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) Monday 11 June 2012 Afternoon 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 P40645A 2012 Pearson Education Ltd. 6/6/7/3/ *P40645A0128*

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 *P40645A0228*

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 Sam wants to find out the types of film people like best. He is going to ask whether they like comedy films or action films or science fiction films or musicals best. (a) Design a suitable table for a data collection sheet he could use to collect this information. (2) Sam collects his data by asking 10 students in his class at school. This might not be a good way to find out the types of film people like best. (b) Give one reason why (1) (Total for Question 1 is 3 marks) *P40645A0328* 3 Turn over

4 2 The diagram shows a patio in the shape of a rectangle. 3 m Diagram NOT accurately drawn 3.6 m The patio is 3.6 m long and 3 m wide. Matthew is going to cover the patio with paving slabs. Each paving slab is a square of side 60 cm. Matthew buys 32 of the paving slabs. (a) Does Matthew buy enough paving slabs to cover the patio? You must show all your working.... (3) The paving slabs cost 8.63 each. (b) Work out the total cost of the 32 paving slabs.... (3) (Total for Question 2 is 6 marks) 4 *P40645A0428*

5 * 3 Bill uses his van to deliver parcels. For each parcel Bill delivers there is a fixed charge plus 1.00 for each mile. You can use the graph to find the total cost of having a parcel delivered by Bill Cost ( ) Distance (miles) (a) How much is the fixed charge? Ed uses a van to deliver parcels. For each parcel Ed delivers it costs 1.50 for each mile. There is no fixed charge. (b) Compare the cost of having a parcel delivered by Bill with the cost of having a parcel delivered by Ed.... (1) (3) (Total for Question 3 is 4 marks) *P40645A0528* 5 Turn over

6 4 Here are the speeds, in miles per hour, of 16 cars Draw an ordered stem and leaf diagram for these speeds. (Total for Question 4 is 3 marks) 6 *P40645A0628*

7 5 Medicine You can work out the amount of medicine, c m, to give to a child by using the formula m is the age of the child, in months. a is an adult dose, in m A child is 30 months old. An adult s dose is 40 m. c ma = 150 Work out the amount of medicine you can give to the child.... m (Total for Question 5 is 2 marks) *P40645A0728* 7 Turn over

8 6 Here are the ingredients needed to make 12 shortcakes. Shortcakes Makes 12 shortcakes 50 g of sugar 200 g of butter 200 g of flour 10 m of milk Liz makes some shortcakes. She uses 25 m of milk. (a) How many shortcakes does Liz make?... (2) Robert has 500 g of sugar 1000 g of butter 1000 g of flour 500 m of milk (b) Work out the greatest number of shortcakes Robert can make.... (2) (Total for Question 6 is 4 marks) 8 *P40645A0828*

9 7 Buses to Acton leave a bus station every 24 minutes. Buses to Barton leave the same bus station every 20 minutes. A bus to Acton and a bus to Barton both leave the bus station at 9 00 am. When will a bus to Acton and a bus to Barton next leave the bus station at the same time?... (Total for Question 7 is 3 marks) 8 (a) Expand 3(2y 5)... (1) (b) Factorise completely 8x 2 + 4xy... (2) (c) Make h the subject of the formula t gh = 10 h =... (2) (Total for Question 8 is 5 marks) *P40645A0928* 9 Turn over

10 9 y A B 2 1 O x Describe fully the single transformation that maps triangle A onto triangle B (Total for Question 9 is 3 marks) 10 *P40645A01028*

11 * 10 Railtickets and Cheaptrains are two websites selling train tickets. Each of the websites adds a credit card charge and a booking fee to the ticket price. Railtickets Credit card charge: 2.25% of ticket price Booking fee: 80 pence Cheaptrains Credit card charge: 1.5% of ticket price Booking fee: 1.90 Nadia wants to buy a train ticket. The ticket price is 60 on each website. Nadia will pay by credit card. Will it be cheaper for Nadia to buy the train ticket from Railtickets or from Cheaptrains? (Total for Question 10 is 4 marks) *P40645A01128* 11 Turn over

12 11 3x 15 2x Diagram NOT accurately drawn 2x 2x + 24 The diagram shows a parallelogram. The sizes of the angles, in degrees, are 2x 3x 15 2x 2x + 24 Work out the value of x. x =... (Total for Question 11 is 3 marks) 12 *P40645A01228*

13 12 Jane has a carton of orange juice. The carton is in the shape of a cuboid. 20 cm Diagram NOT accurately drawn 10 cm 6 cm The depth of the orange juice in the carton is 8 cm. Jane closes the carton. Then she turns the carton over so that it stands on the shaded face. Work out the depth, in cm, of the orange juice now.... cm (Total for Question 12 is 3 marks) *P40645A01328* 13 Turn over

