Mixed Topic Worksheet Grades 8/9: Day 074
- 1
Question 1. Simplify fully √150
Simplifying Surds▶ Show worked answerHide worked answer
- M1: √25 × 6
- A1: 5√6
Answer: 5√6[2 marks] - 2
Question 2. Pupils in Year 9, Year 10 and Year 11 cycle or walk to school. The two-way table shows the results.
One of the pupils who cycle is chosen at random.
Work out the probability that this pupil is in Year 10.Conditional Probability with Two-Way Tables▶ Show worked answerHide worked answer
- M1: 12 + 18 + 15 = 45 pupils who cycle
- A1: 2/5
Answer: dfrac25[2 marks] - 3
Question 3. P(A)=0.5, P(B)=0.4 and P(Acap B)=0.15. Work out P(Bmid A).
Conditional Probability with Venn Diagrams▶ Show worked answerHide worked answer
- M1: P(Bmid A)=0.15/0.5
- A1: 0.3
Answer: 0.3[2 marks] - 4
Question 4. Solve x² - 8x + 3 = 0 by completing the square.
Give your answers in the form a ± √bSolving Quadratics by Completing the Square (a = 1)▶ Show worked answerHide worked answer
- M1: (x - 4)² - 16 + 3 = 0
- A1: (x - 4)² = 13
- M1: x - 4 = ±√13
- A1: x = 4 ± √13
Answer: x = 4 ± √13[4 marks] - 5
Question 5. Rationalise the denominator of dfrac13 + √2
Rationalising Denominators of the Form a ± √b▶ Show worked answerHide worked answer
- M1: dfrac3 - √2(3 + √2)(3 - √2)
- A1: dfrac3 - √27
Answer: dfrac3 - √27[2 marks]
Mixed Topic Worksheet Grades 8/9: Day 074
- 1
Question 1. Simplify fully √150
[2 marks]Simplifying Surds▶ Show worked answerHide worked answer
- M1: √25 × 6
- A1: 5√6
Answer: 5√6 - 2
Question 2. Pupils in Year 9, Year 10 and Year 11 cycle or walk to school. The two-way table shows the results.
[2 marks]
One of the pupils who cycle is chosen at random.
Work out the probability that this pupil is in Year 10.Conditional Probability with Two-Way Tables▶ Show worked answerHide worked answer
- M1: 12 + 18 + 15 = 45 pupils who cycle
- A1: 2/5
Answer: dfrac25 - 3
Question 3. P(A)=0.5, P(B)=0.4 and P(Acap B)=0.15. Work out P(Bmid A).
[2 marks]Conditional Probability with Venn Diagrams▶ Show worked answerHide worked answer
- M1: P(Bmid A)=0.15/0.5
- A1: 0.3
Answer: 0.3 - 4
Question 4. Solve x² - 8x + 3 = 0 by completing the square.
[4 marks]
Give your answers in the form a ± √bSolving Quadratics by Completing the Square (a = 1)▶ Show worked answerHide worked answer
- M1: (x - 4)² - 16 + 3 = 0
- A1: (x - 4)² = 13
- M1: x - 4 = ±√13
- A1: x = 4 ± √13
Answer: x = 4 ± √13 - 5
Question 5. Rationalise the denominator of dfrac13 + √2
[2 marks]Rationalising Denominators of the Form a ± √b▶ Show worked answerHide worked answer
- M1: dfrac3 - √2(3 + √2)(3 - √2)
- A1: dfrac3 - √27
Answer: dfrac3 - √27
Mixed Topic Worksheet Grades 8/9: Day 074
- 1
Question 1. Simplify fully √150
Simplifying Surds▶ Show worked answerHide worked answer
- M1: √25 × 6
- A1: 5√6
Answer: 5√6[2 marks] - 2
Question 2. Pupils in Year 9, Year 10 and Year 11 cycle or walk to school. The two-way table shows the results.
One of the pupils who cycle is chosen at random.
Work out the probability that this pupil is in Year 10.Conditional Probability with Two-Way Tables▶ Show worked answerHide worked answer
- M1: 12 + 18 + 15 = 45 pupils who cycle
- A1: 2/5
Answer: dfrac25[2 marks] - 3
Question 3. P(A)=0.5, P(B)=0.4 and P(Acap B)=0.15. Work out P(Bmid A).
Conditional Probability with Venn Diagrams▶ Show worked answerHide worked answer
- M1: P(Bmid A)=0.15/0.5
- A1: 0.3
Answer: 0.3[2 marks] - 4
Question 4. Solve x² - 8x + 3 = 0 by completing the square.
Give your answers in the form a ± √bSolving Quadratics by Completing the Square (a = 1)▶ Show worked answerHide worked answer
- M1: (x - 4)² - 16 + 3 = 0
- A1: (x - 4)² = 13
- M1: x - 4 = ±√13
- A1: x = 4 ± √13
Answer: x = 4 ± √13[4 marks] - 5
Question 5. Rationalise the denominator of dfrac13 + √2
Rationalising Denominators of the Form a ± √b▶ Show worked answerHide worked answer
- M1: dfrac3 - √2(3 + √2)(3 - √2)
- A1: dfrac3 - √27
Answer: dfrac3 - √27[2 marks]