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

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

1. (a) Given that 20 kg is approximately 44 lb (pounds), complete the statement 1. (a) Given that 20 kg is approximately 44 lb (pounds), complete the statement below. lb (pounds) [1] (b) The label on a pack of cheese reads: 10 litres of milk make 1 lb (pound) of cheese HIGHER Paper 1 GCSE MATHEMATICS - LINEAR 1 kg = Calculate how many litres of milk are needed to make 15 kg of cheese. ASSESSMENT OBJECTIVE Part c 1 (a) AO 1 –Recall and use knowledge of proportion 1(b) AO 2 – Select and apply mathematical methods [3]

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

1 (c) The label on the pack of cheese also states: Typical value per 1 (c) The label on the pack of cheese also states: Typical value per 100 g: Energy Protein Carbohydrate Fat HIGHER Paper 1 GCSE MATHEMATICS - LINEAR [4] 1700 kj 25· 0 g 0· 1 g 34· 4 g 410 kcal Calculate the amount of protein in 1· 5 kg of cheese. Give your answer in grams. [4] Part a & b

1 (c) The label on the pack of cheese also states: Typical value per 1 (c) The label on the pack of cheese also states: Typical value per 100 g: Energy Protein Carbohydrate Fat HIGHER Paper 1 GCSE MATHEMATICS - LINEAR [4] 1700 kj 25· 0 g 0· 1 g 34· 4 g 410 kcal Calculate the amount of protein in 1· 5 kg of cheese. Give your answer in grams. 1. 5 kg = 1500 g Cheese protein 100 g 25. 0 g × 15 1500 g 375 g Answer = 375 g [4] Part a & b Reveal

1 (c) The label on the pack of cheese also states: Typical value per 1 (c) The label on the pack of cheese also states: Typical value per 100 g: Energy Protein Carbohydrate Fat HIGHER Paper 1 GCSE MATHEMATICS - LINEAR [4] 1700 kj 25· 0 g 0· 1 g 34· 4 g 410 kcal Calculate the amount of protein in 1· 5 kg of cheese. Give your answer in grams. ASSESSMENT OBJECTIVE AO 2 –Select and apply mathematical methods [4] Part a & b

1 (c) The label on the pack of cheese also states: Typical value per 1 (c) The label on the pack of cheese also states: Typical value per 100 g: Energy Protein Carbohydrate Fat HIGHER Paper 1 GCSE MATHEMATICS - LINEAR [4] 1700 kj 25· 0 g 0· 1 g 34· 4 g 410 kcal Calculate the amount of protein in 1· 5 kg of cheese. Give your answer in grams. [4] Part a & b

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

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

HIGHER Paper 1 GCSE MATHEMATICS - LINEAR 2. Calculate the size of each of HIGHER Paper 1 GCSE MATHEMATICS - LINEAR 2. Calculate the size of each of the angles marked x, y and z in the diagram below. Diagram not drawn to scale. ASSESSMENT OBJECTIVE x= °, AO 1 – Recall and use knowledge of angle properties y= °, z= ° [3]

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

(a) On the graph paper below, draw a scatter diagram of these results. (b) (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. HIGHER Paper 1 GCSE MATHEMATICS - LINEAR 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] (c) Find an estimate of the average percentage of cloud cover on a day with 0· 6 cm of rainfall clearly showing your method. [2]

Each little square is worth 0. 02 cm (a) On the graph paper below, Each little square is worth 0. 02 cm (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. HIGHER Paper 1 GCSE MATHEMATICS - LINEAR 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. Positive 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 [1] (c) Find an estimate of the average percentage of cloud cover on a day with 0· 6 cm of rainfall clearly showing your method. 64% Each little square is worth 2% 64% Reveal[2]

(a) On the graph paper below, draw a scatter diagram of these results. (b) (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. HIGHER Paper 1 GCSE MATHEMATICS - LINEAR 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. ASSESSMENT OBJECTIVE 3(a) and 3 (b) AO 1 – Recall and use knowledge of scatter diagrams and correlation 3 (c) AO 2 – Select and apply methods to interpret the results derived from the line of best fit [1] (c) Find an estimate of the average percentage of cloud cover on a day with 0· 6 cm of rainfall clearly showing your method. [2]

(a) On the graph paper below, draw a scatter diagram of these results. (b) (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. HIGHER Paper 1 GCSE MATHEMATICS - LINEAR 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] (c) Find an estimate of the average percentage of cloud cover on a day with 0· 6 cm of rainfall clearly showing your method. [2]

Diagram not drawn to scale. HIGHER Paper 1 GCSE MATHEMATICS - LINEAR ^ 4. Diagram not drawn to scale. HIGHER Paper 1 GCSE MATHEMATICS - LINEAR ^ 4. The diagram shows a triangle DEF with EF = 11 cm, DXF = 90° and DX = 7 cm. Find the area of the triangle DEF. State appropriate units for your answer. [3]

It will help to label the diagram 7 cm 11 cm Diagram not drawn It will help to label the diagram 7 cm 11 cm Diagram not drawn to scale. HIGHER Paper 1 GCSE MATHEMATICS - LINEAR ^ 4. The diagram shows a triangle DEF with EF = 11 cm, DXF = 90° and DX = 7 cm. Find the area of the triangle DEF. State appropriate units for your answer. Area of triangle = ½ × base × height = ½ × 11 × 7 = 77 2 = 38. 5 cm 2 Remember, the units of area are squared units [3] Reveal

Diagram not drawn to scale. HIGHER Paper 1 GCSE MATHEMATICS - LINEAR ^ 4. Diagram not drawn to scale. HIGHER Paper 1 GCSE MATHEMATICS - LINEAR ^ 4. The diagram shows a triangle DEF with EF = 11 cm, DXF = 90° and DX = 7 cm. Find the area of the triangle DEF. State appropriate units for your answer. ASSESSMENT OBJECTIVE AO 1 – Recall and use knowledge of area [3]

Diagram not drawn to scale. HIGHER Paper 1 GCSE MATHEMATICS - LINEAR ^ 4. Diagram not drawn to scale. HIGHER Paper 1 GCSE MATHEMATICS - LINEAR ^ 4. The diagram shows a triangle DEF with EF = 11 cm, DXF = 90° and DX = 7 cm. Find the area of the triangle DEF. State appropriate units for your answer. [3]

HIGHER Paper 1 GCSE MATHEMATICS - LINEAR 5. (a) Draw an enlargement of the HIGHER Paper 1 GCSE MATHEMATICS - LINEAR 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. Part b [3]

This is the correct size but drawn in the wrong place. [3] Make sure This is the correct size but drawn in the wrong place. [3] Make sure you use the centre of enlargement, A HIGHER Paper 1 GCSE MATHEMATICS - LINEAR 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. Part b Reveal

HIGHER Paper 1 GCSE MATHEMATICS - LINEAR 5. (a) Draw an enlargement of the HIGHER Paper 1 GCSE MATHEMATICS - LINEAR 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. ASSESSMENT OBJECTIVE Part b AO 1 – Recalling and using knowledge of enlargement [3]