14 13 Diagram NOT accurately drawn x The diagram shows a regular hexagon and a regular octagon. Calculate the size of the angle marked x. You must show all your working.... (Total for Question 13 is 4 marks) 14 *P40645A01428*

15 14 The diagram shows the position of a lighthouse L and a harbour H. N N L H The scale of the diagram is 1 cm represents 5 km. (a) Work out the real distance between L and H.... km (1) (b) Measure the bearing of H from L.... (1) A boat B is 20 km from H on a bearing of 040 (c) On the diagram, mark the position of boat B with a cross ( ). Label it B. (2) (Total for Question 14 is 4 marks) *P40645A01528* 15 Turn over

16 15 Harry grows tomatoes. This year he put his tomato plants into two groups, group A and group B. Harry gave fertiliser to the tomato plants in group A. He did not give fertiliser to the tomato plants in group B. Harry weighed 60 tomatoes from group A. The cumulative frequency graph shows some information about these weights Cumulative frequency Weight (g) (a) Use the graph to find an estimate for the median weight.... g (1) 16 *P40645A01628*

17 The 60 tomatoes from group A had a minimum weight of 153 grams and a maximum weight of 186 grams. (b) Use this information and the cumulative frequency graph to draw a box plot for the 60 tomatoes from group A. Group A Weight (g) (3) Harry did not give fertiliser to the tomato plants in group B. Harry weighed 60 tomatoes from group B. He drew this box plot for his results. Group B Weight (g) (c) Compare the distribution of the weights of the tomatoes from group A with the distribution of the weights of the tomatoes from group B (2) (Total for Question 15 is 6 marks) *P40645A01728* 17 Turn over

18 16 (a) Simplify (m 2 ) 5 (b) Factorise x 2 + 3x (1)... (2) (Total for Question 16 is 3 marks) 17 (a) Write down the value of (1) (b) Write as an ordinary number.... (1) (c) Work out the value of ( ) ( ) Give your answer in standard form.... (2) (Total for Question 17 is 4 marks) 18 *P40645A01828*

19 18 y C A B O x Triangle ABC is drawn on a centimetre grid. A is the point (2, 2). B is the point (6, 2). C is the point (5, 5). Triangle PQR is an enlargement of triangle ABC with scale factor 1 2 and centre (0, 0). Work out the area of triangle PQR.... cm 2 (Total for Question 18 is 3 marks) *P40645A01928* 19 Turn over

20 19 Wendy goes to a fun fair. She has one go at Hoopla. She has one go on the Coconut shy. The probability that she wins at Hoopla is 0.4 The probability that she wins on the Coconut shy is 0.3 (a) Complete the probability tree diagram. Hoopla Coconut shy 0.3 Wendy wins 0.4 Wendy wins... Wendy does not win... Wendy does not win... Wendy wins... Wendy does not win (2) (b) Work out the probability that Wendy wins at Hoopla and also wins on the Coconut shy.... (2) (Total for Question 19 is 4 marks) 20 *P40645A02028*

21 20 Solve the simultaneous equations 5x + 2y = 11 4x 3y = 18 x =... y =... (Total for Question 20 is 4 marks) *P40645A02128* 21 Turn over

22 * 21 D O C Diagram NOT accurately drawn A 50 B B, C and D are points on the circumference of a circle, centre O. AB and AD are tangents to the circle. Angle DAB = 50 Work out the size of angle BCD. Give a reason for each stage in your working. (Total for Question 21 is 4 marks) 22 *P40645A02228*

23 22 The table gives some information about the speeds, in km/h, of 100 cars. Speed (s km/h) Frequency 60 < s < s < s < s (a) On the grid, draw a histogram for the information in the table Speed (s km/h) (3) (b) Work out an estimate for the number of cars with a speed of more than 85 km/h.... (2) (Total for Question 22 is 5 marks) *P40645A02328* 23 Turn over

24 23 (a) Simplify fully x x 4 2x 5x (3) (b) Write 4 x x 2 as a single fraction in its simplest form.... (3) (Total for Question 23 is 6 marks) 24 Express the recurring decimal as a fraction in its simplest form.... (Total for Question 24 is 3 marks) 24 *P40645A02428*

25 25 The diagram shows a solid metal cylinder. Diagram NOT accurately drawn 9x 2x The cylinder has base radius 2x and height 9x. The cylinder is melted down and made into a sphere of radius. Find an expression for in terms of x.... (Total for Question 25 is 3 marks) *P40645A02528* 25 Turn over

