📅 Free live lesson: Tuesday 17th NovemberSave your free place →

Mixed Topic Worksheet Grades 6/7: Day 023

Grades 6/7Non-calculator

  1. Question 1. Is ≤ft(dfrac12)⁻³ greater than ≤ft(dfrac13)⁻²? You must show your working.

    Show worked answerHide worked answer
    1. M1: 2³ = 8 and 3² = 9
    2. A1: No, 9 is greater
    Answer: No. ≤ft(dfrac12)⁻³ = 8 and ≤ft(dfrac13)⁻² = 9
    Fractions with Negative Powers
    [2 marks]

  2. Question 2. Prove that 5(n + 3)² - 5(n + 1)² is a multiple of 20 for all integer values of n.

    Show worked answerHide worked answer
    1. M1: 5(n² + 6n + 9) - 5(n² + 2n + 1)
    2. M1: 20n + 40
    3. C1: 20n + 40 = 20(n + 2), which is a multiple of 20
    Answer: 20(n + 2), a multiple of 20
    Proof with Multiples
    [3 marks]

  3. Question 3. A scientist catches 60 fish in a lake, puts a tag on each fish and returns them to the lake.
    A week later she catches 40 fish from the same lake. 8 of these 40 fish have a tag.
    Work out an estimate for the number of fish in the lake.

    Show worked answerHide worked answer
    1. M1: 60 ÷ N = 8 ÷ 40
    2. M1: 60 × 40 ÷ 8
    3. A1: 300
    Answer: 300
    Capture-Recapture
    [3 marks]

  4. Question 4. Here is triangle XYZ.
    Sam wants to work out the length x.
    Should Sam use the sine rule or the cosine rule?
    Give a reason for your answer.

    Show worked answerHide worked answer
    1. B1: the cosine rule
    2. B1: two sides and the angle between them are given, and the side opposite that angle is unknown
    Answer: The cosine rule, because two sides and the angle between them are given
    Combining the Sine Rule with Other Rules
    7 cmx12 cm64°XYZNot drawn accurately
    [2 marks]

  5. Question 5. f(x) = 2x + 1
    g(x) = x - 9
    fg(a) = 15
    Work out the value of a

    Show worked answerHide worked answer
    1. M1: 2(a - 9) + 1 = 15
    2. M1: a - 9 = 7
    3. A1: a = 16
    Answer: 16
    Composite Functions
    [3 marks]
📅 Free lesson: Tue 17th NovSave your place →

Mixed Topic Worksheet Grades 6/7: Day 023

Grades 6/7Non-calculator

  1. Question 1. Is ≤ft(dfrac12)⁻³ greater than ≤ft(dfrac13)⁻²? You must show your working.

    [2 marks]
    Show worked answerHide worked answer
    1. M1: 2³ = 8 and 3² = 9
    2. A1: No, 9 is greater
    Answer: No. ≤ft(dfrac12)⁻³ = 8 and ≤ft(dfrac13)⁻² = 9
    Fractions with Negative Powers

  2. Question 2. Prove that 5(n + 3)² - 5(n + 1)² is a multiple of 20 for all integer values of n.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: 5(n² + 6n + 9) - 5(n² + 2n + 1)
    2. M1: 20n + 40
    3. C1: 20n + 40 = 20(n + 2), which is a multiple of 20
    Answer: 20(n + 2), a multiple of 20
    Proof with Multiples

  3. Question 3. A scientist catches 60 fish in a lake, puts a tag on each fish and returns them to the lake.
    A week later she catches 40 fish from the same lake. 8 of these 40 fish have a tag.
    Work out an estimate for the number of fish in the lake.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: 60 ÷ N = 8 ÷ 40
    2. M1: 60 × 40 ÷ 8
    3. A1: 300
    Answer: 300
    Capture-Recapture

  4. Question 4. Here is triangle XYZ.
    Sam wants to work out the length x.
    Should Sam use the sine rule or the cosine rule?
    Give a reason for your answer.

    [2 marks]
    7 cmx12 cm64°XYZNot drawn accurately
    Show worked answerHide worked answer
    1. B1: the cosine rule
    2. B1: two sides and the angle between them are given, and the side opposite that angle is unknown
    Answer: The cosine rule, because two sides and the angle between them are given
    Combining the Sine Rule with Other Rules

  5. Question 5. f(x) = 2x + 1
    g(x) = x - 9
    fg(a) = 15
    Work out the value of a

    [3 marks]
    Show worked answerHide worked answer
    1. M1: 2(a - 9) + 1 = 15
    2. M1: a - 9 = 7
    3. A1: a = 16
    Answer: 16
    Composite Functions
📅 Free live lesson: Tuesday 17th NovemberSave your free place →

Mixed Topic Worksheet Grades 6/7: Day 023

Grades 6/7Non-calculator

  1. Question 1. Is ≤ft(dfrac12)⁻³ greater than ≤ft(dfrac13)⁻²? You must show your working.

    Show worked answerHide worked answer
    1. M1: 2³ = 8 and 3² = 9
    2. A1: No, 9 is greater
    Answer: No. ≤ft(dfrac12)⁻³ = 8 and ≤ft(dfrac13)⁻² = 9
    Fractions with Negative Powers
    [2 marks]

  2. Question 2. Prove that 5(n + 3)² - 5(n + 1)² is a multiple of 20 for all integer values of n.

    Show worked answerHide worked answer
    1. M1: 5(n² + 6n + 9) - 5(n² + 2n + 1)
    2. M1: 20n + 40
    3. C1: 20n + 40 = 20(n + 2), which is a multiple of 20
    Answer: 20(n + 2), a multiple of 20
    Proof with Multiples
    [3 marks]

  3. Question 3. A scientist catches 60 fish in a lake, puts a tag on each fish and returns them to the lake.
    A week later she catches 40 fish from the same lake. 8 of these 40 fish have a tag.
    Work out an estimate for the number of fish in the lake.

    Show worked answerHide worked answer
    1. M1: 60 ÷ N = 8 ÷ 40
    2. M1: 60 × 40 ÷ 8
    3. A1: 300
    Answer: 300
    Capture-Recapture
    [3 marks]

  4. Question 4. Here is triangle XYZ.
    Sam wants to work out the length x.
    Should Sam use the sine rule or the cosine rule?
    Give a reason for your answer.

    Show worked answerHide worked answer
    1. B1: the cosine rule
    2. B1: two sides and the angle between them are given, and the side opposite that angle is unknown
    Answer: The cosine rule, because two sides and the angle between them are given
    Combining the Sine Rule with Other Rules
    7 cmx12 cm64°XYZNot drawn accurately
    [2 marks]

  5. Question 5. f(x) = 2x + 1
    g(x) = x - 9
    fg(a) = 15
    Work out the value of a

    Show worked answerHide worked answer
    1. M1: 2(a - 9) + 1 = 15
    2. M1: a - 9 = 7
    3. A1: a = 16
    Answer: 16
    Composite Functions
    [3 marks]