Mixed Topic Worksheet Grades 8/9: Day 085
- 1
Question 1. Simplify √72 + √50. Give your answer in the form a√b.
Simplifying Surds▶ Show worked answerHide worked answer
- M1: √72 = 6√2 and √50 = 5√2
- A1: 11√2
Answer: 11√2[2 marks] - 2
Question 2. Simplify fully dfrac3x8×dfrac49x²
Multiplying & Dividing Algebraic Fractions▶ Show worked answerHide worked answer
- M1: dfrac12x72x²
- A1: dfrac16x
Answer: dfrac16x[2 marks] - 3
Question 3. A, B and C are on a circle, centre O, with C on the major arc AB. Angle ACB = 38°. Find angle AOB, with a reason.
Circle Theorems▶ Show worked answerHide worked answer
- M1: angle at the centre is twice the angle at the circumference
- A1: 76°
Answer: 76°[2 marks] - 4
Question 4. A histogram shows 80 values. The class 0 < x ≤ 10 has frequency 20 and the class 10 < x ≤ 15 has frequency 30. The class 15 < x ≤ 35 has the rest. Work out the height of the last bar if the vertical axis shows frequency density.
Sketching Histograms▶ Show worked answerHide worked answer
- M1: frequency =80-20-30=30
- M1: 30÷20
- A1: 1.5
Answer: 1.5[3 marks] - 5
Question 5. Write 3x² + 18x + 4 in the form a(x + p)² + q.
Solving Quadratics by Completing the Square (a > 1)▶ Show worked answerHide worked answer
- M1: 3(x² + 6x) + 4 = 3(x + 3)² - 27 + 4
- A1: 3(x + 3)² - 23
Answer: 3(x + 3)² - 23[2 marks]
Mixed Topic Worksheet Grades 8/9: Day 085
- 1
Question 1. Simplify √72 + √50. Give your answer in the form a√b.
[2 marks]Simplifying Surds▶ Show worked answerHide worked answer
- M1: √72 = 6√2 and √50 = 5√2
- A1: 11√2
Answer: 11√2 - 2
Question 2. Simplify fully dfrac3x8×dfrac49x²
[2 marks]Multiplying & Dividing Algebraic Fractions▶ Show worked answerHide worked answer
- M1: dfrac12x72x²
- A1: dfrac16x
Answer: dfrac16x - 3
Question 3. A, B and C are on a circle, centre O, with C on the major arc AB. Angle ACB = 38°. Find angle AOB, with a reason.
[2 marks]Circle Theorems▶ Show worked answerHide worked answer
- M1: angle at the centre is twice the angle at the circumference
- A1: 76°
Answer: 76° - 4
Question 4. A histogram shows 80 values. The class 0 < x ≤ 10 has frequency 20 and the class 10 < x ≤ 15 has frequency 30. The class 15 < x ≤ 35 has the rest. Work out the height of the last bar if the vertical axis shows frequency density.
[3 marks]Sketching Histograms▶ Show worked answerHide worked answer
- M1: frequency =80-20-30=30
- M1: 30÷20
- A1: 1.5
Answer: 1.5 - 5
Question 5. Write 3x² + 18x + 4 in the form a(x + p)² + q.
[2 marks]Solving Quadratics by Completing the Square (a > 1)▶ Show worked answerHide worked answer
- M1: 3(x² + 6x) + 4 = 3(x + 3)² - 27 + 4
- A1: 3(x + 3)² - 23
Answer: 3(x + 3)² - 23
Mixed Topic Worksheet Grades 8/9: Day 085
- 1
Question 1. Simplify √72 + √50. Give your answer in the form a√b.
Simplifying Surds▶ Show worked answerHide worked answer
- M1: √72 = 6√2 and √50 = 5√2
- A1: 11√2
Answer: 11√2[2 marks] - 2
Question 2. Simplify fully dfrac3x8×dfrac49x²
Multiplying & Dividing Algebraic Fractions▶ Show worked answerHide worked answer
- M1: dfrac12x72x²
- A1: dfrac16x
Answer: dfrac16x[2 marks] - 3
Question 3. A, B and C are on a circle, centre O, with C on the major arc AB. Angle ACB = 38°. Find angle AOB, with a reason.
Circle Theorems▶ Show worked answerHide worked answer
- M1: angle at the centre is twice the angle at the circumference
- A1: 76°
Answer: 76°[2 marks] - 4
Question 4. A histogram shows 80 values. The class 0 < x ≤ 10 has frequency 20 and the class 10 < x ≤ 15 has frequency 30. The class 15 < x ≤ 35 has the rest. Work out the height of the last bar if the vertical axis shows frequency density.
Sketching Histograms▶ Show worked answerHide worked answer
- M1: frequency =80-20-30=30
- M1: 30÷20
- A1: 1.5
Answer: 1.5[3 marks] - 5
Question 5. Write 3x² + 18x + 4 in the form a(x + p)² + q.
Solving Quadratics by Completing the Square (a > 1)▶ Show worked answerHide worked answer
- M1: 3(x² + 6x) + 4 = 3(x + 3)² - 27 + 4
- A1: 3(x + 3)² - 23
Answer: 3(x + 3)² - 23[2 marks]