Mixed Topic Worksheet Grades 8/9: Day 019
- 1
Question 1. A, B and C are points on a circle, centre O.
AB is a diameter.
Angle ABC = 43^°
Work out the size of angle CAB.
Give reasons for your answer.Circle Theorems▶ Show worked answerHide worked answer
- M1: angle ACB = 90^°
- M1: 180 - 90 - 43
- A1: 47^°, with reasons: the angle in a semicircle is 90^° and the angles in a triangle add up to 180^°
Answer: 47^° (the angle in a semicircle is 90^°; the angles in a triangle add up to 180^°)[3 marks] - 2
Question 2. Ali writes x² + 8x + 3 = (x + 4)² + 3. Is Ali correct? Show how you know, and write the correct form.
Solving Quadratics by Completing the Square (a = 1)▶ Show worked answerHide worked answer
- M1: (x + 4)² = x² + 8x + 16
- A1: No, it should subtract 16 from 3
- B1: (x + 4)² - 13
Answer: No: correct form is (x + 4)² - 13[3 marks] - 3
Question 3. Of 90 pupils, 40 are in Year 10. 18 pupils in Year 10 and 12 pupils in Year 11 have a bike. A pupil with no bike is chosen. Find the probability that they are in Year 10.
Conditional Probability with Two-Way Tables▶ Show worked answerHide worked answer
- M1: no bike: Year 10 = 22, Year 11 = 38, total 60
- M1: dfrac2260
- A1: dfrac1130
Answer: dfrac1130[3 marks] - 4
Question 4. The graph of y = acos(bx) + c for 0^° ≤ x ≤ 360^° is shown.
a, b and c are positive integers.
Work out a, b and c.Transforming Trigonometric Graphs▶ Show worked answerHide worked answer
- M1: a = (4 - (-2)) ÷ 2
- A1: a = 3
- A1: c = 1
- A1: b = 2
Answer: a = 3, b = 2 and c = 1[4 marks] - 5
Question 5. The line 3x + 4y = 48 is a tangent to the circle C at the point P(8, 6). The centre of C is (2, k). Work out the value of k.
Finding Equations of Tangents to Circles▶ Show worked answerHide worked answer
- M1: gradient of the tangent = -dfrac34 so gradient of the radius = dfrac43
- M1: dfrac6 - k8 - 2 = dfrac43
- A1: k = -2
Answer: k = -2[3 marks]
Mixed Topic Worksheet Grades 8/9: Day 019
- 1
Question 1. A, B and C are points on a circle, centre O.
[3 marks]
AB is a diameter.
Angle ABC = 43^°
Work out the size of angle CAB.
Give reasons for your answer.Circle Theorems▶ Show worked answerHide worked answer
- M1: angle ACB = 90^°
- M1: 180 - 90 - 43
- A1: 47^°, with reasons: the angle in a semicircle is 90^° and the angles in a triangle add up to 180^°
Answer: 47^° (the angle in a semicircle is 90^°; the angles in a triangle add up to 180^°) - 2
Question 2. Ali writes x² + 8x + 3 = (x + 4)² + 3. Is Ali correct? Show how you know, and write the correct form.
[3 marks]Solving Quadratics by Completing the Square (a = 1)▶ Show worked answerHide worked answer
- M1: (x + 4)² = x² + 8x + 16
- A1: No, it should subtract 16 from 3
- B1: (x + 4)² - 13
Answer: No: correct form is (x + 4)² - 13 - 3
Question 3. Of 90 pupils, 40 are in Year 10. 18 pupils in Year 10 and 12 pupils in Year 11 have a bike. A pupil with no bike is chosen. Find the probability that they are in Year 10.
[3 marks]Conditional Probability with Two-Way Tables▶ Show worked answerHide worked answer
- M1: no bike: Year 10 = 22, Year 11 = 38, total 60
- M1: dfrac2260
- A1: dfrac1130
Answer: dfrac1130 - 4
Question 4. The graph of y = acos(bx) + c for 0^° ≤ x ≤ 360^° is shown.
[4 marks]
a, b and c are positive integers.
Work out a, b and c.Transforming Trigonometric Graphs▶ Show worked answerHide worked answer
- M1: a = (4 - (-2)) ÷ 2
- A1: a = 3
- A1: c = 1
- A1: b = 2
Answer: a = 3, b = 2 and c = 1 - 5
Question 5. The line 3x + 4y = 48 is a tangent to the circle C at the point P(8, 6). The centre of C is (2, k). Work out the value of k.
[3 marks]Finding Equations of Tangents to Circles▶ Show worked answerHide worked answer
- M1: gradient of the tangent = -dfrac34 so gradient of the radius = dfrac43
- M1: dfrac6 - k8 - 2 = dfrac43
- A1: k = -2
Answer: k = -2
Mixed Topic Worksheet Grades 8/9: Day 019
- 1
Question 1. A, B and C are points on a circle, centre O.
AB is a diameter.
Angle ABC = 43^°
Work out the size of angle CAB.
Give reasons for your answer.Circle Theorems▶ Show worked answerHide worked answer
- M1: angle ACB = 90^°
- M1: 180 - 90 - 43
- A1: 47^°, with reasons: the angle in a semicircle is 90^° and the angles in a triangle add up to 180^°
Answer: 47^° (the angle in a semicircle is 90^°; the angles in a triangle add up to 180^°)[3 marks] - 2
Question 2. Ali writes x² + 8x + 3 = (x + 4)² + 3. Is Ali correct? Show how you know, and write the correct form.
Solving Quadratics by Completing the Square (a = 1)▶ Show worked answerHide worked answer
- M1: (x + 4)² = x² + 8x + 16
- A1: No, it should subtract 16 from 3
- B1: (x + 4)² - 13
Answer: No: correct form is (x + 4)² - 13[3 marks] - 3
Question 3. Of 90 pupils, 40 are in Year 10. 18 pupils in Year 10 and 12 pupils in Year 11 have a bike. A pupil with no bike is chosen. Find the probability that they are in Year 10.
Conditional Probability with Two-Way Tables▶ Show worked answerHide worked answer
- M1: no bike: Year 10 = 22, Year 11 = 38, total 60
- M1: dfrac2260
- A1: dfrac1130
Answer: dfrac1130[3 marks] - 4
Question 4. The graph of y = acos(bx) + c for 0^° ≤ x ≤ 360^° is shown.
a, b and c are positive integers.
Work out a, b and c.Transforming Trigonometric Graphs▶ Show worked answerHide worked answer
- M1: a = (4 - (-2)) ÷ 2
- A1: a = 3
- A1: c = 1
- A1: b = 2
Answer: a = 3, b = 2 and c = 1[4 marks] - 5
Question 5. The line 3x + 4y = 48 is a tangent to the circle C at the point P(8, 6). The centre of C is (2, k). Work out the value of k.
Finding Equations of Tangents to Circles▶ Show worked answerHide worked answer
- M1: gradient of the tangent = -dfrac34 so gradient of the radius = dfrac43
- M1: dfrac6 - k8 - 2 = dfrac43
- A1: k = -2
Answer: k = -2[3 marks]