GCSE Mathematics. Higher Tier. Paper 4C (Calculator) Time: 1 hour and 45 minutes. For Edexcel. Name

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1 For Edexcel Name GCSE Mathematics Paper 4C (Calculator) Higher Tier Time: 1 hour and 45 minutes Materials required Ruler, protractor, compasses, pen, pencil, eraser. Tracing paper may be used. Instructions and Information for Candidates Write your name in the box at the top of the page. Answer all the questions in the spaces provided in this question paper. The marks for each question and for each part of a question are shown in brackets. The total number of marks for this paper is 100. There are 21 questions in this paper. Calculators may be used. If your calculator does not have a π button, take the value of π to be unless the question instructs otherwise. Advice to Candidates Show all stages in any calculation. Work steadily through the paper. Do not spend too long on one question. If you cannot answer a question, leave it and attempt the next one. Return at the end to those you have left out. Written by Shaun Armstrong Only to be copied for use in the purchaser's school or college EH4C Page 1

2 GCSE Mathematics Formulae: Higher Tier Volume of a prism = area of cross section length cross section length Volume of sphere = 4 3 πr3 Surface area of sphere = 4πr 2 Volume of cone = 1 3 πr2 h Curved surface area of cone = πrl r l h r In any triangle ABC b C a The Quadratic Equation The solutions of ax 2 + bx + c = 0 where a 0, are given by x = b± b2 4ac 2a A c B Sine Rule a sin A = b sin B = c sin C Cosine Rule a 2 = b 2 + c 2 2bc cos A Area of triangle = 1 2 ab sin C EH4C Page 2

3 Answer ALL TWENTY ONE questions. Write your answers in the spaces provided. You must write down all the stages in your working. 1. Sol pays a total of 2.24 for 4 baguettes. Liz buys 7 baguettes from the same bakery. Work out how much Liz pays in total. Q1 (Total 2 marks) 2. (a) Work out the exact value of (i) (ii) 5.29 (2) (b) Work out the value of Give your answer correct to 3 significant figures. (Total 5 marks) Q2 EH4C Page 3

4 3. (a) On the grid, draw the graph of y = 5 2x y O x 2 (b) Use your graph to find (i) the value of y when x = 1.4 y = (ii) the value of x when y = 0.6 x = (2) (Total 5 marks) Q3 EH4C Page 4

5 4. (a) Factorise 3x 2 + x (b) Given that y = 3x 5, work out the value of x when y = 10. (1) x = (2) (Total 3 marks) Q4 EH4C Page 5

6 5. In a game, a coin is dropped into a hole. After bouncing on some nails, the coin falls into a slot and scores 1, 2 or 5 points Alice and Brianna each play the game with a number of coins. The table shows their results. Alice Brianna Number of coins 1 Scores Alice says the probability of scoring a 2 is the same as the probability of scoring a 1. (a) (i) Is Alice correct? (ii) Explain your answer. Carol plays the game. She uses 40 coins. (b) Estimate the number of times she will score 5 points. Show clearly how you make your estimate. (Total 6 marks) Q5 EH4C Page 6

7 6. Diagram NOT accurately drawn x x 45 The sizes, in degrees, of the angles of a triangle are 45, (x + 15) and 2x. Work out the value of x. x = Q6 (Total 4 marks) EH4C Page 7

8 7. y P O x 1 Q 2 3 (a) Describe fully the single transformation that maps triangle P onto triangle Q. (b) On the grid, rotate triangle P 180 about the point (4, 3). Label this image R. (2) (Total 5 marks) Q7 EH4C Page 8

9 8. Three friends sold 44 car insurance policies. The number of sales they made are in the ratio 5 : 4 : 2 Gareth made the most sales. (a) Work out the number of sales Gareth made. Gareth's hourly wage increases from 6.50 to 7.20 (b) Work out the percentage increase in his wage. Give your answer to an appropriate degree of accuracy. % (4) (Total 7 marks) Q8 EH4C Page 9

10 9. metres per second O miles per hour The graph is used to convert speeds between miles per hour and metres per second. Using the graph, (a) convert 17 miles per hour into metres per second, m/s (1) (b) convert 54 kilometres per hour into miles per hour. mph (Total 4 marks) Q9 EH4C Page 10

