Mixed Topic Worksheet Grades 8/9: Day 080
- 1
Question 1. Here is the graph of y = x² - x - 6
Use the graph to solve x² - x - 6 < 0Sketching Quadratic Inequalities▶ Show worked answerHide worked answer
- M1: reads the roots x = -2 and x = 3 where the curve crosses the x-axis
- A1: -2 < x < 3, the values of x where the curve is below the x-axis
Answer: -2 < x < 3[2 marks] - 2
Question 2. Solve cos x = 0.25 for -180^° ≤ x ≤ 180^°. Give your answers correct to 1 decimal place.
Solving Trigonometric Equations Using a Graph▶ Show worked answerHide worked answer
- M1: x = cos⁻¹0.25
- A1: symmetry gives x = -75.5^° and x = 75.5^°
Answer: x = -75.5^° and x = 75.5^°[2 marks] - 3
Question 3. PA and PB are tangents to a circle, centre O, touching it at A and B. Angle AOB=110^°. Work out angle APB.
Combining Circle Theorems▶ Show worked answerHide worked answer
- M1: angle OAP=angle OBP=90^°, so APB=360-90-90-110
- A1: 70^°
Answer: 70^°[2 marks] - 4
Question 4. The class 0.4 < m ≤ 0.9 has a frequency of 14. Work out the frequency density of this class.
Sketching Histograms▶ Show worked answerHide worked answer
- M1: class width =0.9-0.4=0.5
- M1: 14÷0.5
- A1: 28
Answer: 28[3 marks] - 5
Question 5. ax² - 18x + c equiv a(x - 3)² + 4 a and c are integers Work out the value of a and the value of c
Solving Quadratics by Completing the Square (a > 1)▶ Show worked answerHide worked answer
- M1: a(x - 3)² + 4 = ax² - 6ax + 9a + 4
- M1: -6a = -18
- A1: a = 3
- A1: c = 31
Answer: a = 3 and c = 31[4 marks]
Mixed Topic Worksheet Grades 8/9: Day 080
- 1
Question 1. Here is the graph of y = x² - x - 6
[2 marks]
Use the graph to solve x² - x - 6 < 0Sketching Quadratic Inequalities▶ Show worked answerHide worked answer
- M1: reads the roots x = -2 and x = 3 where the curve crosses the x-axis
- A1: -2 < x < 3, the values of x where the curve is below the x-axis
Answer: -2 < x < 3 - 2
Question 2. Solve cos x = 0.25 for -180^° ≤ x ≤ 180^°. Give your answers correct to 1 decimal place.
[2 marks]Solving Trigonometric Equations Using a Graph▶ Show worked answerHide worked answer
- M1: x = cos⁻¹0.25
- A1: symmetry gives x = -75.5^° and x = 75.5^°
Answer: x = -75.5^° and x = 75.5^° - 3
Question 3. PA and PB are tangents to a circle, centre O, touching it at A and B. Angle AOB=110^°. Work out angle APB.
[2 marks]Combining Circle Theorems▶ Show worked answerHide worked answer
- M1: angle OAP=angle OBP=90^°, so APB=360-90-90-110
- A1: 70^°
Answer: 70^° - 4
Question 4. The class 0.4 < m ≤ 0.9 has a frequency of 14. Work out the frequency density of this class.
[3 marks]Sketching Histograms▶ Show worked answerHide worked answer
- M1: class width =0.9-0.4=0.5
- M1: 14÷0.5
- A1: 28
Answer: 28 - 5
Question 5. ax² - 18x + c equiv a(x - 3)² + 4 a and c are integers Work out the value of a and the value of c
[4 marks]Solving Quadratics by Completing the Square (a > 1)▶ Show worked answerHide worked answer
- M1: a(x - 3)² + 4 = ax² - 6ax + 9a + 4
- M1: -6a = -18
- A1: a = 3
- A1: c = 31
Answer: a = 3 and c = 31
Mixed Topic Worksheet Grades 8/9: Day 080
- 1
Question 1. Here is the graph of y = x² - x - 6
Use the graph to solve x² - x - 6 < 0Sketching Quadratic Inequalities▶ Show worked answerHide worked answer
- M1: reads the roots x = -2 and x = 3 where the curve crosses the x-axis
- A1: -2 < x < 3, the values of x where the curve is below the x-axis
Answer: -2 < x < 3[2 marks] - 2
Question 2. Solve cos x = 0.25 for -180^° ≤ x ≤ 180^°. Give your answers correct to 1 decimal place.
Solving Trigonometric Equations Using a Graph▶ Show worked answerHide worked answer
- M1: x = cos⁻¹0.25
- A1: symmetry gives x = -75.5^° and x = 75.5^°
Answer: x = -75.5^° and x = 75.5^°[2 marks] - 3
Question 3. PA and PB are tangents to a circle, centre O, touching it at A and B. Angle AOB=110^°. Work out angle APB.
Combining Circle Theorems▶ Show worked answerHide worked answer
- M1: angle OAP=angle OBP=90^°, so APB=360-90-90-110
- A1: 70^°
Answer: 70^°[2 marks] - 4
Question 4. The class 0.4 < m ≤ 0.9 has a frequency of 14. Work out the frequency density of this class.
Sketching Histograms▶ Show worked answerHide worked answer
- M1: class width =0.9-0.4=0.5
- M1: 14÷0.5
- A1: 28
Answer: 28[3 marks] - 5
Question 5. ax² - 18x + c equiv a(x - 3)² + 4 a and c are integers Work out the value of a and the value of c
Solving Quadratics by Completing the Square (a > 1)▶ Show worked answerHide worked answer
- M1: a(x - 3)² + 4 = ax² - 6ax + 9a + 4
- M1: -6a = -18
- A1: a = 3
- A1: c = 31
Answer: a = 3 and c = 31[4 marks]