Mixed Topic Worksheet Grades 6/7: Day 002
- 1
Question 1. Rectangle C and rectangle D are similar.
Rectangle D is 24 cm long and 18 cm wide.
Rectangle C is 6 cm wide.
Work out the length of rectangle C.Similar Side Lengths▶ Show worked answerHide worked answer
- M1: 6 ÷ 18 = dfrac13
- A1: dfrac13 × 24 = 8
Answer: 8 cm[2 marks] - 2
Question 2. Exam marks: minimum 5, lower quartile 52, median 60, upper quartile 70, maximum 95. Work out the range and the IQR, and say which describes the spread of most marks better.
Benefits of IQR & Range▶ Show worked answerHide worked answer
- B1: range 90, IQR = 70 - 52 = 18
- B1: IQR is the better measure for most marks
- B1: it ignores the extreme values 5 and 95
Answer: Range 90, IQR 18; the IQR is better as it ignores extreme values[3 marks] - 3
Question 3. Spinner A has sections numbered 1, 2, 3 and 4.
Spinner B has sections numbered 1, 3 and 5.
Each spinner is spun once and the two scores are added together.
Each section of each spinner is equally likely.
By listing all the outcomes, work out the probability that the total score is at least 6.Calculating Combinations▶ Show worked answerHide worked answer
- M1: lists or counts all 4 × 3 = 12 outcomes
- M1: counts the 6 outcomes with a total of at least 6
- A1: dfrac12
Answer: dfrac12[3 marks] - 4
Question 4. Ben says the point (4, 0) satisfies 3x - 2y < 12.
Cat says it does not.
Who is correct? Show your working.Sketching Linear Inequalities▶ Show worked answerHide worked answer
- M1: substitutes x = 4 and y = 0 to get 3 × 4 - 2 × 0 = 12
- A1: Cat, because 12 is equal to 12 so the point is on the boundary
Answer: Cat is correct[2 marks] - 5
Question 5. Here is triangle XYZ.
Work out the size of angle ZXY.
Give your answer to 1 decimal place.Finding Angles Using the Sine Rule▶ Show worked answerHide worked answer
- M1: dfracsin ZXY6.6 = dfracsin 71^°8.7
- M1: sin ZXY = dfrac6.6 × sin 71^°8.7
- A1: 45.8
Answer: 45.8[3 marks]
Mixed Topic Worksheet Grades 6/7: Day 002
- 1
Question 1. Rectangle C and rectangle D are similar.
[2 marks]
Rectangle D is 24 cm long and 18 cm wide.
Rectangle C is 6 cm wide.
Work out the length of rectangle C.Similar Side Lengths▶ Show worked answerHide worked answer
- M1: 6 ÷ 18 = dfrac13
- A1: dfrac13 × 24 = 8
Answer: 8 cm - 2
Question 2. Exam marks: minimum 5, lower quartile 52, median 60, upper quartile 70, maximum 95. Work out the range and the IQR, and say which describes the spread of most marks better.
[3 marks]Benefits of IQR & Range▶ Show worked answerHide worked answer
- B1: range 90, IQR = 70 - 52 = 18
- B1: IQR is the better measure for most marks
- B1: it ignores the extreme values 5 and 95
Answer: Range 90, IQR 18; the IQR is better as it ignores extreme values - 3
Question 3. Spinner A has sections numbered 1, 2, 3 and 4.
[3 marks]
Spinner B has sections numbered 1, 3 and 5.
Each spinner is spun once and the two scores are added together.
Each section of each spinner is equally likely.
By listing all the outcomes, work out the probability that the total score is at least 6.Calculating Combinations▶ Show worked answerHide worked answer
- M1: lists or counts all 4 × 3 = 12 outcomes
- M1: counts the 6 outcomes with a total of at least 6
- A1: dfrac12
Answer: dfrac12 - 4
Question 4. Ben says the point (4, 0) satisfies 3x - 2y < 12.
[2 marks]
Cat says it does not.
Who is correct? Show your working.Sketching Linear Inequalities▶ Show worked answerHide worked answer
- M1: substitutes x = 4 and y = 0 to get 3 × 4 - 2 × 0 = 12
- A1: Cat, because 12 is equal to 12 so the point is on the boundary
Answer: Cat is correct - 5
Question 5. Here is triangle XYZ.
[3 marks]
Work out the size of angle ZXY.
Give your answer to 1 decimal place.Finding Angles Using the Sine Rule▶ Show worked answerHide worked answer
- M1: dfracsin ZXY6.6 = dfracsin 71^°8.7
- M1: sin ZXY = dfrac6.6 × sin 71^°8.7
- A1: 45.8
Answer: 45.8
Mixed Topic Worksheet Grades 6/7: Day 002
- 1
Question 1. Rectangle C and rectangle D are similar.
Rectangle D is 24 cm long and 18 cm wide.
Rectangle C is 6 cm wide.
Work out the length of rectangle C.Similar Side Lengths▶ Show worked answerHide worked answer
- M1: 6 ÷ 18 = dfrac13
- A1: dfrac13 × 24 = 8
Answer: 8 cm[2 marks] - 2
Question 2. Exam marks: minimum 5, lower quartile 52, median 60, upper quartile 70, maximum 95. Work out the range and the IQR, and say which describes the spread of most marks better.
Benefits of IQR & Range▶ Show worked answerHide worked answer
- B1: range 90, IQR = 70 - 52 = 18
- B1: IQR is the better measure for most marks
- B1: it ignores the extreme values 5 and 95
Answer: Range 90, IQR 18; the IQR is better as it ignores extreme values[3 marks] - 3
Question 3. Spinner A has sections numbered 1, 2, 3 and 4.
Spinner B has sections numbered 1, 3 and 5.
Each spinner is spun once and the two scores are added together.
Each section of each spinner is equally likely.
By listing all the outcomes, work out the probability that the total score is at least 6.Calculating Combinations▶ Show worked answerHide worked answer
- M1: lists or counts all 4 × 3 = 12 outcomes
- M1: counts the 6 outcomes with a total of at least 6
- A1: dfrac12
Answer: dfrac12[3 marks] - 4
Question 4. Ben says the point (4, 0) satisfies 3x - 2y < 12.
Cat says it does not.
Who is correct? Show your working.Sketching Linear Inequalities▶ Show worked answerHide worked answer
- M1: substitutes x = 4 and y = 0 to get 3 × 4 - 2 × 0 = 12
- A1: Cat, because 12 is equal to 12 so the point is on the boundary
Answer: Cat is correct[2 marks] - 5
Question 5. Here is triangle XYZ.
Work out the size of angle ZXY.
Give your answer to 1 decimal place.Finding Angles Using the Sine Rule▶ Show worked answerHide worked answer
- M1: dfracsin ZXY6.6 = dfracsin 71^°8.7
- M1: sin ZXY = dfrac6.6 × sin 71^°8.7
- A1: 45.8
Answer: 45.8[3 marks]