL FOR PAPER IS 100 MARKS 26 *P43598A02628*

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29 Write your name here Surname Other names Edexcel GCSE Centre Number Mathematics A Paper 2 (Calculator) Friday 14 June 2013 Morning Time: 1 hour 45 minutes Candidate Number Higher Tier Paper Reference 1MA0/2H You must have: Ruler graduated in centimetres and millimetres, protractor, pair of compasses, pen, HB pencil, eraser, calculator. Tracing paper may be used. Total Marks 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 there may be more space than you need. Calculators may be used. If your calculator does not have a button, take the value of to be unless the question instructs otherwise. Information The total mark for this paper is 100 The marks for each question are shown in brackets use this as a guide as to how much time to spend on each question. Questions labelled with an asterisk (*) are ones where the quality of your written communication will be assessed. P43600A 2013 Pearson Education Ltd. 6/5/5/ Advice Read each question carefully before you start to answer it. Keep an eye on the time. Try to answer every question. Check your answers if you have time at the end. *P43600A0128* Turn over

30 GCSE Mathematics 1MA0 Formulae: Higher Tier You must not write on this formulae page. Anything you write on this formulae page will gain NO credit. Volume of prism = area of cross section length Area of trapezium = 1 2 (a + b)h cross section h a length b Volume of sphere = Surface area of sphere = 4 2 Volume of cone = h Curved surface area of cone = r l h r In any triangle ABC C The Quadratic Equation The solutions of ax 2 + bx + c = 0 where 0, are given by A b c a B x b b ac = ± ( 4 ) 2a 2 Sine Rule a b c = = sin A sin B sinc Cosine Rule a 2 = b 2 + c 2 2bc cos A Area of triangle = 1 2 ab sin C 2 *P43600A0228*

31 Answer ALL questions. Write your answers in the spaces provided. You must write down all stages in your working. 1 Here is a cuboid. Diagram NOT accurately drawn 1.5 cm 6 cm 1.5 cm The cuboid is 6 cm by 1.5 cm by 1.5 cm. Work out the total surface area of the cuboid.... cm 2 (Total for Question 1 is 3 marks) *P43600A0328* 3 Turn over

32 *2 Here is a list of ingredients for making 18 mince pies. Ingredients for 18 mince pies 225 g of butter 350 g of flour 100 g of sugar 280 g of mincemeat 1 egg Elaine wants to make 45 mince pies. Elaine has 1 kg of butter 1 kg of flour 500 g of sugar 600 g of mincemeat 6 eggs Does Elaine have enough of each ingredient to make 45 mince pies? You must show clearly how you got your answer. (Total for Question 2 is 4 marks) 4 *P43600A0428*

33 3 The scatter graph shows some information about 10 cars, of the same type and make. The graph shows the age (years) and the value ( ) of each car value ( ) age (years) 4 5 The table shows the age and the value of two other cars of the same type and make. age (years) value ( ) (a) On the scatter graph, plot the information from the table. (1) (b) Describe the relationship between the age and the value of the cars (1) A car of the same type and make is years old. (c) Estimate the value of the car.... (2) (Total for Question 3 is 4 marks) *P43600A0528* 5 Turn over

34 4 Rhiana plays a game. The probability that she will lose the game is 0.32 The probability that she will draw the game is 0.05 Rhiana is going to play the game 200 times. Work out an estimate for the number of times Rhiana will win the game.... (Total for Question 4 is 3 marks) 6 *P43600A0628*

35 5 Mason is doing a survey to find out how many magazines people buy. He uses this question on his questionnaire. How many magazines do you buy? 0 to 4 4 to 8 8 to 12 (a) Write down two things wrong with this question (2) (b) Write a better question for Mason to use on his questionnaire to find out how many magazines people buy. Mason asks his friends at school to do his questionnaire. This may not be a good sample to use. (c) Give one reason why. (2) (1) (Total for Question 5 is 5 marks) *P43600A0728* 7 Turn over

36 6 Tame Valley is a company that makes yoghurt. A machine fills trays of 20 pots with yoghurt. In one hour, the machine fills a total of pots. Work out how many seconds the machine takes to fill each tray of 20 pots.... seconds (Total for Question 6 is 4 marks) 8 *P43600A0828*

37 7 Colin, Dave and Emma share some money. Colin gets 3 of the money. 10 Emma and Dave share the rest of the money in the ratio 3 : 2 What is Dave s share of the money?... (Total for Question 7 is 4 marks) *P43600A0928* 9 Turn over

38 8 The diagram shows the plan of a playground. 80 m 30 m Diagram NOT accurately drawn 60 m 50 m 40 m Bill is going to cover the playground with tarmac. It costs 2.56 to cover each square metre with tarmac. Work out the total cost of the tarmac Bill needs.... (Total for Question 8 is 4 marks) 10 *P43600A01028*

