1. 1.(a) Given that 20 kg is approximately 44 lb (pounds), complete the statement below. 1 kg = lb (pounds) [1] (b) The label on a pack of cheese reads: 10 litres of milk make 1lb (pound) of cheese Calculate how many litres of milk are needed to make 15 kg of cheese. [3] GCSE MATHEMATICS - LINEAR Part c HIGHER Paper 1

2. 1.(a) Given that 20 kg is approximately 44 lb (pounds), complete the statement below. 1 kg = lb (pounds) [1] (b) The label on a pack of cheese reads: 10 litres of milk make 1lb (pound) of cheese Calculate how many litres of milk are needed to make 15 kg of cheese. [3] GCSE MATHEMATICS - LINEAR 2.2 15kg = 15 × 2.2 Reveal Part c = 33 lb 33 × 10 = 330 litres This is a 2-step calculation. This is 44 ÷ 20 HIGHER Paper 1

3. 1 (c) The label on the pack of cheese also states: [4] Typical value per 100g: Energy1700kj 410kcal Protein25·0g Carbohydrate0·1g Fat34·4g Typical value per 100g: Energy1700kj 410kcal Protein25·0g Carbohydrate0·1g Fat34·4g Calculate the amount of protein in 1·5 kg of cheese. Give your answer in grams. [4] GCSE MATHEMATICS - LINEAR Part a & b HIGHER Paper 1

4. 1 (c) The label on the pack of cheese also states: [4] Typical value per 100g: Energy1700kj 410kcal Protein25·0g Carbohydrate0·1g Fat34·4g Typical value per 100g: Energy1700kj 410kcal Protein25·0g Carbohydrate0·1g Fat34·4g Calculate the amount of protein in 1·5 kg of cheese. Give your answer in grams. [4] GCSE MATHEMATICS - LINEAR 1.5kg = 1500g Reveal Part a & b Cheese  protein 100g  25.0g 1500g  375g × 15 HIGHER Paper 1 Answer = 375g

5. 2. Calculate the size of each of the angles marked x, y and z in the diagram below. [3] Diagram not drawn to scale. x = °, y = °, z = ° GCSE MATHEMATICS - LINEAR HIGHER Paper 1

6. 2. Calculate the size of each of the angles marked x, y and z in the diagram below. [3] Diagram not drawn to scale. x = °, y = °, z = ° GCSE MATHEMATICS - LINEAR 35 Reveal 35 145 Alternate angles Opposite angles HIGHER Paper 1 x = 35° (opposite angles) y = 35° (alternate angles) z = 180° – 35° (angles on a straight line) z = 145° 35° This angle is 35° too.

7. 3. Every Saturday for 5 weeks in the Autumn the number of centimetres of rainfall and the average percentage of cloud cover were recorded by a group of students. The table below shows the results. [1] (a) On the graph paper below, draw a scatter diagram of these results. (b) Describe the correlation between the average percentage of cloud cover and the amount of rainfall. (c) Find an estimate of the average percentage of cloud cover on a day with 0·6cm of rainfall clearly showing your method. [2] GCSE MATHEMATICS - LINEAR HIGHER Paper 1

8. 3. Every Saturday for 5 weeks in the Autumn the number of centimetres of rainfall and the average percentage of cloud cover were recorded by a group of students. The table below shows the results. [1] (a) On the graph paper below, draw a scatter diagram of these results. (b) Describe the correlation between the average percentage of cloud cover and the amount of rainfall. (c) Find an estimate of the average percentage of cloud cover on a day with 0·6cm of rainfall clearly showing your method. [2] GCSE MATHEMATICS - LINEAR Positive Reveal 64% In order to arrive at an estimate you need to draw a line of best fit on the graph – this does not have to pass through the origin HIGHER Paper 1 Each little square is worth 2% Each little square is worth 0.02 cm

9. 5. (a)Draw an enlargement of the shape shown below using a scale factor of 2. Use the point A as the centre of the enlargement. [3] GCSE MATHEMATICS - LINEAR Part b HIGHER Paper 1

10. 5. (a)Draw an enlargement of the shape shown below using a scale factor of 2. Use the point A as the centre of the enlargement. [3] GCSE MATHEMATICS - LINEAR Reveal Part b HIGHER Paper 1 Make sure you use the centre of enlargement, A This is the correct size but drawn in the wrong place.