26 26 The graph of y = f(x) is shown on each of the grids. (a) On this grid, sketch the graph of y = f(x 3) y O x (2) 26 *P40645A02628*

27 (b) On this grid, sketch the graph of y = 2f(x) y O x (2) (Total for Question 26 is 4 marks) TOTAL FOR PAPER IS 100 MARKS *P40645A02728* 27

28 BLANK PAGE 28 *P40645A02828*

29 Write your name here Surname Other names Edexcel GCSE Centre Number Mathematics A Paper 2 (Calculator) Wednesday 13 June 2012 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. P40647A 2012 Pearson Education Ltd. 6/6/7/3/ 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. *P40647A0124* 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 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 *P40647A0224*

31 Answer ALL questions. Write your answers in the spaces provided. You must write down all stages in your working. 1 A B x C Diagram NOT accurately drawn D E 47 F G ABC and DEF are parallel lines. BEG is a straight line. Angle GEF = 47. Work out the size of the angle marked x. Give reasons for your answer.... (Total for Question 1 is 3 marks) *P40647A0324* 3 Turn over

32 (a) Use your calculator to work out Write down all the figures on your calculator display. You must give your answer as a decimal.... (2) (b) Write your answer to part (a) correct to 1 significant figure.... (1) (Total for Question 2 is 3 marks) 4 *P40647A0424*

33 3 Pradeep wants to find out how much time people spend playing sport. He uses this question on a questionnaire. How much time do you spend playing sport? 0 1 hours 1 2 hours 3 4 hours (a) Write down two things wrong with this question (2) (b) Design a better question for Pradeep s questionnaire to find out how much time people spend playing sport. (2) (Total for Question 3 is 4 marks) *P40647A0524* 5 Turn over

34 4 On the grid, draw the graph of y = 3x 2 for values of x from 1 to 3 y O x (Total for Question 4 is 3 marks) 6 *P40647A0624*

35 * 5 Mr Weaver s garden is in the shape of a rectangle. In the garden there is a patio in the shape of a rectangle and two ponds in the shape of circles with diameter 3.8 m. The rest of the garden is grass. 17 m Diagram NOT accurately drawn patio grass 3.8 m 3.8 m pond 9.5 m pond 2.8 m Mr Weaver is going to spread fertiliser over all the grass. One box of fertiliser will cover 25 m 2 of grass. How many boxes of fertiliser does Mr Weaver need? You must show your working. (Total for Question 5 is 5 marks) *P40647A0724* 7 Turn over

36 * 6 Potatoes cost 9 for a 12.5 kg bag at a farm shop. The same type of potatoes cost 1.83 for a 2.5 kg bag at a supermarket. Where are the potatoes the better value, at the farm shop or at the supermarket? You must show your working. (Total for Question 6 is 4 marks) 8 *P40647A0824*

37 7 The scatter graph shows some information about 8 cars. For each car it shows the engine size, in litres, and the distance, in kilometres, the car travels on one litre of petrol Distance (kilometres) Engine size (litres) (a) What type of correlation does the scatter graph show? A different car of the same type has an engine size of 2.5 litres. (b) Estimate the distance travelled on one litre of petrol by this car.... (1)... kilometres (2) (Total for Question 7 is 3 marks) *P40647A0924* 9 Turn over

38 8 y 4 A O 2 4 x 2 4 (a) Rotate triangle A 90 clockwise, centre O. (2) y B 2 O x (b) Enlarge triangle B by scale factor 3, centre (1, 2). (3) (Total for Question 8 is 5 marks) 10 *P40647A01024*

39 9 Linda is going on holiday to the Czech Republic. She needs to change some money into koruna. She can only change her money into 100 koruna notes. Linda only wants to change up to 200 into koruna. She wants as many 100 koruna notes as possible. The exchange rate is 1 = koruna. How many 100 koruna notes should she get?... (Total for Question 9 is 3 marks) 10 m is an integer such that 2 < m 3 (a) Write down all the possible values of m.... (2) (b) Solve 7x 9 < 3x (2) (Total for Question 10 is 4 marks) *P40647A01124* 11 Turn over

40 11 The equation x 3 6x = 72 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 11 is 4 marks) 12 *P40647A01224*

41 12 The probability that a biased dice will land on a five is 0.3 Megan is going to roll the dice 400 times. Work out an estimate for the number of times the dice will land on a five.... (Total for Question 12 is 2 marks) 13 Bob asked each of 40 friends how many minutes they took to get to work. The table shows some information about his results. Time taken (m minutes) Frequency 0 < m < m < m < m < m 50 9 Work out an estimate for the mean time taken.... minutes (Total for Question 13 is 4 marks) *P40647A01324* 13 Turn over

