Mixed Topic Worksheet Grades 6/7: Day 033
- 1
Question 1. A trader buys a coat for £80.
She sells the coat at a profit of 35% of the price she paid.
Work out the selling price.Profit & Loss▶ Show worked answerHide worked answer
- M1: 35% of 80: 10% = 8 and 5% = 4, so 35% = 28
- M1: 80 + 28
- A1: £108
Answer: £108[3 marks] - 2
Question 2. The table shows information about the times, in minutes, taken by 40 students to complete a puzzle.
Complete the cumulative frequency column of the table.Filling in Cumulative Frequency Tables▶ Show worked answerHide worked answer
- M1: 3 + 9 for the second class, then 12 + 14 for the third
- A1: 12 and 26 correct
- A1: 36 and 40 correct
Answer: 3, 12, 26, 36, 40[3 marks] - 3
Question 3. Two jars are similar.
The volumes of the jars are 480 ml and 1620 ml.
The height of the larger jar is 27 cm.
Work out the height of the smaller jar.Similar Areas & Volumes▶ Show worked answerHide worked answer
- M1: sqrt[3]480 ÷ 1620
- M1: 27 × dfrac23
- A1: 18
Answer: 18 cm[3 marks] - 4
Question 4. Here are three points.
A(1, 2) B(4, 3) C(0, 5)
Which of these points lie in the region defined by
y > 2x - 3 and x + y ≤ 6?
You must show your working.Sketching Linear Inequalities▶ Show worked answerHide worked answer
- M1: substitutes the points into both inequalities
- A1: A: 2 > -1 and 3 ≤ 6; C: 5 > -3 and 5 ≤ 6, so both lie in the region
- A1: B: 3 > 5 is false, so B does not; answer A and C
Answer: A and C[3 marks] - 5
Question 5. Two positive integers differ by 4.
The difference between the squares of the two integers is 112.
Use algebra to work out the two integers.Proof with Square Numbers▶ Show worked answerHide worked answer
- M1: (n + 4)² - n² = 8n + 16
- M1: 8n + 16 = 112
- A1: n = 12 so the integers are 12 and 16
Answer: 12 and 16[3 marks]
Mixed Topic Worksheet Grades 6/7: Day 033
- 1
Question 1. A trader buys a coat for £80.
[3 marks]
She sells the coat at a profit of 35% of the price she paid.
Work out the selling price.Profit & Loss▶ Show worked answerHide worked answer
- M1: 35% of 80: 10% = 8 and 5% = 4, so 35% = 28
- M1: 80 + 28
- A1: £108
Answer: £108 - 2
Question 2. The table shows information about the times, in minutes, taken by 40 students to complete a puzzle.
[3 marks]
Complete the cumulative frequency column of the table.Filling in Cumulative Frequency Tables▶ Show worked answerHide worked answer
- M1: 3 + 9 for the second class, then 12 + 14 for the third
- A1: 12 and 26 correct
- A1: 36 and 40 correct
Answer: 3, 12, 26, 36, 40 - 3
Question 3. Two jars are similar.
[3 marks]
The volumes of the jars are 480 ml and 1620 ml.
The height of the larger jar is 27 cm.
Work out the height of the smaller jar.Similar Areas & Volumes▶ Show worked answerHide worked answer
- M1: sqrt[3]480 ÷ 1620
- M1: 27 × dfrac23
- A1: 18
Answer: 18 cm - 4
Question 4. Here are three points.
[3 marks]
A(1, 2) B(4, 3) C(0, 5)
Which of these points lie in the region defined by
y > 2x - 3 and x + y ≤ 6?
You must show your working.Sketching Linear Inequalities▶ Show worked answerHide worked answer
- M1: substitutes the points into both inequalities
- A1: A: 2 > -1 and 3 ≤ 6; C: 5 > -3 and 5 ≤ 6, so both lie in the region
- A1: B: 3 > 5 is false, so B does not; answer A and C
Answer: A and C - 5
Question 5. Two positive integers differ by 4.
[3 marks]
The difference between the squares of the two integers is 112.
Use algebra to work out the two integers.Proof with Square Numbers▶ Show worked answerHide worked answer
- M1: (n + 4)² - n² = 8n + 16
- M1: 8n + 16 = 112
- A1: n = 12 so the integers are 12 and 16
Answer: 12 and 16
Mixed Topic Worksheet Grades 6/7: Day 033
- 1
Question 1. A trader buys a coat for £80.
She sells the coat at a profit of 35% of the price she paid.
Work out the selling price.Profit & Loss▶ Show worked answerHide worked answer
- M1: 35% of 80: 10% = 8 and 5% = 4, so 35% = 28
- M1: 80 + 28
- A1: £108
Answer: £108[3 marks] - 2
Question 2. The table shows information about the times, in minutes, taken by 40 students to complete a puzzle.
Complete the cumulative frequency column of the table.Filling in Cumulative Frequency Tables▶ Show worked answerHide worked answer
- M1: 3 + 9 for the second class, then 12 + 14 for the third
- A1: 12 and 26 correct
- A1: 36 and 40 correct
Answer: 3, 12, 26, 36, 40[3 marks] - 3
Question 3. Two jars are similar.
The volumes of the jars are 480 ml and 1620 ml.
The height of the larger jar is 27 cm.
Work out the height of the smaller jar.Similar Areas & Volumes▶ Show worked answerHide worked answer
- M1: sqrt[3]480 ÷ 1620
- M1: 27 × dfrac23
- A1: 18
Answer: 18 cm[3 marks] - 4
Question 4. Here are three points.
A(1, 2) B(4, 3) C(0, 5)
Which of these points lie in the region defined by
y > 2x - 3 and x + y ≤ 6?
You must show your working.Sketching Linear Inequalities▶ Show worked answerHide worked answer
- M1: substitutes the points into both inequalities
- A1: A: 2 > -1 and 3 ≤ 6; C: 5 > -3 and 5 ≤ 6, so both lie in the region
- A1: B: 3 > 5 is false, so B does not; answer A and C
Answer: A and C[3 marks] - 5
Question 5. Two positive integers differ by 4.
The difference between the squares of the two integers is 112.
Use algebra to work out the two integers.Proof with Square Numbers▶ Show worked answerHide worked answer
- M1: (n + 4)² - n² = 8n + 16
- M1: 8n + 16 = 112
- A1: n = 12 so the integers are 12 and 16
Answer: 12 and 16[3 marks]