39 9 C R B Diagram NOT accurately drawn A 35 Q x D P ABC, PQR and AQD are straight lines. ABC is parallel to PQR. Angle BAQ = 35 Angle BQA = 90 Work out the size of the angle marked x. Give reasons for each stage of your working. x =... (Total for Question 9 is 4 marks) *P43600A01128* 11 Turn over

40 10 The equation x 3 + 2x = 110 has a solution between 4 and 5 Use a trial and improvement method to find this solution. Give your answer correct to one decimal place. You must show ALL your working. x =... (Total for Question 10 is 4 marks) 12 *P43600A01228*

41 11 XYZ is a right-angled triangle. X 1.35 m Diagram NOT accurately drawn Y 3.25 m Z Calculate the length of XZ. Give your answer correct to 3 significant figures.... m (Total for Question 11 is 3 marks) *P43600A01328* 13 Turn over

42 12 (a) Solve 3(x 2) = x + 7 (b) Solve 2 y = 1 5 x =... (3) y =... (2) (Total for Question 12 is 5 marks) 14 *P43600A01428*

43 13 y B (7, 5) A ( 1, 2) Diagram NOT accurately drawn O x A is the point ( 1, 2) B is the point (7, 5) (a) Find the coordinates of the midpoint of AB. (...,...) (2) P is the point ( 4, 4) Q is the point (1, 5) (b) Find the gradient of PQ.... (2) (Total for Question 13 is 4 marks) *P43600A01528* 15 Turn over

44 *14 Viv wants to invest 2000 for 2 years in the same bank. The International Bank Compound Interest 4% for the first year 1% for each extra year The Friendly Bank Compound Interest 5% for the first year 0.5% for each extra year At the end of 2 years, Viv wants to have as much money as possible. Which bank should she invest her 2000 in? (Total for Question 14 is 4 marks) 16 *P43600A01628*

45 15 (a) Complete the table of values for y = x 2 2x x y (2) (b) On the grid, draw the graph of y = x 2 2x for values of x from 2 to 4 y O x 4 (2) (c) Solve x 2 2x 2 = 1... (2) (Total for Question 15 is 6 marks) *P43600A01728* 17 Turn over

46 *16 Diagram NOT accurately drawn S O S and T are points on the circumference of a circle, centre O. PT is a tangent to the circle. SOP is a straight line. Angle OPT = 32 Work out the size of the angle marked x. Give reasons for your answer. x T 32 P... (Total for Question 16 is 5 marks) 18 *P43600A01828*

47 17 Some girls did a sponsored swim to raise money for charity. The table shows information about the amounts of money ( ) the girls raised. Least amount of money ( ) 10 Greatest amount of money ( ) 45 Median 25 Lower quartile 16 Upper quartile 42 (a) On the grid, draw a box plot for the information in the table Amount of money ( ) (2) Some boys also did the sponsored swim. The box plot shows information about the amounts of money ( ) the boys raised Amount of money ( ) (b) Compare the amounts of money the girls raised with the amounts of money the boys raised (2) (Total for Question 17 is 4 marks) *P43600A01928* 19 Turn over

48 18 Make p the subject of the formula y = 3p (Total for Question 18 is 3 marks) 19 (a) Factorise 6 + 9x... (1) (b) Factorise y (1) (c) Factorise 2p 2 p (2) (Total for Question 19 is 4 marks) 20 *P43600A02028*

49 *20 The diagram shows a ladder leaning against a vertical wall. Diagram NOT accurately drawn 6 m y 2.25 m The ladder stands on horizontal ground. The length of the ladder is 6 m. The bottom of the ladder is 2.25 m from the bottom of the wall. A ladder is safe to use when the angle marked y is about 75. Is the ladder safe to use? You must show all your working. (Total for Question 20 is 3 marks) *P43600A02128* 21 Turn over

50 21 In Holborn School there are 460 students in Key Stage students in Key Stage students in Key Stage 5 Nimer is carrying out a survey. He needs a sample of 100 students stratified by Key Stage. Work out the number of students from Key Stage 3 there should be in the sample.... (Total for Question 21 is 2 marks) 22 h is inversely proportional to the square of. When = 5, h = 3.4 Find the value of h when = 8 h =... (Total for Question 22 is 3 marks) 22 *P43600A02228*

51 23 Dan does an experiment to find the value of. He measures the circumference and the diameter of a circle. He measures the circumference, C, as 170 mm to the nearest millimetre. He measures the diameter, d, as 54 mm to the nearest millimetre. Dan uses = C d Calculate the upper bound and the lower bound for Dan s value of. upper bound =... lower bound =... (Total for Question 23 is 4 marks) *P43600A02328* 23 Turn over