11. 5 (b) Rotate the shape shown below through 90° anticlockwise about the point (2, 1). [2] GCSE MATHEMATICS - LINEAR Part a HIGHER Paper 1

12. 5 (b) Rotate the shape shown below through 90° anticlockwise about the point (2, 1). [2] GCSE MATHEMATICS - LINEAR Reveal Part a HIGHER Paper 1 Remember the three key facts: Angle: 90° Centre: (2, 1) Direction: anticlockwise Remember the three key facts: Angle: 90° Centre: (2, 1) Direction: anticlockwise

13. 6. You will be assessed on the quality of your written communication in part (b) of this question. Mrs. Roberts is travelling to Hong Kong on business. (a) There is a time difference between the UK and Hong Kong. When the time is 6 a.m. in the UK the time is 2 p.m. on the same day in Hong Kong. (i) When it is 10 a.m. in the UK what time is it in Hong Kong? [1] (ii) Mr. Roberts stays in the UK and has given his wife his time schedule, shown below. Mrs. Roberts will be in meetings most of the day in Hong Kong from 8 a.m. until 11 a.m., then from 12 noon to 6 p.m. She plans to telephone her husband at a convenient time during the day. During which time period should Mrs. Roberts telephone her husband? Give your answer in UK and Hong Kong times. [2] GCSE MATHEMATICS - LINEAR Part b HIGHER Paper 1 Part c

14. 6. You will be assessed on the quality of your written communication in part (b) of this question. Mrs. Roberts is travelling to Hong Kong on business. (a) There is a time difference between the UK and Hong Kong. When the time is 6 a.m. in the UK the time is 2 p.m. on the same day in Hong Kong. (i) When it is 10 a.m. in the UK what time is it in Hong Kong? [1] (ii) Mr. Roberts stays in the UK and has given his wife his time schedule, shown below. Mrs. Roberts will be in meetings most of the day in Hong Kong from 8 a.m. until 11 a.m., then from 12 noon to 6 p.m. She plans to telephone her husband at a convenient time during the day. During which time period should Mrs. Roberts telephone her husband? Give your answer in UK and Hong Kong times. [2] GCSE MATHEMATICS - LINEAR HIGHER Paper 1 Reveal Part b HK 2:00 2:30 3:30 7:30 8:30 10:00 0:00 2:00 5:00 6:00 pm meeting am Part c 6am (UK) is 2pm (HK) (+8hrs) so 10am (UK) is 6pm (HK) Between 8:30pm – 10:00pm HK time [Mrs Roberts has finished work] 12:30pm – 2:00pm UK time [Mr Roberts is having lunch] So they are both free to talk. Hong Kong is 8 hours ahead of UK

15. 6 (b) Mrs. Roberts is going to be in Hong Kong for 4 nights. She finds two suitable hotels on the internet. [5] Which hotel should Mrs. Roberts choose? You must show your working and give a reason for your answer. GCSE MATHEMATICS - LINEAR Part a HIGHER Paper 1 Part c

16. 6 (b) Mrs. Roberts is going to be in Hong Kong for 4 nights. She finds two suitable hotels on the internet. [5] Which hotel should Mrs. Roberts choose? You must show your working and give a reason for your answer. GCSE MATHEMATICS - LINEAR Hotel Gelton £80 × 4 = £320 B&B Reveal Part a Hotel Bear £107 × 3 = £321 B&B + dinner Choose Hotel Bear as you also get dinner for 4 nights for an extra £1 HIGHER Paper 1 Part c Remember to include a valid reason for your choice

17. 6 (c) The currency in Hong Kong is dollars, ($). Mrs. Roberts changes £400 into dollars. She returns from Hong Kong with $1500. The bank gives the exchange rates shown below. [3] GCSE MATHEMATICS - LINEAR (i) How much of the £400 did Mrs. Roberts spend when in Hong Kong? Give your answer in dollars. (ii) On return from her business trip Mrs. Roberts exchanges $1500 for pounds. Will she receive more or less than £100? You must give a reason for your answer. [2] Part a HIGHER Paper 1 Part b