42 14 (a) Expand and simplify (p + 9)(p 4) (b) Solve 5 w 8 3 = 4w (2) w =... (3) (c) Factorise x 2 49 (d) Simplify ( xy) (1)... (2) (Total for Question 14 is 8 marks) 14 *P40647A01424*

43 * 15 Henry is thinking about having a water meter. These are the two ways he can pay for the water he uses. Water Meter A charge of per year No Water Meter A charge of 107 per year plus 91.22p for every cubic metre of water used 1 cubic metre = 1000 litres Henry uses an average of 180 litres of water each day. Henry wants to pay as little as possible for the water he uses. Should Henry have a water meter? (Total for Question 15 is 5 marks) *P40647A01524* 15 Turn over

44 16 N L 9.6 cm 6.4 cm Diagram NOT accurately drawn x LMN is a right-angled triangle. MN = 9.6 cm. LM = 6.4 cm. M Calculate the size of the angle marked x. Give your answer correct to 1 decimal place.... (Total for Question 16 is 3 marks) 17 Liam invests 6200 for 3 years in a savings account. He gets 2.5% per annum compound interest. How much money will Liam have in his savings account at the end of 3 years?... (Total for Question 17 is 3 marks) 16 *P40647A01624*

45 18 The diagram shows a quadrilateral ABCD. 16 cm B 40 C Diagram NOT accurately drawn A 12 cm D AB = 16 cm. AD = 12 cm. Angle BCD = 40 Angle ADB = angle CBD = 90 Calculate the length of CD. Give your answer correct to 3 significant figures.... cm (Total for Question 18 is 5 marks) *P40647A01724* 17 Turn over

46 19 p 2 = x y xy x = y = Find the value of p. Give your answer in standard form correct to 2 significant figures.... (Total for Question 19 is 3 marks) 20 Make t the subject of the formula 2(d t) = 4t + 7 t =... (Total for Question 20 is 3 marks) 18 *P40647A01824*

47 21 Prove that (2n + 3) 2 (2n 3) 2 is a multiple of 8 for all positive integer values of n. (Total for Question 21 is 3 marks) 22 Solve 3x 2 4x 2 = 0 Give your solutions correct to 3 significant figures.... (Total for Question 22 is 3 marks) *P40647A01924* 19 Turn over

48 23 (a) Max wants to take a random sample of students from his year group. (i) Explain what is meant by a random sample (ii) Describe a method Max could use to take his random sample (2) (b) The table below shows the numbers of students in 5 year groups at a school. Year Number of students Lisa takes a stratified sample of 100 students by year group. Work out the number of students from Year 9 she has in her sample.... (2) (Total for Question 23 is 4 marks) 20 *P40647A02024*

49 24 A 8.7 cm Diagram NOT accurately drawn 49 B C 64 ABC is a triangle. AB = 8.7 cm. Angle ABC = 49. Angle ACB = 64. Calculate the area of triangle ABC. Give your answer correct to 3 significant figures....cm 2 (Total for Question 24 is 5 marks) *P40647A02124* 21 Turn over

50 25 Carolyn has 20 biscuits in a tin. She has 12 plain biscuits 5 chocolate biscuits 3 ginger biscuits Carolyn takes at random two biscuits from the tin. Work out the probability that the two biscuits were not the same type.... (Total for Question 25 is 4 marks) 22 *P40647A02224*

51 26 B b P Diagram NOT accurately drawn O a A OAB is a triangle. OA = a OB = b (a) Find AB in terms of a and b.... (1) P is the point on AB such that AP : PB = 3 : 1 (b) Find OP in terms of a and b. Give your answer in its simplest form.... (3) (Total for Question 26 is 4 marks) TOTAL FOR PAPER IS 100 MARKS *P40647A02324* 23

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53 Mark Scheme (Results) Summer 2012 GCSE Mathematics (Linear) 1MA0 Higher (Non-Calculator) Paper 1H

54 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, please visit our website at Our website subject pages hold useful resources, support material and live feeds from our subject advisors giving you access to a portal of information. If you have any subject specific questions about this specification that require the help of a subject specialist, you may find our Ask The Expert service helpful. 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 2012 Publications Code UG All the material in this publication is copyright Pearson Education Ltd 2012

55 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.

56 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.