52 24 ABC is a triangle. A 6 cm 60 C 7 cm B Diagram NOT accurately drawn (a) Work out the area of triangle ABC. Give your answer correct to 3 significant figures.... cm 2 (2) (b) Work out the length of the side AB. Give your answer correct to 3 significant figures.... cm (3) (Total for Question 24 is 5 marks) 24 *P43600A02428*

53 25 Solve the simultaneous equations x 2 + y 2 = 9 x + y = 2 Give your answers correct to 2 decimal places. x =... y =... or x =... y =... (Total for Question 25 is 6 marks) TOTAL FOR PAPER IS 100 MARKS *P43600A02528* 25

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57 Mark Scheme (Results) Summer 2013 GCSE Mathematics (Linear) 1MA0 Higher (Non-Calculator) Paper 1H

58 Edexcel and BTEC Qualifications Edexcel and BTEC qualifications come from Pearson, the world s leading learning company. We provide a wide range of qualifications including academic, vocational, occupational and specific programmes for employers. For further information visit our qualifications websites at or for our BTEC qualifications. Alternatively, you can get in touch with us using the details on our contact us page at If you have any subject specific questions about this specification that require the help of a subject specialist, you can speak directly to the subject team at Pearson. Their contact details can be found on this link: You can also use our online Ask the Expert service at You will need an Edexcel username and password to access this service. Pearson: helping people progress, everywhere Our aim is to help everyone progress in their lives through education. We believe in every kind of learning, for all kinds of people, wherever they are in the world. We ve been involved in education for over 150 years, and by working across 70 countries, in 100 languages, we have built an international reputation for our commitment to high standards and raising achievement through innovation in education. Find out more about how we can help you and your students at: Summer 2013 Publications Code UG All the material in this publication is copyright Pearson Education Ltd 2013

59 NOTES ON MARKING PRINCIPLES 1 All candidates must receive the same treatment. Examiners must mark the first candidate in exactly the same way as they mark the last. 2 Mark schemes should be applied positively. Candidates must be rewarded for what they have shown they can do rather than penalised for omissions. 3 All the marks on the mark scheme are designed to be awarded. Examiners should always award full marks if deserved, i.e if the answer matches the mark scheme. Examiners should also be prepared to award zero marks if the candidate s response is not worthy of credit according to the mark scheme. 4 Where some judgement is required, mark schemes will provide the principles by which marks will be awarded and exemplification may be limited. 5 Crossed out work should be marked UNLESS the candidate has replaced it with an alternative response. 6 Mark schemes will indicate within the table where, and which strands of QWC, are being assessed. The strands are as follows: i) ensure that text is legible and that spelling, punctuation and grammar are accurate so that meaning is clear Comprehension and meaning is clear by using correct notation and labeling conventions. ii) select and use a form and style of writing appropriate to purpose and to complex subject matter Reasoning, explanation or argument is correct and appropriately structured to convey mathematical reasoning. iii) organise information clearly and coherently, using specialist vocabulary when appropriate. The mathematical methods and processes used are coherently and clearly organised and the appropriate mathematical vocabulary used.

60 7 With working If there is a wrong answer indicated on the answer line always check the working in the body of the script (and on any diagrams), and award any marks appropriate from the mark scheme. If working is crossed out and still legible, then it should be given any appropriate marks, as long as it has not been replaced by alternative work. If it is clear from the working that the correct answer has been obtained from incorrect working, award 0 marks. Send the response to review, and discuss each of these situations with your Team Leader. If there is no answer on the answer line then check the working for an obvious answer. Any case of suspected misread loses A (and B) marks on that part, but can gain the M marks. Discuss each of these situations with your Team Leader. If there is a choice of methods shown, then no marks should be awarded, unless the answer on the answer line makes clear the method that has been used. 8 Follow through marks Follow through marks which involve a single stage calculation can be awarded without working since you can check the answer yourself, but if ambiguous do not award. Follow through marks which involve more than one stage of calculation can only be awarded on sight of the relevant working, even if it appears obvious that there is only one way you could get the answer given. 9 Ignoring subsequent work It is appropriate to ignore subsequent work when the additional work does not change the answer in a way that is inappropriate for the question: e.g. incorrect canceling of a fraction that would otherwise be correct It is not appropriate to ignore subsequent work when the additional work essentially makes the answer incorrect e.g. algebra. Transcription errors occur when candidates present a correct answer in working, and write it incorrectly on the answer line; mark the correct answer. 10 Probability Probability answers must be given a fractions, percentages or decimals. If a candidate gives a decimal equivalent to a probability, this should be written to at least 2 decimal places (unless tenths). Incorrect notation should lose the accuracy marks, but be awarded any implied method marks. If a probability answer is given on the answer line using both incorrect and correct notation, award the marks. If a probability fraction is given then cancelled incorrectly, ignore the incorrectly cancelled answer.

