Mixed Topic Worksheet Grades 8/9: Day 099
- 1
Question 1. Simplify fully √72
Simplifying Surds▶ Show worked answerHide worked answer
- M1: √36 × 2
- A1: 6√2
Answer: 6√2[2 marks] - 2
Question 2. Show that dfrac3x² - x - 10x² - 4 simplifies to dfrac3x + 5x + 2
Algebraic Fractions Involving Factorising▶ Show worked answerHide worked answer
- M1: dfrac(3x + 5)(x - 2)(x - 2)(x + 2)
- A1: cancel (x - 2) to give dfrac3x + 5x + 2
Answer: Shown[2 marks] - 3
Question 3. The curve y = x² + bx + c has its turning point at (-2, -9). Find the values of b and c.
Solving Quadratics by Completing the Square (a = 1)▶ Show worked answerHide worked answer
- M1: y = (x + 2)² - 9
- M1: expand to x² + 4x + 4 - 9
- A1: b = 4 and c = -5
Answer: b = 4, c = -5[3 marks] - 4
Question 4. Solve dfracx² - 1x ÷ dfracx + 14 = 6
Multiplying & Dividing Algebraic Fractions▶ Show worked answerHide worked answer
- M1 M1: dfrac(x - 1)(x + 1)x × dfrac4x + 1 = dfrac4(x - 1)x
- M1 A1: 4x - 4 = 6x, so x = -2
Answer: x = -2[4 marks] - 5
Question 5. The line y = 2x + k is a tangent to the circle x² + y² = 5. Find the two possible values of k.
Solving Quadratic Simultaneous Equations▶ Show worked answerHide worked answer
- M1 M1: 5x² + 4kx + k² - 5 = 0 and 16k² - 20(k² - 5) = 0
- M1 A1: k² = 25, so k = 5 or k = -5
Answer: k = 5 or k = -5[4 marks]
Mixed Topic Worksheet Grades 8/9: Day 099
- 1
Question 1. Simplify fully √72
[2 marks]Simplifying Surds▶ Show worked answerHide worked answer
- M1: √36 × 2
- A1: 6√2
Answer: 6√2 - 2
Question 2. Show that dfrac3x² - x - 10x² - 4 simplifies to dfrac3x + 5x + 2
[2 marks]Algebraic Fractions Involving Factorising▶ Show worked answerHide worked answer
- M1: dfrac(3x + 5)(x - 2)(x - 2)(x + 2)
- A1: cancel (x - 2) to give dfrac3x + 5x + 2
Answer: Shown - 3
Question 3. The curve y = x² + bx + c has its turning point at (-2, -9). Find the values of b and c.
[3 marks]Solving Quadratics by Completing the Square (a = 1)▶ Show worked answerHide worked answer
- M1: y = (x + 2)² - 9
- M1: expand to x² + 4x + 4 - 9
- A1: b = 4 and c = -5
Answer: b = 4, c = -5 - 4
Question 4. Solve dfracx² - 1x ÷ dfracx + 14 = 6
[4 marks]Multiplying & Dividing Algebraic Fractions▶ Show worked answerHide worked answer
- M1 M1: dfrac(x - 1)(x + 1)x × dfrac4x + 1 = dfrac4(x - 1)x
- M1 A1: 4x - 4 = 6x, so x = -2
Answer: x = -2 - 5
Question 5. The line y = 2x + k is a tangent to the circle x² + y² = 5. Find the two possible values of k.
[4 marks]Solving Quadratic Simultaneous Equations▶ Show worked answerHide worked answer
- M1 M1: 5x² + 4kx + k² - 5 = 0 and 16k² - 20(k² - 5) = 0
- M1 A1: k² = 25, so k = 5 or k = -5
Answer: k = 5 or k = -5
Mixed Topic Worksheet Grades 8/9: Day 099
- 1
Question 1. Simplify fully √72
Simplifying Surds▶ Show worked answerHide worked answer
- M1: √36 × 2
- A1: 6√2
Answer: 6√2[2 marks] - 2
Question 2. Show that dfrac3x² - x - 10x² - 4 simplifies to dfrac3x + 5x + 2
Algebraic Fractions Involving Factorising▶ Show worked answerHide worked answer
- M1: dfrac(3x + 5)(x - 2)(x - 2)(x + 2)
- A1: cancel (x - 2) to give dfrac3x + 5x + 2
Answer: Shown[2 marks] - 3
Question 3. The curve y = x² + bx + c has its turning point at (-2, -9). Find the values of b and c.
Solving Quadratics by Completing the Square (a = 1)▶ Show worked answerHide worked answer
- M1: y = (x + 2)² - 9
- M1: expand to x² + 4x + 4 - 9
- A1: b = 4 and c = -5
Answer: b = 4, c = -5[3 marks] - 4
Question 4. Solve dfracx² - 1x ÷ dfracx + 14 = 6
Multiplying & Dividing Algebraic Fractions▶ Show worked answerHide worked answer
- M1 M1: dfrac(x - 1)(x + 1)x × dfrac4x + 1 = dfrac4(x - 1)x
- M1 A1: 4x - 4 = 6x, so x = -2
Answer: x = -2[4 marks] - 5
Question 5. The line y = 2x + k is a tangent to the circle x² + y² = 5. Find the two possible values of k.
Solving Quadratic Simultaneous Equations▶ Show worked answerHide worked answer
- M1 M1: 5x² + 4kx + k² - 5 = 0 and 16k² - 20(k² - 5) = 0
- M1 A1: k² = 25, so k = 5 or k = -5
Answer: k = 5 or k = -5[4 marks]