HIGHER Paper 1 GCSE MATHEMATICS - LINEAR 5. (a) Draw an enlargement of the HIGHER Paper 1 GCSE MATHEMATICS - LINEAR 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. Part b [3]

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

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

HIGHER Paper 1 GCSE MATHEMATICS - LINEAR 5 (b) Rotate the shape shown below HIGHER Paper 1 GCSE MATHEMATICS - LINEAR 5 (b) Rotate the shape shown below through 90° anticlockwise about the point (2, 1). ASSESSMENT OBJECTIVE Part a AO 1 – Recalling and using knowledge of rotation [2]

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

Mrs. Roberts is travelling to Hong Kong on business. (a) There is a time 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. HIGHER Paper 1 GCSE MATHEMATICS - LINEAR 6. You will be assessed on the quality of your written communication in part (b) of this question. Part b Part c [2]

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

Mrs. Roberts is travelling to Hong Kong on business. (a) There is a time 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. HIGHER Paper 1 GCSE MATHEMATICS - LINEAR 6. You will be assessed on the quality of your written communication in part (b) of this question. ASSESSMENT OBJECTIVE Part b Part c (a) (i) AO 2 – Select and apply appropriate numerical technique to calculate time difference. (ii) AO 3 – Interpret times and select appropriately. [2]

Mrs. Roberts is travelling to Hong Kong on business. (a) There is a time 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. HIGHER Paper 1 GCSE MATHEMATICS - LINEAR 6. You will be assessed on the quality of your written communication in part (b) of this question. Part b Part c [2]

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

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

HIGHER Paper 1 GCSE MATHEMATICS - LINEAR 6 (b) Mrs. Roberts is going to HIGHER Paper 1 GCSE MATHEMATICS - LINEAR 6 (b) Mrs. Roberts is going to be in Hong Kong for 4 nights. She finds two suitable hotels on the internet. Which hotel should Mrs. Roberts choose? You must show your working and give a reason for your answer. ASSESSMENT OBJECTIVE Part a Part c AO 3 – Interpret, analyse and compare both options presented and justify their choice of hotel. [5]

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

(i) How much of the £ 400 did Mrs. Roberts spend when in Hong (i) How much of the £ 400 did Mrs. Roberts spend when in Hong Kong? Give your answer in dollars. HIGHER Paper 1 GCSE MATHEMATICS - LINEAR 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] (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. Part a Part b [2]

(i) How much of the £ 400 did Mrs. Roberts spend when in Hong (i) How much of the £ 400 did Mrs. Roberts spend when in Hong Kong? Give your answer in dollars. 400 15 = $6000 HIGHER Paper 1 GCSE MATHEMATICS - LINEAR 6 (c) The currency in Hong Kong is dollars, ($). Mrs. Roberts changes £ 400 into dollars. She returns from Hong Kong with $1500. The bank gives the exchange rates shown below. 6000 – 1500 = $4500 [3] (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. She will receive less than £ 100 because 1500 ÷ 17 = £ 88. 24 Part a Part b [2] Reveal

(i) How much of the £ 400 did Mrs. Roberts spend when in Hong (i) How much of the £ 400 did Mrs. Roberts spend when in Hong Kong? Give your answer in dollars. HIGHER Paper 1 GCSE MATHEMATICS - LINEAR 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] (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. ASSESSMENT OBJECTIVE Part a Part b AO 2 – Selecting and applying methods involving exchange rates [2]

(i) How much of the £ 400 did Mrs. Roberts spend when in Hong (i) How much of the £ 400 did Mrs. Roberts spend when in Hong Kong? Give your answer in dollars. HIGHER Paper 1 GCSE MATHEMATICS - LINEAR 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] (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. Part a Part b [2]

(a) Fill in the numbers on these houses. [1] HIGHER Paper 1 GCSE MATHEMATICS (a) Fill in the numbers on these houses. [1] HIGHER Paper 1 GCSE MATHEMATICS - LINEAR 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. (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]

7. The houses on one side of a long street have odd numbers and 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. +2 +2 (a) Fill in the numbers on these houses. +2 +2 97 99 101 105 98 100 102 104 106 HIGHER Paper 1 GCSE MATHEMATICS - LINEAR +1 [1] (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? 65 ÷ 5 = 13 [3] This must be the middle house number. So, the solution is: 9 11 13 15 17 (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? The numbers will be consecutive i. e. (number) × (number + 1) = 380 The numbers are 19 and 20. [1] Product means “multiply” Reveal

(a) Fill in the numbers on these houses. [1] HIGHER Paper 1 GCSE MATHEMATICS (a) Fill in the numbers on these houses. [1] HIGHER Paper 1 GCSE MATHEMATICS - LINEAR 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. (b) The numbers on five houses next to. AO 2 other on one side of the street total 65. each – Selecting and applying ASSESSMENT What are the numbers on these five houses? knowledge of numbers and OBJECTIVE properties of numbers [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]

(a) Fill in the numbers on these houses. [1] HIGHER Paper 1 GCSE MATHEMATICS (a) Fill in the numbers on these houses. [1] HIGHER Paper 1 GCSE MATHEMATICS - LINEAR 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. (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]

HIGHER Paper 1 GCSE MATHEMATICS - LINEAR 8. The diagram represents an aerial view HIGHER Paper 1 GCSE MATHEMATICS - LINEAR 8. The diagram represents an aerial view of a building. A dog, D, on a lead is tied to a side of the building at X. Draw the boundary of the region in which the dog can roam. [3]

[3] The lead is shortened by the corner, so the answer is not a [3] The lead is shortened by the corner, so the answer is not a circle. 4. 9 cm 1. 9 cm 3 cm HIGHER Paper 1 GCSE MATHEMATICS - LINEAR 8. The diagram represents an aerial view of a building. A dog, D, on a lead is tied to a side of the building at X. Draw the boundary of the region in which the dog can roam. Reveal

HIGHER Paper 1 GCSE MATHEMATICS - LINEAR 8. The diagram represents an aerial view HIGHER Paper 1 GCSE MATHEMATICS - LINEAR 8. The diagram represents an aerial view of a building. A dog, D, on a lead is tied to a side of the building at X. Draw the boundary of the region in which the dog can roam. ASSESSMENT OBJECTIVE AO 2 - Select and apply appropriate rules of loci [3]

HIGHER Paper 1 GCSE MATHEMATICS - LINEAR 8. The diagram represents an aerial view HIGHER Paper 1 GCSE MATHEMATICS - LINEAR 8. The diagram represents an aerial view of a building. A dog, D, on a lead is tied to a side of the building at X. Draw the boundary of the region in which the dog can roam. [3]

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

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

9. y (4 y 3+ 1) [2] HIGHER Paper 1 GCSE MATHEMATICS - LINEAR 9. y (4 y 3+ 1) [2] HIGHER Paper 1 GCSE MATHEMATICS - LINEAR (a) Expand (b) Simplify ASSESSMENT t 6 t 2 OBJECTIVE AO 1 – Recall and use knowledge of indices and expanding brackets [1]