61 11 Linear equations Full marks can be gained if the solution alone is given on the answer line, or otherwise unambiguously indicated in working (without contradiction elsewhere). Where the correct solution only is shown substituted, but not identified as the solution, the accuracy mark is lost but any method marks can be awarded. 12 Parts of questions Unless allowed by the mark scheme, the marks allocated to one part of the question CANNOT be awarded in another. 13 Range of answers Unless otherwise stated, when an answer is given as a range (e.g ) then this is inclusive of the end points (e.g 3.5, 4.2) and includes all numbers within the range (e.g 4, 4.1) Guidance on the use of codes within this mark scheme M1 method mark A1 accuracy mark B1 Working mark C1 communication mark QWC quality of written communication oe or equivalent cao correct answer only ft follow through sc special case dep dependent (on a previous mark or conclusion) indep independent isw ignore subsequent working

62 PAPER: 1MA0_1H Question Working Answer Mark Notes 1 (a) B1 cao (b) B1 cao M1 for ( = 36) oe M1 for 240 ( = 180) oe M1 (dep on both prev M1) for A1 cao OR M1 for 15(%) + 75(%) ( = 90(%)) M1 for 100(%) 90(%) ( = 10(%)) M1 (dep on both prev M1) for 240 oe A1 cao OR M1 for ( = 0.9) oe M1 for ( = 216) oe M1 (dep on both prev M1) for A1 cao OR M1 for ( = 0.9) oe M1 for ( = 0.1) oe M1 (dep on both prev M1) for oe A1 cao

63 PAPER: 1MA0_1H Question Working Answer Mark Notes Key,eg 4 1 is 4.1(kg) 3 B2 for correct ordered stem and leaf (B1 for fully correct unordered or ordered with one error or omission) B1 (indep) for key (units not required) 4 (a) 6 + 3t 1 B1 for 6 + 3t (b) 6x x 2 B2 for 6x x (B1 for 6x 2 or 15x) (c) m m + 3m + 30 m m M1 for all 4 terms (and no additional terms) correct with or without signs or 3 out of no more than four terms correct with signs A1 for m m M1 for continual prime factorisation (at least first 2 steps correct) or first two stages of a factor tree correct M1 for fully correct factor tree or list 3, 5, 5, 7 A or

64 PAPER: 1MA0_1H Question Working Answer Mark Notes x M1 for 4 10 or 40 or 4 M1 for a complete correct method A1 cao or a correct equation 7 (a) (4,0) (3, 0) (3, -1) (2, -1) (2, 2) (4, 2) Correct position 2 B2 for correct shape in correct position (B1 for any incorrect translation of correct shape) (b) Rotation 180 (0,1) 3 B1 for rotation B1 for 180 (ignore direction) B1 for (0, 1) OR B1 for enlargement B1 for scale factor -1 B1 for (0, 1) (NB: a combination of transformations gets B0)

65 PAPER: 1MA0_1H Question Working Answer Mark Notes B1 for 20 or 300 used M1 for or " ". " " or, values do not. need to be rounded A1 for answer in the range SC B3 for with or without working 9 LCM (80, 50) = 400 Matt = 8 Dan = 5 OR 50 = 2 5 ( 5) 80 = 2 5 ( 2 2 2) Matt 8 Dan 5 3 M1 lists multiples of both 80 (seconds) and 50 (seconds) (at least 3 of each but condone errors if intention is clear, can be in minutes and seconds) or use of 400 seconds oe. M1 (dep on M1) for a division of "LCM" by 80 or 50 or counts up multiples (implied if one answer is correct or answers reversed) A1 Matt 8 and Dan 5 SC B1 for Matt 7, Dan 4 OR M1 for expansion of both 80 and 50 into prime factors. M1 demonstrates that both expansions include 10 oe A1 Matt 8 and Dan 5 SC B1 for Matt 7, Dan 4

66 PAPER: 1MA0_1H Question Working Answer Mark Notes M1 for correct expression for perimeter eg x + x x + x + 6 oe M1 for forming a correct equation eg x + x x + x + 6= 32 oe M1 for 8x = 12 or 12 8 A1 for 1.5 oe OR M1 for correct expression for semi-perimeter eg x + x + 6 oe M1 for forming a correct equation eg x + x + 6 = 16 oe M1 for 4x = 6 or 6 4 A1 for 1.5 oe

67 PAPER: 1MA0_1H Question Working Answer Mark Notes *11 60 = 75 Debbie + 4 M1 for reading 24 (mins) and 30 (km) or a pair of explanation other values for Debbie M1 for correct method to calculate speed eg oe A1 for or for and 1.1 C1 (dep on M2) for correct conclusion, eg Debbie is fastest from comparison of with 66 (kph) or and 1.1 (km per minute) OR M1 for using an appropriate pair of values for Ian s speed eg 66 and 60, 33 and 30, 11 and 10 M1 for pair of values plotted on graph A1 for correct line drawn C1 (dep on M2) for Debbie is fastest from comparison of gradients. OR M1 for reading 24 (mins) and 30 (km) or a pair other values for Debbie M1 for Ian s time for same distance or Ian s distance for same time. A1 for a pair of comparable values. C1 (dep on M2) for Debbie is fastest from comparison of comparable values.

