Mixed Topic Worksheet Grades 8/9: Day 062
- 1
Question 1. A graph has equation y = 4sin x - 1. Work out the value of y when x = 210°.
Transforming Trigonometric Graphs▶ Show worked answerHide worked answer
- M1: 4 × sin 210° - 1 = 4 × (-0.5) - 1
- A1: -3
Answer: -3[2 marks] - 2
Question 2. Show that 2x = x + 4 has a solution between x = 2.5 and x = 3
Change of Signs▶ Show worked answerHide worked answer
- M1: work out f(2.5) and f(3) for f(x) = 2x - x - 4
- A1: -0.843 and 1, a sign change, so a solution lies between them
Answer: Change of sign shows a solution between 2.5 and 3[2 marks] - 3
Question 3. The histogram shows the times, t minutes, of 100 fun run finishers. Assume times are spread evenly in each class. 90% finished in T minutes or less. Work out an estimate for T.
Median from a Histogram▶ Show worked answerHide worked answer
- M1: 1.0 × 10 + 3.0 × 15 + 2.0 × 15
- M1: 40 + (90 - 85) ÷ 0.5
- A1: 50
Answer: 50[3 marks] - 4
Question 4. ABCD is a cyclic quadrilateral. Angle ABC = 82^°
Ravi says angle ADC = 96^°. Is Ravi correct?
Show your working.Circle Theorems▶ Show worked answerHide worked answer
- M1: 180 - 82
- A1: 98, not 96
- B1: No, opposite angles of a cyclic quadrilateral sum to 180^°
Answer: No. Angle ADC = 180 - 82 = 98^°, not 96^°, because opposite angles of a cyclic quadrilateral add up to 180^°[3 marks] - 5
Question 5. AB is a diameter of a circle. A is the point (-1, 2) and B is the point (5, -6).
Find an equation of the tangent to the circle at B.
Give your answer in the form ax + by = c where a, b and c are integers.Finding Equations of Tangents to Circles▶ Show worked answerHide worked answer
- M1: gradient of AB = dfrac-6 - 25 - (-1) = -dfrac43
- M1: gradient of the tangent = dfrac34 and y + 6 = dfrac34(x - 5)
- A1: 3x - 4y = 39
Answer: 3x - 4y = 39[3 marks]
Mixed Topic Worksheet Grades 8/9: Day 062
- 1
Question 1. A graph has equation y = 4sin x - 1. Work out the value of y when x = 210°.
[2 marks]Transforming Trigonometric Graphs▶ Show worked answerHide worked answer
- M1: 4 × sin 210° - 1 = 4 × (-0.5) - 1
- A1: -3
Answer: -3 - 2
Question 2. Show that 2x = x + 4 has a solution between x = 2.5 and x = 3
[2 marks]Change of Signs▶ Show worked answerHide worked answer
- M1: work out f(2.5) and f(3) for f(x) = 2x - x - 4
- A1: -0.843 and 1, a sign change, so a solution lies between them
Answer: Change of sign shows a solution between 2.5 and 3 - 3
Question 3. The histogram shows the times, t minutes, of 100 fun run finishers. Assume times are spread evenly in each class. 90% finished in T minutes or less. Work out an estimate for T.
[3 marks]Median from a Histogram▶ Show worked answerHide worked answer
- M1: 1.0 × 10 + 3.0 × 15 + 2.0 × 15
- M1: 40 + (90 - 85) ÷ 0.5
- A1: 50
Answer: 50 - 4
Question 4. ABCD is a cyclic quadrilateral. Angle ABC = 82^°
[3 marks]
Ravi says angle ADC = 96^°. Is Ravi correct?
Show your working.Circle Theorems▶ Show worked answerHide worked answer
- M1: 180 - 82
- A1: 98, not 96
- B1: No, opposite angles of a cyclic quadrilateral sum to 180^°
Answer: No. Angle ADC = 180 - 82 = 98^°, not 96^°, because opposite angles of a cyclic quadrilateral add up to 180^° - 5
Question 5. AB is a diameter of a circle. A is the point (-1, 2) and B is the point (5, -6).
[3 marks]
Find an equation of the tangent to the circle at B.
Give your answer in the form ax + by = c where a, b and c are integers.Finding Equations of Tangents to Circles▶ Show worked answerHide worked answer
- M1: gradient of AB = dfrac-6 - 25 - (-1) = -dfrac43
- M1: gradient of the tangent = dfrac34 and y + 6 = dfrac34(x - 5)
- A1: 3x - 4y = 39
Answer: 3x - 4y = 39
Mixed Topic Worksheet Grades 8/9: Day 062
- 1
Question 1. A graph has equation y = 4sin x - 1. Work out the value of y when x = 210°.
Transforming Trigonometric Graphs▶ Show worked answerHide worked answer
- M1: 4 × sin 210° - 1 = 4 × (-0.5) - 1
- A1: -3
Answer: -3[2 marks] - 2
Question 2. Show that 2x = x + 4 has a solution between x = 2.5 and x = 3
Change of Signs▶ Show worked answerHide worked answer
- M1: work out f(2.5) and f(3) for f(x) = 2x - x - 4
- A1: -0.843 and 1, a sign change, so a solution lies between them
Answer: Change of sign shows a solution between 2.5 and 3[2 marks] - 3
Question 3. The histogram shows the times, t minutes, of 100 fun run finishers. Assume times are spread evenly in each class. 90% finished in T minutes or less. Work out an estimate for T.
Median from a Histogram▶ Show worked answerHide worked answer
- M1: 1.0 × 10 + 3.0 × 15 + 2.0 × 15
- M1: 40 + (90 - 85) ÷ 0.5
- A1: 50
Answer: 50[3 marks] - 4
Question 4. ABCD is a cyclic quadrilateral. Angle ABC = 82^°
Ravi says angle ADC = 96^°. Is Ravi correct?
Show your working.Circle Theorems▶ Show worked answerHide worked answer
- M1: 180 - 82
- A1: 98, not 96
- B1: No, opposite angles of a cyclic quadrilateral sum to 180^°
Answer: No. Angle ADC = 180 - 82 = 98^°, not 96^°, because opposite angles of a cyclic quadrilateral add up to 180^°[3 marks] - 5
Question 5. AB is a diameter of a circle. A is the point (-1, 2) and B is the point (5, -6).
Find an equation of the tangent to the circle at B.
Give your answer in the form ax + by = c where a, b and c are integers.Finding Equations of Tangents to Circles▶ Show worked answerHide worked answer
- M1: gradient of AB = dfrac-6 - 25 - (-1) = -dfrac43
- M1: gradient of the tangent = dfrac34 and y + 6 = dfrac34(x - 5)
- A1: 3x - 4y = 39
Answer: 3x - 4y = 39[3 marks]