Mixed Topic Worksheet Grades 8/9: Day 059
- 1
Question 1. sin 30° = 1/2. Write down the exact value of sin 330°.
Sketching sin, cos & tan▶ Show worked answerHide worked answer
- B1: -1/2
Answer: -1/2[1 mark] - 2
Question 2. The histogram shows the times, t minutes, that 115 customers waited in a queue.
Work out the number who waited more than 20 minutes.Interpreting Histograms▶ Show worked answerHide worked answer
- M1: 3 × (30 - 20), 2.5 × (50 - 30), 1 × (60 - 50) (at least two correct)
- M1: 30 + 50 + 10
- A1: 90
Answer: 90[3 marks] - 3
Question 3. A rectangle has width x cm and length (x + 6) cm Its area is less than 91 cm² Find the range of possible values of x
Sketching Quadratic Inequalities▶ Show worked answerHide worked answer
- M1: x(x + 6) < 91 so x² + 6x < 91
- M1: (x + 13)(x - 7) < 0 so -13 < x < 7
- A1: 0 < x < 7 because x is a length
Answer: 0 < x < 7[3 marks] - 4
Question 4. The line y = x + 6 meets the curve y = x² at two points. Find their coordinates.
Solving Quadratic Simultaneous Equations▶ Show worked answerHide worked answer
- M1: x² = x + 6, so (x - 3)(x + 2) = 0
- M1 A1 A1: (3, 9) and (-2, 4)
Answer: (3, 9) and (-2, 4)[4 marks] - 5
Question 5. overrightarrowAB=2mathbfa+6mathbfb and overrightarrowBC=kmathbfa+9mathbfb. A, B and C lie on a straight line. Find k.
Vectors Along a Straight Line▶ Show worked answerHide worked answer
- M1: overrightarrowBC=3/2overrightarrowAB (compare the mathbfb terms)
- A1: k=3
Answer: k=3[2 marks]
Mixed Topic Worksheet Grades 8/9: Day 059
- 1
Question 1. sin 30° = 1/2. Write down the exact value of sin 330°.
[1 mark]Sketching sin, cos & tan▶ Show worked answerHide worked answer
- B1: -1/2
Answer: -1/2 - 2
Question 2. The histogram shows the times, t minutes, that 115 customers waited in a queue.
[3 marks]
Work out the number who waited more than 20 minutes.Interpreting Histograms▶ Show worked answerHide worked answer
- M1: 3 × (30 - 20), 2.5 × (50 - 30), 1 × (60 - 50) (at least two correct)
- M1: 30 + 50 + 10
- A1: 90
Answer: 90 - 3
Question 3. A rectangle has width x cm and length (x + 6) cm Its area is less than 91 cm² Find the range of possible values of x
[3 marks]Sketching Quadratic Inequalities▶ Show worked answerHide worked answer
- M1: x(x + 6) < 91 so x² + 6x < 91
- M1: (x + 13)(x - 7) < 0 so -13 < x < 7
- A1: 0 < x < 7 because x is a length
Answer: 0 < x < 7 - 4
Question 4. The line y = x + 6 meets the curve y = x² at two points. Find their coordinates.
[4 marks]Solving Quadratic Simultaneous Equations▶ Show worked answerHide worked answer
- M1: x² = x + 6, so (x - 3)(x + 2) = 0
- M1 A1 A1: (3, 9) and (-2, 4)
Answer: (3, 9) and (-2, 4) - 5
Question 5. overrightarrowAB=2mathbfa+6mathbfb and overrightarrowBC=kmathbfa+9mathbfb. A, B and C lie on a straight line. Find k.
[2 marks]Vectors Along a Straight Line▶ Show worked answerHide worked answer
- M1: overrightarrowBC=3/2overrightarrowAB (compare the mathbfb terms)
- A1: k=3
Answer: k=3
Mixed Topic Worksheet Grades 8/9: Day 059
- 1
Question 1. sin 30° = 1/2. Write down the exact value of sin 330°.
Sketching sin, cos & tan▶ Show worked answerHide worked answer
- B1: -1/2
Answer: -1/2[1 mark] - 2
Question 2. The histogram shows the times, t minutes, that 115 customers waited in a queue.
Work out the number who waited more than 20 minutes.Interpreting Histograms▶ Show worked answerHide worked answer
- M1: 3 × (30 - 20), 2.5 × (50 - 30), 1 × (60 - 50) (at least two correct)
- M1: 30 + 50 + 10
- A1: 90
Answer: 90[3 marks] - 3
Question 3. A rectangle has width x cm and length (x + 6) cm Its area is less than 91 cm² Find the range of possible values of x
Sketching Quadratic Inequalities▶ Show worked answerHide worked answer
- M1: x(x + 6) < 91 so x² + 6x < 91
- M1: (x + 13)(x - 7) < 0 so -13 < x < 7
- A1: 0 < x < 7 because x is a length
Answer: 0 < x < 7[3 marks] - 4
Question 4. The line y = x + 6 meets the curve y = x² at two points. Find their coordinates.
Solving Quadratic Simultaneous Equations▶ Show worked answerHide worked answer
- M1: x² = x + 6, so (x - 3)(x + 2) = 0
- M1 A1 A1: (3, 9) and (-2, 4)
Answer: (3, 9) and (-2, 4)[4 marks] - 5
Question 5. overrightarrowAB=2mathbfa+6mathbfb and overrightarrowBC=kmathbfa+9mathbfb. A, B and C lie on a straight line. Find k.
Vectors Along a Straight Line▶ Show worked answerHide worked answer
- M1: overrightarrowBC=3/2overrightarrowAB (compare the mathbfb terms)
- A1: k=3
Answer: k=3[2 marks]