68 PAPER: 1MA0_1H Question Working Answer Mark Notes 12 x y = y (Table of values/calculation of values) M1 for at least 2 correct attempts to find points by drawn substituting values of x. M1 ft for plotting at least 2 of their points (any points plotted from their table must be plotted correctly) A1 for correct line between x = -2 and x = 4 (No table of values) M1 for at least 2 correct points with no more than 2 incorrect points M1 for at least 2 correct points (and no incorrect points) plotted OR line segment of y = x + 5 drawn A1 for correct line between x = -2 and x = 4 (Use of y=mx+c) M1 for line drawn with gradient 0.5 OR line drawn with y intercept at 5 M1 for line drawn with gradient 0.5 AND line drawn with y intercept at 5 A1 For correct line between x = -2 and x = 4 *13 Yes with explanation SC B2 for a correct line from x = 0 to x = 4 3 M1 for bearing ± 2 within overlay M1 for use of scale to show arc within overlay or line drawn from C to ship s course with measurement C1(dep M1) for comparison leading to a suitable conclusion from a correct method

69 PAPER: 1MA0_1H Question Working Answer Mark Notes 14 (a) Line joins an empty circle at 2 to a solid circle at 3 diagram 2 B2 cao (B1 for line from 2 to 3) (b) 2x 7 x M1 for correct method to isolate variable and number terms (condone use of =, >,, or <) or (x =) 3.5 A1 for x 3.5 oe as final answer *Q15 No + explanation 3 M1 for oe A1 for 4.5 C1 (dep M1) for correct decision based on comparison of their paper height with 4 OR M1 for oe A1 for C1 (dep M1) for correct decision based on comparison of their paper thickness with OR M1 for 4 ( ) oe A1 for 444(.4...) C1 (dep M1) for correct decision based on comparison of their number of sheets of paper with M1 for 70% = 350 or M1 for 100 oe A1 cao

70 PAPER: 1MA0_1H Question Working Answer Mark Notes 17 1 hour 45 mins 6 M1 for method to find volume of pond, eg 2 1 ( ) 2 1 (= 1.8) M1 for method to find the volume of water emptied in 30 minutes, eg (= 0.4), (= ) A1 for correct rate, eg 0.8 m³/hr, 0.4 m³ in 30 minutes M1 for correct method to find total time taken to empty the pond, eg M1 for method to find extra time, eg 2 hrs 15 minutes 30 minutes A1 for 1.75 hours, 1 hours, 1 hour 45 mins or 105 mins OR M1 for method to find volume of water emptied in 30 minutes,.eg (= 0.4), (= ) M1 for method to work out rate of water loss eg A1 for correct rate, eg 0.8 m³/hr M1 for correct method to work out remaining volume of water eg. ( ) 2 1 (= 1.4) M1 for method to work out time, eg A1 for 1.75 hours, 1 hours, 1 hour 45 mins or 105 mins NB working could be in 3D or in 2D and in metres or cm throughout

71 PAPER: 1MA0_1H Question Working Answer Mark Notes 18 12x + 21y = 3 12x + 40y = 60 19y = 57 y= 3 3x = 15 3x = 15 x= -5, y = 3 4 M1 for a correct process to eliminate either x or y or rearrangement of one equation leading to substitution (condone one arithmetic error) A1 for either x = 5 or y = 3 M1 (dep) for correct substitution of their found value A1 cao Alternative method x = y = y +40y = 60 19y = 57 x = 19 5, 0.2, 0.5, 1-5, 5-1, 0.5, M1 for either 5-1 or 5 0 evaluated correctly A1 for a fully correct list from correct working, accept original numbers or evaluated (SC B1 for one error in position or correct list in reverse order)

72 PAPER: 1MA0_1H Question Working Answer Mark Notes 20 5x 2 4 M1 for 4x 4x M1 for (2x 4x)/2 or (2x x)/2 or(3x 4x)/2 M1(dep M2) for 16 x 2 4 x 2 x 2 6 x 2 A1 for 5x 2 OR M1 for 2x ² 4x ² (= 20 ² = 20 x) M1 for ² 2 ² (= 5 ² = 5 x) " " " " M1(dep M2) for (= ² A1 for 5x 2 21 (a) Cf table: 4, 9, 25, 52, 57,60 cf graph Correct Cf graph 3 B1 Correct cumulative frequencies (may be implied by correct heights on the grid) M1 for at least 5 of 6 points plotted consistently within each interval A1 for a fully correct CF graph (b)(i) B1 for 172 or read off at cf = 30 or 30.5 from a cf graph, ft provided M1 is awarded in (a) (ii) IQR = UQ LQ M1 for readings from graph at cf = 15 or and cf = 45or from a cf graph with at least one of LQ or UQ correct from graph (± ½ square). A1ft provided M1 is awarded in (a)