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

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

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

10. (a) A teacher recorded the time taken by each of 30 pupils in 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. (i) On the graph paper below draw a frequency polygon for this data. HIGHER Paper 1 GCSE MATHEMATICS - LINEAR [2] (ii) Using the table, give the class interval which contains the median time taken. ASSESSMENT OBJECTIVE Part b 10 (a) AO 1 – Recall and use knowledge of grouped frequency [1]

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

Use the cumulative frequency diagram to find an estimate for the interquartile range. HIGHER Use the cumulative frequency diagram to find an estimate for the interquartile range. HIGHER Paper 1 GCSE MATHEMATICS - LINEAR 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. [2] (c )Is it possible for the median times of the two classes to be the same? Give a reason for your answer. [2] Part a

A quarter of 32 is 8. Use the cumulative frequency diagram to find an A quarter of 32 is 8. Use the cumulative frequency diagram to find an estimate for the interquartile range. Interquartile range = UQ – LQ Interquartile range = 19. 5 – 11. 5 UQ: at 24 HIGHER Paper 1 GCSE MATHEMATICS - LINEAR 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. Interquartile range = 8 [2] Median: at 16 (c )Is it possible for the median times of the two classes to be the same? Give a reason for your answer. [2] Median time for this class ≈ 15. 5 LQ: at 8 Part a Your answer Both medians are in the range 10 < t ≤ 20, must be justified so yes it is possible that they could be the using results same. 15. 5 11. 5 19. 5 Reveal

Use the cumulative frequency diagram to find an estimate for the interquartile range. HIGHER Use the cumulative frequency diagram to find an estimate for the interquartile range. HIGHER Paper 1 GCSE MATHEMATICS - LINEAR 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. [2] (c )Is it possible for the median times of the two classes to be the same? Give a reason for your answer. [2] ASSESSMENT OBJECTIVE Part a 10 (b) AO 1– Recall and use AO 1 knowledge of cumulative frequency 10 (c) AO 3 – Interpret and analyse results gained

Use the cumulative frequency diagram to find an estimate for the interquartile range. HIGHER Use the cumulative frequency diagram to find an estimate for the interquartile range. HIGHER Paper 1 GCSE MATHEMATICS - LINEAR 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. [2] (c )Is it possible for the median times of the two classes to be the same? Give a reason for your answer. [2] Part a

11. A pyramid has a perpendicular height of x cm and a base area 11. A pyramid has a perpendicular height of x cm and a base area of 18 cm 2. A cuboid of height 10 cm has a base in the shape of a square of side x cm. [1] HIGHER Paper 1 GCSE MATHEMATICS - LINEAR (a) Show that the volume of the pyramid is 6 x cm 3. (b) Write down an expression for the volume of the cuboid in terms of x. [1] Part b

11. A pyramid has a perpendicular height of x cm and a base area 11. A pyramid has a perpendicular height of x cm and a base area of 18 cm 2. A cuboid of height 10 cm has a base in the shape of a square of side x cm. Volume of pyramid = ⅓ × (Area of base) × height = ⅓ × 18 × x = 6 x cm 3 [1] HIGHER Paper 1 GCSE MATHEMATICS - LINEAR (a) Show that the volume of the pyramid is 6 x cm 3. (b) Write down an expression for the volume of the cuboid in terms of x. Volume of cuboid = length × breadth × height = x × 10 = 10 x 2 cm 3 [1] Part b Reveal

11. A pyramid has a perpendicular height of x cm and a base area 11. A pyramid has a perpendicular height of x cm and a base area of 18 cm 2. A cuboid of height 10 cm has a base in the shape of a square of side x cm. [1] HIGHER Paper 1 GCSE MATHEMATICS - LINEAR (a) Show that the volume of the pyramid is 6 x cm 3. (b) Write down an expression for the volume of the cuboid in terms of x. AO 2 – Select and apply geometric ASSESSMENT OBJECTIVE formulae to form algebraic expressions [1] Part b

11. A pyramid has a perpendicular height of x cm and a base area 11. A pyramid has a perpendicular height of x cm and a base area of 18 cm 2. A cuboid of height 10 cm has a base in the shape of a square of side x cm. [1] HIGHER Paper 1 GCSE MATHEMATICS - LINEAR (a) Show that the volume of the pyramid is 6 x cm 3. (b) Write down an expression for the volume of the cuboid in terms of x. [1] Part b

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

Scales Vertical: 1 small square = 0. 2 Horizontal: 1 small square = 0. Scales Vertical: 1 small square = 0. 2 Horizontal: 1 small square = 0. 02 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. HIGHER Paper 1 GCSE MATHEMATICS - LINEAR 11 (c) On the diagram below, the graph drawn shows the volume of the pyramid for values of x from 0 to 1. 0 0. 4 1. 6 3. 6 6. 4 10 Substitute each value of x from the table into 10 x 2 to calculate the volume (e. g. 10 × 0. 2² = 10 × 0. 04 = 0. 4) [3] (d) Explain what the intersection of the two graphs tells you. At the point of intersection the cuboid and the pyramid have the same volume. Part a [1] Reveal

On the same diagram, draw a graph to show the volume of the cuboid 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. HIGHER Paper 1 GCSE MATHEMATICS - LINEAR 11 (c) On the diagram below, the graph drawn shows the volume of the pyramid for values of x from 0 to 1. ASSESSMENT OBJECTIVE AO 2 – Select and apply mathematical methods using the formula to plot the graph [3] (d) Explain what the intersection of the two graphs tells you. ASSESSMENT OBJECTIVE Part a AO 3 – Interpret the intersection of the two graphs [1]

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

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

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

12. When Dylan has lunch the probability that he has a dessert is 1. 12. When Dylan has lunch the probability that he has a dessert is 1. 4 Whether or not he has a dessert the probability that he has coffee is 2. 5 HIGHER Paper 1 GCSE MATHEMATICS - LINEAR (a) Complete the following tree diagram. ASSESSMENT OBJECTIVE AO 1 – Recall and use knowledge of tree diagrams and probability law of independent events (b) Calculate the probability that Dylan has a dessert or coffee, but not both. [2]

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

13. A bag contains 16 red beads, 4 green beads and 1 yellow bead. 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. HIGHER Paper 1 GCSE MATHEMATICS - LINEAR (a) Calculate the probability that the two beads are of the same colour. (b) Calculate the probability that one of the two beads selected is yellow. [3] [2]

13. A bag contains 16 red beads, 4 green beads and 1 yellow bead. 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. Remember there is NO replacement P(r) = 16 21 P(g) = 4 21 = 15 20 = 16 20 P(g) = 3 [3] P(r, r) + P(g, g) + P(y, y) 15 = 16 × + 21 20 P(r) HIGHER Paper 1 GCSE MATHEMATICS - LINEAR (a) Calculate the probability that the two beads are of the same colour. 4 × 3 21 20 + 1 × 0 21 12 = 240 + 420 20 = 252 420 P(y) = 1 21 = 3 5 P(y) = 0 (b) Calculate the probability that one of the two beads selected is yellow. P(r, y) + P(g, y) + P(y, r) + P(y, g) 1 = 16 × + 4 × 1 + 1 × 16 20 21 21 20 4 4 = 16 + + 16 + 420 420 = 40 420 = 2 21 + 1 × 4 21 20 [2] Remember to consider all options. e. g. ‘red, yellow’ is different to ‘yellow, red’ Reveal

