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 Thursday 24 May 2018 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. *jun1 3001H01* IB/M/Jun18/E8 8300/1H Answer all questions in the spaces provided outside the box 1 Work out Circle your answer. 40 80 400 4000 2 The vector  2  translates A to B. [1 mark]    3  Circle the vector that translates B to A.  2     3   3     2   3   2    2   3   3 Circle the expression that is equivalent to 3a – a × 4a + 2a [1 mark] [1 mark] 8a2 + 2a 12a2 5a – 4a2 3a – 6a2 4 Circle the number that is closest in value to 9.8 0.0195 [1 mark] outside the box 5 50 500 5000 5 Solve 5(x + 3) 60 [2 marks] Answer Turn over for the next question Turn over ► box 7 A (0, 2) and B (6, 5) are points on the straight line ABCD. AB = BC = CD Work out the coordinates of D. Not drawn accurately [3 marks] box Answer ( , ) Turn over for the next question Turn over ► 8 A coin is thrown 50 times. It lands on heads 31 times. 8 (a) Write down the relative frequency it lands on heads. [1 mark] Answer 8 (b) Raj says, “The coin is biased towards heads.” Use the data to give a reason why he might be correct. [1 mark] 9 The range of a set of numbers is 15 1 4 The smallest number is –2 7 8 Work out the largest number. [3 marks] Answer 10 y is inversely proportional to x. Complete the table. [2 marks] x 12 6 y 4 8 Turn over for the next question *07* Turn over ► 11 A large rectangle is made by joining three identical small rectangles as shown. Not drawn accurately The perimeter of one small rectangle is 15 cm Work out the perimeter of the large rectangle. [4 marks] Answer cm *0* 12 Put these numbers in order from smallest to largest. 8 × 10–4 4 × 10–2 6 × 10–4 0.07 [2 marks] Smallest Largest 13 Circle the volume that is the same as 15 cm3 [1 mark] 15 000 mm3 1.5 mm3 0.0015 mm3 150 mm3 Turn over for the next question Turn over ► 14 (a) More rows are added to Pattern B so that number of straight lines : number of arcs = 10 : 9 How many rows are added? [2 marks] Answer 14 (b) A different pattern is made using 20 straight lines and 16 arcs. The straight lines and arcs are made from metal. 20 straight lines cost £12 cost of one straight line : cost of one arc = 2 : 3 Work out the total cost of the metal in the pattern. [3 marks] Answer £ Turn over for the next question Turn over ► 15 A biased dice is thrown. Here are the probabilities of each score. box Score 1 2 3 4 5 6 Probability 0.25 0.05 0.15 0.05 0.3 0.2 The dice is thrown 200 times. Work out the expected number of times the score will be odd. [3 marks] Answer 16 The value of y is 20% more than the value of x. Circle the ratio x : y 5 : 6 6 : 5 4 : 5 5 : 4 17 Here is a triangle. [1 mark] box Circle the correct equation. Not drawn accurately [1 mark] sin x = sin 15º 42 104 x = 15 sin 42º sin 104º sin x = sin 15º 34 104 x = 15 sin 42º sin 34º Turn over ► 18 Here is a tunnel for a toy train. The diagram below shows the cross section of the tunnel. Not drawn accurately AD is a semicircular arc of radius 10 cm BC is a semicircular arc of radius 7 cm The length of the tunnel is 30 cm Work out the total area of all six faces of the tunnel. Give your answer in terms of π. [5 marks] Turn over ► 19 Type A batteries and type B batteries were tested. The cumulative frequency diagram shows information about the battery life of type A. 19 (a) Estimate the interquartile range for type A. [2 marks] Answer hours 19 (b) Estimate the number of type A batteries that had a battery life of more than 1600 hours. [1 mark] Answer 19 (c) The box plot shows information about the battery life of type B. On average, which type had the greater battery life? Tick a box. type A type B Using data from both diagrams, state how you chose your answer. [2 marks] *17* Turn over ► 20 A linear sequence starts a + 2b a + 6b a + 10b …….. …….. The 2nd term has value 8 The 5th term has value 44 Work out the values of a and b. [4 marks] a = b = *1* 21 Enlarge triangle ABC by scale factor –2, centre (4, 1) [2 marks] 22 Which of these represents the shaded region? Circle your answer. [1 mark] A ∩ B/ B/ A U B/ A/ U B/ Turn over ► 23 A shopkeeper compares the income from sales of a