Excel / Education. GCSE Mathematics. Paper 3A (Non-Calculator) Higher Tier. Time: 2 hours. Turn over

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1 Excel / Education GCSE Mathematics Paper 3A (Non-Calculator) Higher Tier Time: 2 hours 3A Materials required for examination Ruler graduated in centimetres and millimetres, protractor, compasses, pen, HB pencil, eraser. Tracing paper may be used. Items included with question papers Formulae sheet Instructions to Candidates Answer ALL the questions in the spaces provided in this question paper. Supplementary answer sheets may be used. Information for Candidates The total mark for this paper is 100. The marks for questions and parts of questions are shown in round brackets: e.g.. Calculators must not be used. Advice to Candidates Show all your working.

2 1. Given that x is an integer and -1 x < 5 Write down all the possible values of x A tractor wheel has a circumference of 4m. While ploughing a field, the tractor travels a total of 1.1 km. How many complete turns does the tractor wheel make? 3. The equation of a line is y = 8 2x.. (4) (a) Complete the following table of values for this equation. x y 8 (b) Use the grid on the next page to plot the graph of y = 8 2x

3 y x (c) What is the gradient of this line?.. (1) 4. The following table gives ages of contestants in a painting competition. Age Number of contestants Cumulative frequency

4 (a) Complete the cumulative frequency column of the table (b) On the grid (below), draw a cumulative frequency diagram to represent the data. cf age (c) Use your diagram to estimate; (4) (i) (ii) The median The inter-quartile range (1)

5 5. The diagram below shows a regular pentagon; x Calculate the size of an interior angle of the regular pentagon (marked x in the diagram). 6. (a) Write the following in standard form; (i) 2,000,000.. (4) (ii) (1) (b) Using your answers to part (a) or otherwise, work out (1) 2,000,000 x (1)

6 7. In a class, 1 4 of the students have blonde hair and 1 have black hair. 3 3 of the blonde students wear glasses and no other students wear glasses. 5 (a) What fraction of the students have neither blonde nor black hair? (b) What fraction of the students wear glasses? 8. y 65 o x (a) Calculate the size of angle x. Give a reason for your answer. (b) Calculate the size of angle y. Give a reason for your answer.

7 9. Solve; (a) 4x + 5 = x + 17 (b) 4(5x 2) = 2 x = (c) x = 8 x = (d) 2x 10 4 = 3x x = x = 10. On her way to work, Jackie passes two sets of traffic lights. The probability 2 1 that the first set is red is and the probability that the second set is red is 5 3. (a) Complete the probability tree over the page;

8 Red 2 / 5. 1 / 3 Red. Not Red Red Not Red. (b) Not Red. Work out the probability that exactly one of the sets of lights is red Solve 4 < x

9 12. A C Diagram NOT accurately drawn O B 50 D O is the centre of the circle and AB is the diameter. DB and DC are tangents to the circle at B and C respectively. (a) Calculate the size of angle ABC. Give reasons for your answer. (b) Calculate the size of angle BDC. Give reasons for your answer. (c) Calculate the size of angle BAC. Give reasons for your answer.

10 13. A ship sails from port P, 10km north and 10km east to an island Q. O 10km Q 10km P On what bearing must the ship sail to return directly to port P? 14. x is proportional to y. When x = 100, y = 5 o (4) (a) Find an equation connecting x and y (b) Find the value of y when x =

11 15. y A x (a) Draw the image of triangle A after it has been rotated 90 o anticlockwise about the point (1, 2). Label this triangle B.... (b) Draw the image of triangle A after an enlargement, scale factor 1.5, centre the origin. Label this triangle C. 16. Show that the sum of any four consecutive even numbers is always divisible by (4)

12 17. r This hemisphere has a total surface area of 27π cm 2. Find the value of r. (4) 18. (x 3) m x m 2 m x m 2 m (x + 2)m The cube and the triangular prism above have the same volume. (i) Find the value of x. m (4)

13 (ii) Hence find the volume of the cuboid. m (i) Write x 2 + 4x + 6 in the form (x + p) 2 + q where p and q are integers to be found. (ii).. Use your answer to (i) to explain why the equation x 2 + 4x + 6 = 0 has no real solutions. End of Questions (Total Marks: 100)

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