57 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

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59 1MA0_1H Question Working Answer Mark Notes 1 (a) Type of film Tally Frequency 2 B2 for a table with all 3 aspects: Column/row heading type of film or list of at least 3 film types Column/row heading tally or tally marks (or key) Column/row heading frequency or totals oe (B1 for a table with 2 of the 3 aspects) (b) 1 B1 for acceptable reason eg. all same age, sample too small, biased, same school

60 1MA0_1H Question Working Answer Mark Notes 2 (a) = = = Yes and 30 3 M1 for dividing side of patio by side of paving slab eg or or or or 6 and 5 seen (may be on a diagram) or 6 divisions seen on length of diagram or 5 divisions seen on width of diagram M1 for correct method to find number of paving slabs eg. (360 60) (300 60) oe or 6 5 or 30 squares seen on diagram (units may not be consistent) A1 for Yes and 30 (or 2 extra) with correct calculations OR M1 for correct method to find area of patio or paving slab eg or seen or or 3600 seen or or 10.8 seen or or 0.36 seen M1 for dividing area of patio by area of a paving slab eg. (3.6 3) ( ) oe (units may not be consistent) A1 for Yes and 30 (or 2 extra) with correct calculations OR M1 for method to find area of patio or area of 32 slabs eg or M1 for method to find both area of patio and area of 32 slabs eg and (units may not be consistent) A1 for Yes and and OR Yes and and 10.8 NB : Throughout the question, candidates could be working in metres or centimetres

61 1MA0_1H Question Working Answer Mark Notes (b) = M1 for complete correct method with relative place value correct. Condone 1 multiplication error, addition not necessary. OR M1 for a complete grid. Condone 1 multiplication error, addition not necessary. OR M1 for sight of a complete partitioning method, condone 1 multiplication error. Final addition not necessary. A1 for digits A1 ft (dep on M1) for correct placement of decimal point after addition (of appropriate values) (SC: B1 for attempting to add 32 lots of 8.63)

62 1MA0_1H Question Working Answer Mark Notes 3 (a) 10 1 B1 cao (b) y Ed is cheaper up to 20 miles, Bill is cheaper for more than 20 miles 3 M1 for correct line for Ed intersecting at (20,30) ±1 sq tolerance or 10 + x = 1.5x oe C2 (dep on M1) for a correct full statement ft from graph eg. Ed cheaper up to 20 miles and Bill cheaper for more than 20 miles (C1 (dep on M1) for a correct conclusion ft from graph eg. cheaper at 10 miles with Ed ; eg. cheaper at 50 miles with Bill eg. same cost at 20 miles; eg for 5 go further with Bill OR A general statement covering short and long distances eg. Ed is cheaper for shorter distances and Bill is cheaper for long distances) x Miles Ed Bill OR M1 for correct method to work out Ed's delivery cost for at least 2 values of n miles where 0 < n 50 OR for correct method to work out Ed and Bill's delivery cost for n miles where 0 < n 50 C2 (dep on M1) for 20 miles linked with 30 for Ed and Bill with correct full statement eg. Ed cheaper up to 20 miles and Bill cheaper for more than 20 miles (C1 (dep on M1) for a correct conclusion eg. cheaper at 10 miles with Ed; eg. cheaper at 50 miles with Bill eg. same cost at 20 miles; eg for 5 go further with Bill OR A general statement covering short and long distances eg. Ed is cheaper for shorter distances and Bill is cheaper for long distances) SC : B1 for correct full statement seen with no working eg. Ed cheaper up to 20 miles and Bill cheaper for more than 20 miles QWC: Decision and justification should be clear with working clearly presented and attributable

63 1MA0_1H Question Working Answer Mark Notes OR Key: 2 9 = 29 3 B3 for fully correct diagram with appropriate key (B2 for ordered leaves, with at most two errors or omissions and a key OR correct unordered leaves and a key OR correct ordered leaves) (B1 for unordered or ordered leaves, with at most two errors or omissions OR key) NB : Order of stem may be reversed; condone commas between leaves 5 c = M1 for A1 cao or 1200 seen 6 (a) 30 2 M1 for or 2.5 seen or or 0.4 seen or oe or a complete method eg oe A1 cao (b) M1 for or or OR correct scale factor clearly linked with one ingredient eg. 10 with sugar or 5 with butter or flour or 50 with milk OR answer of 120 or 600 A1 cao

