Mixed Topic Worksheet Grades 6/7: Day 077
- 1
Question 1. 50 people each chose tea or coffee. The two-way table shows the results.
One of the people is chosen at random.
Work out the probability that the person is a man who chose tea.Finding Probabilities with Two-Way Tables▶ Show worked answerHide worked answer
- B1: 14/50 or 7/25
Answer: dfrac725[1 mark] - 2
Question 2. Tia says: “A rotation of 90^° about (2, 1) has no invariant points, because every point moves.”
Is Tia correct? You must explain your answer.Invariant Points▶ Show worked answerHide worked answer
- B1: No
- B1: the point (2, 1), the centre of rotation, does not move
Answer: No. The centre of rotation, (2, 1), does not move, so it is invariant.[2 marks] - 3
Question 3. (n + p)² - (n - 1)² is a multiple of 8 for all integer values of n. p is a positive integer less than 10. Work out the smallest possible value of p.
Proof with Multiples▶ Show worked answerHide worked answer
- M1: (n + p)² - (n - 1)² = (2n + p - 1)(p + 1)
- M1: tries values of p, for example p = 3 gives 8(n + 1) and p = 1 and p = 2 do not give a multiple of 8
- A1: 3
Answer: 3[3 marks] - 4
Question 4. A cube has side length (2x - 1) cm.
Work out an expression for the volume of the cube.
Give your answer in expanded form.Expanding Triple Brackets▶ Show worked answerHide worked answer
- M1: (2x - 1)² = 4x² - 4x + 1
- M1: (2x - 1)(4x² - 4x + 1) = 8x³ - 8x² + 2x - 4x² + 4x - 1
- A1: 8x³ - 12x² + 6x - 1
Answer: 8x³ - 12x² + 6x - 1[3 marks] - 5
Question 5. Write dfrac713 as a decimal to find which of dfrac713 and 0.dot5dot4 is greater.
Which number is greater?
You must show all your working.Writing Fractions as Recurring Decimals▶ Show worked answerHide worked answer
- M1: 7 ÷ 13 = 0.538461...
- M1: 0.5384... compared with 0.5454...
- A1: 0.dot5dot4 is greater
Answer: 0.dot5dot4 is greater[3 marks]
Mixed Topic Worksheet Grades 6/7: Day 077
- 1
Question 1. 50 people each chose tea or coffee. The two-way table shows the results.
[1 mark]
One of the people is chosen at random.
Work out the probability that the person is a man who chose tea.Finding Probabilities with Two-Way Tables▶ Show worked answerHide worked answer
- B1: 14/50 or 7/25
Answer: dfrac725 - 2
Question 2. Tia says: “A rotation of 90^° about (2, 1) has no invariant points, because every point moves.”
[2 marks]
Is Tia correct? You must explain your answer.Invariant Points▶ Show worked answerHide worked answer
- B1: No
- B1: the point (2, 1), the centre of rotation, does not move
Answer: No. The centre of rotation, (2, 1), does not move, so it is invariant. - 3
Question 3. (n + p)² - (n - 1)² is a multiple of 8 for all integer values of n. p is a positive integer less than 10. Work out the smallest possible value of p.
[3 marks]Proof with Multiples▶ Show worked answerHide worked answer
- M1: (n + p)² - (n - 1)² = (2n + p - 1)(p + 1)
- M1: tries values of p, for example p = 3 gives 8(n + 1) and p = 1 and p = 2 do not give a multiple of 8
- A1: 3
Answer: 3 - 4
Question 4. A cube has side length (2x - 1) cm.
[3 marks]
Work out an expression for the volume of the cube.
Give your answer in expanded form.Expanding Triple Brackets▶ Show worked answerHide worked answer
- M1: (2x - 1)² = 4x² - 4x + 1
- M1: (2x - 1)(4x² - 4x + 1) = 8x³ - 8x² + 2x - 4x² + 4x - 1
- A1: 8x³ - 12x² + 6x - 1
Answer: 8x³ - 12x² + 6x - 1 - 5
Question 5. Write dfrac713 as a decimal to find which of dfrac713 and 0.dot5dot4 is greater.
[3 marks]
Which number is greater?
You must show all your working.Writing Fractions as Recurring Decimals▶ Show worked answerHide worked answer
- M1: 7 ÷ 13 = 0.538461...
- M1: 0.5384... compared with 0.5454...
- A1: 0.dot5dot4 is greater
Answer: 0.dot5dot4 is greater
Mixed Topic Worksheet Grades 6/7: Day 077
- 1
Question 1. 50 people each chose tea or coffee. The two-way table shows the results.
One of the people is chosen at random.
Work out the probability that the person is a man who chose tea.Finding Probabilities with Two-Way Tables▶ Show worked answerHide worked answer
- B1: 14/50 or 7/25
Answer: dfrac725[1 mark] - 2
Question 2. Tia says: “A rotation of 90^° about (2, 1) has no invariant points, because every point moves.”
Is Tia correct? You must explain your answer.Invariant Points▶ Show worked answerHide worked answer
- B1: No
- B1: the point (2, 1), the centre of rotation, does not move
Answer: No. The centre of rotation, (2, 1), does not move, so it is invariant.[2 marks] - 3
Question 3. (n + p)² - (n - 1)² is a multiple of 8 for all integer values of n. p is a positive integer less than 10. Work out the smallest possible value of p.
Proof with Multiples▶ Show worked answerHide worked answer
- M1: (n + p)² - (n - 1)² = (2n + p - 1)(p + 1)
- M1: tries values of p, for example p = 3 gives 8(n + 1) and p = 1 and p = 2 do not give a multiple of 8
- A1: 3
Answer: 3[3 marks] - 4
Question 4. A cube has side length (2x - 1) cm.
Work out an expression for the volume of the cube.
Give your answer in expanded form.Expanding Triple Brackets▶ Show worked answerHide worked answer
- M1: (2x - 1)² = 4x² - 4x + 1
- M1: (2x - 1)(4x² - 4x + 1) = 8x³ - 8x² + 2x - 4x² + 4x - 1
- A1: 8x³ - 12x² + 6x - 1
Answer: 8x³ - 12x² + 6x - 1[3 marks] - 5
Question 5. Write dfrac713 as a decimal to find which of dfrac713 and 0.dot5dot4 is greater.
Which number is greater?
You must show all your working.Writing Fractions as Recurring Decimals▶ Show worked answerHide worked answer
- M1: 7 ÷ 13 = 0.538461...
- M1: 0.5384... compared with 0.5454...
- A1: 0.dot5dot4 is greater
Answer: 0.dot5dot4 is greater[3 marks]