AQA GCSE MATHEMATICS Higher Tier Paper 1 Non-Calculator

AQA GCSE MATHEMATICS Higher Tier Paper 1 Non-Calculator Please write clearly in block capitals. Centre number Candidate number Surname Forename(s) Candidate signat ure H Tuesday 21 May 2019 Morning Time allowed: 1 hour 30 minutes Materials For this paper you must have: • mathematical instruments You must not use a calculator. Instructions • Use black ink or black ball-point pen. Draw diagrams in pencil. • Fill in the boxes at the top of this page. • Answer all questions. • You must answer the questions in the spaces provided. Do not write outside the box around each page or on blank pages. • Do all rough work in this book. Cross through any work you do not want to be marked. Information • The marks for questions are shown in brackets. • The maximum mark for this paper is 80. • You may ask for more answer paper, graph paper and tracing paper. These must be tagged securely to this answer book. Advice In all calculations, show clearly how you work out your answer. *Jun19 3001H01* IB/M/Jun19/E8 8300/1H Answer all questions in the spaces provided box 1 Here are two right-angled triangles. Circle the value of y. Not drawn accurately [1 mark] 11 7.5 9 4  2  2 2 Work out the value of 13    Circle your answer. [1 mark] 1 4 9 3 1 3 2 4 9 2 7 9 3 Work out the arc length, in metres, of a semicircle of radius 6 metres. Circle your answer. [1 mark] 3π 6π 12π 18π 4 Circle the fraction that is equivalent to 4.625 [1 mark] box 39 8 37 8 185 4 17 4 5 (a) Write 0.000 97 in standard form. [1 mark] Answer 5 (b) 3  105 Work out 4  103 Give your answer as an ordinary number. [2 marks] Answer Turn over ► 6 Anna plays a game with an ordinary, fair dice. If she rolls 1 she wins. If she rolls 2 or 3 she loses. If she rolls 4, 5 or 6 she rolls again. When she has to roll again, if she rolls an odd number she wins if she rolls an even number she loses. 6 (a) Complete the tree diagram with the four missing probabilities. [2 marks] 6 (b) Is Anna more likely to win or to lose? You must work out the probability that she wins. [4 marks] Turn over for the next question Turn over ► 7 Three friends arrive at a party. Their arrival increases the number of people at the party by 20% In total, how many people are now at the party? [2 marks] Answer 8 Work out the value of (312 ÷ 35) ÷ (32 × 3) [3 marks] Answer 9 A shaded semicircle is inside a circle as shown. Not drawn accurately The radius of the circle is 10 cm The diameter of the semicircle is 8 cm How many times bigger is the unshaded area than the shaded area? [4 marks] Answer Turn over for the next question *07* Turn over ► 10 The number of items, n, made in 1 hour by a machine is given by n = 60 t t is the time in minutes the machine takes to make one item. The value of t changes for different types of item. 10 (a) On the grid below, draw the graph of n = 60 for values of t from 1 to 4 t [2 marks] 10 (b) The machine takes 3 minutes 30 seconds to make one item. Use your graph to estimate the value of n. [2 marks] Answer *0* 11 Ed and Fay shared £330 in the ratio 7 : 4 Ed gives Fay some of his money. Fay now has the same amount as Ed. How much does Ed give Fay? [3 marks] Answer £ 12 The next term of a sequence is made by adding the previous two terms. Which of these sequences follows this rule? Circle your answer. [1 mark] –9 2 –7 –5 –12 –3 5 –2 3 1 0 –3 –3 0 –3 –1 –1 –2 –3 1 Turn over ► 13 The triangular cross section of a prism is an isosceles right-angled triangle. The volume of the prism is 102 cm3 Use approximations to estimate the value of x. You must show your working. [3 marks] Answer 14 Here is a quadrilateral. box a = 90° and a : b = 5 : 3 x : y = 1 : 3 Show that b = x Not drawn accurately [3 marks] Turn over ► 15 Here is some information about the test marks of 120 students. box Mark, m 0 < m ⩽ 10 10 < m ⩽ 20 20 < m ⩽ 30 30 < m ⩽ 40 40 < m ⩽ 50 Frequency 20 28 40 20 12 15 (a) Complete the cumulative frequency table. [1 mark] Mark, m m ⩽ 10 m ⩽ 20 m ⩽ 30 m ⩽ 40 m ⩽ 50 Cumulative frequency 20 48 15 (b) Draw a cumulative frequency graph. [2 marks] 15 (c) Students who scored 15 marks or fewer take another test. Use your graph to estimate how many students take another test. [2 marks] Answer 16 Simplify fully 4x  8x2 12x  6 [3 marks] Answer Turn over for the next question Turn over ► 17 Toby is forming and solving equations. 17 (a) The product of half of a number and three more than the number is the same as the square of the number Toby uses y to represent the number. Write an equation that Toby could form. [2 marks] Answer 17 (b) Toby forms another equation. x = 9 8x He wants to work out the values of x. Here is his working. x = 9 8x 8x2 = 9 8x = 3 or 8x = –3 x = 3 or x = – 3 8 8 What error has he made in his working? [1 mark] 18 Here is an identity. x2 – y2  (x + y)(x – y) 18 (a) Use the identity to work out the value of 1932 – 72 You must show your working. [2 marks] Answer 18 (b) Factorise 100a2 – 81b2 [1 mark] Answer 19 Circle the fraction that is equivalent to • 0.1 [1 mark] 1 9 1 99 1 10 11 100 Turn over ► 20 A, B and C are points on a circle. CD is a tangent. Not drawn accurately 20 (a) Assume that triangle ABC is isosceles with AC = BC Prove that AB is parallel to DC. [4 marks] 20 (b) In fact, triangle ABC is equilateral. Tick the two boxes for the statements that must be correct. [1 mark] box AB is parallel to DC AC bisects angle BCD AC bisects angle BAD *17* Turn over ► 22 ABC and ACD are triangles. k is a constant. Not drawn accurately 22 (a) Show that C�D�⃗ = 6a + 4.5b [1 mark] 22 (b) BCD is a straight line. Work out the value of k. You must show your working. [3 marks] Answer *1* 23 2 Simplify 84 ÷ 32 5 Give your answer in the form 2m where m is an integer. [3 marks] Answer 24 f(x) = sin(x – 90°) Circle the value of f(0°) [1 mark] 1 0  1 2 –1 Turn over for the next question Turn over ► 25 P (4, 8) is a point on a circle, centre O. The tangent at P intersects the axes at points A and B. Not drawn accurately 25 (a) Show that the gradient of the tangent is – 1 2 [2 marks] 25 (b) Work out the length AB. Give your answer in the form a 5 where a is an integer. You must show your working. [4 marks] Answer units Turn over for the next question Turn over ► 26 The turning point of the graph y = (x + a)2 + b has x-coordinate –2 (3, 1) is another point on the graph. Work out the y-coordinate of the turning point. [3 marks] Answer 27 Angle x is acute. cos x = sin 60° × tan 30° Work out the size of angle x. You must show your working. [3 marks] Answer degrees END OF QUESTIONS *23* There are no questions printed on this page DO NOT WRITE ON THIS PAGE ANSWER IN THE SPACES PROVIDED box Copyright information For confidentiality purposes, from the November 2015 examination series, acknowledgements of third-party copyright material are published in a separate booklet rather than including them on the examination paper or support materials. This booklet is published after each examination series and is available for free download from after the live examination series. Permission to reproduce all copyright material has been applied for. In some cases, efforts to contact copyright-holders may have been unsuccessful and AQA will be happy to rectify any omissions of acknowledgements. If you have any queries please contact the Copyright Team, AQA, Stag Hill House, Guildford, GU2 7XJ. Copyright © 2019 AQA and its licensors. All rights reserved. *24* *196g 300/1h*