18. 6 (c) The currency in Hong Kong is dollars, ($). Mrs. Roberts changes £400 into dollars. She returns from Hong Kong with $1500. The bank gives the exchange rates shown below. [3] GCSE MATHEMATICS - LINEAR (i) How much of the £400 did Mrs. Roberts spend when in Hong Kong? Give your answer in dollars. (ii) On return from her business trip Mrs. Roberts exchanges $1500 for pounds. Will she receive more or less than £100? You must give a reason for your answer. [2] Reveal Part a HIGHER Paper 1 Part b 400  15 = $6000 6000 – 1500 = $4500 She will receive less than £100 because 1500 ÷ 17 = £88.24

19. 7. The houses on one side of a long street have odd numbers and the houses on the other side of the street have even numbers. [1] (a) Fill in the numbers on these houses. (b) The numbers on five houses next to each other on one side of the street total 65. What are the numbers on these five houses? [3] (c) The product of the numbers on two houses which are directly opposite each other is 380. What are the numbers on these two houses? [1] GCSE MATHEMATICS - LINEAR HIGHER Paper 1

20. 7. The houses on one side of a long street have odd numbers and the houses on the other side of the street have even numbers. [1] (a) Fill in the numbers on these houses. (b) The numbers on five houses next to each other on one side of the street total 65. What are the numbers on these five houses? [3] (c) The product of the numbers on two houses which are directly opposite each other is 380. What are the numbers on these two houses? [1] GCSE MATHEMATICS - LINEAR 65 ÷ 5 = 13 Reveal (number) × (number + 1) = 380 +1 +2 9799101105 98100102106 104 911 13 15 17 The numbers are 19 and 20. HIGHER Paper 1 This must be the middle house number. So, the solution is: The numbers will be consecutive i.e. Product means “multiply”

21. 9. [2] (a) Expand y (4y 3 + 1) (b) Simplify t 6t 6 t 2t 2 [1] GCSE MATHEMATICS - LINEAR HIGHER Paper 1

22. 9. [2] (a) Expand y (4y 3 + 1) (b) Simplify t 6t 6 t 2t 2 [1] GCSE MATHEMATICS - LINEAR = 4y 4 + y Reveal = t 4 subtract the powers HIGHER Paper 1 Remember – everything in the bracket is multiplied by the y

23. 10.(a) A teacher recorded the time taken by each of 30 pupils in her class to complete a task. The table below shows a summary of her results. [2] (i) On the graph paper below draw a frequency polygon for this data. (ii) Using the table, give the class interval which contains the median time taken. [1] GCSE MATHEMATICS - LINEAR Part b HIGHER Paper 1

24. 10.(a) A teacher recorded the time taken by each of 30 pupils in her class to complete a task. The table below shows a summary of her results. [2] (i) On the graph paper below draw a frequency polygon for this data. (ii) Using the table, give the class interval which contains the median time taken. [1] GCSE MATHEMATICS - LINEAR 30 pupils  median is between 15th and 16th pupil, both of whom are in the interval Reveal Mid point 5 15 25 35 10 < t ≤ 20 Remember: Plot the mid-points The frequency polygon starts at the first point and ends at the last point HIGHER Paper 1 Part b

25. 10 (b) Another teacher recorded the times taken to complete the same task for his class of 32 pupils and he drew the following cumulative frequency diagram. Use the cumulative frequency diagram to find an estimate for the interquartile range. [2] (c )Is it possible for the median times of the two classes to be the same? Give a reason for your answer. [2] GCSE MATHEMATICS - LINEAR Part a HIGHER Paper 1

26. 10 (b) Another teacher recorded the times taken to complete the same task for his class of 32 pupils and he drew the following cumulative frequency diagram. Use the cumulative frequency diagram to find an estimate for the interquartile range. [2] (c )Is it possible for the median times of the two classes to be the same? Give a reason for your answer. [2] GCSE MATHEMATICS - LINEAR Interquartile range = 19.5 – 11.5 Reveal Part a UQ: at 24 Median: at 16 LQ: at 8 11.5 15.5 19.5 Interquartile range = 8 Median time for this class ≈ 15.5 Both medians are in the range 10 < t ≤ 20, so yes it is possible that they could be the same. Your answer must be justified using results HIGHER Paper 1 A quarter of 32 is 8. Interquartile range = UQ – LQ

27. On the same diagram, draw a graph to show the volume of the cuboid for values of x from 0 to 1 using the values in the following table. [3] [1] 11 (c) On the diagram below, the graph drawn shows the volume of the pyramid for values of x from 0 to 1. (d) Explain what the intersection of the two graphs tells you. GCSE MATHEMATICS - LINEAR Part a HIGHER Paper 1