64 1MA0_1H Question Working Answer Mark Notes 7 Acton after 24, 48, 72, 96, 120 Barton after 20, 40, 60, 80, 100, 120 LCM of 20 and 24 is 120 9: 00 am minutes OR Acton after 24, 48, 1h 12 m, 1h 36m, 2h Barton after 20, 40, 1 h, 1h 20m, 1h 40m, 2h LCM is 2 hours 9: 00 am + 2 hours OR Times from 9: 00 am when each bus leaves the bus station Acton at 9: 24, 9: 48, 10: 12, 10:36, 11:00 Barton at 9: 20, 9: 40, 10: 00, 10:20, 10:40, 11:00 OR 20 = = = : 00 am 3 M1 for listing multiples of 20 and 24 with at least 3 numbers in each list ; multiples could be given in minutes or in hours and minutes (condone one addition error in total in first 3 numbers in lists) A1 identify 120 (mins) or 2 (hours) as LCM A1 for 11: 00 (am) or 11(am) or 11 o'clock OR M1 for listing times after 9am when each bus leaves the bus station, with at least 3 times in each list (condone one addition error in total in first 3 times after 9am in lists) A1 for correct times in each list up to and including 11: 00 A1 for 11: 00 (am) or 11(am) or 11 o'clock OR M1 for correct method to write 20 and 24 in terms of their prime factors 2, 2, 5 and 2, 2, 2, 3 (condone one error) A1 identify 120 as LCM A1 for 11: 00 (am) or 11(am) or 11 o'clock

65 1MA0_1H Question Working Answer Mark Notes 8 (a) 6y 15 1 B1 cao (b) 4x(2x + y) 2 B2 cao (B1 for x(8x + 4y) or 2x(4x +2y) or 4(2x 2 + xy) or 4x(ax + by) where a, b are positive integers or ax(2x + y) where a is a positive integer or 4x(2x y)) (c) 10t = gh h = 10t g 10t g 2 M1 for clear intention to multiply both sides of the equation by 10 (eg. 10 seen on both sides of equation) or clear intention to divide both sides of the equation by g (eg. g seen on both sides of equation) t h or 10t = gh or g = 10 or fully correct reverse flow diagram eg. 10 g A1 for 10t g oe

66 1MA0_1H Question Working Answer Mark Notes 9 Rotation 180 Centre (3, 3) 3 B1 for rotation B1 for 180 B1 for (3, 3) or Enlargement Scale factor -1 Centre (3, 3) OR B1 for enlargement B1 for scale factor -1 B1 for (3, 3) B0 for a combination of transformations

67 1MA0_1H Question Working Answer Mark Notes = 1.35 Railtickets with 4 NB. All work may be done in pence throughout = 2.15 correct calculations = 0.90 M1 for correct method to find credit card charge for one = 2.80 company eg (=1.35) oe or (=0.9) oe M1 (dep) for correct method to find total additional charge or total price for one company eg or or 2.15 or 2.8(0) or or 62.8(0) A1 for 2.15 and 2.8(0) or and 62.8(0) C1 (dep on M1) for a statement deducing the cheapest company, but figures used for the comparison must also be stated somewhere, and a clear association with the name of each company OR M1 for correct method to find percentage of (60+booking fee) eg (=1.368) oe or (=0.9285) M1 (dep) for correct method to find total cost or total additional cost eg. '1.368' (=62.168) or '1.368' (=2.168) or '0.9285' (= ) or '0.9285' +1.9 (=2.8285) A1 for or AND or OR or 2.17 AND or 2.83 C1 (dep on M1) for a statement deducing the cheapest company, but figures used for the comparison must also be stated somewhere, and a clear association with the name of each company OR OR

68 1MA0_1H Question Working Answer Mark Notes = = = < 1.90 M1 for correct method to find difference in cost of credit card charge eg. ( ) oe or 0.45 seen M1 (dep) for using difference with booking fee or finding difference between booking fees eg (=1.25) or (=1.45) or (=1.1(0)) A and 1.9(0) or 0.45 and 1.1(0) C1 (dep on M1) for a statement deducing the cheapest company, but figures used for the comparison must also be stated somewhere, and a clear association with the name of each company QWC: Decision and justification should be clear with working clearly presented and attributable

69 1MA0_1H Question Working Answer Mark Notes 11 3x 15 = 2x+24 x = M1 for forming an appropriate equation eg. 3x 15 = 2x + 24 OR 2x+3x 15 +2x+ 2x+24 = 360 9x + 9 = 360 9x = 351 x = 39 OR 2x + 2x+24 = 180 4x + 24 = 180 4x = 156 x = 39 OR 2x + 3x 15 = 180 5x 15 = 180 5x = 195 x = 39 OR 2x + 3x x + 2x + 24 = 360 OR 2x + 2x + 24 = 180 OR 2x + 3x 15 = 180 OR 2x + 3x 15 = 2x + 2x + 24 M1 (dep) for correct operation(s) to isolate x and non-x terms in an equation to get to ax = b A1 cao OR M2 for oe or 9 5 A1 cao oe or oe

