Mathematics Module N6 Paper 1 (Non-calculator) Higher Tier am am [GMN61] 1 hour 15 minutes.

Transcription

1 Centre Number 71 Candidate Number General Certificate of Secondary Education 009 Mathematics Module N6 Paper 1 (Non-calculator) Higher Tier [GMN61] GMN61 MONDAY 1 JUNE 9.15 am am TIME 1 hour 15 minutes. INSTRUCTIONS TO CANDIDATES Write your Centre Number and Candidate Number in the spaces provided at the top of this page. Write your answers in the spaces provided in this question paper. Answer all twelve questions. Any working should be clearly shown in the spaces provided since marks may be awarded for partially correct solutions. You must not use a calculator for this paper. INFORMATION FOR CANDIDATES The total mark for this paper is 56. Figures in brackets printed down the right-hand side of pages indicate the marks awarded to each question or part question. You should have a ruler, compasses, set-square and protractor. The Formula Sheet is on page. 464 For Examiner s use only Question Number Total

2 Formula Sheet Area of trapezium = 1 (a + b)h a h b Volume of prism = area of cross section length In any triangle ABC Cross section A length Area of triangle = 1 ab sin C a b c Sine rule : = = sin A sin B sin C Cosine rule: a = b + c bc cos A B c a b C Volume of sphere = 4 3 πr 3 Surface area of sphere = 4πr r Volume of cone = 1 3 πr h Curved surface area of cone = πrl l r h Quadratic equation: The solutions of ax + bx + c = 0, where a 0, are given by x = b± b 4ac a 464 [Turn over

3 1 A spinner can point to the colours Red, Green, Yellow, Blue or Black. The probabilities for some of these are given in the table. Colour Red Green Yellow Blue Black Probability (a) What is the probability of getting the colour Yellow? Answer [] (b) If the spinner is spun 600 times, estimate how many times you would expect the colour to be Green. Answer [] Use the formula P QS = ( ) 8 to find the value of P when Q = 1 and S = 4 Answer [3] [Turn over

4 3 Side view Front view The diagram shows the front and side views of a 3-D solid consisting of 6 cubes. Draw (a) the plan of the solid, [] (b) the side elevation of the solid. [] [Turn over

5 4 (a) Estimate the answer to (i) Answer [] (ii) ( ) Answer [3] (b) Given that find = 15484, Answer [1] [Turn over

6 5 y B A D x 3 C (a) Describe fully the single transformation which takes Triangle A to Triangle B. [3] (b) Describe fully the single transformation which takes Triangle A to Triangle C. [] (c) Describe fully the single transformation which takes Triangle A to Triangle D. [3] [Turn over

7 6 (a) Make g the subject of the formula v = u + gt. Answer [] (b) Solve the inequality 6 < 3n for integer values of n. Answer n = [4] Diagrams not drawn accurately x The triangles are congruent. What is the size of angle x? Answer x = [1] [Turn over

8 8 (a) Prove that the square of any even number is a multiple of 4 [] (b) If x < 1 then x < 1 Give a counter example to disprove this statement. Answer [1] (c) Prove that (n 1)(n + 1) + n (n 1) n 1 [] [Turn over

9 9 (a) Write in standard form. Answer [1] (b) Write in standard form. Answer [1] (c) Find, in standard form, the value of (3 10 ) ( ) Answer [] [Turn over

10 10 On her way to work Rebekah passes through two sets of traffic lights. The probability that the first set is green when she reaches them is 0.7 and the probability that the second set is green is 0.6 (a) Complete the tree diagram for these events. 0.6 Green Green 0.7 Not Green Green Not Green Not Green [1] [Turn over

11 (b) Use the tree diagram to find the probability that, on a work day chosen at random, Rebekah had to stop at only one set of traffic lights. Answer [] [Turn over

12 11 (a) Show that ( ) = 50 [] (b) Change into a fraction. Answer [3] [Turn over

13 1 Mike takes cubes at random without replacement from a bag containing 7 red, 3 yellow and white cubes. What is the probability that (a) the first two cubes he takes are both yellow, Answer [3] (b) the first two cubes are the same colour as each other but the third is a different colour? Answer [4] THIS IS THE END OF THE QUESTION PAPER [Turn over

