Mixed Topic Worksheet Grades 8/9: Day 044
- 1
Question 1. Simplify fully √98
Simplifying Surds▶ Show worked answerHide worked answer
- B1: 7√2
Answer: 7√2[1 mark] - 2
Question 2. Simplify fully dfracx²-256×dfrac3x+5
Multiplying & Dividing Algebraic Fractions▶ Show worked answerHide worked answer
- M1: (x-5)(x+5)
- M1: dfrac3(x-5)(x+5)6(x+5)
- A1: dfracx-52
Answer: dfracx-52[3 marks] - 3
Question 3. x² + bx + 10 equiv (x + p)² - 6
b is a positive number
Work out the value of b and the value of pSolving Quadratics by Completing the Square (a = 1)▶ Show worked answerHide worked answer
- M1: expand: x² + 2px + p² - 6
- M1: p² - 6 = 10 so p = 4 (as b > 0)
- A1: p = 4 and b = 8
Answer: b = 8, p = 4[3 marks] - 4
Question 4. PA and PB are tangents from P to a circle, centre O, touching it at A and B. Angle OAB = 28°. Work out angle APB.
Circle Theorems▶ Show worked answerHide worked answer
- M1: isosceles triangle OAB: 180 - 2 × 28
- M1 A1: angle AOB = 124°, then 360 - 90 - 90 - 124 = 56°
Answer: 56°[3 marks] - 5
Question 5. Solve (x + 3)² > 16
Solving Quadratic Inequalities▶ Show worked answerHide worked answer
- M1: boundaries from x + 3 = 4 and x + 3 = -4
- M1: critical values x = 1 and x = -7
- A1: x < -7 or x > 1
Answer: x < -7 or x > 1[3 marks]
Mixed Topic Worksheet Grades 8/9: Day 044
- 1
Question 1. Simplify fully √98
[1 mark]Simplifying Surds▶ Show worked answerHide worked answer
- B1: 7√2
Answer: 7√2 - 2
Question 2. Simplify fully dfracx²-256×dfrac3x+5
[3 marks]Multiplying & Dividing Algebraic Fractions▶ Show worked answerHide worked answer
- M1: (x-5)(x+5)
- M1: dfrac3(x-5)(x+5)6(x+5)
- A1: dfracx-52
Answer: dfracx-52 - 3
Question 3. x² + bx + 10 equiv (x + p)² - 6
[3 marks]
b is a positive number
Work out the value of b and the value of pSolving Quadratics by Completing the Square (a = 1)▶ Show worked answerHide worked answer
- M1: expand: x² + 2px + p² - 6
- M1: p² - 6 = 10 so p = 4 (as b > 0)
- A1: p = 4 and b = 8
Answer: b = 8, p = 4 - 4
Question 4. PA and PB are tangents from P to a circle, centre O, touching it at A and B. Angle OAB = 28°. Work out angle APB.
[3 marks]Circle Theorems▶ Show worked answerHide worked answer
- M1: isosceles triangle OAB: 180 - 2 × 28
- M1 A1: angle AOB = 124°, then 360 - 90 - 90 - 124 = 56°
Answer: 56° - 5
Question 5. Solve (x + 3)² > 16
[3 marks]Solving Quadratic Inequalities▶ Show worked answerHide worked answer
- M1: boundaries from x + 3 = 4 and x + 3 = -4
- M1: critical values x = 1 and x = -7
- A1: x < -7 or x > 1
Answer: x < -7 or x > 1
Mixed Topic Worksheet Grades 8/9: Day 044
- 1
Question 1. Simplify fully √98
Simplifying Surds▶ Show worked answerHide worked answer
- B1: 7√2
Answer: 7√2[1 mark] - 2
Question 2. Simplify fully dfracx²-256×dfrac3x+5
Multiplying & Dividing Algebraic Fractions▶ Show worked answerHide worked answer
- M1: (x-5)(x+5)
- M1: dfrac3(x-5)(x+5)6(x+5)
- A1: dfracx-52
Answer: dfracx-52[3 marks] - 3
Question 3. x² + bx + 10 equiv (x + p)² - 6
b is a positive number
Work out the value of b and the value of pSolving Quadratics by Completing the Square (a = 1)▶ Show worked answerHide worked answer
- M1: expand: x² + 2px + p² - 6
- M1: p² - 6 = 10 so p = 4 (as b > 0)
- A1: p = 4 and b = 8
Answer: b = 8, p = 4[3 marks] - 4
Question 4. PA and PB are tangents from P to a circle, centre O, touching it at A and B. Angle OAB = 28°. Work out angle APB.
Circle Theorems▶ Show worked answerHide worked answer
- M1: isosceles triangle OAB: 180 - 2 × 28
- M1 A1: angle AOB = 124°, then 360 - 90 - 90 - 124 = 56°
Answer: 56°[3 marks] - 5
Question 5. Solve (x + 3)² > 16
Solving Quadratic Inequalities▶ Show worked answerHide worked answer
- M1: boundaries from x + 3 = 4 and x + 3 = -4
- M1: critical values x = 1 and x = -7
- A1: x < -7 or x > 1
Answer: x < -7 or x > 1[3 marks]