Mixed Topic Worksheet Grades 8/9: Day 050
- 1
Question 1. The histogram shows the ages, a years, of some people. The vertical axis is not numbered. The frequency for 0 < a ≤ 10 is 18. Work out the frequency for 20 < a ≤ 40.
Interpreting Histograms▶ Show worked answerHide worked answer
- M1: 18 ÷ (3 × 10) for the area scale
- M1: 4 × 20 × 0.6
- A1: 48
Answer: 48[3 marks] - 2
Question 2. ABCDEFGH is a cuboid.
Work out the size of the angle between the line BG and the plane ABCD.
Give your answer to 1 decimal place.3D Trigonometry▶ Show worked answerHide worked answer
- M1: tan GBC = dfracCGBC
- M1: tan GBC = dfrac69
- A1: angle GBC = 33.7
Answer: 33.7[3 marks] - 3
Question 3. A cylinder has radius 3.2 cm, correct to 1 decimal place, and height 15 cm, correct to the nearest cm.
Work out the lower bound of its volume. volume = π r² h
Give your answer to 3 significant figures.Combining Upper & Lower Bounds▶ Show worked answerHide worked answer
- M1: 3.2 - 0.05 and 15 - 0.5
- M1: π × 3.15² × 14.5
- A1: 452
Answer: 452[3 marks] - 4
Question 4. Simplify fully dfracx²-6x+8x²-2x-8
Algebraic Fractions Involving Factorising▶ Show worked answerHide worked answer
- M1: (x-2)(x-4)
- M1: (x-4)(x+2)
- A1: dfracx-2x+2
Answer: dfracx-2x+2[3 marks] - 5
Question 5. Solve 2x² - 8x - 3 = 0 by completing the square. Give your solutions in the form dfraca ± √bc.
Solving Quadratics by Completing the Square (a > 1)▶ Show worked answerHide worked answer
- M1: 2(x - 2)² - 8 - 3 = 0
- M1: (x - 2)² = dfrac112
- A1: x = dfrac4 ± √222
Answer: x = dfrac4 ± √222[3 marks]
Mixed Topic Worksheet Grades 8/9: Day 050
- 1
Question 1. The histogram shows the ages, a years, of some people. The vertical axis is not numbered. The frequency for 0 < a ≤ 10 is 18. Work out the frequency for 20 < a ≤ 40.
[3 marks]Interpreting Histograms▶ Show worked answerHide worked answer
- M1: 18 ÷ (3 × 10) for the area scale
- M1: 4 × 20 × 0.6
- A1: 48
Answer: 48 - 2
Question 2. ABCDEFGH is a cuboid.
[3 marks]
Work out the size of the angle between the line BG and the plane ABCD.
Give your answer to 1 decimal place.3D Trigonometry▶ Show worked answerHide worked answer
- M1: tan GBC = dfracCGBC
- M1: tan GBC = dfrac69
- A1: angle GBC = 33.7
Answer: 33.7 - 3
Question 3. A cylinder has radius 3.2 cm, correct to 1 decimal place, and height 15 cm, correct to the nearest cm.
[3 marks]
Work out the lower bound of its volume. volume = π r² h
Give your answer to 3 significant figures.Combining Upper & Lower Bounds▶ Show worked answerHide worked answer
- M1: 3.2 - 0.05 and 15 - 0.5
- M1: π × 3.15² × 14.5
- A1: 452
Answer: 452 - 4
Question 4. Simplify fully dfracx²-6x+8x²-2x-8
[3 marks]Algebraic Fractions Involving Factorising▶ Show worked answerHide worked answer
- M1: (x-2)(x-4)
- M1: (x-4)(x+2)
- A1: dfracx-2x+2
Answer: dfracx-2x+2 - 5
Question 5. Solve 2x² - 8x - 3 = 0 by completing the square. Give your solutions in the form dfraca ± √bc.
[3 marks]Solving Quadratics by Completing the Square (a > 1)▶ Show worked answerHide worked answer
- M1: 2(x - 2)² - 8 - 3 = 0
- M1: (x - 2)² = dfrac112
- A1: x = dfrac4 ± √222
Answer: x = dfrac4 ± √222
Mixed Topic Worksheet Grades 8/9: Day 050
- 1
Question 1. The histogram shows the ages, a years, of some people. The vertical axis is not numbered. The frequency for 0 < a ≤ 10 is 18. Work out the frequency for 20 < a ≤ 40.
Interpreting Histograms▶ Show worked answerHide worked answer
- M1: 18 ÷ (3 × 10) for the area scale
- M1: 4 × 20 × 0.6
- A1: 48
Answer: 48[3 marks] - 2
Question 2. ABCDEFGH is a cuboid.
Work out the size of the angle between the line BG and the plane ABCD.
Give your answer to 1 decimal place.3D Trigonometry▶ Show worked answerHide worked answer
- M1: tan GBC = dfracCGBC
- M1: tan GBC = dfrac69
- A1: angle GBC = 33.7
Answer: 33.7[3 marks] - 3
Question 3. A cylinder has radius 3.2 cm, correct to 1 decimal place, and height 15 cm, correct to the nearest cm.
Work out the lower bound of its volume. volume = π r² h
Give your answer to 3 significant figures.Combining Upper & Lower Bounds▶ Show worked answerHide worked answer
- M1: 3.2 - 0.05 and 15 - 0.5
- M1: π × 3.15² × 14.5
- A1: 452
Answer: 452[3 marks] - 4
Question 4. Simplify fully dfracx²-6x+8x²-2x-8
Algebraic Fractions Involving Factorising▶ Show worked answerHide worked answer
- M1: (x-2)(x-4)
- M1: (x-4)(x+2)
- A1: dfracx-2x+2
Answer: dfracx-2x+2[3 marks] - 5
Question 5. Solve 2x² - 8x - 3 = 0 by completing the square. Give your solutions in the form dfraca ± √bc.
Solving Quadratics by Completing the Square (a > 1)▶ Show worked answerHide worked answer
- M1: 2(x - 2)² - 8 - 3 = 0
- M1: (x - 2)² = dfrac112
- A1: x = dfrac4 ± √222
Answer: x = dfrac4 ± √222[3 marks]