laptop in March and April. box April Price 1 more than March 5 Number sold 1 less than March 4 By what fraction does the income from these sales decrease in April? [3 marks] Answer 24 (a) 14  9 2 Work out the value of 2 ÷  2    Give your answer as a fraction in its simplest form. [3 marks] Answer 24 (b) 3 Work out the value of 25 2 [2 marks] Answer Turn over for the next question Turn over ► 25 Here is a sketch of the graph of y = cos x for values of x from 0° to 360° 25 (a) cos x = cos 60° Work out the value of x when 90° ⩽ x ⩽ 360° [1 mark] Answer degrees 25 (b) cos x = – cos 60° Work out the value of x when 180° ⩽ x ⩽ 360° [1 mark] Answer degrees 26 b is two thirds of c. 5a = 4c Work out the ratio a : b : c Give your answer in its simplest form where a, b and c are integers. [3 marks] box Answer : : Turn over for the next question Turn over ► 27 (a) Jo wants to work out the solutions of x2 + 3x – 5 = 0 She says, ‘‘The solutions cannot be worked out because x2 + 3x – 5 does not factorise to (x + a)(x + b) where a and b are integers.’’ Is Jo correct? Tick a box. Yes No Give a reason for your answer. [1 mark] 27 (b) Without expanding any brackets, show how to work out the exact solutions of 9(x + 3)2 = 4 Give the solutions. [3 marks] 2 28 Simplify 80 + 2 9 Give your answer in the form a 5 where a and b are integers. b [3 marks] Answer Turn over for the next question Turn over ► 29 Here are sketches of two graphs. The graph of y = x2 – 1 is translated 3 units to the left to give graph A. 29 (a) The equation of graph A can be written in the form Work out the values of b and c. y = x2 + bx + c [3 marks] b = c = 29 (b) The graph of y = x2 – 1 is reflected in the x-axis to give graph B. Work out the equation of graph B. [1 mark] Answer 30 Show that the value of cos 30° × tan 60° + sin 30° is an integer. [3 marks] END OF QUESTIONS *27* There are no questions printed on this page Please write clearly in block capitals. Centre number Candidate number Surname Forename(s) Candidate signat ure H Thursday 24 May 2018 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. *jun1 3001H01* IB/M/Jun18/E8 8300/1H Answer all questions in the spaces provided outside the box 1 Work out Circle your answer. 40 80 400 4000 2 The vector  2  translates A to B. [1 mark]    3  Circle the vector that translates B to A.  2     3   3     2   3   2    2   3   3 Circle the expression that is equivalent to 3a – a × 4a + 2a [1 mark] [1 mark] 8a2 + 2a 12a2 5a – 4a2 3a – 6a2 4 Circle the number that is closest in value to 9.8 0.0195 [1 mark] outside the box 5 50 500 5000 5 Solve 5(x + 3) 60 [2 marks] Answer Turn over for the next question Turn over ► box 7 A (0, 2) and B (6, 5) are points on the straight line ABCD. AB = BC = CD Work out the coordinates of D. Not drawn accurately [3 marks] box Answer ( , ) Turn over for the next question Turn over ► 8 A coin is thrown 50 times. It lands on heads 31 times. 8 (a) Write down the relative frequency it lands on heads. [1 mark] Answer 8 (b) Raj says, “The coin is biased towards heads.” Use the data to give a reason why he might be correct. [1 mark] 9 The range of a set of numbers is 15 1 4 The smallest number is –2 7 8 Work out the largest number. [3 marks] Answer 10 y is inversely proportional to x. Complete the table. [2 marks] x 12 6 y 4 8 Turn over for the next question *07* Turn over ► 11 A large rectangle is made by joining three identical small rectangles as shown. Not drawn accurately The perimeter of one small rectangle is 15 cm Work out the perimeter of the large rectangle. [4 marks] Answer cm *0* 12 Put these numbers in order from smallest to largest. 8 × 10–4 4 × 10–2 6 × 10–4 0.07 [2 marks] Smallest Largest 13 Circle the volume that is the same as 15 cm3 [1 mark] 15 000 mm3 1.5 mm3 0.0015 mm3 150 mm3 Turn over for the next question Turn over ► 14 (a) More rows are added to Pattern B so that number of straight lines : number of arcs = 10 : 9 How many rows are added? [2 marks] Answer 14 (b) A different pattern is made using 20 straight lines and 16 arcs. The straight lines and arcs are made from metal. 