13. A bag contains 16 red beads, 4 green beads and 1 yellow bead. 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. ASSESSMENT HIGHER Paper 1 GCSE MATHEMATICS - LINEAR (a) Calculate the probability that the two beads are of the same colour. OBJECTIVE [3] AO 1 – Recall and use knowledge of conditional probability (b) Calculate the probability that one of the two beads selected is yellow. [2]

13. A bag contains 16 red beads, 4 green beads and 1 yellow bead. 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. HIGHER Paper 1 GCSE MATHEMATICS - LINEAR (a) Calculate the probability that the two beads are of the same colour. (b) Calculate the probability that one of the two beads selected is yellow. [3] [2]

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

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

x 2 + 5 x + 6 3 x + 6 ASSESSMENT OBJECTIVE (b) x 2 + 5 x + 6 3 x + 6 ASSESSMENT OBJECTIVE (b) Simplify HIGHER Paper 1 GCSE MATHEMATICS - LINEAR 14. (a) Simplify AO 1 – Recall and use knowledge of quadratic factorisation and simplification of algebraic expressions [3] (3 ab 7)3 ASSESSMENT OBJECTIVE AO 1 – Recall and use knowledge of rules of indices (c) Make d the subject of the following formula. de – c 2 d + g ASSESSMENT OBJECTIVE [2] =5 AO 1 – Recall and use knowledge of change of subject of formula when the subject appears twice [4]

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

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

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

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

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

The diagram shows two circles. The line OA is a radius of the larger The diagram shows two circles. The line OA is a radius of the larger circle and a diameter of the smaller circle. Find, in its simplest form, the area of the smaller circle as a fraction of the area of the larger circle. HIGHER Paper 1 GCSE MATHEMATICS - LINEAR 15 (b) [2] Part a

The diagram shows two circles. The line OA is a radius of the larger The diagram shows two circles. The line OA is a radius of the larger circle and a diameter of the smaller circle. 2 r HIGHER Paper 1 GCSE MATHEMATICS - LINEAR 15 (b) Find, in its simplest form, the area of the smaller circle as a fraction of the area of the larger circle. We will need the radius of the small circle. Call this r. Then OA will be 2 r. Let OA = 2 r. [2] Remember to square all of 2 r Area of large circle = (2 r) 2 = × 4 r 2 = 4 r 2 Part a = r 2 4 r 2 = Area of small circle Area of large circle Area of small circle = r 2 r O A 1 4 Reveal

The diagram shows two circles. The line OA is a radius of the larger The diagram shows two circles. The line OA is a radius of the larger circle and a diameter of the smaller circle. Find, in its simplest form, the area of the smaller circle as a fraction of the area of the larger circle. HIGHER Paper 1 GCSE MATHEMATICS - LINEAR 15 (b) [2] ASSESSMENT OBJECTIVE Part a AO 3 – Interpret and analyse the problem and generate a strategy to find and compare expressions for the areas of the circles

The diagram shows two circles. The line OA is a radius of the larger The diagram shows two circles. The line OA is a radius of the larger circle and a diameter of the smaller circle. Find, in its simplest form, the area of the smaller circle as a fraction of the area of the larger circle. HIGHER Paper 1 GCSE MATHEMATICS - LINEAR 15 (b) [2] Part a

HIGHER Paper 1 GCSE MATHEMATICS - LINEAR 16. (a) The diagram shows a sketch HIGHER Paper 1 GCSE MATHEMATICS - LINEAR 16. (a) The diagram shows a sketch of y = – x 3. On the same diagram, sketch the curve y = – 2 x 3. [1] (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] Part c

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

HIGHER Paper 1 GCSE MATHEMATICS - LINEAR 16. (a) The diagram shows a sketch HIGHER Paper 1 GCSE MATHEMATICS - LINEAR 16. (a) The diagram shows a sketch of y = – x 3. On the same diagram, sketch the curve y = – 2 x 3. [1] (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. ASSESSMENT OBJECTIVE Part c AO 1 – Recall and use knowledge of transformations of graphs and functions [2]

HIGHER Paper 1 GCSE MATHEMATICS - LINEAR 16. (a) The diagram shows a sketch HIGHER Paper 1 GCSE MATHEMATICS - LINEAR 16. (a) The diagram shows a sketch of y = – x 3. On the same diagram, sketch the curve y = – 2 x 3. [1] (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] Part c

The diagram shows a sketch of y = f (x). On the same diagram, 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. HIGHER Paper 1 GCSE MATHEMATICS - LINEAR 16 (c) Part a&b [2]

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

The diagram shows a sketch of y = f (x). On the same diagram, 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. HIGHER Paper 1 GCSE MATHEMATICS - LINEAR 16 (c) ASSESSMENT OBJECTIVE Part a&b AO 1 – Recall and use knowledge of transformations of graphs and functions [2]

The diagram shows a sketch of y = f (x). On the same diagram, 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. HIGHER Paper 1 GCSE MATHEMATICS - LINEAR 16 (c) Part a&b [2]

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

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

HIGHER Paper 1 GCSE MATHEMATICS - LINEAR 17. Solve ASSESSMENT OBJECTIVE AO 1 – HIGHER Paper 1 GCSE MATHEMATICS - LINEAR 17. Solve ASSESSMENT OBJECTIVE AO 1 – Recall and use knowledge of solving algebraic fractions [7]

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

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

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

Pattern 1 Pattern 2 Pattern 3 Pattern 4 Diagrams not drawn to scale. HIGHER Pattern 1 Pattern 2 Pattern 3 Pattern 4 Diagrams not drawn to scale. HIGHER Paper 1 GCSE MATHEMATICS - LINEAR 18. Patterns are generated as shown in the diagram. Find the perimeter of Pattern 6 in the form a + √b , where a and b are whole numbers. Show your working. ASSESSMENT OBJECTIVE AO 3 – Interpret and analyse the problem and generate a strategy to find a numerical expression in surd form for the perimeter [4]

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

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

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

1. The numbers on opposite faces of a dice add up to 7. HIGHER 1. The numbers on opposite faces of a dice add up to 7. HIGHER Paper 2 GCSE MATHEMATICS - LINEAR Complete the following diagrams for nets of dice. ASSESSMENT OBJECTIVE AO 2 – Select and apply mathematical methods using knowledge of nets [4]

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

2. The owner of a takeaway coffee shop uses two types of paper cups. 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. HIGHER Paper 2 GCSE MATHEMATICS - LINEAR They can be stacked like this. . . (a) How high is a stack of 25 Hi-rim cups? [2] (b) A stack of Base-stay cups is 18. 6 cm high. How many Base-stay cups are in the stack? [2] Part (c)