28. On the same diagram, draw a graph to show the volume of the cuboid for values of x from 0 to 1 using the values in the following table. [3] [1] 11 (c) On the diagram below, the graph drawn shows the volume of the pyramid for values of x from 0 to 1. (d) Explain what the intersection of the two graphs tells you. GCSE MATHEMATICS - LINEAR Reveal Part a 00.41.63.66.410 At the point of intersection the cuboid and the pyramid have the same volume. Substitute each value of x from the table into 10x 2 to calculate the volume (e.g. 10 × 0.2² = 10 × 0.04 = 0.4) HIGHER Paper 1 Scales Vertical: 1 small square = 0.2 Horizontal: 1 small square = 0.02

29. 12. When Dylan has lunch the probability that he has a dessert is. Whether or not he has a dessert the probability that he has coffee is. (a) Complete the following tree diagram. [2] 2 5 1 4 (b) Calculate the probability that Dylan has a dessert or coffee, but not both. [2] GCSE MATHEMATICS - LINEAR HIGHER Paper 1

30. 12. When Dylan has lunch the probability that he has a dessert is. Whether or not he has a dessert the probability that he has coffee is. (a) Complete the following tree diagram. [2] 2 5 1 4 (b) Calculate the probability that Dylan has a dessert or coffee, but not both. [2] GCSE MATHEMATICS - LINEAR P(dessert and NOT coffee) or P(NOT dessert and coffee) Reveal 3 4 2 5 3 5 2 5 3 5 Remember each set of branches total 1 HIGHER Paper 1 9 20 = 3 6 + = 1 4 3 5 3 4 2 5 × + × =

31. 13. A bag contains 16 red beads, 4 green beads and 1 yellow bead. Two beads are drawn at random without replacement from the bag. (a) Calculate the probability that the two beads are of the same colour. [2] (b) Calculate the probability that one of the two beads selected is yellow. [3] GCSE MATHEMATICS - LINEAR HIGHER Paper 1

32. 13. A bag contains 16 red beads, 4 green beads and 1 yellow bead. Two beads are drawn at random without replacement from the bag. (a) Calculate the probability that the two beads are of the same colour. [2] (b) Calculate the probability that one of the two beads selected is yellow. [3] GCSE MATHEMATICS - LINEAR HIGHER Paper 1 P(r,r) + P(g,g) + P(y,y) P(r)P(r) = 16 21 P(g)P(g) P(y)P(y) = 4 = 1 P(r)P(r) = 15 20 P(r) = 16 20 P(g)P(g) = 3 P(y)P(y) = 0 = 240 420 + 12 420 = 252 420 = 3 5 P(r,y) + P(g,y) + P(y,r) + P(y,g) = 16 420 + 4 16 420 + 4 + = 40 420 = 2 21 Remember there is NO replacement Remember to consider all options. e.g. ‘red, yellow’ is different to ‘yellow, red’ = 16 21 ×+ 4 1 20 1 × + 1 21 16 20 × + 1 21 4 20 × Reveal = 16 21 × + 4 15 20 3 × + 1 21 × 0

33. 14. (a) Simplify [4] (c) Make d the subject of the following formula. (b) Simplify (3ab 7 ) 3 [3] x 2 + 5x + 6 3x + 6 [2] de – c 2d + g = 5 GCSE MATHEMATICS - LINEAR HIGHER Paper 1

34. 14. (a) Simplify [4] (c) Make d the subject of the following formula. (b) Simplify (3ab 7 ) 3 [3] x 2 + 5x + 6 3x + 6 [2] de – c 2d + g = 5 GCSE MATHEMATICS - LINEAR Reveal 27a 3 b 21 = 3 (x + 2) (x + 3) (x + 2) (x + 3) = 3 de – c = 5(2d + g) de – c = 10d + 5g de – 10d = 5g + c d(e – 10) = 5g + c (e – 10) = 5g + c d Numerator and denominator both need to be factorised before you can cancel The 3, the a and the b 7 need to be cubed HIGHER Paper 1 Multiply by denominator factorise Collect d terms together on left hand side