73 PAPER: 1MA0_1H Question Working Answer Mark Notes cm 3 4 M1 for and 15 2 M1 for A1 for 1200 B1 (indep) for cm 3 OR M1 for or 2 3 or 8 indicated as scale factor M1 for A1 for 1200 B1 (indep) for cm SC B2 for 600 cm 3 (B1 for 600) 2 M1 for (x ± 5)(x±3) A1 for = = = = = 0.2 Histogram 3 B3 for fully correct histogram (B2 for 4 correct blocks) (B1 for 3 correct blocks) (If B0, SC B1 for correct key eg 1cm 2 = 2 (calls) Or frequency class interval for at least 3 frequencies) NB Apply the same mark scheme if a different frequency density is used.

74 PAPER: 1MA0_1H Question Working Answer Mark Notes 25 (a) a = 4, b = 5 3 M1 for sight of (x 4) 2 (b) (4, 5) 1 B1 ft M1 for (x 4) A1 for a = 4, b = 5 OR M1 for x 2 2ax + a 2 + b M1 for 2a = 8 and a 2 + b =21 A1 for a = 4, b = M1 for 3 fractions,, where a < 10, b < 9 and c < 8 M1 for or or (= M1 for + + or 3 A1 for oe. eg. Alternative Scheme for With Replacement M1 for (= M1 for 3 (= M0 A0 No further marks

75 PAPER: 1MA0_1H Question Working Answer Mark Notes 27 (a) a - b 1 B1 for a - b oe (b) a + b 3 M1 for a correct vector statement for eg. ( =) NQ + QR or ( =) NS + SR M1 for SQ (+ QR) or QS (+ SR) (SQ, QR, QS, SR may be written in terms of a and b) A1 for (a b) + b oe or (b a) + a oe 28 (a) (90, 0) 1 B1 for (90, 0) (condone (, 0)) (b) Correct graph 1 B1 for graph through (0, 2) (90, 0) (180, -2) (270, 0) (360, 2) professional judgement

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78 Further copies of this publication are available from Edexcel Publications, Adamsway, Mansfield, Notts, NG18 4FN Telephone Fax Order Code UG Summer 2013 For more information on Edexcel qualifications, please visit our website Pearson Education Limited. Registered company number with its registered office at Edinburgh Gate, Harlow, Essex CM20 2JE

79 Mark Scheme (Results) Summer 2013 GCSE Mathematics (Linear) 1MA0 Higher (Calculator) Paper 2H

80 Edexcel and BTEC Qualifications Edexcel and BTEC qualifications come from Pearson, the world s leading learning company. We provide a wide range of qualifications including academic, vocational, occupational and specific programmes for employers. For further information visit our qualifications websites at or for our BTEC qualifications. Alternatively, you can get in touch with us using the details on our contact us page at If you have any subject specific questions about this specification that require the help of a subject specialist, you can speak directly to the subject team at Pearson. Their contact details can be found on this link: You can also use our online Ask the Expert service at You will need an Edexcel username and password to access this service. Pearson: helping people progress, everywhere Our aim is to help everyone progress in their lives through education. We believe in every kind of learning, for all kinds of people, wherever they are in the world. We ve been involved in education for over 150 years, and by working across 70 countries, in 100 languages, we have built an international reputation for our commitment to high standards and raising achievement through innovation in education. Find out more about how we can help you and your students at: Summer 2013 Publications Code UG All the material in this publication is copyright Pearson Education Ltd 2013

81 NOTES ON MARKING PRINCIPLES 1 All candidates must receive the same treatment. Examiners must mark the first candidate in exactly the same way as they mark the last. 2 Mark schemes should be applied positively. Candidates must be rewarded for what they have shown they can do rather than penalised for omissions. 3 All the marks on the mark scheme are designed to be awarded. Examiners should always award full marks if deserved, i.e if the answer matches the mark scheme. Examiners should also be prepared to award zero marks if the candidate s response is not worthy of credit according to the mark scheme. 4 Where some judgement is required, mark schemes will provide the principles by which marks will be awarded and exemplification may be limited. 5 Crossed out work should be marked UNLESS the candidate has replaced it with an alternative response. 6 Mark schemes will indicate within the table where, and which strands of QWC, are being assessed. The strands are as follows: i) ensure that text is legible and that spelling, punctuation and grammar are accurate so that meaning is clear Comprehension and meaning is clear by using correct notation and labeling conventions. ii) select and use a form and style of writing appropriate to purpose and to complex subject matter Reasoning, explanation or argument is correct and appropriately structured to convey mathematical reasoning. iii) organise information clearly and coherently, using specialist vocabulary when appropriate. The mathematical methods and processes used are coherently and clearly organised and the appropriate mathematical vocabulary used.