2. The owner of a takeaway coffee shop uses two types of paper cups. 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. HIGHER Paper 2 GCSE MATHEMATICS - LINEAR They can be stacked like this. . . (a) How high is a stack of 25 Hi-rim cups? Remember there are 24 cups above the bottom cup Therefore 24 × 0. 5 NOT 25 × 0. 5 Height of cup 1 = 14 cm Height of cups 2 to 25 = 24 × 0. 5 = 12 cm Add height of bottom cup Total height = 14 + 12 = 26 cm [2] (b) A stack of Base-stay cups is 18. 6 cm high. How many Base-stay cups are in the stack? Remove cup 1: 18. 6 – 9 = 9. 6 Number of cups 9. 6 ÷ 1. 2 = 8 8 cups + 1 cup = 9 cups [2] Part (c) Reveal

2. The owner of a takeaway coffee shop uses two types of paper cups. 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. HIGHER Paper 2 GCSE MATHEMATICS - LINEAR They can be stacked like this. . . (a) How high is a stack of 25 Hi-rim cups? [2] (b) A stack of Base-stay cups is 18. 6 cm high. How many Base-stay cups are in the stack? ASSESSMENT OBJECTIVE Part (c) AO 2 – Select and apply mathematical methods using the visual information of how the cups are stacked [2]

2. The owner of a takeaway coffee shop uses two types of paper cups. 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. HIGHER Paper 2 GCSE MATHEMATICS - LINEAR They can be stacked like this. . . (a) How high is a stack of 25 Hi-rim cups? [2] (b) A stack of Base-stay cups is 18. 6 cm high. How many Base-stay cups are in the stack? [2] Part (c)

HIGHER Paper 2 GCSE MATHEMATICS - LINEAR 2 (c) A stack of Hi-rim cups HIGHER Paper 2 GCSE MATHEMATICS - LINEAR 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? [3] Part (a) & (b)

Height of Base-stay 20 × 1. 2 + 9 = 33 cm To find 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 HIGHER Paper 2 GCSE MATHEMATICS - LINEAR 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? [3] Part (a) & (b) Reveal

HIGHER Paper 2 GCSE MATHEMATICS - LINEAR 2 (c) A stack of Hi-rim cups HIGHER Paper 2 GCSE MATHEMATICS - LINEAR 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? [3] ASSESSMENT OBJECTIVE Part (a) & (b) AO 3 – Interpret and analyse the problem and generate a strategy to find the number of cups

HIGHER Paper 2 GCSE MATHEMATICS - LINEAR 2 (c) A stack of Hi-rim cups HIGHER Paper 2 GCSE MATHEMATICS - LINEAR 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? [3] Part (a) & (b)

HIGHER Paper 2 GCSE MATHEMATICS - LINEAR 3. Mrs Evans received an electricity bill HIGHER Paper 2 GCSE MATHEMATICS - LINEAR 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. [6]

Change to £ HIGHER Paper 2 GCSE MATHEMATICS - LINEAR 3. Mrs Evans received Change to £ HIGHER Paper 2 GCSE MATHEMATICS - LINEAR 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. [6] 1100 156. 20 Add on 191. 08 9. 55 Check your answer makes sense, an electricity bill isn’t usually thousands of pounds 200. 63 This means that they paid too much on their last bill. 188. 63 Reveal

HIGHER Paper 2 GCSE MATHEMATICS - LINEAR 3. Mrs Evans received an electricity bill HIGHER Paper 2 GCSE MATHEMATICS - LINEAR 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. [6] ASSESSMENT OBJECTIVE AO 2 – Select and apply mathematical methods using basic principles of household finance

HIGHER Paper 2 GCSE MATHEMATICS - LINEAR 3. Mrs Evans received an electricity bill HIGHER Paper 2 GCSE MATHEMATICS - LINEAR 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. [6]

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

(a) Are there any balls of another colour in the bag? Give a reason (a) Are there any balls of another colour in the bag? Give a reason for your answer. 0. 25 + 0. 14 + 0. 06 + 0. 15 + 0. 40 = 1 HIGHER Paper 2 GCSE MATHEMATICS - LINEAR 4. The table below shows the probabilities of selecting one ball at random from a bag of coloured balls. There are no balls of any other colour because the probabilities add up to 1. (b) What is the probability of selecting either a yellow or a purple ball? P(yellow or purple) = P(yellow) + P(purple) = 0. 06 + 0. 40 = 0. 46 [2] The ball can’t be yellow and purple at the same time, so the rule P(A or B) = P(A) + P(B) works. [2] Reveal

(a) Are there any balls of another colour in the bag? Give a reason (a) Are there any balls of another colour in the bag? Give a reason for your answer. HIGHER Paper 2 GCSE MATHEMATICS - LINEAR 4. The table below shows the probabilities of selecting one ball at random from a bag of coloured balls. ASSESSMENT OBJECTIVE AO 3 – Generating a strategy involving the law of total probability to solve the problem (b) What is the probability of selecting either a yellow or a purple ball? ASSESSMENT OBJECTIVE [2] AO 2 – Select and apply the probability law for mutually exclusive events [2]

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

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

12 + 10 = 11 22 + 10 = 14 Start with n = 12 + 10 = 11 22 + 10 = 14 Start with n = 1 32 + 10 = 19 [2] (b) Solve 8 x + 7 = 2 x + 10. 8 x – 2 x = 10 – 7 HIGHER Paper 2 GCSE MATHEMATICS - LINEAR 5. (a) Write down the first three terms of the sequence with an nth term of n 2 + 10. 6 x = 3 Be careful with signs x =3 6 x =1 2 [3] Reveal

5. (a) Write down the first three terms of the sequence with an nth 5. (a) Write down the first three terms of the sequence with an nth term of n 2 + 10. OBJECTIVE AO 1 – Recall and use knowledge of generating a number sequence from the nth term [2] (b) Solve 8 x + 7 = 2 x + 10. HIGHER Paper 2 GCSE MATHEMATICS - LINEAR ASSESSMENT OBJECTIVE AO 1 – Recall and use knowledge of solving linear equations with x on both sides [3]

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

[2] (b) Calculate 5. 6 × 3. 4 8. 1 – 2. 7 giving [2] (b) Calculate 5. 6 × 3. 4 8. 1 – 2. 7 giving your answer correct to two decimal places. HIGHER Paper 2 GCSE MATHEMATICS - LINEAR 6. (a) Express 104 as a percentage of 260. [2] (c) Two friends share £ 280 in the ratio 3: 4. Find how much each friend receives. [2]

6. (a) Express 104 as a percentage of 260. = 40% (b) Calculate 5. 6. (a) Express 104 as a percentage of 260. = 40% (b) Calculate 5. 6 × 3. 4 ( 8. 1 – 2. 7 ) Put brackets around the denominator when you put it into your calculator [2] giving your answer correct to two decimal places. HIGHER Paper 2 GCSE MATHEMATICS - LINEAR 104 × 100 % 260 3. 53 As this number is 5 or higher, 3. 52 rounds up to 3. 53 3. 52592592…. [2] (c) Two friends share £ 280 in the ratio 3: 4. Find how much each friend receives. 3+4=7 280 = 40 7 Total number of parts 3 × 40 = £ 120 4 × 40 = £ 160 How much each part is worth [2] Reveal

