www.themathsprofessor.com Write your name here Surname Other names Pearson Edexcel Level 1/Level GCSE (9-1) Centre Number Candidate Number Mathematics Paper (Calculator) Specimen Papers Set Time: 1 hour 30 minutes Higher Tier Paper Reference 1MA1/H You must have: Ruler graduated in centimetres and millimetres, protractor, pair of compasses, pen, HB pencil, eraser, calculator. Total Marks Instructions Information 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 π button, take the value of π to be 3.14 unless the question instructs otherwise. Diagrams are NOT accurately drawn, unless otherwise indicated. You must show all your working out. 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. Keep an eye on the time. Try to answer every question. Check your answers if you have time at the end. S50158A 015 Pearson Education Ltd. 6/6/4/ *S50158A014* Pearson Edexcel Level 1/Level GCSE (9-1) in Mathematics - Specimen Papers Set - September 015 Pearson Education Limited 015 11
14 Joseph travels to work each day by train. The weekly cost of his train journey is 45 Joseph s weekly pay is 65 (a) Work out 45 as a percentage of 65 45 65 x 100 = 7. % (b) The weekly cost of his train journey increases by 8%. Increase 45 by 8%. 45 x 0.08 = 3.6 45 + 3.6 = 48.6 (3) (c) Joseph s weekly pay increases to 640 Calculate the percentage increase from 65 to 640 change original x 100 15 65 x 100 =.4 % (3) (d) Joseph decides to cycle to work. He cycles 18 km to work. His journey to work takes 1 hour 0 minutes. Calculate his average speed in kilometres per hour. S D T? 18 1 /3 10.8 km/h (3) (Total for Question 14 is 11 marks) *P41035A0150* 15
6 y 6 4 Q P -6-4 - O 4 6 x (a) Describe fully the single transformation which maps triangle P onto triangle Q. Rotation 90 degrees clockwise from (0,0)... (b) Reflect triangle Q in the line y = x. Label the new triangle R. vertices should be at (4,4) (4,) and (5,) (Total for Question 6 is 5 marks) 73 The perimeter of a triangle is 90 cm. The lengths of the sides of the triangle are in the ratios 3 : 5 : 7 Work out the length of the longest side of the triangle. (3) 90 15 = 6 so 18 : 30 : 4 4... cm (Total for Question 7 is 3 marks) *P38579A074* 7
84 E = {, 3, 4, 5, 6, 7, 8, 9, 10, 11, 1} A = {odd numbers} P = {prime numbers} List the members of the set (i) A P, 3 5 7 11... (ii) A P. 3 5 7 9 11... (Total for Question 8 is marks) 95 Ella invested $8000 for 3 years at 5% per annum compound interest. Calculate the value of her investment at the end of 3 years. 8000 x 1.05^3 = 961 961 $... (Total for Question 9 is 3 marks) 8 *P38579A084*
19 6 The table shows information about the numbers of text messages sent by 40 teenagers in one day. Number of text messages Number of teenagers Mid-interval value 0 to 3 1 3 to 5 6 4 3 4 10 9 to 11 15 1 to 14 5 15 to 17 1 7 10 13 16 70 150 65 16 (a) Write down the modal class. 40 38 9 to 11 (1) (b) Work out an estimate for the mean number of texts sent by the 40 teenagers in one day. 38 divided by 40 = 8. 8. (4) (Total for Question 19 is 5 marks) *P40610A0190* 19
15 7 (a) Simplify 8( x 3) 4( x 3) (x-3) 8 and 4 cancel (x-3) cancels at top and bottom (x-3) (b) Factorise a 144 Difference of two squares! (a+ 1) (a-1) (c) Make q the subject of the formula p = q 5r p + 5r = /q -- square each term (d) Solve 4 y 4 = 5 p^ + 5r^ = q q = P^ + 5r^ 4 = 5(y-4) 4 = 5y - 0 4 = 5y y = 4.8 y = 4.8 (3) (Total for Question 15 is 9 marks) *P38577A0134* 13