20 straight lines cost £12 cost of one straight line : cost of one arc = 2 : 3 Work out the total cost of the metal in the pattern. [3 marks] Answer £ Turn over for the next question Turn over ► 15 A biased dice is thrown. Here are the probabilities of each score. box Score 1 2 3 4 5 6 Probability 0.25 0.05 0.15 0.05 0.3 0.2 The dice is thrown 200 times. Work out the expected number of times the score will be odd. [3 marks] Answer 16 The value of y is 20% more than the value of x. Circle the ratio x : y 5 : 6 6 : 5 4 : 5 5 : 4 17 Here is a triangle. [1 mark] box Circle the correct equation. Not drawn accurately [1 mark] sin x = sin 15º 42 104 x = 15 sin 42º sin 104º sin x = sin 15º 34 104 x = 15 sin 42º sin 34º Turn over ► 18 Here is a tunnel for a toy train. The diagram below shows the cross section of the tunnel. Not drawn accurately AD is a semicircular arc of radius 10 cm BC is a semicircular arc of radius 7 cm The length of the tunnel is 30 cm Work out the total area of all six faces of the tunnel. Give your answer in terms of π. [5 marks] Turn over ► 19 Type A batteries and type B batteries were tested. The cumulative frequency diagram shows information about the battery life of type A. 19 (a) Estimate the interquartile range for type A. [2 marks] Answer hours 19 (b) Estimate the number of type A batteries that had a battery life of more than 1600 hours. [1 mark] Answer 19 (c) The box plot shows information about the battery life of type B. On average, which type had the greater battery life? Tick a box. type A type B Using data from both diagrams, state how you chose your answer. [2 marks] *17* Turn over ► 20 A linear sequence starts a + 2b a + 6b a + 10b …….. …….. The 2nd term has value 8 The 5th term has value 44 Work out the values of a and b. [4 marks] a = b = *1* 21 Enlarge triangle ABC by scale factor –2, centre (4, 1) [2 marks] 22 Which of these represents the shaded region? Circle your answer. [1 mark] A ∩ B/ B/ A U B/ A/ U B/ Turn over ► 23 A shopkeeper compares the income from sales of a laptop in March and April. box April Price 1 more than March 5 Number sold 1 less than March 4 By what fraction does the income from these sales decrease in April? [3 marks] Answer 24 (a) 14  9 2 Work out the value of 2 ÷  2    Give your answer as a fraction in its simplest form. [3 marks] Answer 24 (b) 3 Work out the value of 25 2 [2 marks] Answer Turn over for the next question Turn over ► 25 Here is a sketch of the graph of y = cos x for values of x from 0° to 360° 25 (a) cos x = cos 60° Work out the value of x when 90° ⩽ x ⩽ 360° [1 mark] Answer degrees 25 (b) cos x = – cos 60° Work out the value of x when 180° ⩽ x ⩽ 360° [1 mark] Answer degrees 26 b is two thirds of c. 5a = 4c Work out the ratio a : b : c Give your answer in its simplest form where a, b and c are integers. [3 marks] box Answer : : Turn over for the next question Turn over ► 27 (a) Jo wants to work out the solutions of x2 + 3x – 5 = 0 She says, ‘‘The solutions cannot be worked out because x2 + 3x – 5 does not factorise to (x + a)(x + b) where a and b are integers.’’ Is Jo correct? Tick a box. Yes No Give a reason for your answer. [1 mark] 27 (b) Without expanding any brackets, show how to work out the exact solutions of 9(x + 3)2 = 4 Give the solutions. [3 marks] 2 28 Simplify 80 + 2 9 Give your answer in the form a 5 where a and b are integers. b [3 marks] Answer Turn over for the next question Turn over ► 29 Here are sketches of two graphs. The graph of y = x2 – 1 is translated 3 units to the left to give graph A. 29 (a) The equation of graph A can be written in the form Work out the values of b and c. y = x2 + bx + c [3 marks] b = c = 29 (b) The graph of y = x2 – 1 is reflected in the x-axis to give graph B. Work out the equation of graph B. [1 mark] Answer 30 Show that the value of cos 30° × tan 60° + sin 30° is an integer. [3 marks] END OF QUESTIONS *27* 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 will be 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 © 2018 AQA and its licensors. All rights reserved. *2* Please write clearly in block capitals. Centre number Candidate number Surname Forename(s) Candidate signat ure H Thursday 24 May 2018 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. *jun1 3001H01* IB/M/Jun18/E8 8300/1H Answer all questions in the spaces provided outside the box 1 Work out Circle your answer. 