6. (a) Express 104 as a percentage of 260. OBJECTIVE AO 1 – Recall 6. (a) Express 104 as a percentage of 260. OBJECTIVE AO 1 – Recall and use knowledge of expressing one number as a percentage of another [2] (b) Calculate 5. 6 × 3. 4 8. 1 – 2. 7 giving your answer correct to two decimal places. HIGHER Paper 2 GCSE MATHEMATICS - LINEAR ASSESSMENT OBJECTIVE AO 1 - Recall and use knowledge of how a calculator orders its operations [2] (c) Two friends share £ 280 in the ratio 3: 4. Find how much each friend receives. ASSESSMENT OBJECTIVE AO 1 - Recall and use knowledge of sharing amounts in a given ratio [2]

[2] (b) Calculate 5. 6 × 3. 4 8. 1 – 2. 7 giving [2] (b) Calculate 5. 6 × 3. 4 8. 1 – 2. 7 giving your answer correct to two decimal places. HIGHER Paper 2 GCSE MATHEMATICS - LINEAR 6. (a) Express 104 as a percentage of 260. [2] (c) Two friends share £ 280 in the ratio 3: 4. Find how much each friend receives. [2]

HIGHER Paper 2 GCSE MATHEMATICS - LINEAR 7. The test scores of 20 people HIGHER Paper 2 GCSE MATHEMATICS - LINEAR 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. [3]

7. The test scores of 20 people were recorded and the results are summarised 7. The test scores of 20 people were recorded and the results are summarised in the following table. 4. 5 0 + 9 = 4. 5 2 14. 5 24. 5 Total = 20 HIGHER Paper 2 GCSE MATHEMATICS - LINEAR Mid-point Calculate an estimate for the mean of the test scores. mean = total of ‘mid-point × frequency’ total frequency = 4. 5 × 7 + 14. 5 × 11 + 24. 5 × 2 20 = 240 20 = 12 [3] Reveal

HIGHER Paper 2 GCSE MATHEMATICS - LINEAR 7. The test scores of 20 people HIGHER Paper 2 GCSE MATHEMATICS - LINEAR 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. ASSESSMENT OBJECTIVE AO 1 - Recall and use knowledge of estimating the mean from a grouped frequency table [3]

HIGHER Paper 2 GCSE MATHEMATICS - LINEAR 7. The test scores of 20 people HIGHER Paper 2 GCSE MATHEMATICS - LINEAR 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. [3]

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

3 – 3 [2] (b) On the graph paper below, draw the graph of 3 – 3 [2] (b) On the graph paper below, draw the graph of y = 2 x 2 – 5 for values of x between – 2 and 2. [2] (– 2)2 = 4, So, 2(4) – 5 = 3 HIGHER Paper 2 GCSE MATHEMATICS - LINEAR 8. The table shows some of the values of y = 2 x 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. (c) Write down the x-coordinates of the points of intersection of y = 2 x 2 – 5 with the x-axis. x ≈ 1. 6 and x ≈ – 1. 6 [2] (d) Write down the minimum value of y. – 5 Reveal [1]

[2] (b) On the graph paper below, draw the graph of y = 2 [2] (b) On the graph paper below, draw the graph of y = 2 x 2 – 5 for values of x between – 2 and 2. [2] ASSESSMENT HIGHER Paper 2 GCSE MATHEMATICS - LINEAR 8. The table shows some of the values of y = 2 x 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. OBJECTIVE AO 1 - Recall and use knowledge of drawing and interpreting quadratic equations (c) Write down the x-coordinates of the points of intersection of y = 2 x 2 – 5 with the x-axis. [2] (d) Write down the minimum value of y. [1]

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

A number is written on each of five cards. The cards are arranged in 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. HIGHER Paper 2 GCSE MATHEMATICS - LINEAR 9. You will be assessed on the quality of your written communication in this question. [3]

4 6 10 12 16 A number is written on each of five cards. 4 6 10 12 16 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. HIGHER Paper 2 GCSE MATHEMATICS - LINEAR 9. You will be assessed on the quality of your written communication in this question. [3] The median is 10. Therefore, the number on the middle card is 10. The largest number is 16. 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. Reveal

A number is written on each of five cards. The cards are arranged in 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. HIGHER Paper 2 GCSE MATHEMATICS - LINEAR 9. You will be assessed on the quality of your written communication in this question. ASSESSMENT OBJECTIVE AO 3 – Interpret and analyse the problem to generate a strategy using knowledge of mean, median and range [3]

A number is written on each of five cards. The cards are arranged in 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. HIGHER Paper 2 GCSE MATHEMATICS - LINEAR 9. You will be assessed on the quality of your written communication in this question. [3]

Diagram not drawn to scale. The lengths of all the edges of the cuboid Diagram not drawn to scale. The lengths of all the edges of the cuboid are increased by 20%. Find the percentage increase in the volume of the cuboid. HIGHER Paper 2 GCSE MATHEMATICS - LINEAR 10. The diagram shows a cuboid. [4]

Diagram not drawn to scale. The lengths of all the edges of the cuboid Diagram not drawn to scale. The lengths of all the edges of the cuboid are increased by 20%. Find the percentage increase in the volume of the cuboid. HIGHER Paper 2 GCSE MATHEMATICS - LINEAR 10. The diagram shows a cuboid. Original length is 100% Then, scale factor is 120% = 1. 23 = 1. 728 As there are 3 dimensions, we need to cube the scale factor Percentage increase = 1. 728 – 1 = 0. 728 × 100% = 72. 8% [4] Reveal

Diagram not drawn to scale. The lengths of all the edges of the cuboid Diagram not drawn to scale. The lengths of all the edges of the cuboid are increased by 20%. Find the percentage increase in the volume of the cuboid. HIGHER Paper 2 GCSE MATHEMATICS - LINEAR 10. The diagram shows a cuboid. ASSESSMENT OBJECTIVE AO 2 – Select and apply mathematical methods to calculate the percentage increase [4]

Diagram not drawn to scale. The lengths of all the edges of the cuboid Diagram not drawn to scale. The lengths of all the edges of the cuboid are increased by 20%. Find the percentage increase in the volume of the cuboid. HIGHER Paper 2 GCSE MATHEMATICS - LINEAR 10. The diagram shows a cuboid. [4]

HIGHER Paper 2 GCSE MATHEMATICS - LINEAR 11. The diagram below shows an ornamental HIGHER Paper 2 GCSE MATHEMATICS - LINEAR 11. The diagram below shows an ornamental archway, which is 8 m wide, 6. 5 m high and 2 m deep, over a cycle path. The arch has a semi-circular cross-section with diameter 5 m. Given that one tin of paint is sufficient to cover a surface of area 5 m 2, find the number of tins of paint needed to paint all the surfaces of the archway. [9]

