Mixed Topic Worksheet Grades 8/9: Day 016
- 1
Question 1. Expand and simplify (√12 + √3)².
Simplifying Surds▶ Show worked answerHide worked answer
- M1: 12 + 2√36 + 3 (or (3√3)²)
- M1: 12 + 12 + 3
- A1: 27
Answer: 27[3 marks] - 2
Question 2. A cuboid is 5 cm by 12 cm and 9 cm high. Work out the angle between a space diagonal and a vertical edge of the cuboid. Give your answer correct to 1 decimal place.
3D Trigonometry▶ Show worked answerHide worked answer
- M1: base diagonal = 13
- M1: tanθ = 13/9
- A1: 55.3°
Answer: 55.3°[3 marks] - 3
Question 3. P(A) = 0.5, P(B) = 0.35 and P(A cup B) = 0.7. Work out P(A mid B'). Give your answer to 3 decimal places.
Conditional Probability with Venn Diagrams▶ Show worked answerHide worked answer
- M1: P(A cap B) = 0.15, so P(A cap B') = 0.35, P(B') = 0.65
- M1: dfrac0.350.65
- A1: 0.538
Answer: 0.538[3 marks] - 4
Question 4. y is directly proportional to the square of x.
y = 20 when x = 2
Work out the value of y when x = 3Direct & Inverse Proportion with Functions▶ Show worked answerHide worked answer
- M1: y = kx²
- M1: 20 = k × 2²
- A1: k = 5
- A1: y = 5 × 3² = 45
Answer: y = 45[4 marks] - 5
Question 5. Solve x(2x - 1) < 15
Solving Quadratic Inequalities▶ Show worked answerHide worked answer
- M1: 2x²-x-15 < 0
- M1: (2x + 5)(x - 3) < 0
- A1: -dfrac52 < x < 3
Answer: -dfrac52 < x < 3[3 marks]
Mixed Topic Worksheet Grades 8/9: Day 016
- 1
Question 1. Expand and simplify (√12 + √3)².
[3 marks]Simplifying Surds▶ Show worked answerHide worked answer
- M1: 12 + 2√36 + 3 (or (3√3)²)
- M1: 12 + 12 + 3
- A1: 27
Answer: 27 - 2
Question 2. A cuboid is 5 cm by 12 cm and 9 cm high. Work out the angle between a space diagonal and a vertical edge of the cuboid. Give your answer correct to 1 decimal place.
[3 marks]3D Trigonometry▶ Show worked answerHide worked answer
- M1: base diagonal = 13
- M1: tanθ = 13/9
- A1: 55.3°
Answer: 55.3° - 3
Question 3. P(A) = 0.5, P(B) = 0.35 and P(A cup B) = 0.7. Work out P(A mid B'). Give your answer to 3 decimal places.
[3 marks]Conditional Probability with Venn Diagrams▶ Show worked answerHide worked answer
- M1: P(A cap B) = 0.15, so P(A cap B') = 0.35, P(B') = 0.65
- M1: dfrac0.350.65
- A1: 0.538
Answer: 0.538 - 4
Question 4. y is directly proportional to the square of x.
[4 marks]
y = 20 when x = 2
Work out the value of y when x = 3Direct & Inverse Proportion with Functions▶ Show worked answerHide worked answer
- M1: y = kx²
- M1: 20 = k × 2²
- A1: k = 5
- A1: y = 5 × 3² = 45
Answer: y = 45 - 5
Question 5. Solve x(2x - 1) < 15
[3 marks]Solving Quadratic Inequalities▶ Show worked answerHide worked answer
- M1: 2x²-x-15 < 0
- M1: (2x + 5)(x - 3) < 0
- A1: -dfrac52 < x < 3
Answer: -dfrac52 < x < 3
Mixed Topic Worksheet Grades 8/9: Day 016
- 1
Question 1. Expand and simplify (√12 + √3)².
Simplifying Surds▶ Show worked answerHide worked answer
- M1: 12 + 2√36 + 3 (or (3√3)²)
- M1: 12 + 12 + 3
- A1: 27
Answer: 27[3 marks] - 2
Question 2. A cuboid is 5 cm by 12 cm and 9 cm high. Work out the angle between a space diagonal and a vertical edge of the cuboid. Give your answer correct to 1 decimal place.
3D Trigonometry▶ Show worked answerHide worked answer
- M1: base diagonal = 13
- M1: tanθ = 13/9
- A1: 55.3°
Answer: 55.3°[3 marks] - 3
Question 3. P(A) = 0.5, P(B) = 0.35 and P(A cup B) = 0.7. Work out P(A mid B'). Give your answer to 3 decimal places.
Conditional Probability with Venn Diagrams▶ Show worked answerHide worked answer
- M1: P(A cap B) = 0.15, so P(A cap B') = 0.35, P(B') = 0.65
- M1: dfrac0.350.65
- A1: 0.538
Answer: 0.538[3 marks] - 4
Question 4. y is directly proportional to the square of x.
y = 20 when x = 2
Work out the value of y when x = 3Direct & Inverse Proportion with Functions▶ Show worked answerHide worked answer
- M1: y = kx²
- M1: 20 = k × 2²
- A1: k = 5
- A1: y = 5 × 3² = 45
Answer: y = 45[4 marks] - 5
Question 5. Solve x(2x - 1) < 15
Solving Quadratic Inequalities▶ Show worked answerHide worked answer
- M1: 2x²-x-15 < 0
- M1: (2x + 5)(x - 3) < 0
- A1: -dfrac52 < x < 3
Answer: -dfrac52 < x < 3[3 marks]