35. 15.(a) [2] Diagram not drawn to scale. The points A, B, C and D are on the circumference of a circle with centre O and BOD = 6x. Find the size of BCD in terms of x. GCSE MATHEMATICS - LINEAR Part b HIGHER Paper 1

36. 15.(a) [2] Diagram not drawn to scale. The points A, B, C and D are on the circumference of a circle with centre O and BOD = 6x. Find the size of BCD in terms of x. GCSE MATHEMATICS - LINEAR Reveal Part b BAD + BCD = 180° (opposite angles of a cyclic quadrilateral) 3x + BCD = 180° Remember, the angle at circumference is half the angle at the centre BAD = 3x (angle at circumference is half angle at centre) HIGHER Paper 1 BCD = 180° – 3x 3x3x

37. [1] 16.(a)The diagram shows a sketch of y = – x 3. On the same diagram, sketch the curve y = – 2x 3. (b) The diagram shows a sketch of y = f (x). On the same diagram, sketch the curve y = f (x + 5).Indicate the coordinates of one point on the curve. [2] GCSE MATHEMATICS - LINEAR Part c HIGHER Paper 1

38. [1] 16.(a)The diagram shows a sketch of y = – x 3. On the same diagram, sketch the curve y = – 2x 3. (b) The diagram shows a sketch of y = f (x). On the same diagram, sketch the curve y = f (x + 5).Indicate the coordinates of one point on the curve. [2] GCSE MATHEMATICS - LINEAR Reveal Part c (– 5, 0) Graph stretches this way: As the + 5 is inside the bracket, you move the graph to the LEFT 5 HIGHER Paper 1 Every point will end up being twice as far from the x-axis than it was.

39. 16 (c) [2] The diagram shows a sketch of y = f (x). On the same diagram, sketch the curve y = f (x) – 3. Indicate the coordinates of one point on the curve. GCSE MATHEMATICS - LINEAR Part a&b HIGHER Paper 1

40. 16 (c) [2] The diagram shows a sketch of y = f (x). On the same diagram, sketch the curve y = f (x) – 3. Indicate the coordinates of one point on the curve. GCSE MATHEMATICS - LINEAR (0, – 3) Reveal Part a&b As the – 3 is outside the bracket, you move the graph DOWN 3 HIGHER Paper 1

41. 17. Solve [7] GCSE MATHEMATICS - LINEAR HIGHER Paper 1

42. 17. Solve [7] GCSE MATHEMATICS - LINEAR Reveal 20(n + 3) + 5n(n + 1) (n + 1)(n + 3) 6 = 20(n + 3) + 5n(n + 1) = 6(n + 1)(n + 3) 20n + 60 + 5n 2 + 5n = 6n 2 + 24n + 18 n 2 – n – 42 = 0 (n – 7)(n + 6) = 0 n = 7 or n = – 6 Either n – 7 = 0 or n + 6 = 0 See mark scheme for alternative start to this question HIGHER Paper 1 Rearrange so that right hand side is equal to zero 0 = n 2 – n – 42 Write the two fractions as one on left hand side Multiply throughout by denominator Expand all brackets Collect all terms on right hand side (more n 2 )

43. 18. Patterns are generated as shown in the diagram. [4] Pattern 1 Pattern 2 Pattern 3 Pattern 4 Diagrams not drawn to scale. Find the perimeter of Pattern 6 in the form a + √b, where a and b are whole numbers. Show your working. GCSE MATHEMATICS - LINEAR HIGHER Paper 1

44. 18. Patterns are generated as shown in the diagram. [4] Pattern 1 Pattern 2 Pattern 3 Pattern 4 Diagrams not drawn to scale. Find the perimeter of Pattern 6 in the form a + √b, where a and b are whole numbers. Show your working. GCSE MATHEMATICS - LINEAR Reveal HIGHER Paper 1 P 1 = 1 + 1 + √2 = 2 + √2 P 2 = 1 + 1 + 1 + √3 = 3 + √3 Note: P n = (n+1) + √(n+1) P 3 = …………… = 4 + √4 P 4 = …………… = 5 + √5 P 6 = 7 + √7

45. [4] 1. The numbers on opposite faces of a dice add up to 7. Complete the following diagrams for nets of dice. GCSE MATHEMATICS - LINEAR HIGHER Paper 2