16 8 The incomplete table shows information about the times, in minutes, that runners took to complete a race. Time (t minutes) 30 t 35 35 t 40 40 t 50 50 t 60 60 t 80 Number of runners 1 0 1 16.4 (a) Use the histogram to calculate the number 4 of runners who 3took between 40 and 50 1.6 minutes to complete the race. 10 x 3 (3 is FD) = 30 (b) Complete the histogram for the remaining results. Frequency density 3..8.4 1.6 1. 0.8 0.4 30 40 50 60 70 80 Time (t minutes) 16 *P4061A0160*
Runners who achieved a time between 37 and 48 minutes to complete the race were each awarded a silver medal. (c) Calculate an estimate of the number of runners awarded silver medals. 0.6 x 0 + 0.8 x 30 36 (Total for Question 16 is 6 marks) 17 9 Show that the recurring decimal x = 0.177777777777 10x = 1.7777777777 9x = 1.6 x = 1.6/9 x = 16 90 (Total for Question 17 is marks) *P4061A0170* 17
3+ 7 10 19 Show that State the value of k. can be expressed in the form k where k is an integer. 3 3 + 3 + 3 3 x = 4 3 x 4 3 48 k = 4 (Total for Question 19 is 3 marks) 0 11 Simplify fully 4 3 + x x 4 ( - x) x(-x) + 3(x) x(-x) 8-4x + 3x x(-x) 8 - x x(-x) can expand denominator if you want! (Total for Question 0 is 3 marks) *P4061A0190* 19
1 1 B x cm (x + 5) cm 4 C 5 Diagram NOT accurately drawn A (x + 8) cm The diagram shows a trapezium ABCD with AD parallel to BC. AB = x cm, BC = (x + 5) cm and AD = (x + 8) cm. The area of the trapezium is 4 cm. 3 D (a) Show that x +13x 84 = 0 x + 13 divided by = x + 6.5 (x + 6.5) x height = x^ + 6.5x x^ + 6.5x = 4 x^ + 6.5x - 4 = 0 Double the numbers (b) Calculate the perimeter of the trapezium. Use the quadratic formula whenever you see a quadratic equation! which gives x = 4 or -10.5 and as it is a length is has to be positive If x is 4 3 x 4 + 13 + 5 = 30! You have to do pythagoras on the end of the trapezium cm (5) (Total for Question 1 is 7 marks) TOTAL FOR PAPER IS 100 MARKS 0 *P4061A000*
13 1 ABCDE is a square-based pyramid. B 15 cm AE = BE = CE = DE = 1 cm AB = 15 cm Calculate the size of angle DEB. Give your answer to the nearest degree. BD = the root of 15^ + 15^ so BD = 450 BD = 1. C Cos EBD = 0.5 x 1. 1 1 use cosine rule so DEB = cos-1 which is 14 E A 1^ + 1^ - 450 x 1 x 1 1 cm Diagram NOT accurately drawn D... DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA (Total for Question 1 is 4 marks) 0 *P46917A004*
14 1 The functions g and h are defined as g(x) x x 5 h(x) x + 4 (a) Find the value of g(1) 1-3 or - 1/3... (1) (b) State which value of x must be excluded from any domain of g.5 as the denominator can't be 0! (1)... (c) Find gh(x) Simplify your answer. x + 4 (x + 4) - 5 x + 4 x + 8-5 = x + 4 x + 3 gh(x)... (d) Express the inverse function g 1 in the form g 1 (x)... y y - 5 = x y = x(y - 5) so y = xy - 5x xy - y = 5x y(x - 1) = 5x so y = 5x/ x-1 g 1 (x)... (3) (Total for Question 1 is 7 marks) *P44619A0170* 17
18 15 C B Diagram NOT accurately drawn 9 cm A 9 cm O 35 D AOD is a diameter of a circle, with centre O and radius 9 cm. ABC is an arc of the circle. AC is a chord. Angle ADC = 35 Calculate the area of the shaded segment. Give your answer correct to 3 significant figures. AOC = 70 as OCD is isosceles pi x 9^ x 70/360 = 49.48 1/ x 9^ x sin70 = 38.057 Subtract them = 11.4! cm (Total for Question 18 is 65 marks) 18 *P4061A0180*
19 16 y y = kx A( p, q) y = N x O x The diagram shows the straight line with equation y = kx intersecting N the curve with equation y = at the point A(p, q). x (a) Find p and find q. Give each answer in its simplest form, in terms of k and N. kx = n/x kp = n/p Whenever you see lines intersecting set them equal to each other! p = n/k q = nk p =... Given that p = q (b) find the value of k. q =... (3) or q n/k = nk n/k = k x = q nk n/k = 4nk 1/ p = kp n = 4nk^ if 1/ p = x p then the missing value is also 1/ 1/ k =... (Total for Question 19 is 5 marks) *P4460A034* 3