14 Centre Number 71 Candidate Number General Certificate of Secondary Education 009 Mathematics Module N6 Paper (With calculator) Higher Tier [GMN6] GMN6 TIME 1 hour 15 minutes. 465 MONDAY 1 JUNE am 1.00 noon INSTRUCTIONS TO CANDIDATES Write your Centre Number and Candidate Number in the spaces provided at the top of this page. Write your answers in the spaces provided in this question paper. Answer all sixteen questions. Any working should be clearly shown in the spaces provided since marks may be awarded for partially correct solutions. INFORMATION FOR CANDIDATES The total mark for this paper is 56. Figures in brackets printed down the right-hand side of pages indicate the marks awarded to each question or part question. You should have a calculator, ruler, compasses, set-square and protractor. The Formula Sheet is on page. For Examiner s use only Question Number Total

15 Formula Sheet Area of trapezium = 1 (a + b)h a h b Volume of prism = area of cross section length In any triangle ABC Cross section A length Area of triangle = 1 ab sin C a b c Sine rule : = = sin A sin B sin C Cosine rule: a = b + c bc cos A B c a b C Volume of sphere = 4 3 πr 3 Surface area of sphere = 4πr r Volume of cone = 1 3 πr h Curved surface area of cone = πrl l r h Quadratic equation: The solutions of ax + bx + c = 0, where a 0, are given by x = b± b 4ac a 465 [Turn over

16 1 A bag of 5 potatoes selected at random in a store has 4 bad potatoes. How many potatoes are expected to be bad out of a bag of 00 potatoes? Answer [] WXYZ is a trapezium. W 1.6 cm X 6.1 cm Z 8.5 cm Y Calculate the area of the trapezium. Give your answer to an appropriate degree of accuracy. Answer cm [3] [Turn over

17 3 (a) To feed 30 people John makes 0 beef sandwiches 36 cheese sandwiches 5 ham sandwiches How many of each would he need to make for 45 people? (b) 1 = $ and $5 = 3 Answer beef Answer cheese Answer ham [3] Which is cheaper, a camera bought for 36 or another bought for 4? Show your working. Answer: The camera bought for [] [Turn over

18 4 (a) Complete the table of values for y = x 3 x y [] (b) Hence draw the graph of y = x 3 y x 4 6 [] [Turn over

19 5 A piece of metal has a volume of 600 cm 3 and weighs 700 g. Calculate its density. Answer g/cm 3 [] [Turn over

20 6 An athlete goes for a run from Newtown to Oldtown and back. His journey is illustrated on the graph. Oldtown 1 10 distance from Newtown (km) Newtown Time (a) What is the athlete s speed on the return journey from Oldtown to Newtown? Answer km/hr [] (b) A second athlete leaves Oldtown at 1030 and runs towards Newtown, at a speed of 7 km/hr. (i) Illustrate his journey on the graph above. [3] (ii) At what time do the two athletes pass each other? Answer [1] [Turn over

21 7 In Westwood School there are 550 girls and 450 boys. The probability that a girl plays the piano is 0.3 and the probability that a boy plays the piano is 0.18 How many pupils at Westwood School play the piano? Answer [4] is divided between Lisa, Mikey and Richard in the ratio 8:1:6 How much does each get? Answer Lisa Answer Mikey Answer Richard [3] 9 Simplify (a) t 3 t 3 Answer [1] (b) r 6 r Answer [1] (c) 4x 1 y 3 x y Answer [] [Turn over

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23 1 h, l and r represent lengths. Complete the table below indicating whether the expressions could represent length area volume none of these 3πr h rl πrlh r 3 4πr (l + h) (l + r)(h r) [3] 50( q+ r) 13 Make r the subject of the formula p =. r Answer r = [4] [Turn over

24 14 The diagram shows a sector of a circle, radius 0 cm. Angle AOB = 144 A 0 cm O Diagram not drawn accurately B (a) Find, in terms of π, the arc length of the sector. Answer cm [3] The straight edges of the sector are joined together to form a cone with slant height 0 cm as shown below. 0 cm r (b) Find the radius, r, of the base of the cone. Answer cm [] [Turn over

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26 (b) Sketch the function y = f(3x) y x 1 3 [1] (c) Sketch the function y = f(x) 3 y x 1 3 [1] THIS IS THE END OF THE QUESTION PAPER