46. [4] 1. The numbers on opposite faces of a dice add up to 7. Complete the following diagrams for nets of dice. GCSE MATHEMATICS - LINEAR 5 or 2 Reveal 2 or 5 5 or 2 2 or 5 HIGHER Paper 2 These faces are opposite each other and must add up to 7

47. [2] 2. The owner of a takeaway coffee shop uses two types of paper cups. Hi-rim cup Base-stay cup Diagrams are not drawn to scale. They can be stacked like this... Hi-rim cup Base-stay cup (a) How high is a stack of 25 Hi-rim cups? (b) A stack of Base-stay cups is 18.6 cm high. How many Base-stay cups are in the stack? [2] GCSE MATHEMATICS - LINEAR Part (c) HIGHER Paper 2

48. [2] 2. The owner of a takeaway coffee shop uses two types of paper cups. Hi-rim cup Base-stay cup Diagrams are not drawn to scale. They can be stacked like this... Hi-rim cup Base-stay cup (a) How high is a stack of 25 Hi-rim cups? (b) A stack of Base-stay cups is 18.6 cm high. How many Base-stay cups are in the stack? [2] GCSE MATHEMATICS - LINEAR Reveal Part (c) HIGHER Paper 2 Height of cup 1 = 14 cm Remove cup 1: 18.6 – 9 = 9.6 Height of cups 2 to 25 = 24 × 0.5 = 12 cm Total height = 14 + 12 = 26 cm Number of cups 9.6 ÷ 1.2 = 8 8 cups + 1 cup = 9 cups Remember there are 24 cups above the bottom cup Therefore 24 × 0.5 NOT 25 × 0.5 Add height of bottom cup

49. [3] 2 (c) A stack of Hi-rim cups is the same height as a stack of Base-stay cups. There are 21 Base-stay cups in the stack. How many cups are there in the stack of Hi-rim cups? GCSE MATHEMATICS - LINEAR Part (a) & (b) HIGHER Paper 2

50. [3] 2 (c) A stack of Hi-rim cups is the same height as a stack of Base-stay cups. There are 21 Base-stay cups in the stack. How many cups are there in the stack of Hi-rim cups? GCSE MATHEMATICS - LINEAR Reveal Part (a) & (b) HIGHER Paper 2 Height of Base-stay 20 × 1.2 + 9 = 33 cm To find number of Hi-rim 33 – 14 = 19 19 ÷ 0.5 = 38 cups 38 + 1 = 39 cups Don’t forget the bottom cup

51. [6] 3. Mrs Evans received an electricity bill from Wales Electricity Company. The bill, with some of the entries removed, is shown below. Use the information given on the bill to complete all of the missing entries and calculate the total amount that Mrs Evans has to pay. GCSE MATHEMATICS - LINEAR HIGHER Paper 2

52. [6] 3. Mrs Evans received an electricity bill from Wales Electricity Company. The bill, with some of the entries removed, is shown below. Use the information given on the bill to complete all of the missing entries and calculate the total amount that Mrs Evans has to pay. GCSE MATHEMATICS - LINEAR 1100 Reveal 156.20 191.08 9.55 200.63 188.63 HIGHER Paper 2 Change to £ Add on This means that they paid too much on their last bill. Check your answer makes sense, an electricity bill isn’t usually thousands of pounds

53. [2] 4. The table below shows the probabilities of selecting one ball at random from a bag of coloured balls. (a)Are there any balls of another colour in the bag? Give a reason for your answer. (b) What is the probability of selecting either a yellow or a purple ball? [2] GCSE MATHEMATICS - LINEAR HIGHER Paper 2

54. [2] 4. The table below shows the probabilities of selecting one ball at random from a bag of coloured balls. (a)Are there any balls of another colour in the bag? Give a reason for your answer. (b) What is the probability of selecting either a yellow or a purple ball? [2] GCSE MATHEMATICS - LINEAR Reveal HIGHER Paper 2 0.25 + 0.14 + 0.06 + 0.15 + 0.40 = 1 P(yellow or purple) There are no balls of any other colour because the probabilities add up to 1. = 0.06 + 0.40 = 0.46 The ball can’t be yellow and purple at the same time, so the rule P(A or B) = P(A) + P(B) works. = P(yellow) + P(purple)

55. [3] 5. (a) Write down the first three terms of the sequence with an nth term of n 2 + 10. [2] (b) Solve 8x + 7 = 2x + 10. GCSE MATHEMATICS - LINEAR HIGHER Paper 2