There are 6 surfaces: 8 m Top 2 m HIGHER Paper 2 GCSE MATHEMATICS There are 6 surfaces: 8 m Top 2 m HIGHER Paper 2 GCSE MATHEMATICS - LINEAR 11. The diagram below shows an ornamental archway, which is 8 m wide, 6. 5 m high and 2 m deep, over a cycle path. The arch has a semi-circular cross-section with diameter 5 m. Given that one tin of paint is sufficient to cover a surface of area 5 m 2, find the number of tins of paint needed to paint all the surfaces of the archway. × 2 6. 5 m 2 m 6. 5 × 2 = 26 m 2 Sides 8 m × 2 8 × 2 = 16 m 2 Front and back Under the arch [9] Under the arch is the curved surface area of half a cylinder Two equal semicircles 2 × rectangle – circle = 2 × 6. 5 × 8 – ( × 2. 52) = 84. 37 m 2 Part of cylinder surface = ½ circumference of circle × depth of bridge = ½ × × 5 × 2 = 15. 71 m 2 Total = 16 + 26 + 84. 37 + 15. 71 = 142. 08 m 2 Number of tins of paint = 142. 08 = 28. 42 or 29 full tins of paint 5 Reveal

HIGHER Paper 2 GCSE MATHEMATICS - LINEAR 11. The diagram below shows an ornamental HIGHER Paper 2 GCSE MATHEMATICS - LINEAR 11. The diagram below shows an ornamental archway, which is 8 m wide, 6. 5 m high and 2 m deep, over a cycle path. The arch has a semi-circular cross-section with diameter 5 m. Given that one tin of paint is sufficient to cover a surface of area 5 m 2, find the number of tins of paint needed to paint all the surfaces of the archway. ASSESSMENT OBJECTIVE AO 2 – Select and apply surface area formulae to find the number of tins of paint needed [9]

HIGHER Paper 2 GCSE MATHEMATICS - LINEAR 11. The diagram below shows an ornamental HIGHER Paper 2 GCSE MATHEMATICS - LINEAR 11. The diagram below shows an ornamental archway, which is 8 m wide, 6. 5 m high and 2 m deep, over a cycle path. The arch has a semi-circular cross-section with diameter 5 m. Given that one tin of paint is sufficient to cover a surface of area 5 m 2, find the number of tins of paint needed to paint all the surfaces of the archway. [9]

HIGHER Paper 2 GCSE MATHEMATICS - LINEAR 12. The dimensions of a rectangle are: HIGHER Paper 2 GCSE MATHEMATICS - LINEAR 12. The dimensions of a rectangle are: Length (x + 5) cm Width (x – 2) cm The area of the rectangle is 120 cm 2. Find the value of x. [4]

x– 2 x+5 HIGHER Paper 2 GCSE MATHEMATICS - LINEAR 12. The dimensions of x– 2 x+5 HIGHER Paper 2 GCSE MATHEMATICS - LINEAR 12. The dimensions of a rectangle are: Length (x + 5) cm Width (x – 2) cm The area of the rectangle is 120 cm 2. Find the value of x. (x + 5)(x – 2) = 120 x 2 + 3 x – 10 = 120 x 2 + 3 x – 130 = 0 (x + 13)(x – 10) = 0 Remember to equate to zero before factorizing x = – 13 or x = 10 Cannot be x = – 13, so x = 10 [4] Reveal

HIGHER Paper 2 GCSE MATHEMATICS - LINEAR 12. The dimensions of a rectangle are: HIGHER Paper 2 GCSE MATHEMATICS - LINEAR 12. The dimensions of a rectangle are: Length (x + 5) cm Width (x – 2) cm The area of the rectangle is 120 cm 2. Find the value of x. ASSESSMENT OBJECTIVE AO 2 – Select and apply mathematical methods using knowledge of area of a rectangle [4]

HIGHER Paper 2 GCSE MATHEMATICS - LINEAR 12. The dimensions of a rectangle are: HIGHER Paper 2 GCSE MATHEMATICS - LINEAR 12. The dimensions of a rectangle are: Length (x + 5) cm Width (x – 2) cm The area of the rectangle is 120 cm 2. Find the value of x. [4]

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

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

Make sure that you clearly indicate the region that represents your answer. [4] HIGHER Make sure that you clearly indicate the region that represents your answer. [4] HIGHER Paper 2 GCSE MATHEMATICS - LINEAR 13. On the graph paper below, draw the region which satisfies all of the following inequalities. ASSESSMENT OBJECTIVE AO 1 – Recall and use knowledge of use of straight line graphs to locate regions given by linear inequalities

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

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

14. (a) Factorise 6 x 2 + 18 xy. Difference of two squares [2] 14. (a) Factorise 6 x 2 + 18 xy. Difference of two squares [2] (b) Factorise x 2 – 25. (x + 5)(x – 5) (c) Solve 4 n – 5 < n + 22. HIGHER Paper 2 GCSE MATHEMATICS - LINEAR 6 x (x + 3 y) 4 n – n < 22 + 5 3 n < 27 3 (d) Solve the equation decimal places. 3 x 2 [1] Use inequality sign throughout [2] + 19 x + 11 = 0, giving your solutions correct to two b 2 x = – b ± √ – 4 ac 2 a with a = 3, b = 19, c = 11 2 x = – 19 ± √ 19 – (4 × 3 × 11) 2× 3 x = – 19 ± √ 229 6 x = – 0. 64, x = – 5. 69 [3] If the question asks for solutions to a given number of decimal places, don’t try and factorise, use the formula. Reveal

14. (a) Factorise 6 x 2 + 18 xy. (b) Factorise x 2 – 14. (a) Factorise 6 x 2 + 18 xy. (b) Factorise x 2 – 25. ASSESSMENT OBJECTIVE (a) and (b): AO 1 – Recall and use knowledge of factorising quadratics [1] (c) Solve 4 n – 5 < n + 22. HIGHER Paper 2 GCSE MATHEMATICS - LINEAR [2] (c): AO 1 – Recall and use knowledge of solving linear OBJECTIVE inequalities (d) Solve the equation 3 x 2 + 19 x + 11 = 0, giving your solutions correct to two ASSESSMENT decimal places. ASSESSMENT OBJECTIVE [2] [3] (d): AO 1 – Recall and use knowledge of solving quadratic equations using the quadratic formula

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

(a) Find an estimate for the median of this distribution. [1] (b) Draw a (a) Find an estimate for the median of this distribution. [1] (b) Draw a histogram to illustrate the distribution on the graph below. HIGHER Paper 2 GCSE MATHEMATICS - LINEAR 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. [2]

15. There are 100 pupils in Year 10. The time taken by each pupil 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. 10 10 50 10 10 (a) Find an estimate for the median of this distribution. Median 20 50 30 [1] (b) Draw a histogram to illustrate the distribution on the graph below. HIGHER Paper 2 GCSE MATHEMATICS - LINEAR Interval width Frequency density 4 3 2 1 Areas of bars show the frequency (no. of pupils) [2] frequency = density interval width 6 = 0. 6 10 14 = 0. 7 20 0. 6, 1. 9, 2. 5, 3. 6, 0. 7 Use these values to decide on a scale Reveal

