Mixed Topic Worksheet Grades 8/9: Day 009
- 1
Question 1. a = 12 and b = 5
Each value is correct to the nearest integer.
Work out the upper bound of a - b.Combining Upper & Lower Bounds▶ Show worked answerHide worked answer
- M1: 12 + 0.5 and 5 - 0.5
- M1: 12.5 - 4.5
- A1: 8
Answer: 8[3 marks] - 2
Question 2. The graph of y = sin 2x and the line y = 0.5 are shown for 0^° ≤ x ≤ 360^°. sin 30^° = 0.5. Solve sin 2x = 0.5 in this range.
Solving Trigonometric Equations Using a Graph▶ Show worked answerHide worked answer
- M1: 2x = 30 and 2x = 150 (symmetry of the graph)
- M1: add 360: 2x = 390 and 2x = 510
- A1: x = 15, x = 75, x = 195 and x = 255
Answer: x = 15, x = 75, x = 195 and x = 255[3 marks] - 3
Question 3. The curve y = f(x) has a maximum point at (3, 8) Write down the coordinates of the turning point of the curve y = -f(-x) and say whether it is a maximum or a minimum
Reflections in the x- & y-Axes▶ Show worked answerHide worked answer
- M1: f(-x) reflects in the y-axis, -f(-x) then reflects in the x-axis
- A1: (-3, -8)
- B1: minimum
Answer: (-3, -8), a minimum[3 marks] - 4
Question 4. The diagram shows a circle.
PAB is a straight line.
PT is a tangent to the circle at T.
Prove that triangles PTA and PBT are similar.Combining Circle Theorems▶ Show worked answerHide worked answer
- B1: angle TPA = angle BPT (common to both triangles)
- B1: angle PTA = angle PBT (alternate segment theorem)
- C1: two pairs of equal angles, so the triangles are similar
Answer: Two pairs of equal angles, so triangles PTA and PBT are similar[3 marks] - 5
Question 5. Write 2x² + 12x + 5 in the form a(x + p)² + q
Solving Quadratics by Completing the Square (a > 1)▶ Show worked answerHide worked answer
- M1: 2(x² + 6x) + 5
- M1: 2≤ft((x + 3)² - 9) + 5
- A1: 2(x + 3)² - 13
Answer: 2(x + 3)² - 13[3 marks]
Mixed Topic Worksheet Grades 8/9: Day 009
- 1
Question 1. a = 12 and b = 5
[3 marks]
Each value is correct to the nearest integer.
Work out the upper bound of a - b.Combining Upper & Lower Bounds▶ Show worked answerHide worked answer
- M1: 12 + 0.5 and 5 - 0.5
- M1: 12.5 - 4.5
- A1: 8
Answer: 8 - 2
Question 2. The graph of y = sin 2x and the line y = 0.5 are shown for 0^° ≤ x ≤ 360^°. sin 30^° = 0.5. Solve sin 2x = 0.5 in this range.
[3 marks]Solving Trigonometric Equations Using a Graph▶ Show worked answerHide worked answer
- M1: 2x = 30 and 2x = 150 (symmetry of the graph)
- M1: add 360: 2x = 390 and 2x = 510
- A1: x = 15, x = 75, x = 195 and x = 255
Answer: x = 15, x = 75, x = 195 and x = 255 - 3
Question 3. The curve y = f(x) has a maximum point at (3, 8) Write down the coordinates of the turning point of the curve y = -f(-x) and say whether it is a maximum or a minimum
[3 marks]Reflections in the x- & y-Axes▶ Show worked answerHide worked answer
- M1: f(-x) reflects in the y-axis, -f(-x) then reflects in the x-axis
- A1: (-3, -8)
- B1: minimum
Answer: (-3, -8), a minimum - 4
Question 4. The diagram shows a circle.
[3 marks]
PAB is a straight line.
PT is a tangent to the circle at T.
Prove that triangles PTA and PBT are similar.Combining Circle Theorems▶ Show worked answerHide worked answer
- B1: angle TPA = angle BPT (common to both triangles)
- B1: angle PTA = angle PBT (alternate segment theorem)
- C1: two pairs of equal angles, so the triangles are similar
Answer: Two pairs of equal angles, so triangles PTA and PBT are similar - 5
Question 5. Write 2x² + 12x + 5 in the form a(x + p)² + q
[3 marks]Solving Quadratics by Completing the Square (a > 1)▶ Show worked answerHide worked answer
- M1: 2(x² + 6x) + 5
- M1: 2≤ft((x + 3)² - 9) + 5
- A1: 2(x + 3)² - 13
Answer: 2(x + 3)² - 13
Mixed Topic Worksheet Grades 8/9: Day 009
- 1
Question 1. a = 12 and b = 5
Each value is correct to the nearest integer.
Work out the upper bound of a - b.Combining Upper & Lower Bounds▶ Show worked answerHide worked answer
- M1: 12 + 0.5 and 5 - 0.5
- M1: 12.5 - 4.5
- A1: 8
Answer: 8[3 marks] - 2
Question 2. The graph of y = sin 2x and the line y = 0.5 are shown for 0^° ≤ x ≤ 360^°. sin 30^° = 0.5. Solve sin 2x = 0.5 in this range.
Solving Trigonometric Equations Using a Graph▶ Show worked answerHide worked answer
- M1: 2x = 30 and 2x = 150 (symmetry of the graph)
- M1: add 360: 2x = 390 and 2x = 510
- A1: x = 15, x = 75, x = 195 and x = 255
Answer: x = 15, x = 75, x = 195 and x = 255[3 marks] - 3
Question 3. The curve y = f(x) has a maximum point at (3, 8) Write down the coordinates of the turning point of the curve y = -f(-x) and say whether it is a maximum or a minimum
Reflections in the x- & y-Axes▶ Show worked answerHide worked answer
- M1: f(-x) reflects in the y-axis, -f(-x) then reflects in the x-axis
- A1: (-3, -8)
- B1: minimum
Answer: (-3, -8), a minimum[3 marks] - 4
Question 4. The diagram shows a circle.
PAB is a straight line.
PT is a tangent to the circle at T.
Prove that triangles PTA and PBT are similar.Combining Circle Theorems▶ Show worked answerHide worked answer
- B1: angle TPA = angle BPT (common to both triangles)
- B1: angle PTA = angle PBT (alternate segment theorem)
- C1: two pairs of equal angles, so the triangles are similar
Answer: Two pairs of equal angles, so triangles PTA and PBT are similar[3 marks] - 5
Question 5. Write 2x² + 12x + 5 in the form a(x + p)² + q
Solving Quadratics by Completing the Square (a > 1)▶ Show worked answerHide worked answer
- M1: 2(x² + 6x) + 5
- M1: 2≤ft((x + 3)² - 9) + 5
- A1: 2(x + 3)² - 13
Answer: 2(x + 3)² - 13[3 marks]