56. [3] 5. (a) Write down the first three terms of the sequence with an nth term of n 2 + 10. [2] (b) Solve 8x + 7 = 2x + 10. GCSE MATHEMATICS - LINEAR 1 2 + 10 = 11 Reveal 8x – 2x = 10 – 7 2 2 + 10 = 14 3 2 + 10 = 19 6x = 3 x = 3 6 x = 1 2 HIGHER Paper 2 Be careful with signs Start with n = 1

57. [2] 6. (a) Express 104 as a percentage of 260. [2] (b) Calculate giving your answer correct to two decimal places. 5.6 × 3.4 8.1 – 2.7 (c) Two friends share £280 in the ratio 3:4. Find how much each friend receives. [2] GCSE MATHEMATICS - LINEAR HIGHER Paper 2

58. [2] 6. (a) Express 104 as a percentage of 260. [2] (b) Calculate giving your answer correct to two decimal places. 5.6 × 3.4 8.1 – 2.7 (c) Two friends share £280 in the ratio 3:4. Find how much each friend receives. [2] GCSE MATHEMATICS - LINEAR Reveal 3.53 104 260 × 100 % = 40% 3 + 4 = 7280 = 40 7 3 × 40 = £120 4 × 40 = £160 HIGHER Paper 2 3.52592592…. As this number is 5 or higher, 3.52 rounds up to 3.53 Put brackets around the denominator when you put it into your calculator ( ) Total number of parts How much each part is worth

59. [3] 7. The test scores of 20 people were recorded and the results are summarised in the following table. Calculate an estimate for the mean of the test scores. GCSE MATHEMATICS - LINEAR HIGHER Paper 2

60. [3] 7. The test scores of 20 people were recorded and the results are summarised in the following table. Calculate an estimate for the mean of the test scores. GCSE MATHEMATICS - LINEAR Reveal Mid-point 4.5 14.5 24.5 Total = 20 HIGHER Paper 2 mean = total of ‘mid-point × frequency’ total frequency = 4.5 × 7 + 14.5 ×11 + 24.5 × 2 20 = 240 20 = 12 0 + 9 = 4.5 2

61. [1] 8. The table shows some of the values of y = 2x 2 – 5 for values of x from –2 to 2. (a) Complete the table by finding the value of y for x = –2 and x = 1. [2] (b) On the graph paper below, draw the graph of y = 2x 2 – 5 for values of x between – 2 and 2. (c) Write down the x-coordinates of the points of intersection of y = 2x 2 – 5 with the x-axis. (d) Write down the minimum value of y. [2] GCSE MATHEMATICS - LINEAR HIGHER Paper 2

62. [1] 8. The table shows some of the values of y = 2x 2 – 5 for values of x from –2 to 2. (a) Complete the table by finding the value of y for x = –2 and x = 1. [2] (b) On the graph paper below, draw the graph of y = 2x 2 – 5 for values of x between – 2 and 2. (c) Write down the x-coordinates of the points of intersection of y = 2x 2 – 5 with the x-axis. (d) Write down the minimum value of y. [2] GCSE MATHEMATICS - LINEAR 3 Reveal x ≈ 1.6 and x ≈ – 1.6 –3 –5 HIGHER Paper 2 (– 2) 2 = 4, So, 2(4) – 5 = 3

63. [3] 9. You will be assessed on the quality of your written communication in this question. A number is written on each of five cards. The cards are arranged in ascending order. It is known that the mean of the five numbers is 9.6, the range is 12, the median is 10, the greatest number is 16 and the fourth number is twice the second number. Explaining your reasoning, find the five numbers written on the cards. GCSE MATHEMATICS - LINEAR HIGHER Paper 2

64. [3] 9. You will be assessed on the quality of your written communication in this question. A number is written on each of five cards. The cards are arranged in ascending order. It is known that the mean of the five numbers is 9.6, the range is 12, the median is 10, the greatest number is 16 and the fourth number is twice the second number. Explaining your reasoning, find the five numbers written on the cards. GCSE MATHEMATICS - LINEAR Reveal HIGHER Paper 2 46101216 The median is 10. Therefore, the number on the middle card is 10. The range is 12. Therefore, the smallest number is 16 – 12 = 4 Now, mean × number of cards = total So, 9.6 × 5 = 48 total of 5 cards – total of 3 cards = 48 – (4 + 10 + 16) = 18 The fourth number is twice the second, and the two add up to 18. The fourth number is 12, the second is 6. The largest number is 16.