AO 1 - Recall and (a) Find an estimate for the median of this AO 1 - Recall and (a) Find an estimate for the median of this distribution. ASSESSMENT OBJECTIVE use knowledge of median from grouped frequency table [1] (b) Draw a histogram to illustrate the distribution on the graph below. HIGHER Paper 2 GCSE MATHEMATICS - LINEAR 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. [2] ASSESSMENT OBJECTIVE AO 1 - Recall and use knowledge of calculating frequency density to construct a histogram

(a) Find an estimate for the median of this distribution. [1] (b) Draw a (a) Find an estimate for the median of this distribution. [1] (b) Draw a histogram to illustrate the distribution on the graph below. HIGHER Paper 2 GCSE MATHEMATICS - LINEAR 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. [2]

The height of the frustum is 10 cm, the radius of the base is The height of the frustum is 10 cm, the radius of the base is 8 cm and the radius of the top is 3 cm. Find the volume of the frustum. Diagram not drawn to scale. HIGHER Paper 2 GCSE MATHEMATICS - LINEAR 16. The diagram shows a frustum of a cone. [6]

The height of the frustum is 10 cm, the radius of the base is The height of the frustum is 10 cm, the radius of the base is 8 cm and the radius of the top is 3 cm. Find the volume of the frustum. Ratio of radii is 3 : 8 Ratio of heights is h : h + 10 Diagram not drawn to scale. Start by letting height of small cone be h Ratio of radii = Ratio of heights HIGHER Paper 2 GCSE MATHEMATICS - LINEAR 16. The diagram shows a frustum of a cone. h h + 10 3 cm 16 cm 8 cm 3 = h. 8 h + 10 3(h + 10) = 8 h 3 h + 30 = 8 h 30 = 5 h h =6 6 cm 8 cm 3 cm Volume of frustum = Volume of large cone – Volume of small cone = ⅓ π 82 × 16 – ⅓ π 32 × 6 = 1015. 78 cm 3 [6] Reveal

The height of the frustum is 10 cm, the radius of the base is The height of the frustum is 10 cm, the radius of the base is 8 cm and the radius of the top is 3 cm. Find the volume of the frustum. Diagram not drawn to scale. HIGHER Paper 2 GCSE MATHEMATICS - LINEAR 16. The diagram shows a frustum of a cone. ASSESSMENT OBJECTIVE AO 1 - Recall and use knowledge of similar shapes and formula for the volume of a cone [6]

The height of the frustum is 10 cm, the radius of the base is The height of the frustum is 10 cm, the radius of the base is 8 cm and the radius of the top is 3 cm. Find the volume of the frustum. Diagram not drawn to scale. HIGHER Paper 2 GCSE MATHEMATICS - LINEAR 16. The diagram shows a frustum of a cone. [6]

HIGHER Paper 2 GCSE MATHEMATICS - LINEAR 17. (a) Using the axes below, sketch HIGHER Paper 2 GCSE MATHEMATICS - LINEAR 17. (a) Using the axes below, sketch the graph of y = sin x for values of x from – 180° to 360°. [2] (b) Find all solutions of the following equation in the range – 180° to 360°. sin x = – 0. 788 [3]

17. (a) Using the axes below, sketch Plot – 1 and = sin x 17. (a) Using the axes below, sketch Plot – 1 and = sin x the graph of y 1 on the for values of x from – 180° to 360°. [2] 1 – 180 HIGHER Paper 2 GCSE MATHEMATICS - LINEAR y-axis and – 180º, – 90º, 180º, 270º, 360º at even intervals on the x-axis. – 90 180 270 360 – 0. 788 – 1 Use your calculator to find first value of x (b) Find all solutions of the following equation in the range – 180° to 360°. sin x = – 0. 788 [3] x = sin (– 0. 788) x = – 52º (to the nearest º) Using graph … x = – 180º + 52º, x = 360º – 52º x = – 128º, x = 232º, x = 308º Reveal

ASSESSMENT OBJECTIVE HIGHER Paper 2 GCSE MATHEMATICS - LINEAR 17. (a) Using the axes ASSESSMENT OBJECTIVE HIGHER Paper 2 GCSE MATHEMATICS - LINEAR 17. (a) Using the axes below, sketch the graph of y = sin x for values of x from – 180° to 360°. [2] AO 1 – Recall and use knowledge of sketching trigonometric graphs (b) Find all solutions of the following equation in the range – 180° to 360°. – 0. 788 ASSESSMENTsin x = AO 1 – Recall and use knowledge of interpreting trigonometric graphs OBJECTIVE with the aid of a calculator [3]

HIGHER Paper 2 GCSE MATHEMATICS - LINEAR 17. (a) Using the axes below, sketch HIGHER Paper 2 GCSE MATHEMATICS - LINEAR 17. (a) Using the axes below, sketch the graph of y = sin x for values of x from – 180° to 360°. [2] (b) Find all solutions of the following equation in the range – 180° to 360°. sin x = – 0. 788 [3]

18. Diagram not drawn to scale. HIGHER Paper 2 GCSE MATHEMATICS - LINEAR In 18. Diagram not drawn to scale. HIGHER Paper 2 GCSE MATHEMATICS - LINEAR In the diagram the circle has centre O and radius 5. 2 cm. Calculate the perimeter of the shaded region. [8]

18. The perimeter is the line AB added to the arc AB Diagram not 18. The perimeter is the line AB added to the arc AB Diagram not drawn to scale. HIGHER Paper 2 GCSE MATHEMATICS - LINEAR In the diagram the circle has centre O and radius 5. 2 cm. Calculate the perimeter of the shaded region. The arc AB is 68 of the circumference. 360 arc AB = 68 × 2π × 5. 2 = 6. 1714…. . 360 Don’t round answers too early Use the cosine rule to work out the length of AB. AB 2 = 5. 22 + 5. 22 – 2 × 5. 2 × cos 68º AB = 5. 8156…. Perimeter = 5. 8156…+ 6. 1714… = 11. 99 cm (correct to 2 decimal places) [8] Reveal

18. Diagram not drawn to scale. HIGHER Paper 2 GCSE MATHEMATICS - LINEAR In 18. Diagram not drawn to scale. HIGHER Paper 2 GCSE MATHEMATICS - LINEAR In the diagram the circle has centre O and radius 5. 2 cm. Calculate the perimeter of the shaded region. ASSESSMENT OBJECTIVE AO 3 – Interpret and analyse the problem and generate a strategy to find the length of the chord AB and the length of the minor arc AB [8]

18. Diagram not drawn to scale. HIGHER Paper 2 GCSE MATHEMATICS - LINEAR In 18. Diagram not drawn to scale. HIGHER Paper 2 GCSE MATHEMATICS - LINEAR In the diagram the circle has centre O and radius 5. 2 cm. Calculate the perimeter of the shaded region. [8]