GCSE Mathematics. Higher Tier. Paper 3G (Non-Calculator) Time: 1 hour and 45 minutes. For Edexcel. Name

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1 For Edexcel Name GCSE Mathematics Paper 3G (Non-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 23 questions in this paper. Calculators must not be used. 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 EH3G 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 EH3G Page 2

3 Answer ALL TWENTY THREE questions. Write your answers in the spaces provided. You must write down all the stages in your working. You must NOT use a calculator. 1. Solve 3(x 2) = 5x + 8 x = Q1 (Total 3 marks) 2. (a) Simplify (i) r 2 r 5 (ii) 4a + b + 2a 2b (b) Work out the value of 5p + 2q when p = 3 and q = 4.5 (Total 4 marks) Q2 EH3G Page 3

4 3. Nabeel wants to find out how often people send text messages. He plans to ask 50 people who have mobile phones this question. How many text messages have you sent? (a) Write down two reasons why this is not a good question. First reason Second reason (b) Design a better question that Nabeel could use. You should include response boxes. (Total 4 marks) Q3 EH3G Page 4

5 4. A library has 600 history books. 15% of these books are paperbacks. (a) Work out 15% of of the history books have been borrowed in the last six months. (b) Work out 192 as a percentage of 600. % (Total 4 marks) Q4 5. Use the information that = 7958 to find the value of (a) (1) (b) (1) (c) (1) (Total 3 marks) Q5 EH3G Page 5

6 6. This is a map of part of Wales. N Pembroke Cardiff Scale: 1 cm represents 15 km (a) Measure and write down the bearing of Pembroke from Cardiff. (1) A furniture store in Pembroke will deliver to anywhere within 90 km of Pembroke. Another furniture store in Cardiff will deliver to anywhere within 60 km of Cardiff. (b) On the diagram, shade the region where deliveries will be made by both stores. (Total 3 marks) Q6 EH3G Page 6

7 7. Diagram NOT accurately drawn 32 Q P S 109 R 141 T Sally says that the lines PQ and ST are parallel. Is Sally correct? You must show working to justify your answer. Q7 (Total 3 marks) EH3G Page 7

8 8. A group of people each choose one of three desserts. Some information about their choices is shown in the table. Ice cream Male 28 Cake 20 Fruit bowl Female A female is picked at random. (a) Find the probability that she chose the ice cream. Give your answer as a fraction in its simplest form. A male is to be picked at random. The probability that he chose the fruit bowl is 1 4. (b) Work out how many males chose the fruit bowl. (3) (Total 5 marks) Q8 EH3G Page 8

9 9. Ann opens a bank account and pays in 100. She then pays in another 5 each week. (a) Write down an expression for the total amount, in pounds, that Ann will have paid into her account after n weeks. Emma opens a bank account at the same time as Ann and pays in 40. She then pays in another 8 each week. (b) Work out how many weeks it will take for Emma to have paid the same amount in total into her account as Ann. (3) (Total 5 marks) Q9 EH3G Page 9

10 10. (a) List all the possible integer values of n such that 4 < n 2 (b) On the grid below, show by shading the region which satisfies all three of these inequalities. x > 2 y < 6 y > x Label the region R. y O x 2 (3) (Total 5 marks) Q10 EH3G Page 10

11 11. Solve the simultaneous equations x y = 5 3x 4y = 13 x = y = Q11 (Total 3 marks) 12. (a) Work out Give your answer as a fraction in its simplest form. (b) Work out (3) (Total 5 marks) Q12 EH3G Page 11

12 13. Diagram NOT A 7 cm accurately drawn 3.1 cm B 12.8 cm E C 14 cm D AB is parallel to CD. The straight lines AD and BC intersect at E. AB = 7 cm. CD = 14 cm. AE = 3.1 cm. CE = 12.8 cm. (a) Work out the length of DE. cm (b) Work out the length of BE. cm (Total 4 marks) Q13 EH3G Page 12

13 14. Diagram NOT B accurately drawn 39 O C A D A, B, C and D are points on the circumference of a circle, centre O. AOB is a diameter of the circle. Angle ABC = 39. (a) (i) Write down the size of angle AOC. (ii) Give a reason for your answer. (b) (i) Write down the size of angle ADC. (ii) Give a reason for your answer. (Total 4 marks) Q14 EH3G Page 13

14 people were asked to estimate the time between two bells ringing. The results are shown in the table. Estimated time (t s) Frequency 20 t < t < t < t < t < 70 8 (a) Complete the cumulative frequency table. Estimated time (t s) Cumulative Frequency 20 t < t < t < t < t < 70 (1) EH3G Page 14

15 (b) On the grid, draw a cumulative frequency graph for your table. Cumulative Frequency Estimated time (t s) (c) Use your graph to estimate the median time estimated by the people. s (1) The actual time between the bells was 53 s. (d) Use your graph to estimate how many people estimated a time of more than 53 s. (1) (Total 5 marks) Q15 EH3G Page 15

16 16. (a) Write in standard form (i) (ii) (iii) 1 20 (3) (b) Work out an estimate for the value of ( ) ( ) Give your answer in standard form. (3) (Total 6 marks) Q16 EH3G Page 16

17 17. (a) Expand 2y(y 2 + 4y) (b) Expand and simplify (p + 1)(p 3) (c) Factorise a 2 16 (Total 6 marks) Q17 EH3G Page 17

18 18. (a) Evaluate (i) (2 3 ) (ii) 9 (3) (b) Rationalise the denominator of 15 5 Give your answer in its simplest form. (Total 5 marks) Q Diagram NOT accurately drawn A 160 O 6 cm B OAB is a sector of a circle, centre O. Angle AOB = 160. The radius of the sector is 6 cm. Find the area of the sector. Give your answer in terms of π and state the units of your answer. Q19 (Total 4 marks) EH3G Page 18

19 20. Diagram NOT L 6b M accurately drawn 2a X O Y N OLMN is a trapezium with LM parallel to ON. OL = 2a, LM = 6b, and ON = 8b. X is the midpoint of OM. Y is the midpoint of ON. (a) Express, in terms of a and b, (i) (ii) OM OX (b) Show that XY is parallel to MN. (4) (Total 6 marks) Q20 EH3G Page 19

20 21. (a) On the grid, sketch the graph of y = sin x for 0 x 360. y 1 O x 1 (b) Here is a sketch of part of the graph of y = 3 cos x 1. y O x P Write down the coordinates of P. (, ) (Total 4 marks) Q21 EH3G Page 20

21 22. Solve the equation x 2 2x 7 = 0 Give your answers in the form a + b 2, where a and b are integers. Q22 (Total 4 marks) EH3G Page 21

22 23. (a) On the grid below, draw the graphs of x 2 + y 2 = 36 and y = 2x + 4 y O x (3) (b) Use your graphs to estimate the solutions of the simultaneous equations x 2 + y 2 = 36 y = 2x + 4 x = y = or x = y = (Total 5 marks) Q23 TOTAL FOR PAPER: 100 MARKS END EH3G Page 22