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

Mixed Topic Worksheet Grades 6/7: Day 073

Grades 6/7Non-calculator

  1. Question 1. On a distance-time graph, a cyclist's line is horizontal from 10:00 to 10:30 at a distance of 12 km from home.
    What does this tell you about the cyclist? [1]

    Show worked answerHide worked answer
    1. B1: stationary (stopped) for 30 minutes, 12 km from home
    Answer: The cyclist stopped for 30 minutes, 12 km from home
    Key Regions on Distance-Time Graphs
    [1 mark]

  2. Question 2. Seals on an island are caught and each is given a tag. The tagged seals are returned to the island.
    70 seals are tagged.
    A month later, 36 seals are caught.
    9 of these 36 seals have a tag.
    Work out an estimate for the number of seals on the island.

    Show worked answerHide worked answer
    1. M1: dfrac936 or dfrac70N equated, or 70 × 36 ÷ 9
    2. A1: 280
    Answer: 280
    Capture-Recapture
    [2 marks]

  3. Question 3. The point C(-1, 4) is enlarged by scale factor -2, centre (1, 2).
    Work out the coordinates of the image of C.

    Show worked answerHide worked answer
    1. M1: from the centre to C is 2 left and 2 up
    2. M1: times -2: 4 right and 4 down from the centre
    3. A1: (5, -2)
    Answer: (5, -2)
    Enlargements with Negative Integer Scale Factors
    [3 marks]

  4. Question 4. x¹/³ = 5. Work out the value of x.

    Show worked answerHide worked answer
    1. M1: cubes both sides, x = 5³
    2. A1: 125
    Answer: 125
    Fractional Powers
    [2 marks]

  5. Question 5. The table shows the first five terms of a quadratic sequence.
    Find an expression, in terms of n, for the nth term of this sequence.

    Show worked answerHide worked answer
    1. M1: differences 7, 11, 15, 19 so the second difference is 4 and a = 2
    2. M1: 2n² gives 2, 8, 18, 32, 50 and the remainders 3, 4, 5, 6, 7 are n + 2
    3. A1: 2n² + n + 2
    Answer: 2n² + n + 2
    nth Term of Quadratic Sequences
    n12345Term512233857
    [3 marks]
📅 Free lesson: Tue 17th NovSave your place →

Mixed Topic Worksheet Grades 6/7: Day 073

Grades 6/7Non-calculator

  1. Question 1. On a distance-time graph, a cyclist's line is horizontal from 10:00 to 10:30 at a distance of 12 km from home.
    What does this tell you about the cyclist? [1]

    [1 mark]
    Show worked answerHide worked answer
    1. B1: stationary (stopped) for 30 minutes, 12 km from home
    Answer: The cyclist stopped for 30 minutes, 12 km from home
    Key Regions on Distance-Time Graphs

  2. Question 2. Seals on an island are caught and each is given a tag. The tagged seals are returned to the island.
    70 seals are tagged.
    A month later, 36 seals are caught.
    9 of these 36 seals have a tag.
    Work out an estimate for the number of seals on the island.

    [2 marks]
    Show worked answerHide worked answer
    1. M1: dfrac936 or dfrac70N equated, or 70 × 36 ÷ 9
    2. A1: 280
    Answer: 280
    Capture-Recapture

  3. Question 3. The point C(-1, 4) is enlarged by scale factor -2, centre (1, 2).
    Work out the coordinates of the image of C.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: from the centre to C is 2 left and 2 up
    2. M1: times -2: 4 right and 4 down from the centre
    3. A1: (5, -2)
    Answer: (5, -2)
    Enlargements with Negative Integer Scale Factors

  4. Question 4. x¹/³ = 5. Work out the value of x.

    [2 marks]
    Show worked answerHide worked answer
    1. M1: cubes both sides, x = 5³
    2. A1: 125
    Answer: 125
    Fractional Powers

  5. Question 5. The table shows the first five terms of a quadratic sequence.
    Find an expression, in terms of n, for the nth term of this sequence.

    [3 marks]
    n12345Term512233857
    Show worked answerHide worked answer
    1. M1: differences 7, 11, 15, 19 so the second difference is 4 and a = 2
    2. M1: 2n² gives 2, 8, 18, 32, 50 and the remainders 3, 4, 5, 6, 7 are n + 2
    3. A1: 2n² + n + 2
    Answer: 2n² + n + 2
    nth Term of Quadratic Sequences
📅 Free live lesson: Tuesday 17th NovemberSave your free place →

Mixed Topic Worksheet Grades 6/7: Day 073

Grades 6/7Non-calculator

  1. Question 1. On a distance-time graph, a cyclist's line is horizontal from 10:00 to 10:30 at a distance of 12 km from home.
    What does this tell you about the cyclist? [1]

    Show worked answerHide worked answer
    1. B1: stationary (stopped) for 30 minutes, 12 km from home
    Answer: The cyclist stopped for 30 minutes, 12 km from home
    Key Regions on Distance-Time Graphs
    [1 mark]

  2. Question 2. Seals on an island are caught and each is given a tag. The tagged seals are returned to the island.
    70 seals are tagged.
    A month later, 36 seals are caught.
    9 of these 36 seals have a tag.
    Work out an estimate for the number of seals on the island.

    Show worked answerHide worked answer
    1. M1: dfrac936 or dfrac70N equated, or 70 × 36 ÷ 9
    2. A1: 280
    Answer: 280
    Capture-Recapture
    [2 marks]

  3. Question 3. The point C(-1, 4) is enlarged by scale factor -2, centre (1, 2).
    Work out the coordinates of the image of C.

    Show worked answerHide worked answer
    1. M1: from the centre to C is 2 left and 2 up
    2. M1: times -2: 4 right and 4 down from the centre
    3. A1: (5, -2)
    Answer: (5, -2)
    Enlargements with Negative Integer Scale Factors
    [3 marks]

  4. Question 4. x¹/³ = 5. Work out the value of x.

    Show worked answerHide worked answer
    1. M1: cubes both sides, x = 5³
    2. A1: 125
    Answer: 125
    Fractional Powers
    [2 marks]

  5. Question 5. The table shows the first five terms of a quadratic sequence.
    Find an expression, in terms of n, for the nth term of this sequence.

    Show worked answerHide worked answer
    1. M1: differences 7, 11, 15, 19 so the second difference is 4 and a = 2
    2. M1: 2n² gives 2, 8, 18, 32, 50 and the remainders 3, 4, 5, 6, 7 are n + 2
    3. A1: 2n² + n + 2
    Answer: 2n² + n + 2
    nth Term of Quadratic Sequences
    n12345Term512233857
    [3 marks]