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

Mixed Topic Worksheet Grades 6/7: Day 059

Grades 6/7Non-calculator

  1. Question 1. n(xi)=40, n(A')=26, n(B)=15 and n(A cap B)=6. Work out n(A cup B).

    Show worked answerHide worked answer
    1. M1: n(A)=40-26=14
    2. M1: n(A cup B)=14+15-6
    3. A1: 23
    Answer: 23
    Fundamentals of Set Notation
    [3 marks]

  2. Question 2. Ages at two clubs. Youth club: minimum 11, lower quartile 13, median 15, upper quartile 17, maximum 19. Walking club: minimum 20, lower quartile 45, median 60, upper quartile 68, maximum 79. Compare the ages using the median and the interquartile range.

    Show worked answerHide worked answer
    1. B1: median: walking club 60 > youth club 15
    2. B1: IQR: walking club 23 > youth club 4, so the ages vary more
    Answer: The walking club has the higher median age (60 > 15) and the larger interquartile range (23 > 4), so its ages vary more.
    Comparing Data Using Box Plots
    [2 marks]

  3. Question 3. Zoe says that a reflection in the line y = x and a rotation of 180^° about (0, 0) each have exactly one invariant point, which is (0, 0).
    Is Zoe correct? You must give a reason.

    Show worked answerHide worked answer
    1. B1: No
    2. B1: every point on y = x is invariant under the reflection, so it has more than one invariant point (the rotation has only (0, 0))
    Answer: No. Every point on the line y = x is invariant under the reflection, for example (3, 3).
    Invariant Points
    [2 marks]

  4. Question 4. f(x) = 3x + 1
    fg(x) = 12x - 5
    Find g(x)

    Show worked answerHide worked answer
    1. M1: 3g(x) + 1 = 12x - 5
    2. M1: 3g(x) = 12x - 6
    3. A1: g(x) = 4x - 2
    Answer: 4x - 2
    Composite Functions
    [3 marks]

  5. Question 5. x²/³ = 16 and x is positive. Work out the value of x.

    Show worked answerHide worked answer
    1. M1: raises both sides to the power dfrac32
    2. M1: 16³/² = 4³
    3. A1: 64
    Answer: 64
    Fractional Powers
    [3 marks]
📅 Free lesson: Tue 17th NovSave your place →

Mixed Topic Worksheet Grades 6/7: Day 059

Grades 6/7Non-calculator

  1. Question 1. n(xi)=40, n(A')=26, n(B)=15 and n(A cap B)=6. Work out n(A cup B).

    [3 marks]
    Show worked answerHide worked answer
    1. M1: n(A)=40-26=14
    2. M1: n(A cup B)=14+15-6
    3. A1: 23
    Answer: 23
    Fundamentals of Set Notation

  2. Question 2. Ages at two clubs. Youth club: minimum 11, lower quartile 13, median 15, upper quartile 17, maximum 19. Walking club: minimum 20, lower quartile 45, median 60, upper quartile 68, maximum 79. Compare the ages using the median and the interquartile range.

    [2 marks]
    Show worked answerHide worked answer
    1. B1: median: walking club 60 > youth club 15
    2. B1: IQR: walking club 23 > youth club 4, so the ages vary more
    Answer: The walking club has the higher median age (60 > 15) and the larger interquartile range (23 > 4), so its ages vary more.
    Comparing Data Using Box Plots

  3. Question 3. Zoe says that a reflection in the line y = x and a rotation of 180^° about (0, 0) each have exactly one invariant point, which is (0, 0).
    Is Zoe correct? You must give a reason.

    [2 marks]
    Show worked answerHide worked answer
    1. B1: No
    2. B1: every point on y = x is invariant under the reflection, so it has more than one invariant point (the rotation has only (0, 0))
    Answer: No. Every point on the line y = x is invariant under the reflection, for example (3, 3).
    Invariant Points

  4. Question 4. f(x) = 3x + 1
    fg(x) = 12x - 5
    Find g(x)

    [3 marks]
    Show worked answerHide worked answer
    1. M1: 3g(x) + 1 = 12x - 5
    2. M1: 3g(x) = 12x - 6
    3. A1: g(x) = 4x - 2
    Answer: 4x - 2
    Composite Functions

  5. Question 5. x²/³ = 16 and x is positive. Work out the value of x.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: raises both sides to the power dfrac32
    2. M1: 16³/² = 4³
    3. A1: 64
    Answer: 64
    Fractional Powers
📅 Free live lesson: Tuesday 17th NovemberSave your free place →

Mixed Topic Worksheet Grades 6/7: Day 059

Grades 6/7Non-calculator

  1. Question 1. n(xi)=40, n(A')=26, n(B)=15 and n(A cap B)=6. Work out n(A cup B).

    Show worked answerHide worked answer
    1. M1: n(A)=40-26=14
    2. M1: n(A cup B)=14+15-6
    3. A1: 23
    Answer: 23
    Fundamentals of Set Notation
    [3 marks]

  2. Question 2. Ages at two clubs. Youth club: minimum 11, lower quartile 13, median 15, upper quartile 17, maximum 19. Walking club: minimum 20, lower quartile 45, median 60, upper quartile 68, maximum 79. Compare the ages using the median and the interquartile range.

    Show worked answerHide worked answer
    1. B1: median: walking club 60 > youth club 15
    2. B1: IQR: walking club 23 > youth club 4, so the ages vary more
    Answer: The walking club has the higher median age (60 > 15) and the larger interquartile range (23 > 4), so its ages vary more.
    Comparing Data Using Box Plots
    [2 marks]

  3. Question 3. Zoe says that a reflection in the line y = x and a rotation of 180^° about (0, 0) each have exactly one invariant point, which is (0, 0).
    Is Zoe correct? You must give a reason.

    Show worked answerHide worked answer
    1. B1: No
    2. B1: every point on y = x is invariant under the reflection, so it has more than one invariant point (the rotation has only (0, 0))
    Answer: No. Every point on the line y = x is invariant under the reflection, for example (3, 3).
    Invariant Points
    [2 marks]

  4. Question 4. f(x) = 3x + 1
    fg(x) = 12x - 5
    Find g(x)

    Show worked answerHide worked answer
    1. M1: 3g(x) + 1 = 12x - 5
    2. M1: 3g(x) = 12x - 6
    3. A1: g(x) = 4x - 2
    Answer: 4x - 2
    Composite Functions
    [3 marks]

  5. Question 5. x²/³ = 16 and x is positive. Work out the value of x.

    Show worked answerHide worked answer
    1. M1: raises both sides to the power dfrac32
    2. M1: 16³/² = 4³
    3. A1: 64
    Answer: 64
    Fractional Powers
    [3 marks]