Mixed Topic Worksheet Grades 8/9: Day 096
- 1
Question 1. Simplify √200 - √18
Simplifying Surds▶ Show worked answerHide worked answer
- M1: 10√2 - 3√2
- A1: 7√2
Answer: 7√2[2 marks] - 2
Question 2. E = frac12 mv². m = 6.0 and v = 3.2, both correct to 1 decimal place. Work out the upper bound of E. Give your answer to 3 significant figures.
Combining Upper & Lower Bounds▶ Show worked answerHide worked answer
- M1: use the upper bound of both m and v
- M1: frac12 × 6.05 × 3.25²
- A1: 32.0 (31.95...)
Answer: 32.0 (3 s.f.)[3 marks] - 3
Question 3. Simplify fully dfrac2x² - 8xx² - 16
Algebraic Fractions Involving Factorising▶ Show worked answerHide worked answer
- M1: dfrac2x(x - 4)(x - 4)(x + 4)
- M1 A1: dfrac2xx + 4
Answer: dfrac2xx + 4[3 marks] - 4
Question 4. Solve x² - 6x - 2 = 0 by completing the square
Give the solutions in the form a ± √b where a and b are integers.Solving Quadratics by Completing the Square (a = 1)▶ Show worked answerHide worked answer
- M1: (x - 3)² - 9 - 2 = 0
- M1: (x - 3)² = 11
- M1: x - 3 = ±√11
- A1: Both solutions: 3 + √11 and 3 - √11
Answer: x = 3 ± √11[4 marks] - 5
Question 5. The solution of x²-kx+24 ≤ 0 is 3 ≤ x ≤ 8. Work out the value of k.
Solving Quadratic Inequalities▶ Show worked answerHide worked answer
- M1: (x-3)(x-8) = x²-11x+24
- A1: k = 11
Answer: 11[2 marks]
Mixed Topic Worksheet Grades 8/9: Day 096
- 1
Question 1. Simplify √200 - √18
[2 marks]Simplifying Surds▶ Show worked answerHide worked answer
- M1: 10√2 - 3√2
- A1: 7√2
Answer: 7√2 - 2
Question 2. E = frac12 mv². m = 6.0 and v = 3.2, both correct to 1 decimal place. Work out the upper bound of E. Give your answer to 3 significant figures.
[3 marks]Combining Upper & Lower Bounds▶ Show worked answerHide worked answer
- M1: use the upper bound of both m and v
- M1: frac12 × 6.05 × 3.25²
- A1: 32.0 (31.95...)
Answer: 32.0 (3 s.f.) - 3
Question 3. Simplify fully dfrac2x² - 8xx² - 16
[3 marks]Algebraic Fractions Involving Factorising▶ Show worked answerHide worked answer
- M1: dfrac2x(x - 4)(x - 4)(x + 4)
- M1 A1: dfrac2xx + 4
Answer: dfrac2xx + 4 - 4
Question 4. Solve x² - 6x - 2 = 0 by completing the square
[4 marks]
Give the solutions in the form a ± √b where a and b are integers.Solving Quadratics by Completing the Square (a = 1)▶ Show worked answerHide worked answer
- M1: (x - 3)² - 9 - 2 = 0
- M1: (x - 3)² = 11
- M1: x - 3 = ±√11
- A1: Both solutions: 3 + √11 and 3 - √11
Answer: x = 3 ± √11 - 5
Question 5. The solution of x²-kx+24 ≤ 0 is 3 ≤ x ≤ 8. Work out the value of k.
[2 marks]Solving Quadratic Inequalities▶ Show worked answerHide worked answer
- M1: (x-3)(x-8) = x²-11x+24
- A1: k = 11
Answer: 11
Mixed Topic Worksheet Grades 8/9: Day 096
- 1
Question 1. Simplify √200 - √18
Simplifying Surds▶ Show worked answerHide worked answer
- M1: 10√2 - 3√2
- A1: 7√2
Answer: 7√2[2 marks] - 2
Question 2. E = frac12 mv². m = 6.0 and v = 3.2, both correct to 1 decimal place. Work out the upper bound of E. Give your answer to 3 significant figures.
Combining Upper & Lower Bounds▶ Show worked answerHide worked answer
- M1: use the upper bound of both m and v
- M1: frac12 × 6.05 × 3.25²
- A1: 32.0 (31.95...)
Answer: 32.0 (3 s.f.)[3 marks] - 3
Question 3. Simplify fully dfrac2x² - 8xx² - 16
Algebraic Fractions Involving Factorising▶ Show worked answerHide worked answer
- M1: dfrac2x(x - 4)(x - 4)(x + 4)
- M1 A1: dfrac2xx + 4
Answer: dfrac2xx + 4[3 marks] - 4
Question 4. Solve x² - 6x - 2 = 0 by completing the square
Give the solutions in the form a ± √b where a and b are integers.Solving Quadratics by Completing the Square (a = 1)▶ Show worked answerHide worked answer
- M1: (x - 3)² - 9 - 2 = 0
- M1: (x - 3)² = 11
- M1: x - 3 = ±√11
- A1: Both solutions: 3 + √11 and 3 - √11
Answer: x = 3 ± √11[4 marks] - 5
Question 5. The solution of x²-kx+24 ≤ 0 is 3 ≤ x ≤ 8. Work out the value of k.
Solving Quadratic Inequalities▶ Show worked answerHide worked answer
- M1: (x-3)(x-8) = x²-11x+24
- A1: k = 11
Answer: 11[2 marks]