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

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1 For Edexcel Name GCSE Mathematics Paper 4D (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 22 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 EH4D 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 EH4D Page 2

3 Answer ALL TWENTY TWO questions. Write your answers in the spaces provided. You must write down all the stages in your working. 1. (a) Solve 2x + 3 = 4 (b) Solve 3(y + 5) = 21 x = y = (3) (Total 5 marks) Q1 2. Calculate how long it takes to travel a distance of 6 km at a speed of 90 km/h. Give your answer in minutes. minutes Q2 (Total 3 marks) EH4D Page 3

4 kg of coal is to be divided in the ratio 2 : 3 Work out the weight of the smaller share. kg Q3 (Total 2 marks) 4. (a) Simplify fully (i) 2r 3s 6r + 4s (ii) ( x 3 ) 2 (iii) 2ab 4 3a 5 b 1 (5) (b) Factorise fully 2p 2 8p (Total 7 marks) Q4 EH4D Page 4

5 5. Use your calculator to work out the value of Give your answer correct to 1 decimal place Q5 (Total 2 marks) 6. The density of diamond is 3.5 grams per cm 3. (a) Work out the mass of a diamond with a volume of 0.2 cm 3. A granite sculpture weighs 5.4 kilograms and has a volume of 2000 cm 3. grams (b) Work out the density of granite. Give your answer in grams per cm 3. grams per cm 3 (Total 4 marks) Q6 EH4D Page 5

6 7. The table shows information about the weight lost by 120 men over two months. Weight lost (W kg) Frequency 0 W < W < W < W < W < 20 9 (a) Work out an estimate for the mean weight lost by the men. kg (4) (b) Complete the cumulative frequency table. Weight lost (W kg) Cumulative Frequency 0 W < W < 8 0 W < 12 0 W < 16 0 W < 20 (1) EH4D Page 6

7 (c) On the grid, draw a cumulative frequency graph for your table. Cumulative Frequency O Weight lost (W kg) (d) Use your graph to estimate the median weight lost by the men. kg (1) (Total 8 marks) Q7 EH4D Page 7

8 8. Diagram NOT D accurately drawn E 77 A C 28 B A, B, C and D lie on the circumference of a circle. AC and BD intersect at E. Angle AED = 77. Angle ACB = 28. (a) (i) Write down the size of angle ADB. (ii) Give a reason for your answer. (b) (i) Find the size of angle CBD. (ii) Give reasons for your answer. (3) (Total 5 marks) Q8 EH4D Page 8

9 9. C D Diagram NOT accurately drawn 1.5 cm B 5.5 cm A E 8.5 cm The diagram show a company identity card. The card is rectangular in shape but one corner has been rounded. AE = 8.5 cm. DE = 5.5 cm. BC is a quarter-circle of radius 1.5 cm. Find the area of the card. State the units of your answer. Q9 (Total 5 marks) EH4D Page 9

10 10. Peter says For all prime numbers, n, the value of n 2 + n 1 is also a prime number Give an example to show that Peter is wrong. Q10 (Total 4 marks) 11. Q Diagram NOT accurately drawn 5 cm P 18 cm R PQR is a right-angled triangle. PR = 18 cm. QR = 5 cm. Work out the size of angle QPR. Give your answer correct to 1 decimal place. Q11 (Total 3 marks) EH4D Page 10

11 12. Sally invests 2000 in an account that pays 5% compound interest per year. Work out the amount of interest she earns over 2 years. Q12 (Total 3 marks) 13. The equation x 2 + x = 16 has a solution between 3 and 4. Use a trial and improvement method to find this solution. Give your answer correct to 1 decimal place. You must show all your working. x = Q13 (Total 4 marks) EH4D Page 11

12 14. B Diagram NOT accurately drawn 75 A 2x y C ABC is a triangle. (a) Explain why 2x + y = 105. (1) E 100 Diagram NOT F accurately drawn 2y D 3x 70 G DEFG is a quadrilateral. (b) Find the value of 3x + 2y. 3x + 2y = (c) Use algebra to find the value of x and the value of y. x = y = (3) (Total 6 marks) Q14 EH4D Page 12

13 15. (a) Solve x x x 2 = 1 x = (4) (b) Hence solve y 2 y y 2 2 = 1 y = or y = (Total 6 marks) Q Describe fully the single transformation that would transform the curve with equation y = x 2 to give (a) the curve with equation y = 2x 2 (b) the curve with equation y = (x + 3) 2 (Total 4 marks) Q16 EH4D Page 13

14 17. A sack of potatoes weighs 10 kg correct to the nearest kilogram. Calculate the maximum weight of 20 sacks of potatoes. kg Q17 (Total 2 marks) 18. L is directly proportional to the square root of m. When m = 9, L = 42 Find the value of L when m = 100 L = Q18 (Total 4 marks) EH4D Page 14

15 19. Diagram NOT accurately drawn cm The diagram shows a square and a sector of a circle of radius 5 cm. The angle at the centre of the sector is 135. The square and the sector have the same perimeter. Find the area of the square. Give your answer correct to an appropriate degree of accuracy. cm 2 Q19 (Total 5 marks) EH4D Page 15

16 20. A game at a fair consists of throwing a ball at a coconut on a stand. If you knock the coconut off, you win a prize. You can throw up to three balls at the coconut. If you knock it off with your first or second throw then you do not get any more throws. Darren plays the game. The probability that he knocks the coconut off with his first throw is 0.1 If his first throw is not successful, the probability that he knocks the coconut off with his second throw is 0.12 If his first two throws are not successful, the probability that he knocks the coconut off with his third throw is 0.15 (a) Complete the tree diagram. first throw second throw third throw Success... Success... Fail... Success... Fail... Fail (b) Work out the probability that Darren wins a prize. (3) EH4D Page 16

17 It costs 1 to play the game. Each prize costs 2. (c) Work out an estimate of the profit made by the stall when 50 people with the same chance of winning as Darren play the game. (Total 7 marks) Q The Earth is approximately a sphere of radius m. (a) Write in standard form. (b) Calculate the volume of the Earth in m 3. Give your answer in standard form correct to 3 significant figures. (1) m 3 (3) (Total 4 marks) Q21 EH4D Page 17

18 22. D Diagram NOT accurately drawn C B A 4 cm 6 cm H G F E The shapes ABGH, BCFG and CDEF are mathematically similar. AH = 4 cm and BG = 6 cm. (a) Calculate the length of CF. cm (b) Calculate the length of DE. cm (c) Find the ratio Area of CDEF : Area of ABGH (3) (Total 7 marks) Q22 TOTAL FOR PAPER: 100 MARKS END EH4D Page 18

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