82 7 With working If there is a wrong answer indicated on the answer line always check the working in the body of the script (and on any diagrams), and award any marks appropriate from the mark scheme. If working is crossed out and still legible, then it should be given any appropriate marks, as long as it has not been replaced by alternative work. If it is clear from the working that the correct answer has been obtained from incorrect working, award 0 marks. Send the response to review, and discuss each of these situations with your Team Leader. If there is no answer on the answer line then check the working for an obvious answer. Any case of suspected misread loses A (and B) marks on that part, but can gain the M marks. Discuss each of these situations with your Team Leader. If there is a choice of methods shown, then no marks should be awarded, unless the answer on the answer line makes clear the method that has been used. 8 Follow through marks Follow through marks which involve a single stage calculation can be awarded without working since you can check the answer yourself, but if ambiguous do not award. Follow through marks which involve more than one stage of calculation can only be awarded on sight of the relevant working, even if it appears obvious that there is only one way you could get the answer given. 9 Ignoring subsequent work It is appropriate to ignore subsequent work when the additional work does not change the answer in a way that is inappropriate for the question: e.g. incorrect canceling of a fraction that would otherwise be correct It is not appropriate to ignore subsequent work when the additional work essentially makes the answer incorrect e.g. algebra. Transcription errors occur when candidates present a correct answer in working, and write it incorrectly on the answer line; mark the correct answer. 10 Probability Probability answers must be given a fractions, percentages or decimals. If a candidate gives a decimal equivalent to a probability, this should be written to at least 2 decimal places (unless tenths). Incorrect notation should lose the accuracy marks, but be awarded any implied method marks. If a probability answer is given on the answer line using both incorrect and correct notation, award the marks. If a probability fraction is given then cancelled incorrectly, ignore the incorrectly cancelled answer.

83 11 Linear equations Full marks can be gained if the solution alone is given on the answer line, or otherwise unambiguously indicated in working (without contradiction elsewhere). Where the correct solution only is shown substituted, but not identified as the solution, the accuracy mark is lost but any method marks can be awarded. 12 Parts of questions Unless allowed by the mark scheme, the marks allocated to one part of the question CANNOT be awarded in another. 13 Range of answers Unless otherwise stated, when an answer is given as a range (e.g ) then this is inclusive of the end points (e.g 3.5, 4.2) and includes all numbers within the range (e.g 4, 4.1) Guidance on the use of codes within this mark scheme M1 method mark A1 accuracy mark B1 Working mark C1 communication mark QWC quality of written communication oe or equivalent cao correct answer only ft follow through sc special case dep dependent (on a previous mark or conclusion) indep independent isw ignore subsequent working

84 PAPER: 1MA0_2H Question Working Answer Mark Notes M1 for or M1 for adding area of 5 or 6 faces provided at least 3 are the correct area A1 cao NB: anything that leads to a volume calculation 0 marks. *2 Not enough mincemeat since 600<700 OR Only able to make 38 mince pies since insufficient mincemeat 4 M1 for (= 2.5) M1 for 2.5 used as factor or divisor A1 for ingredients as and 875 and 250 and 700 and 2.5 (accept 2 or 3) OR for availables as 400, 400, , 2.4 (accept 2 or 3) C1 ft (dep on at least M1) for identifying and stating which ingredient is insufficient for the recipe (with some supportive evidence) OR M1 for a correct method to determine the number of pies one ingredient could produce M1 for a correct method to determine the number of pies all ingredient could produce A1 for 80 and 51 and 90 and 38 and 108 C1 ft (dep on at least M1) for identifying and stating which ingredient is insufficient for the recipe. (with some supportive evidence)

85 PAPER: 1MA0_2H Question Working Answer Mark Notes 3 (a) Points plotted at (1,8200) and (3.5,5000) 1 B1 for points accurately plotted ±1/2 square tolerance (b) the older the car the lower the value the greater the value the newer the car 1 B1 for an acceptable relationship eg. the older the car the lower the value (accept negative correlation but not just negative ) (c) 5200 to M1 for a single line segment with negative gradient that could be used as a line of best fit or a vertical line from 2.5 or a point at (2.5,y) where y is from 5200 to 6600 A1 for given answer in the range M1 for (= 0.63) M1 for A1 cao OR M1 for (= 10) or (= 64) or (=74) M1 for A1 cao OR M1 for (= 63) M1 for "63" A1 cao SC: B2 for 126 as the answer. 200