40 80 400 4000 2 The vector  2  translates A to B. [1 mark]    3  Circle the vector that translates B to A.  2     3   3     2   3   2    2   3   3 Circle the expression that is equivalent to 3a – a × 4a + 2a [1 mark] [1 mark] 8a2 + 2a 12a2 5a – 4a2 3a – 6a2 4 Circle the number that is closest in value to 9.8 0.0195 [1 mark] outside the box 5 50 500 5000 5 Solve 5(x + 3) 60 [2 marks] Answer Turn over for the next question Turn over ► box 7 A (0, 2) and B (6, 5) are points on the straight line ABCD. AB = BC = CD Work out the coordinates of D. Not drawn accurately [3 marks] box Answer ( , ) Turn over for the next question Turn over ► 8 A coin is thrown 50 times. It lands on heads 31 times. 8 (a) Write down the relative frequency it lands on heads. [1 mark] Answer 8 (b) Raj says, “The coin is biased towards heads.” Use the data to give a reason why he might be correct. [1 mark] 9 The range of a set of numbers is 15 1 4 The smallest number is –2 7 8 Work out the largest number. [3 marks] Answer 10 y is inversely proportional to x. Complete the table. [2 marks] x 12 6 y 4 8 Turn over for the next question *07* Turn over ► 11 A large rectangle is made by joining three identical small rectangles as shown. Not drawn accurately The perimeter of one small rectangle is 15 cm Work out the perimeter of the large rectangle. [4 marks] Answer cm *0* 12 Put these numbers in order from smallest to largest. 8 × 10–4 4 × 10–2 6 × 10–4 0.07 [2 marks] Smallest Largest 13 Circle the volume that is the same as 15 cm3 [1 mark] 15 000 mm3 1.5 mm3 0.0015 mm3 150 mm3 Turn over for the next question Turn over ► 14 (a) More rows are added to Pattern B so that number of straight lines : number of arcs = 10 : 9 How many rows are added? [2 marks] Answer 14 (b) A different pattern is made using 20 straight lines and 16 arcs. The straight lines and arcs are made from metal. 20 straight lines cost £12 cost of one straight line : cost of one arc = 2 : 3 Work out the total cost of the metal in the pattern. [3 marks] Answer £ Turn over for the next question Turn over ► 15 A biased dice is thrown. Here are the probabilities of each score. box Score 1 2 3 4 5 6 Probability 0.25 0.05 0.15 0.05 0.3 0.2 The dice is thrown 200 times. Work out the expected number of times the score will be odd. [3 marks] Answer 16 The value of y is 20% more than the value of x. Circle the ratio x : y 5 : 6 6 : 5 4 : 5 5 : 4 17 Here is a triangle. [1 mark] box Circle the correct equation. Not drawn accurately [1 mark] sin x = sin 15º 42 104 x = 15 sin 42º sin 104º sin x = sin 15º 34 104 x = 15 sin 42º sin 34º Turn over ► 18 Here is a tunnel for a toy train. The diagram below shows the cross section of the tunnel. Not drawn accurately AD is a semicircular arc of radius 10 cm BC is a semicircular arc of radius 7 cm The length of the tunnel is 30 cm Work out the total area of all six faces of the tunnel. Give your answer in terms of π. [5 marks] Turn over ► 19 Type A batteries and type B batteries were tested. The cumulative frequency diagram shows information about the battery life of type A. 19 (a) Estimate the interquartile range for type A. [2 marks] Answer hours 19 (b) Estimate the number of type A batteries that had a battery life of more than 1600 hours. [1 mark] Answer 19 (c) The box plot shows information about the battery life of type B. On average, which type had the greater battery life? Tick a box. type A type B Using data from both diagrams, state how you chose your answer. [2 marks] *17* Turn over ► 20 A linear sequence starts a + 2b a + 6b a + 10b …….. …….. The 2nd term has value 8 The 5th term has value 44 Work out the values of a and b. [4 marks] a = b = *1* 21 Enlarge triangle ABC by scale factor –2, centre (4, 1) [2 marks] 22 Which of these represents the shaded region? Circle your answer. [1 mark] A ∩ B/ B/ A U B/ A/ U B/ Turn over ► 23 A shopkeeper compares the income from sales of a laptop in March and April. box April Price 1 more than March 5 Number sold 1 less than March 4 By what fraction does the