70 1MA0_1H Question Working Answer Mark Notes = (6 20) = 4 3 M1 for or 480 seen M1 (dep) for '480' (6 20) oe A1 cao OR M1 for (=2) or (= 1 2 ) or 8 20 M1 (dep) for 8 '2' or or 8 10 oe or A1 cao oe or 20 8 oe SC : B2 for answer of 16 coming from oe 10 6

71 1MA0_1H Question Working Answer Mark Notes (360 6) = (360 8) = = NB. Do remember to look at the diagram when marking this question. Looking at the complete method should confirm if interior or exterior angles are being calculated OR = = = M1 for a correct method to work out the interior angle of a regular hexagon eg. 180 (360 6) oe or (6-2) oe or 120 as interior angle of the hexagon M1 for a correct method to work out the interior angle of a regular octagon 180 (360 8) oe or (8-2) oe or 135 as interior angle of the octagon M1 (dep on at least M1) for a complete method eg A1 cao OR M1 for a correct method to work out an exterior angle of a regular hexagon eg or 60 as exterior angle of the hexagon M1 for a correct method to work out an exterior angle of a regular hexagon or 45 as exterior angle of the octagon M1 (dep on at least M1) for a complete method eg A1 cao SC : B1 for answer of 255

72 1MA0_1H Question Working Answer Mark Notes 14 (a) 35 1 B1 for (b) B1 for (c) Position of B marked 2 B1 for a point marked on a bearing of 40 (±2 ) from H or for a line on a bearing of 40 (±2 ) (use straight line guidelines on overlay) B1 for a point 4 cm (± 0.2cm) from H or for a line of length 4 cm (± 0.2cm) from H (use circular guidelines on overlay) NB. No label needed for point 15 (a) B1 accept answers in range inclusive (b) 3 B3 for box plot with all 3 aspects correct (overlay) aspect 1 : ends of whiskers at 153 and 186 aspect 2 : ends of box at 165 and 175 aspect 3 : median marked at 170 or ft (a) provided 165<(a)<175 (B2 for box plot with two aspects correct) (B1 for one aspect or correct quartiles and median identified) SC : B2 for all 5 values (153, 165, '170', 175, 186) plotted (c) Two correct comparisons 2 B1 ft from (b) for a correct comparison of range or inter-quartile range eg. the range / iqr is smaller for group B than group A B1 ft from (b) for a correct comparison of median or upper quartile or lower quartile or minimum or maximum eg. the median in group A is greater than the median in group B

73 1MA0_1H Question Working Answer Mark Notes 16 (a) m B1 for m 10 or 10 m (b) (x + 5)(x 2) 2 M1 for (x ± 5)(x ± 2) or x(x 2) + 5(x 2) or x(x + 5) 2(x + 5) A1 17 (a) 1 1 B1 cao (b) B1 cao (c) M1 for or oe or an answer of n where n is an integer or an answer of a where 1 a < 10 A1 cao

74 1MA0_1H Question Working Answer Mark Notes = 6 M1 for oe = 1 M1 for 2 6 A1 cao OR M2 for oe (M1 for triangle with all lengths 1 2 corresponding lengths of triangle ABC seen in any position or vertices seen at (1, 1) (3,1) and (2.5, 2.5) or stated) A1 cao 19 (a) , 0.3, B1 for 0.6 in correct position on tree diagram B1 for 0.7, 0.3, 0.7 in correct positions on tree diagram (b) = M1 for oe or a complete alternative method ft from tree diagram A1 for 0.12 oe

75 1MA0_1H Question Working Answer Mark Notes 20 15x + 6y = 33 8x 6y = 36 x = 3 y = 2 4 M1 for coefficients of x or y the same followed by correct operation (condone one arithmetic error) A1 cao for first solution 23x = 69 M1 (dep on M1) for correct substitution of found value into one of the equations or appropriate method after starting again (condone y = 11 one arithmetic error) A1 cao for second solution OR 11 2y x = y 4 3y = y 15y = = 23y y = 2 OR M1 for full method to rearrange and substitute to eliminate x or y, (condone one arithmetical error) A1 cao for first solution M1 (dep on M1) for correct substitution of found value into one of the equations or appropriate method after starting again (condone one arithmetic error) A1 cao for second solution Trial and improvement 0 marks unless both x and y correct values found

