3301/1H. General Certificate of Secondary Education June MATHEMATICS (SPECIFICATION A) 3301/1H Higher Tier Paper 1 Non-Calculator

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1 Surname Other Names Leave blank Centre Number Candidate Number Candidate Signature General Certificate of Secondary Education June 006 MATHEMATICS (SPECIFICATION A) 0/H Higher Tier Paper Non-Calculator H Monday 5 June pm to.0 pm For this paper you must have: mathematical instruments You must not use a calculator. Time allowed: hours Instructions Use blue or black ink or ball-point pen. Draw diagrams in pencil. Fill in the boxes at the top of this page. Answer all questions. Answer the questions in the spaces provided. Do all rough work in this booklet. Information The maximum mark for this paper is 00. The marks for questions are shown in brackets. You may ask for more answer paper, graph paper and tracing paper. This must be tagged securely to this answer booklet. Advice In all calculations, show clearly how you work out your answer. For Examiner s Use Pages Mark TOTAL Examiner s Initials 0/H

2 Formulae Sheet: Higher Tier You may need to use the following formulae: Volume of prism = area of cross-section length crosssection length 4 Volume of sphere = π r r Surface area of sphere = 4 π r Volume of cone = π r h Curved surface area of cone = π rl l r h In any triangle ABC Area of triangle = ab sin C a b c Sine rule = = sin A sin B sin C Cosine rule a = b + c bc cos A A b c C a B The Quadratic Equation The solutions of ax + bx + c = 0, where a 0, are given by b ± (b 4ac) x = a

3 Answer all questions in the spaces provided. The diagrams show a sequence of rectangles. Area = Diagram Area = 6 Diagram Area = Diagram Area = 0 Diagram 4 (a) Write down an expression for the area of Diagram n. (b) A rectangle in the sequence has an area of 0 cm. What is its perimeter? Answer... cm Turn over for the next question Turn over 4

4 4 (a) Expand and simplify 7(x y) (x y) 4 x (b) Solve = 5 Answer x =... (c) (i) Factorise y 5y + 6 (ii) Hence solve the equation y 5y + 6 = 0 ( mark) (x + ) (d) Simplify 8(x + )

5 5 (e) Simplify (m p) 4 (a) Work out the reciprocal of.5 Give your answer as a fraction in its simplest form. (b) Use approximations to estimate the value of You must show your working ( marks) 5 (c) Work out 4 ( marks) Turn over 9

6 6 4 The diagram shows four shapes, A, B, C and D. y B C A 4 O x D 4 (a) Describe fully the single transformation that takes shape A onto shape B.

7 7 (b) Describe fully the single transformation that takes shape B onto shape C. ( marks) (c) Describe fully the single transformation that takes shape C onto shape D. ( marks) (a) Which one of, and is a recurring decimal? 9 0 Show clearly how you made your decision. (b) Change to a recurring decimal. Turn over

8 8 6 The frequency polygon shows the number of hours of television watched each week by 0 teachers Frequency Number of hours (h) (a) The number of hours of television watched each week by 0 students is shown below. Number of hours (h) Frequency 0 h 5 5 h 0 0 h h h h 0 4 On the same grid draw a frequency polygon to show this information.

9 9 (b) Give two comparisons between the number of hours of television watched by these teachers and students. Comparison Comparison 7 (a) The ratio : 50 can be written in the form n : Work out the value of n. Give your answer in standard form. Answer n =... (b) Solve the equation y 0 6 =.5 0 Give your answer in standard form. Answer y =... Turn over 8

10 0 8 Match each of the shaded regions to one of these inequalities. A y x + D y x 4 B y x + E y x 4 C y x y 6 y O x O x 6 y 6 y O x O x Region... Region... Region... Region 4... (4 marks)

11 9 Make u the subject of the formula s = (u + v) t Answer u =... ( marks) 0 In the diagram SR is parallel to PT. SQT and RQP are straight lines. SR = 0 cm and PT = 0 cm The total height of the two triangles is 40 cm. S 0 cm R Not drawn accurately Q 40 cm h P 0 cm T Use similar triangles to calculate the height, h cm, of triangle PQT Answer h =... cm ( marks) Turn over 0

12 A factory employs 50 men and 00 women. Each person s job is given a grade, A, B, C or D. The diagrams show the proportion at each grade for both men and women. Men (50 employees) A B C D 0% 4% 60% 88% 00% Women (00 employees) A B C D 0% 9% 48% 8% 00% A 0% sample is taken of the employees, stratified by sex and by grade. Complete the table to show how many of each group should be sampled. Men Women A B C D (4 marks)

13 XYZ is an isosceles triangle in which XZ = XY M and N are points on XZ and XY such that angle MYZ = angle NZY X N M Y Z Prove that triangles YMZ and ZNY are congruent (4 marks) Turn over 8

14 4 The grid shows the graph of y = x + x 5 y 4 4 O x 4 6 By drawing an appropriate straight line, solve the equation x + x 5 = x ( marks)

15 5 4 The diagram shows a cuboid. AB = cm, AE = 4 cm, BC = cm. H G E D 4 cm F C A cm B y x cm Not drawn accurately (a) Find the length of BH. Answer... cm (b) The angle between BH and BD is x and the angle between BH and BC is y. Which angle is bigger, x or y? You must show your working. ( marks) Turn over 8

16 6 5 Ian and Simon play each other in a darts match. The match consists of three games. The winner of the match is the first player to win two games. The tree diagram shows all the possible outcomes. I wins means that Ian wins the game. S wins means that Simon wins the game. st game nd game rd game 0.5 I wins I wins S wins I wins S wins 0.5 S wins I wins S wins I wins S wins The probability that Ian wins the first game is 0.5 Whenever Ian wins a game the probability that he wins the next game is 0.7 Whenever Simon wins a game the probability that he wins the next game is 0.6 (a) (b) Complete the tree diagram. Calculate the probability that Ian wins the darts match. (4 marks)

17 7 6 (a) Simplify (i) w w 6 ( mark) (ii) w 0 w 4 ( mark) (iii) ( w 4 ) ( mark) (b) If x = p and y = q Express in terms of x and/or y (i) p q ( mark) (ii) p ( mark) (iii) q + ( mark) Turn over

18 8 7 In an experiment measurements of t and m were taken. The results were as follows: t.4 m The results are connected by one of these rules. A t α m B t α C t α m m Which rule is the correct one? State your answer clearly. You must show your working (4 marks)

19 9 8 (a) Show that ( + ) = 7 (b) In the diagram PQ = ( + ) cm QS = ( 8 + ) cm SR = cm P Not drawn accurately ( + ) cm Q ( 8 + ) cm S cm R (i) Show that PS = cm (4 marks) (ii) Find the area of triangle PQR giving your answer in the form a, where a is a positive integer. Answer... cm ( marks) Turn over

20 0 9 A sphere has radius r. A cone has base radius r and perpendicular height x. The volume of the sphere is double the volume of the cone. Not drawn accurately r x r (a) Show that x = r (b) Calculate the ratio of the surface area of the sphere to the curved surface area of the cone. Give your answer in surd form. (4 marks) END OF QUESTIONS Copyright 006 AQA and its licensors. All rights reserved. 6