income from these sales decrease in April? [3 marks] Answer 24 (a) 14  9 2 Work out the value of 2 ÷  2    Give your answer as a fraction in its simplest form. [3 marks] Answer 24 (b) 3 Work out the value of 25 2 [2 marks] Answer Turn over for the next question Turn over ► 25 Here is a sketch of the graph of y = cos x for values of x from 0° to 360° 25 (a) cos x = cos 60° Work out the value of x when 90° ⩽ x ⩽ 360° [1 mark] Answer degrees 25 (b) cos x = – cos 60° Work out the value of x when 180° ⩽ x ⩽ 360° [1 mark] Answer degrees 26 b is two thirds of c. 5a = 4c Work out the ratio a : b : c Give your answer in its simplest form where a, b and c are integers. [3 marks] box Answer : : Turn over for the next question Turn over ► 27 (a) Jo wants to work out the solutions of x2 + 3x – 5 = 0 She says, ‘‘The solutions cannot be worked out because x2 + 3x – 5 does not factorise to (x + a)(x + b) where a and b are integers.’’ Is Jo correct? Tick a box. Yes No Give a reason for your answer. [1 mark] 27 (b) Without expanding any brackets, show how to work out the exact solutions of 9(x + 3)2 = 4 Give the solutions. [3 marks] 2 28 Simplify 80 + 2 9 Give your answer in the form a 5 where a and b are integers. b [3 marks] Answer Turn over for the next question Turn over ► 29 Here are sketches of two graphs. The graph of y = x2 – 1 is translated 3 units to the left to give graph A. 29 (a) The equation of graph A can be written in the form Work out the values of b and c. y = x2 + bx + c [3 marks] b = c = 29 (b) The graph of y = x2 – 1 is reflected in the x-axis to give graph B. Work out the equation of graph B. [1 mark] Answer 30 Show that the value of cos 30° × tan 60° + sin 30° is an integer. [3 marks] END OF QUESTIONS *27* 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 will be 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 © 2018 AQA and its licensors. All rights reserved. *2* Please write clearly in block capitals. Centre number Candidate number Surname Forename(s) Candidate signat ure H Thursday 24 May 2018 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. *jun1 3001H01* IB/M/Jun18/E8 8300/1H Answer all questions in the spaces provided outside the box 1 Work out Circle your answer. 40 80 400 4000 2 The vector  2  translates A to B. [1 mark]    3  Circle the vector that translates B to A.  2     3   3     2   3   2    2   3   3 Circle the expression that is equivalent to 3a – a × 4a + 2a [1 mark] [1 mark] 8a2 + 2a 12a2 5a – 4a2 3a – 6a2 4 Circle the number that is closest in value to 9.8 0.0195 [1 mark] outside the box 5 50 500 5000 5 Solve 5(x + 3) 60 [2 marks] Answer Turn over for the next question Turn over ► box 7 A (0, 2) and B (6, 5) are points on the straight line ABCD. AB = BC = CD Work out the coordinates of D. Not drawn accurately [3 marks] box Answer ( , ) Turn over for the next question Turn over ► 8 A coin is thrown 50 times. It lands on heads 31 times. 8 (a) Write down the relative frequency it lands on heads. [1 mark] Answer 8 (b) Raj says, “The coin is biased towards heads.” Use the data to give a reason why he might be correct. [1 mark] 9 The range of a set of numbers is 15 1 4 The smallest number is –2 7 8 Work out the largest number. [3 marks] Answer 10 y is inversely proportional to x. Complete the table. [2 marks] x 12 6 y 4 8 Turn over for the next question *07* Turn over ► 11 A large rectangle is made by joining three identical small rectangles as shown. Not drawn accurately The perimeter of one small rectangle is 15 cm Work out the perimeter of the large rectangle. [4 marks] Answer cm *0* 12 Put these numbers in order from smallest to largest. 8 × 10–4 4 × 10–2 6 × 10–4 0.07 [2 marks] Smallest Largest 13 Circle the volume that is the same as 15 cm3 [1 mark] 15 000 mm3 1.5 mm3 0.0015 mm3 150 mm3 Turn over for the next question Turn over ► 14 (a) More rows are added to Pattern B so that number of straight lines : number of arcs = 10 : 9 How many rows are added? [2 marks] Answer 14 (b) A different pattern is made using 20 straight lines and 16 arcs. The straight lines and arcs are made from metal. 