76 1MA0_1H Question Working Answer Mark Notes 21* ABO = ADO = 90 (Angle between tangent and radius is 90 ) DOB = (Angles in a quadrilateral add up to 360 ) BCD = (Angle at centre is twice angle at circumference) 65 o 4 B1 for ABO = 90 or ADO = 90 (may be on diagram) B1 for BCD = 65 (may be on diagram) C2 for BCD = 65 o stated or DCB = 65 o stated or angle C = 65 o stated with all reasons: angle between tangent and radius is 90 o ; angles in a quadrilateral sum to 360 o ; angle at centre is twice angle at circumference (accept angle at circumference is half (or 1 ) the angle at the centre) 2 (C1 for one correct and appropriate circle theorem reason) QWC: Working clearly laid out and reasons given using correct language OR ABD = (180 50) 2 (Base angles of an isosceles triangle) BCD = 65 (Alternate segment theorem) OR B1 for ABD = 65 or ADB = 65 (may be on diagram) B1 for BCD = 65 (may be on diagram) C2 for BCD = 65 o stated or DCB = 65 o stated or angle C = 65 o stated with all reasons: base angles of an isosceles triangle are equal; angles in a triangle sum to 180 o ; tangents from an external point are equal; alternate segment theorem (C1 for one correct and appropriate circle theorem reason) QWC: Working clearly laid out and reasons given using correct language

77 1MA0_1H Question Working Answer Mark Notes 22 (a) Correct histogram 3 B3 for fully correct histogram (overlay) (B2 for 3 correct blocks) F (B1 for 2 correct blocks of different widths) Fd SC : B1 for correct key, eg. 1 cm 2 = 5 (cars) or correct values for (freq class interval) for at least 3 frequencies (3, 5, 3.6, 1.2) NB: The overlay shows one possible histogram, there are other correct solutions. (b) M1 for (=18) oe or 1 24 (=6) oe 4 A1 cao OR M1 ft histogram for or 5 "1.2" A1 ft

78 1MA0_1H Question Working Answer Mark Notes 23 (a) ( x+ 4)( x 1) x M1 for (x + 4)(x 1) M1 for (2x 3)(x 1) (2x 3)( x 1) 2x 3 A1 cao (b) 4( x 2) 3( x+ 2) + ( x+ 2)( x 2) ( x+ 2)( x 2) 7x 2 ( x+ 2)( x 2) 3 M1 for denominator (x + 2)(x 2) oe or x 2 4 4( x 2) 3( x + 2) M1 for oe or oe ( x+ 2)( x 2) ( x+ 2)( x 2) (NB. The denominator must be (x + 2)(x - 2) or x 2 4 or another suitable common denominator) A1 for 7x 2 ( x+ 2)( x 2) 7x 2 or 2 x 4 SC: If no marks awarded then award B1 for 4( x 2) 3( x+ 2) + oe 2 2 x 2 x 2

79 1MA0_1H Question Working Answer Mark Notes 24 eg M1 for (...) or (...) or x = evidence of correct recurring decimal eg (...) x = M1 for two correct recurring decimals that, when subtracted, would result in a terminating decimal, and 99x = 27.9 attempting the subtraction eg. 100x = , x = and subtracting eg. 1000x = , 10x = and subtracting OR A1 cao or oe 25 Vol cylinder = π (2x) 2 9x = 36πx π x = π r 3 r 3 = 27x x 3 M1 for sub. into πr 2 h eg. π (2x) 2 9x oe M1 for ( ) π 2x 9x= π r oe x A1 oe eg NB : For both method marks condone missing brackets around the 2x

80 1MA0_1H Question Working Answer Mark Notes 26 (a) Parabola through (4, 1), (2, 3), (6, 3) (3, 0) (5, 0) 2 B2 for a parabola with min (4, 1), through (2, 3), (6, 3),(3, 0), (5, 0) (B1 for a parabola with min (4, 1) or a parabola through (2, 3) and (6, 3) or a parabola through (3, 0) and (5, 0) or a translation of the given parabola along the x-axis by any value other than +3 with the points ( 1, 3) (0, 0) (1, 1) (2, 0) (3, 3) all translated by the same amount) (b) Parabola through (1, 2), (0, 0), (2, 0) 2 B2 parabola with min (1, 2), through (0, 0) and (2, 0) (B1 parabola with min (1, 2) or parabola through (0, 0), (2, 0) (-1, 6) and (3, 6))

81

82 Further copies of this publication are available from Edexcel Publications, Adamsway, Mansfield, Notts, NG18 4FN Telephone Fax Order Code UG Summer 2012 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

83 Mark Scheme (Results) Summer 2012 GCSE Mathematics (Linear) 1MA0 Higher (Calculator) Paper 2H

84 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, please visit our website at Our website subject pages hold useful resources, support material and live feeds from our subject advisors giving you access to a portal of information. If you have any subject specific questions about this specification that require the help of a subject specialist, you may find our Ask The Expert service helpful. 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 2012 Publications Code UG All the material in this publication is copyright Pearson Education Ltd 2012

85 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 labelling 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.

86 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 cancelling 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.