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1 For Edexcel Name GCSE Mathematics Paper 4F (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 25 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 EH4F 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 EH4F Page 2

3 Answer ALL TWENTY FIVE questions. Write your answers in the spaces provided. You must write down all the stages in your working. 1. (a) Expand 2x(3 x) (b) Solve 4y 3 = 7 (1) y = (2) (Total 3 marks) Q1 2. Ray buys 20 tins of baked beans at Foods4U for 7.20 Wes buys 14 tins of baked beans at Quickshop for 4.90 Find out which shop sells tins of baked beans for the lowest price. You must show all your working. Q2 (Total 3 marks) EH4F Page 3

4 3. P = πr 2 + 2rl r = 2.5 l = 6.1 Work out the value of P. Give your answer correct to 3 significant figures. P = Q3 (Total 3 marks) 4. 8 cm Diagram NOT accurately drawn 6 cm 7 cm 13 cm 5 cm 9 cm In the shape shown above, all the corners are right-angles. Work out the perimeter of the shape. cm Q4 (Total 3 marks) EH4F Page 4

5 5. N A N N C B A, B and C are three houses on the edge of a lake. The bearing of a boat from A is 106. The bearing of the same boat from B is 022. (a) Mark with a cross ( ) the position of the boat on the diagram. (3) (b) Measure and write down the bearing of the boat from C. (1) (Total 4 marks) Q5 EH4F Page 5

6 6. 60 families coming out of a supermarket were asked how much they had spent. The results are shown in the table. Amount spent ( P) Frequency 60 < P < P < P < P < P < P (a) On the grid, draw a frequency diagram to represent the data Frequency Amount spent ( P) (2) (b) Find the class interval in which the median lies. (2) EH4F Page 6

7 (c) Write down the letter of the graph below which could be the cumulative frequency graph for the data. Graph A Graph B Cumulative Frequency Cumulative Frequency Graph C Graph D Cumulative Frequency Cumulative Frequency Graph (1) (Total 5 marks) Q6 EH4F Page 7

8 7. (a) Factorise (i) y 2 + 7y (ii) x 2 2x 8 (3) (b) Work out the value of 2p + pq when p = 7 and q = 5. (2) (Total 5 marks) Q7 8. A cattery charges a 3 booking fee and 8 per night that a cat stays. The total cost when a cat stays n nights is C pounds. Write down a formula for C in terms of n. Q8 (Total 3 marks) EH4F Page 8

9 9. Kate makes scarves. She sells each scarf for 6.40 plus VAT at %. She sells 450 scarves. Work out how much money Kate receives. Q9 (Total 4 marks) 10. Solve the simultaneous equations 3x + 4y = 2 2x + 6y = 7 x = y = Q10 (Total 4 marks) EH4F Page 9

10 11. In June 2007 there were 3000 penguins in a colony. Each year the number of penguins decreases by 10%. Mel says that means there won't be any penguins left in the colony after 10 years. (a) Explain why Mel is wrong. (2) (b) Calculate the number of penguins there will be in the colony in June (3) (Total 5 marks) Q11 EH4F Page 10

11 12. The table shows some rows of a number pattern. Value Row = 9 Row = 16 Row = 25 Row 4 Row n (a) Complete row 4 of the number pattern. (1) (b) Find an expression, in terms of n, for the value of Row n. Give your answer in its simplest form. (2) (Total 3 marks) Q A straight line has the equation y = 3x 4 (a) Write down the equation of a straight line parallel to y = 3x 4 which passes through the point (0, 2). (1) (b) Find the equation of a straight line parallel to y = 3x 4 which passes through the point ( 2, 0). (3) (Total 4 marks) Q13 EH4F Page 11

12 14. The equation x 3 + 2x = 14 has only one solution. (a) Explain why the solution cannot be a negative number. (1) (b) Use a trial and improvement method to find the solution. Give your answer correct to 1 decimal place. You must show all your working. x = (4) (Total 5 marks) Q14 EH4F Page 12