11 10. Alison is using trial and improvement to find a solution to the equation x 3 5x = 60 She puts her trials in a table: x x 3 5x comment 4 44 too small too big Continue the table to find a solution to the equation. Give your answer correct to 1 decimal place. x = Q10 (Total 3 marks) EH4C Page 11

12 11. Water is poured at a constant rate into each of three containers. For each container, one of these four sketch graphs shows how the depth, d, of the water, changes with time, t. d Graph P d Graph Q d Graph R t d Graph S t t t Write down the letter of the correct graph for each container. (a) Graph (1) (b) Graph (1) (c) Graph (1) (Total 3 marks) Q11 EH4C Page 12

13 12. A coin is biased so that when it is flipped, the probability of getting a head is 0.6 Josh flips the coin twice. (a) Complete the tree diagram. 1 st flip 2 nd flip... head head... tail... tail... head... tail (2) (b) Find the probability that Josh gets two heads. (2) (c) Find the probability that Josh gets at least one head. (2) (Total 6 marks) Q12 EH4C Page 13

14 13. Solve the simultaneous equations a + 2b = 3 3a 4b = 14 a = b = Q13 (Total 3 marks) EH4C Page 14

15 14. R S Diagram NOT accurately drawn P x 130 Q P, Q and R are points on the circumference of a circle. The tangents to the circle at Q and R meet at S. The lines PQ and RS are parallel. Angle PQS = 130. Work out the size of angle x. Q14 (Total 4 marks) EH4C Page 15

16 15. A bulb has a resistance of a ohms and a buzzer has a resistance of b ohms. They are connected so that their total resistance, R ohms, is given by the formula R = ab a b (a) Find the value of R when a = 4.5 and b = 8.1 Give your answer correct to 3 significant figures. R = (2) (b) Make a the subject of the formula R = ab a b a = (4) (Total 6 marks) Q15 EH4C Page 16

17 16. Brad joins a golf club. He decides to keep a record of his score for each round he plays. After 6 rounds, his mean score is M. In his seventh round he scores 90 and this raises his mean score to (M + 2). Find the value of M. M = Q16 (Total 4 marks) EH4C Page 17

18 17. C Diagram NOT accurately drawn B cm A 64 D Quadrilateral ABCD is made up of 2 isosceles triangles. AB = BD = 8.4 cm. BC = CD. Angle BAD = 64. Angle BCD = 38. (a) Calculate the length of AD. Give your answer correct to 3 significant figures. cm (b) Calculate the perimeter of ABCD. Give your answer correct to 3 significant figures. cm (4) (Total 7 marks) Q17 EH4C Page 18

19 18. (a) Expand x(4x 3) (1) (b) Expand and simplify 4(3x 2) 2(2x 5) (2) (c) Simplify fully x 2 3 x 2 2 x 2 2 x (Total 6 marks) Q18 EH4C Page 19

20 19. C Diagram NOT accurately drawn B O D 6 cm 72 A E ABCDE is a regular pentagon. It is made up of 5 identical isosceles triangles which meet at O. OA = 6 cm. Angle AOE = 72. (a) Calculate the area of pentagon ABCDE. Give your answer correct to 3 significant figures. cm 2 (b) Calculate the perimeter of pentagon ABCDE. Give your answer correct to 3 significant figures. cm (Total 6 marks) Q19 EH4C Page 20

21 20. The power P transmitted to a light bulb in an electrical ciruit is given by P = V 2 where V is the potential difference and R is the resistance. A student records these values: V = 9 R = 4 Both values are correct to 1 significant figure. Calculate the greatest value of P. Give your answer correct to 3 significant figures. R P = Q20 (Total 4 marks) EH4C Page 21

22 21. Diagram NOT accurately drawn cm x The diagram shows a giant comma to be used on a sign. The shape of the comma is made up of a triangle and a sector of a circle. The triangle is right-angled and has a height of 12 cm. The sector of a circle has a radius of 12 cm and the angle at its centre is 300. (a) Work out the length, x, of the base of the triangle. Give your answer correct to 1 decimal place. x = cm (b) Work out the area of the comma. cm 2 (4) (Total 7 marks) Q21 TOTAL FOR PAPER: 100 MARKS END EH4C Page 22