65. [4] 13. On the graph paper below, draw the region which satisfies all of the following inequalities. Make sure that you clearly indicate the region that represents your answer. GCSE MATHEMATICS - LINEAR HIGHER Paper 2

66. [4] 13. On the graph paper below, draw the region which satisfies all of the following inequalities. Make sure that you clearly indicate the region that represents your answer. GCSE MATHEMATICS - LINEAR Draw: Reveal y = x + 7 y = 1 – 2x y = 3 x = 4 x – 5 0 5 y 2 7 12 x – 5 0 5 y 11 1 – 9 Check : Consider point within region (0, 5) 5 ≤ 0 + 7 5 ≥ 1 – 0 5 ≥ 3 0 ≤ 4 HIGHER Paper 2

67. [3] 14. (a) Factorise 6x 2 + 18xy. [2] (b) Factorise x 2 – 25. [1] (c) Solve 4n – 5 < n + 22. [2] (d) Solve the equation 3x 2 + 19x + 11 = 0, giving your solutions correct to two decimal places. GCSE MATHEMATICS - LINEAR HIGHER Paper 2

68. [3] 14. (a) Factorise 6x 2 + 18xy. [2] (b) Factorise x 2 – 25. [1] (c) Solve 4n – 5 < n + 22. [2] (d) Solve the equation 3x 2 + 19x + 11 = 0, giving your solutions correct to two decimal places. GCSE MATHEMATICS - LINEAR 6x (x + 3y) Reveal Difference of two squares (x + 5)(x – 5) 4n – n < 22 + 5 3n < 27 n < 27 3 Use inequality sign throughout with a = 3, b = 19, c = 11 x – 19 ± √ 229 = 6 x = – 0.64, x = – 5.69 HIGHER Paper 2 x= – b ± √ b 2 – 4ac 2a2a x = – 19 ± √ 19 2 – (4 × 3 × 11) 2 × 3 If the question asks for solutions to a given number of decimal places, don’t try and factorise, use the formula.

69. [2] 15. There are 100 pupils in Year 10. The time taken by each pupil to answer a question was recorded. The following grouped frequency distribution was obtained. (a) Find an estimate for the median of this distribution. [1] (b) Draw a histogram to illustrate the distribution on the graph below. GCSE MATHEMATICS - LINEAR HIGHER Paper 2

70. [2] 15. There are 100 pupils in Year 10. The time taken by each pupil to answer a question was recorded. The following grouped frequency distribution was obtained. (a) Find an estimate for the median of this distribution. [1] (b) Draw a histogram to illustrate the distribution on the graph below. GCSE MATHEMATICS - LINEAR Reveal 50 Median 30 Interval width 10 10 10 10 20 frequency density interval width = frequency 0.6, 1.9, 2.5, 3.6, 0.7 1 2 3 4 Frequency density HIGHER Paper 2 Areas of bars show the frequency (no. of pupils) 6 = 0.6 10 14 = 0.7 20 Use these values to decide on a scale

71. [3] 17. (a) Using the axes below, sketch the graph of y = sin x for values of x from – 180° to 360°. (b) Find all solutions of the following equation in the range – 180° to 360°. sin x = – 0.788 [2] GCSE MATHEMATICS - LINEAR HIGHER Paper 2

72. [3] 17. (a) Using the axes below, sketch the graph of y = sin x for values of x from – 180° to 360°. (b) Find all solutions of the following equation in the range – 180° to 360°. sin x = – 0.788 [2] GCSE MATHEMATICS - LINEAR x = sin (– 0.788) Reveal 1 –1 – 180  – 90  90  180  270  360  – 0.788 x = – 52º (to the nearest º) Using graph … x = –180º + 52º, x = 180º + 52º, x = 360º – 52º x = –128º, x = 232º, x = 308º HIGHER Paper 2 Plot – 1 and 1 on the y-axis and – 180º, – 90º, 0º, 90º, 180º, 270º, 360º at even intervals on the x-axis. Plot – 1 and 1 on the y-axis and – 180º, – 90º, 0º, 90º, 180º, 270º, 360º at even intervals on the x-axis. Use your calculator to find first value of x