Pearson Edexcel Merged Question Paper + Mark Scheme (Results) Summer 2022 Pearson Edexcel GCSE (9 – 1) In Mathematics (1MA1) Higher (Calculator) Paper 3H *P66381A0124* Turn over Candidate surn

Pearson Edexcel Merged Question Paper + Mark Scheme (Results) Summer 2022 Pearson Edexcel GCSE (9 – 1) In Mathematics (1MA1) Higher (Calculator) Paper 3H *P66381A0124* Turn over Candidate surname Other names Total Marks Centre Number Candidate Number Please check the examination details below before entering your candidate information Time Paper reference P66381A ©2021 Pearson Education Ltd. 1/1/1/1/1/ 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. • You must show all your working. • Diagrams are NOT accurately drawn, unless otherwise indicated. • Calculators may be used. • If your calculator does not have a π button, take the value of π to be 3.142 unless the question instructs otherwise. Information • The total mark for this paper is 80 • The marks for each question are shown in brackets – use this as a guide as to how much time to spend on each question. Advice • Read each question carefully before you start to answer it. • Try to answer every question. • Check your answers if you have time at the end. • Good luck with your examination. You must have: Ruler graduated in centimetres and millimetres, protractor, pair of compasses, pen, HB pencil, eraser, calculator, Formulae Sheet (enclosed). Tracing paper may be used. Mathematics PAPER 3 (Calculator) Higher Tier 1 hour 30 minutes 1MA1/3H Pearson Edexcel Level 1/Level 2 GCSE (9–1) *P66381A0224* 2 Answer ALL questions. Write your answers in the spaces provided. You must write down all the stages in your working. 1 Here is a right-angled triangle. 8.5 cm x cm 4 cm Work out the value of x. x = ...................................................... (Total for Question 1 is 2 marks) *P66381A0324* Turn over 3 2 T = 4m2 − 11 (a) Work out the value of T when m = − 3 T = ...................................................... (2) (b) Make p the subject of the formula d = 3p + 4 ...................................................... (2) (Total for Question 2 is 4 marks) *P66381A0424* 4 3 Rick, Selma and Tony are playing a game with counters. Rick has some counters. Selma has twice as many counters as Rick. Tony has 6 counters less than Selma. In total they have 54 counters. the number of counters Rick has : the number of counters Tony has = 1 : p Work out the value of p. p = ...................................................... (Total for Question 3 is 5 marks) *P66381A0524* Turn over 5 4 Jo is going to buy 15 rolls of wallpaper. Here is some information about the cost of rolls of wallpaper from each of two shops. Chic Decor 3 rolls for £36 Style Papers Pack of 5 rolls normal price £70 12% off the normal price Jo wants to buy the 15 rolls of wallpaper as cheaply as possible. Should Jo buy the wallpaper from Chic Decor or from Style Papers? You must show how you get your answer. (Total for Question 4 is 4 marks) *P66381A0624* 6 5 The table gives information about the lengths, in cm, of some pieces of string. Length (t cm) Frequency 0 < t  10 15 10 < t  20 20 20 < t  30 50 30 < t  40 25 40 < t  50 5 Amos draws a frequency polygon for the information in the table. Lengths of pieces of string 60 50 30 20 10 0 00 Length (cm) Frequency Write down two mistakes that Amos has made. 1............................................................................................................................................................................................................................................... .................................................................................................................................................................................................................................................. 2............................................................................................................................................................................................................................................... .................................................................................................................................................................................................................................................. (Total for Question 5 is 2 marks) *P66381A0724* Turn over 7 6 Jessica runs for 15 minutes at an average speed of 6 miles per hour. She then runs for 40 minutes at an average speed of 9 miles per hour. It takes Amy 45 minutes to run the same total distance that Jessica runs. Work out Amy’s average speed. Give your answer in miles per hour. ...................................................... miles per hour (Total for Question 6 is 4 marks) *P66381A0824* 8 7 The diagram shows rectangle STUV. TQU and SRV are straight lines. All measurements are in cm. T Q U S R V 2x 4x 3x 5 The area of trapezium QUVR is Acm2 Show that A = 2x2 + 20x (Total for Question 7 is 3 marks) *P66381A0924* Turn over 9 8 An electricity company charges the same fixed amount for each unit of electricity used. David uses this graph to work out the total cost of the electricity he has used. 20 16 12 8 4 0 0100 110 Number of units used Cost (£) (a) Work out the gradient of the straight line. ...................................................... (2) (b) What does the gradient of this line represent? .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. (1) (Total for Question 8 is 3 marks) *P66381A01024* 10 9 (a) Express 10 10 10 360 150 90 × as a power of 10 ...................................................... (3) Liam was asked to express (1250)2 as a power of 12 Liam wrote (1250)2 = 12502 = Liam’s method is wrong. (b) Explain why. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. (1) (Total for Question 9 is 4 marks) *P66381A01124* Turn over 11 10 Jane bought a new car three years ago. At the end of the first year the value of the car had decreased by 12.5% The value of the car then decreased by 10% each year for the next two years. At the end of the three years, the value of the car was £17010 Work out the value of the car when Jane bought it three years ago. £...................................................... (Total for Question 10 is 3 marks) *P66381A01224* 12 11 Rayheem has 16 shirts 5 pairs of jeans 3 jackets Rayheem chooses an outfit to wear. An outfit is 1 shirt, 1 pair of jeans and 1 jacket. Work out how many different outfits Rayheem can choose. ...................................................... (Total for Question 11 is 2 marks) *P66381A01324* Turn over 13 12 ABC and ACD are right-angled triangles. A D 8 cm C B 45° 20° DC = 8 cm Angle ADC = 45° Angle ABC = 20° Work out the length of AB. Give your answer correct to 3 significant figures. ...................................................... cm (Total for Question 12 is 3 marks) *P66381A01424* 14 13 a and b are vectors such that a = 2 −3          and    3a − 2b = 8 −17       Find b as a column vector. ............. ............. (Total for Question 13 is 3 marks) *P66381A01524* Turn over 15 14 (a) Factorise fully 4p2 − 36 ...................................................... (2) (b) Show that (m + 4)(2m − 5)(3m + 1) can be written in the form am3 + bm2 + cm + d where a, b, c and d are integers. (3) (Total for Question 14 is 5 marks) *P66381A01624* 16 15 P, Q, R and S are four points on a circle. P X S R Q PXR and SXQ are straight lines. Prove that triangle PQX and triangle SRX are similar. (Total for Question 15 is 3 marks) *P66381A01724* Turn over 17 16 p = 2e f e = 6.8 correct to 1 decimal place. f = 0.05 correct to 1 significant figure. Work out the upper bound for the value of p. Give your answer correct to 3 significant figures. You must show all your working. ...................................................... (Total for Question 16 is 3 marks) *P66381A01824* 18 17 The table gives information about the distances, in miles, that some Year 10 students live from school. Distance (d miles) Frequency 0 < d  1.0 90 1.0 < d  1.5 48 1.5 < d  2.0 22 2.0 < d  3.0 8 3.0 < d  5.0 12 (a) On the grid, draw a histogram for this information. Frequency density 0 1 2 3 4 5 Distance (d miles) (3) *P66381A01924* Turn over 19 Turn over The histogram below shows information about the distances, in miles, that some Year 11 students live from school. Frequency density 0 1 2 3 4 5 Distance (d miles) The number of Year 11 students who live between 1 and 2 miles from school is n. (b) Find an expression, in terms of n, for the number of Year 11 students who live between 3 and 5 miles from school