13 15. Diagram NOT Q accurately drawn P 7.6 cm 41 R PQR is a right-angled triangle. PR = 7.6 cm. Angle PRQ = 41. Work out the length of PQ. Give your answer correct to an appropriate degree of accuracy. cm Q15 (Total 3 marks) EH4F Page 13

14 16. Some boxes of Chocobite cereal contain a golden star. If you collect 5 of these stars, you can claim a prize. The probability of a 300 g box of Chocobite containing a star is 1 8. The probability of a 600 g box of Chocobite containing a star is 1 3. Taimur buys one 300 g box and one 600 g box of Chocobite. (a) Complete the tree diagram. 300 g box 600 g box... star star... no star... star... no star... no star (2) (b) Work out the probability that Taimur gets exactly one star from his two boxes. (3) (Total 5 marks) Q16 EH4F Page 14

15 17. y O x On the grid, enlarge the shaded shape by a scale factor of 2 1, centre ( 3, 6). 2 Q17 (Total 3 marks) EH4F Page 15

16 18. (a) Expand and simplify (x + y)(x + 3y) (2) (b) Simplify fully p 2 4 p 2 2 p (3) (Total 5 marks) Q A school has 1200 pupils. The table shows information about the type of lunch pupils have. Hot lunch Male 378 Packed lunch 219 Female The headteacher wants to get opinions on a change to the hot lunches offered. He decides to survey a sample of 100 pupils, stratified by both gender and type of lunch they have. Calculate the number of females who have a hot lunch that should be in the sample. Q19 (Total 2 marks) EH4F Page 16

17 20. Diagram NOT accurately drawn The diagram shows a rectangle. The lengths of the sides are given in centimetres. Giving your answers in the form p + q 3, where p and q are integers, work out (a) the perimeter of the rectangle, cm (3) (b) the area of the rectangle. cm 2 (3) (Total 6 marks) Q20 EH4F Page 17

18 21. B Diagram NOT accurately drawn cm C 25.6 cm A ABC is a triangle. AB = 21.3 cm. AC = 25.6 cm. Angle ABC = 63. Work out the size of angle ACB. Give your answer correct to 1 decimal place. Q21 (Total 3 marks) EH4F Page 18

19 22. Will wants to lay a single row of paving stones to make a path to his greenhouse. The path is straight and 8 m long correct to 1 significant figure. The paving stones are square and of side 60 cm correct to 1 significant figure. Assuming there are no gaps between the paving stones, work out the maximum number of paving stones that he will need to buy. Q22 (Total 4 marks) EH4F Page 19

20 23. Diagram NOT accurately drawn 8 cm A semicircle has a diameter of 8 cm. (a) Work out the area of the semicircle. Give your answer correct to 3 significant figures. cm 2 Diagram NOT accurately drawn (2) The semicircle is then cut into 3 identical sectors. These are arranged as shown to form an equilateral triangle. (b) Work out the area of the shaded region of the triangle. cm 2 (3) (Total 5 marks) Q23 EH4F Page 20

21 24. The histogram shows information about the ages of teachers at a school. Frequency density Age (years) There are 27 teachers aged less than 35 years. Find the number of teachers aged less than 40 years. Q24 (Total 3 marks) EH4F Page 21

22 25. (a) Diagram NOT accurately drawn 6 cm 6 cm x 6 cm The diagram shows an equilateral triangle of side 6 cm. Find the height, x, of the triangle. Give your answer correct to 3 significant figures. E cm (3) (b) Diagram NOT accurately drawn B D F 9 cm A 6 cm C ABCDEF is a prism of length 9 cm. The cross-section of the prism is an equilateral triangle of side 6 cm. Calculate the size of the angle BF makes with the plane ACFD. Give your answer correct to 1 decimal place. (4) (Total 7 marks) Q25 TOTAL FOR PAPER: 100 MARKS END EH4F Page 22

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