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

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1 For Edexcel Name GCSE Mathematics Paper 3C (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 EH3C 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 EH3C 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. Fiona and Javed are doing a project on pets. (a) Fiona writes a questionnaire for people who own a cat. This is one of her questions. Is your cat an indoor cat a short-haired cat a playful cat Write down one way in which this is not a good question. Javed wants to find out how often people who own a dog take it for a walk. Design a suitable question he could use. You should include response boxes. (Total 3 marks) Q1 EH3C Page 3

4 2. (a) Write down the inequality represented by the following diagram x Solve the inequality 4x + 3 < 15 (Total 3 marks) Q2 EH3C Page 4

5 3. B Diagram NOT accurately drawn 8 cm 8 cm A 6 cm C The diagram shows a sketch of an isosceles triangle, ABC. AB = BC = 8 cm. AC = 6 cm. (a) Make an accurate drawing of triangle ABC. The side AC has been drawn for you. You must show all your construction lines. A C Measure the size of angle ABC on your diagram. (Total 3 marks) Q3 EH3C Page 5

6 4. Students in Class P and Class Q complete the same homework. The two-way table shows information about the grades the students were given. Grade A Grade B Grade C Total Class P 8 7 Class Q 4 30 Total (a) Complete the two-way table. (3) A student is picked at random from Class Q. Write down the probability that the student got a Grade C on the homework. A student is picked at random from all those that got a Grade A on the homework. (c) Write down the probability that the student is in Class Q. (Total 6 marks) Q4 EH3C Page 6

7 5. (a) Diagram NOT A accurately drawn y C B x The lines AB and CD are parallel. (i) Write down the size of the angle marked x. (ii) Find the size of the angle marked y. D (3) z H 52 Diagram NOT accurately drawn G F E EFG is a straight line and EH = FH = FG. Angle EHF = 52. Find the size of the angle marked z. (3) (Total 6 marks) Q5 EH3C Page 7

8 6. y O x (a) Reflect the shaded rectangle in the y-axis. Label this image A. Rotate the shaded rectangle 180 about O. Label this image B. (Total 4 marks) Q6 EH3C Page 8

9 7. This cumulative frequency graph shows information about the ages of 40 cars. Cumulative Frequency O Age in years Use the graph to estimate (a) the median age of the cars, years the percentage of the cars that are more than 3 years old. % (3) (Total 4 marks) Q7 EH3C Page 9

10 8. y = x 5 x 3 (a) Work out the value of y when x = 4. y = Work out the value of x when y = 2. x = (3) (Total 5 marks) Q8 9. A company buys 16 computer monitors for 3464 Work out the cost of each monitor. Q9 (Total 3 marks) EH3C Page 10

11 10. (a) Solve 6x 7 = 17 x = Solve y y 1 2 = 1 y = (4) (Total 6 marks) Q (a) Work out Give your answer as a fraction in its simplest form. Work out Give your answer as a fraction in its simplest form. (3) (Total 5 marks) Q11 EH3C Page 11

12 12. Diagram NOT accurately drawn 8 cm 6 cm 4 cm The diagram shows the net of a triangular prism. Calculate the volume of the prism that can be formed from this net. State the units of your answer. Q12 (Total 4 marks) EH3C Page 12

13 13. Here are some expressions. a + 2c b + 2π ab + c 2 a(b + c) 2πb 3 c + 2 ab(c + 2) 2b(a 2 + c 2 ) a, b and c represent lengths. π and 2 are numbers which have no dimensions. Write down one of the expressions above which could be (a) a length, an area, (c) a volume. Q13 (Total 3 marks) 14. (a) Write 200 in standard form. Write as an ordinary number. (c) Work out ( ) ( ) Give your answer in standard form. (Total 4 marks) Q14 EH3C Page 13

14 15. Diagram NOT C D accurately drawn 10 cm B A 4 cm E ABCD is a square. ADE is a triangle. AE = 4cm. DE = 10 cm. Angle AED = 90. Work out the area of pentagon ABCDE. cm 2 Q15 (Total 4 marks) EH3C Page 14

15 16. Exton College has 420 students in year 12. This is 5% more than last year. Rhona says You can work out the number of year 12 students last year by calculating (a) Explain why Rhona is wrong. Work out the number of students in year 12 last year. (3) (Total 4 marks) Q16 EH3C Page 15

16 17. Solve the simultaneous equations y = 2x 2 y = 5x + 3 x = y = or x = y = Q17 (Total 4 marks) EH3C Page 16

17 18. In this question you may use the grid provided below but you are not required to do so. The locus of the point P is such that the distance of P from the point (1, 0) is equal to the distance of P from the point (5, 0). (a) Find an equation for the locus of P. The locus of the point Q is such that the distance of Q from the point (3, 1) is equal to the distance of Q from the point (6, 2). Find an equation for the locus of Q. (3) Q18 (Total 5 marks) EH3C Page 17

18 19. (a) Evaluate (i) (ii) 49 Write 20 in the form k 5, where k is an integer. (Total 4 marks) Q M is inversely proportional to f. When f = 3, M = 14. Find the value of f when M = 6. f = Q20 (Total 5 marks) EH3C Page 18

19 21. A Diagram NOT accurately drawn x B 3x 9 C Angle ABC = 90. AB = x cm. BC = 3x 9 cm. The area of triangle ABC is 15 cm 2. (a) Show that x 2 3x 10 = 0 (3) (i) Solve the equation x 2 3x 10 = 0 x = or x = (ii) Hence find the length of BC. cm (3) (Total 6 marks) Q21 EH3C Page 19

20 22. The histogram gives information about the distance, in metres, of 100 goalkicks. Frequency density (kicks per metre) O Distance (d m) Use the histogram to complete the table. Distance (d m) Frequency 0 d < d < d < d < d < 100 Q22 (Total 3 marks) EH3C Page 20

21 23. A Diagram NOT accurately drawn R P S O Q B OAB is a triangle. P lies on OA such that OP : OA = 1 : 3 Q lies on OB such that OQ : OB = 1 : 3 OP = p and OQ = q. (a) Find, in terms of p and q, the vectors (i) (ii) OA AB R and S lie on AB such AR = RS = SB. Prove that PR and QS are parallel. (4) (Total 6 marks) Q23 TOTAL FOR PAPER: 100 MARKS END EH3C Page 21