86 PAPER: 1MA0_2H Question Working Answer Mark Notes 5 (a) Response boxes overlap and are not exhaustive 2 B2 for TWO aspects from: No time frame given Non-exhaustive responses Response boxes over-lapping (B1 for ONE correct aspect) (b) How many magazines do you buy each month? over 8 2 B1 for a question with a time frame B1 for at least 3 correctly labelled response boxes (nonoverlapping, need not be exhaustive) or for a set of response boxes that are exhaustive (could be overlapping) [Do not allow inequalities in response boxes] (c) One reason 1 B1 for ONE reason Eg. All the same age, may all be males, may all like same types of magazines, sample too small, biased M1 for (=3600) M1 for (=750) or (= ) or (=0.24) or (=4.16..) M1 for 3600 ( ) or oe A1 cao

87 PAPER: 1MA0_2H Question Working Answer Mark Notes 7 28% or 4 M1 for (= 70) or 1 M1 for 70 (3 + 2) (= 14) or " " (3+2) (= ) M1 for 14 2 or 2 A1 for 28% or oe OR M1 for a correct method to find (100-30)% of any actual sum of money M1 for 350 (3 + 2) (= 70) M1 for 70 2 A1 for 28% or oe OR M1 for starting with two numbers in ratio 3:2, eg 21 and 14 M1 for equating sum of their numbers to (=70%), eg (=35) M1 for scaling sum of their numbers to 100%, eg (=50) A1 for 28% or oe SC: award B3 for oe answers expressed in an incorrect form eg.

88 PAPER: 1MA0_2H Question Working Answer Mark Notes M1 for splitting the pentagon (or show the recognition of the absent triangle) and using a correct method to find the area of one shape M1 for a complete and correct method to find the total area M1 (dep on at least one prev M1) for multiplying their total area by 2.56 (where total area is a calculation involving at least two areas) A1 cao M1 for a correct method to find a different angle using 35 M1 for setting up a complete process to calculate angle x A1 cao B1 states one of the following reasons relating to their chosen method: Alternate angles are equal; Corresponding angles are equal; Allied angles / Co-interior angles add up to 180; the exterior angle of a triangle is equal to the sum of the interior opposite angles.

89 PAPER: 1MA0_2H Question Working Answer Mark Notes 10 x x 3 + 2x (121) (488) (107) (984) (125) (536) (223) No working scores 0 marks (192) (449) (44625) (14696) (87563) (63232) (41709) B2 for a trial 4.6 x 4.7 evaluated correctly (B1 for a trial evaluated correctly for 4 x 5 ) B1 for a different trial evaluated correctly for 4.65 x < 4.7 B1 (dep on at least one previous B1) for 4.7 [Note: Trials should be evaluated to at least accuracy shown in table, truncated or rounded] M1 for M1 (dep) for ( ) (= ) A1 for answer in the range 3.51 to 3.52

90 PAPER: 1MA0_2H Question Working Answer Mark Notes 12 (a) 3x 6 = x M1 for 3 x 3 2 (=3x 6) or 2x = 13 M1 for correct method to isolate the terms in x or the number terms on opposite sides of an equation A1 for 6.5 oe (b) 2 y = M1 for intention to multiply both sides by 5 (to give 2 y = 1 5) A1 cao 13 (a) (3, 3.5) oe 2 M1 for a correct method to find the value of either the x coordinate or the y coordinate of the midpoint or x = 3 or y = 3.5 A1 cao (b) -1.8 oe 2 M1 for correct method to find the gradient OR (+)1.8 A1 for -1.8 oe

91 PAPER: 1MA0_2H Question Working Answer Mark Notes *14 The Friendly Bank 4 M1 for a correct method to find interest for the first year for either bank OR correct method to find the value of investment after one year for either bank OR use of the multiplier 1.04 or 1.05 M1 for a correct full method to find the value of the investment (or the value of the total interest) at the end of 2 years in either bank A1 for (0) and (0) (accept 100.8(0) and 110.5(0)) C1 (dep on M1) ft for a correct comparison of their total amounts, identifying the bank from their calculations OR M1 for either or M1 for and A1 for and C1 (dep on M1) ft for a correct comparison of their total multiplying factors identifying the bank from their calculations

92 PAPER: 1MA0_2H Question Working Answer Mark Notes 15 (a) B2 for 8, -1, 0, 8 (B1 for at least two of 8, -1, 0, 8) (b) Correct curve 2 M1 (ft) for at least 5 points plotted correctly A1 for a fully correct curve (c) x 2 2x 3 = 0 OR (x 3)(x + 1) = 0 3 and 1 2 M1 for the straight line y = 3 drawn to intersect the graph from (a) A1 for both solutions OR M1 for identifying y = 3 from the table A1 for both solutions OR M1 for (x ± 3)(x ± 1) A1 for both solutions