Mixed Topic Worksheet Grades 6/7: Day 046
- 1
Question 1. A cylinder lies on its side.
The length of the cylinder is 9 m and the radius of each end is 1.5 m.
Work out the total surface area of the cylinder.
Give your answer to 1 decimal place.Surface Area of Cylinders▶ Show worked answerHide worked answer
- M1: 2 × π × 1.5 × 9 and 2 × π × 1.5²
- M1: 84.82... + 14.13...
- A1: 99.0
Answer: 99.0 m²[3 marks] - 2
Question 2. Delays, in minutes, of two bus companies. X: minimum 0, lower quartile 2, median 4, upper quartile 7, maximum 15. Y: minimum 1, lower quartile 3, median 5, upper quartile 6, maximum 9. Compare the delays.
Comparing Data Using Box Plots▶ Show worked answerHide worked answer
- B1: median: X (4) is lower than Y (5), so X has the shorter typical delay
- B1: IQR: X is 5 and Y is 3, so Y is more consistent
Answer: X has the lower median delay (4 < 5) but a larger interquartile range (5 > 3), so Y's delays are more consistent.[2 marks] - 3
Question 3. Simplify fully dfracx² + 7x + 10x² + 2x
Simplifying Algebraic Fractions▶ Show worked answerHide worked answer
- M1: numerator (x + 2)(x + 5)
- M1: denominator x(x + 2)
- A1: dfracx + 5x
Answer: dfracx + 5x[3 marks] - 4
Question 4. Express 0.dot3dot4 as a fraction in its simplest form.
You must show all your working.Writing Recurring Decimals as Fractions▶ Show worked answerHide worked answer
- M1: multiplies by 100 and subtracts x, so the recurring parts cancel
- A1: 99x = 34, so x = dfrac3499
Answer: dfrac3499[2 marks] - 5
Question 5. Here is triangle ABC.
Work out the size of angle ABC.
Give your answer to 1 decimal place.Finding Angles Using the Cosine Rule▶ Show worked answerHide worked answer
- M1: 16² = 19² + 13² - 2 × 19 × 13 × cos ABC
- M1: cos ABC = dfrac19² + 13² - 16²2 × 19 × 13 = 0.5547
- A1: ABC = 56.3^°
Answer: 56.3^°[3 marks]
Mixed Topic Worksheet Grades 6/7: Day 046
- 1
Question 1. A cylinder lies on its side.
[3 marks]
The length of the cylinder is 9 m and the radius of each end is 1.5 m.
Work out the total surface area of the cylinder.
Give your answer to 1 decimal place.Surface Area of Cylinders▶ Show worked answerHide worked answer
- M1: 2 × π × 1.5 × 9 and 2 × π × 1.5²
- M1: 84.82... + 14.13...
- A1: 99.0
Answer: 99.0 m² - 2
Question 2. Delays, in minutes, of two bus companies. X: minimum 0, lower quartile 2, median 4, upper quartile 7, maximum 15. Y: minimum 1, lower quartile 3, median 5, upper quartile 6, maximum 9. Compare the delays.
[2 marks]Comparing Data Using Box Plots▶ Show worked answerHide worked answer
- B1: median: X (4) is lower than Y (5), so X has the shorter typical delay
- B1: IQR: X is 5 and Y is 3, so Y is more consistent
Answer: X has the lower median delay (4 < 5) but a larger interquartile range (5 > 3), so Y's delays are more consistent. - 3
Question 3. Simplify fully dfracx² + 7x + 10x² + 2x
[3 marks]Simplifying Algebraic Fractions▶ Show worked answerHide worked answer
- M1: numerator (x + 2)(x + 5)
- M1: denominator x(x + 2)
- A1: dfracx + 5x
Answer: dfracx + 5x - 4
Question 4. Express 0.dot3dot4 as a fraction in its simplest form.
[2 marks]
You must show all your working.Writing Recurring Decimals as Fractions▶ Show worked answerHide worked answer
- M1: multiplies by 100 and subtracts x, so the recurring parts cancel
- A1: 99x = 34, so x = dfrac3499
Answer: dfrac3499 - 5
Question 5. Here is triangle ABC.
[3 marks]
Work out the size of angle ABC.
Give your answer to 1 decimal place.Finding Angles Using the Cosine Rule▶ Show worked answerHide worked answer
- M1: 16² = 19² + 13² - 2 × 19 × 13 × cos ABC
- M1: cos ABC = dfrac19² + 13² - 16²2 × 19 × 13 = 0.5547
- A1: ABC = 56.3^°
Answer: 56.3^°
Mixed Topic Worksheet Grades 6/7: Day 046
- 1
Question 1. A cylinder lies on its side.
The length of the cylinder is 9 m and the radius of each end is 1.5 m.
Work out the total surface area of the cylinder.
Give your answer to 1 decimal place.Surface Area of Cylinders▶ Show worked answerHide worked answer
- M1: 2 × π × 1.5 × 9 and 2 × π × 1.5²
- M1: 84.82... + 14.13...
- A1: 99.0
Answer: 99.0 m²[3 marks] - 2
Question 2. Delays, in minutes, of two bus companies. X: minimum 0, lower quartile 2, median 4, upper quartile 7, maximum 15. Y: minimum 1, lower quartile 3, median 5, upper quartile 6, maximum 9. Compare the delays.
Comparing Data Using Box Plots▶ Show worked answerHide worked answer
- B1: median: X (4) is lower than Y (5), so X has the shorter typical delay
- B1: IQR: X is 5 and Y is 3, so Y is more consistent
Answer: X has the lower median delay (4 < 5) but a larger interquartile range (5 > 3), so Y's delays are more consistent.[2 marks] - 3
Question 3. Simplify fully dfracx² + 7x + 10x² + 2x
Simplifying Algebraic Fractions▶ Show worked answerHide worked answer
- M1: numerator (x + 2)(x + 5)
- M1: denominator x(x + 2)
- A1: dfracx + 5x
Answer: dfracx + 5x[3 marks] - 4
Question 4. Express 0.dot3dot4 as a fraction in its simplest form.
You must show all your working.Writing Recurring Decimals as Fractions▶ Show worked answerHide worked answer
- M1: multiplies by 100 and subtracts x, so the recurring parts cancel
- A1: 99x = 34, so x = dfrac3499
Answer: dfrac3499[2 marks] - 5
Question 5. Here is triangle ABC.
Work out the size of angle ABC.
Give your answer to 1 decimal place.Finding Angles Using the Cosine Rule▶ Show worked answerHide worked answer
- M1: 16² = 19² + 13² - 2 × 19 × 13 × cos ABC
- M1: cos ABC = dfrac19² + 13² - 16²2 × 19 × 13 = 0.5547
- A1: ABC = 56.3^°
Answer: 56.3^°[3 marks]