AQA A-LEVEL BUSINESS 1 PAPER 1 MARK SCHEME

AQA GCSE MATHEMATICS HIGHER TIER PAPER 3 H Monday 8 June 2020 Morning Time allowed: 1 hour 30 minutes Materials For this paper you must have: a calculator • mathematical instruments. 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. • If you need extra space for your answer(s), use the lined pages at the end of this book. Write the question number against your answer(s). • 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. *Jun20 3003H01* IB/M/Jun20/E7 8300/3H Answer all questions in the spaces provided. box 1 What does A U B represent in P(A U B) ? Circle your answer. [1 mark] A or B or both A but not B not A and not B A and B 2 Circle the equation of the line that is parallel to y = 1 x + 3 2 [1 mark] y = –2x y = 2x y = 1 x 2 y = – 1 x 2 3 Work out 320 as a percentage of 80 Circle your answer. [1 mark] 25% 75% 300% 400% 4 A fair coin is spun four times. Circle the probability of getting four Heads. [1 mark] box 1 2 2 1 8 1 16 5 To the nearest 1000, there are 18 000 people at a festival. 5 (a) Write down the minimum possible number of people at the festival. [1 mark] Answer 5 (b) Write down the maximum possible number of people at the festival. [1 mark] Answer Turn over for the next question Turn over ► box 7 Use Pythagoras’ theorem to work out the value of x. box Not drawn accurately [3 marks] Answer cm Turn over for the next question Turn over ► 8 Chris visits a library. He cycles to the library in half an hour at a speed of 12 miles per hour. He stays at the library for one hour. He then cycles home. The sketch graph represents his visit. Work out the speed, in miles per hour, at which Chris cycles home. [3 marks] Answer mph 9 These two triangles are similar. Not drawn accurately Work out the value of a. [2 marks] Answer cm 10 Expand and simplify fully 4(2c + 3) – (5c – 1) [2 marks] Answer *07* Turn over ► 11 A spinner can land on red, blue or green. After 350 spins relative frequency of red = 0.18 relative frequency of blue = 0.62 Work out the number of times the spinner landed on green. [3 marks] Answer *0* 12 Here is some information about 26 houses. a, b and c are all different numbers. box Number of bedrooms Number of houses 1 7 2 a 3 b 4 c 5 8 The median number of bedrooms is 3.5 Work out a possible set of values for a, b and c. [3 marks] a = b = c = Turn over ► 13 (a) Simplify 25a × 2a 8 5 Give your answer as a single fraction in its simplest form. [2 marks] Answer 13 (b) Sofia is trying to simplify 6c  10 2 Her method is divide 6c by 2 then add 10 Evaluate her method. [1 mark] 14 A rectangle has length 60 cm and width 40 cm Not drawn accurately The length decreases by 15% The width decreases by 10% Sue says, ‘‘The perimeter decreases by 25% because 15% + 10% is 25%’’ Is she correct? You must show calculations to support your answer. [4 marks] Turn over ► 15 Solve 4 > 11 – x 3 [2 marks] Answer 16 The number of goals scored by 20 players in a season is shown. Number of goals Frequency Midpoint 0 to 4 6 5 to 9 11 10 to 14 3 Total = 20 Work out an estimate of the mean number of goals per player. Give your answer as a decimal. [3 marks] Answer 17 Here are two rectangles. Not drawn accurately The area of the shaded rectangle is 1 the area of the large rectangle. 4 Work out the value of x. [4 marks] Answer Turn over ► 18 The pressure in a tyre is 30 pounds per square inch. Convert the pressure into kilograms per square centimetre. Use 1 pound = 0.45 kilograms and 1 inch = 2.54 centimetres [3 marks] Answer kg/cm2 19 The sketch shows the lines x = 1 and y = –3 Which pair of inequalities describes the shaded region? Tick one box. [1 mark] box x < 1 and y < –3 x < 1 and y > –3 x > 1 and y > –3 x > 1 and y < –3 Turn over for the next question Turn over ► 20 Amari and Ben each play a game. 20 (a) Here is some information about Amari’s scores. Lowest 12 Highest 20 Lower quartile 13 Upper quartile 19 Median 17 Draw a box plot to represent his scores. [2 marks] 20 (b) This box plot represents Ben’s scores. Who had more consistent scores, Amari or Ben? Work out the interquartile ranges to support your answer. [2 marks] Turn over for the next question *17* Turn over ► 21 (a) A and B are points on a circle. PA and PB are tangents. Not drawn accurately Work out the size of angle APB. [2 marks] Answer degrees *1* 21 (b) C, D and E are points on a different circle. Not drawn accurately Is X the centre of the circle? Tick a box. Yes No Show working to support your answer. [2 marks] Turn over for the next question Turn over ► 22 Visitors to a museum buy a child ticket or an adult ticket. Here is some information about two groups of visitors. Group X 250 visitors, including 120 children Group Y number of children : number of adults = 17 : 15 One visitor from each group is picked at random. Is this statement correct? box You must show your working. [4 marks] 23 In triangle JKL M is the midpoint of JK JN : NL = 3 : 2 K�L⃗ = 7a N�L⃗ = 4b Not drawn accurately Work out J��M�⃗ in terms of a and b. Give your answer in its simplest form. [3 marks] Answer Turn over for the next question Turn over ► 24 A and B are points on a curve. A is (2, 7) B is (12, 0) 24 (a) Work out the instantaneous rate of change of y with respect to x at point A. [2 marks] Answer 24 (b) The average rate of change of y with respect to x between points A and B is worked out. box Which statement is correct? Tick one box. [1 mark] It is positive. It is zero. It is negative. You cannot tell if it is positive or negative. 25 The equation of a circle is x2 + y2 = 9 Work out the length of the diameter. Circle your answer. 3 6 9 18 Turn over for the next question [1 mark] Turn over ► 26 • 313 Prove algebraically that 3.47 = 90 [3 marks] 27 The equation of a curve is y = (x – 1)2 – 6 Circle the coordinates of the turning point. [1 mark] (–1, –6) (1, 6) (–1, 6) (1, –6) 28 Line A has equation y = 4x – 1 Line B is perpendicular to line A and passes through the point (8, 5) Work out the coordinates of the point where line B intersects the x-axis. [4 marks] Answer ( , ) Turn over for the next question Turn over ► 29 A shape is made by joining triangle ABC to a semicircle with diameter AC. Not drawn accurately Work out the total area of the shape. [5 marks] Answer cm2 30 f(x) = 1 x g(x) = x – x2 2 Solve f –1(x) = gf(x) [4 marks] Answer END OF QUESTIONS *27* There are no questions printed on this page DO NOT WRITE ON THIS PAGE ANSWER IN THE SPACES PROVIDED box *2* box box Question number Additional page, if required. Write the question numbers in the left-hand margin. *31* box 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, all acknowledgements of third-party copyright material are published in a separate booklet. This booklet is published after each live examination series and is available for free download from . 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. Copyright © 2020 AQA and its licensors. All rights reserved. *32* *206g 300/3h*