20 straight lines cost £12 cost of one straight line : cost of one arc = 2 : 3 Work out the total cost of the metal in the pattern. [3 marks] Answer £ Turn over for the next question Turn over ► 15 A biased dice is thrown. Here are the probabilities of each score. box Score 1 2 3 4 5 6 Probability 0.25 0.05 0.15 0.05 0.3 0.2 The dice is thrown 200 times. Work out the expected number of times the score will be odd. [3 marks] Answer 16 The value of y is 20% more than the value of x. Circle the ratio x : y 5 : 6 6 : 5 4 : 5 5 : 4 17 Here is a triangle. [1 mark] box Circle the correct equation. Not drawn accurately [1 mark] sin x = sin 15º 42 104 x = 15 sin 42º sin 104º sin x = sin 15º 34 104 x = 15 sin 42º sin 34º Turn over ► 18 Here is a tunnel for a toy train. The diagram below shows the cross section of the tunnel. Not drawn accurately AD is a semicircular arc of radius 10 cm BC is a semicircular arc of radius 7 cm The length of the tunnel is 30 cm Work out the total area of all six faces of the tunnel. Give your answer in terms of π. [5 marks] Turn over ► 19 Type A batteries and type B batteries were tested. The cumulative frequency diagram shows information about the battery life of type A. 19 (a) Estimate the interquartile range for type A. [2 marks] Answer hours 19 (b) Estimate the number of type A batteries that had a battery life of more than 1600 hours. [1 mark] Answer 19 (c) The box plot shows information about the battery life of type B. On average, which type had the greater battery life? Tick a box. type A type B Using data from both diagrams, state how you chose your answer. [2 marks] *17* Turn over ► 20 A linear sequence starts a + 2b a + 6b a + 10b …….. …….. The 2nd term has value 8 The 5th term has value 44 Work out the values of a and b. [4 marks] a = b = *1* 21 Enlarge triangle ABC by scale factor –2, centre (4, 1) [2 marks] 22 Which of these represents the shaded region? Circle your answer. [1 mark] A ∩ B/ B/ A U B/ A/ U B/ Turn over ► 23 A shopkeeper compares the income from sales of a laptop in March and April. box April Price 1 more than March 5 Number sold 1 less than March 4 By what fraction does the income from these sales decrease in April? [3 marks] Answer 24 (a) 14  9 2 Work out the value of 2 ÷  2    Give your answer as a fraction in its simplest form. [3 marks] Answer 24 (b) 3 Work out the value of 25 2 [2 marks] Answer Turn over for the next question Turn over ► 25 Here is a sketch of the graph of y = cos x for values of x from 0° to 360° 25 (a) cos x = cos 60° Work out the value of x when 90° ⩽ x ⩽ 360° [1 mark] Answer degrees 25 (b) cos x = – cos 60° Work out the value of x when 180° ⩽ x ⩽ 360° [1 mark] Answer degrees 26 b is two thirds of c. 5a = 4c Work out the ratio a : b : c Give your answer in its simplest form where a, b and c are integers. [3 marks] box Answer : : Turn over for the next question Turn over ► 27 (a) Jo wants to work out the solutions of x2 + 3x – 5 = 0 She says, ‘‘The solutions cannot be worked out because x2 + 3x – 5 does not factorise to (x + a)(x + b) where a and b are integers.’’ Is Jo correct? Tick a box. Yes No Give a reason for your answer. [1 mark] 27 (b) Without expanding any brackets, show how to work out the exact solutions of 9(x + 3)2 = 4 Give the solutions. [3 marks] 2 28 Simplify 80 + 2 9 Give your answer in the form a 5 where a and b are integers. b [3 marks] Answer Turn over for the next question Turn over ► 29 Here are sketches of two graphs. The graph of y = x2 – 1 is translated 3 units to the left to give graph A. 29 (a) The equation of graph A can be written in the form Work out the values of b and c. y = x2 + bx + c [3 marks] b = c = 29 (b) The graph of y = x2 – 1 is reflected in the x-axis to give graph B. Work out the equation of graph B. [1 mark] Answer 30 Show that the value of cos 30° × tan 60° + sin 30° is an integer. [3 marks] END OF QUESTIONS *27* 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 will be 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 © 2018 AQA and its licensors. All rights reserved. *2* 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 will be 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 © 2018 AQA and its licensors. All rights reserved. *2*