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

Mixed Topic Worksheet Grades 6/7: Day 069

Grades 6/7Non-calculator

  1. Question 1. The graph shows the cost of hiring a bike for different numbers of hours.
    (a) Write down the cost of hiring the bike for 0 hours. [1]
    (b) Work out the extra cost for each hour of hire. [2]

    Show worked answerHide worked answer
    1. (a) B1: Read the value where the line meets the vertical axis: 20
    2. (b) M1: (50 − 20) ÷ 5
    3. (b) A1: 6
    Answer: (a) 20; (b) 6
    Gradient as a Rate of Change
    Time (hours)Cost (£)010203040500123456
    [3 marks]

  2. Question 2. A reflection maps the point (2, 9) onto the point (2, 1).
    Write down the equation of the line of invariant points of this reflection.

    Show worked answerHide worked answer
    1. M1: the mirror line is halfway between the y-coordinates, (9 + 1) ÷ 2
    2. A1: y = 5
    Answer: y = 5
    Invariant Points
    [2 marks]

  3. Question 3. The number of hedgehogs in a park is estimated to be 540.
    The estimate was found by marking 60 hedgehogs in a first catch.
    In a second catch, 45 hedgehogs were caught.
    Some of these 45 hedgehogs were marked.
    Work out how many of the 45 hedgehogs were marked.

    Show worked answerHide worked answer
    1. M1: dfracm45 = dfrac60540 or 60 × 45 ÷ 540
    2. A1: 5
    Answer: 5
    Capture-Recapture
    [2 marks]

  4. Question 4. Expand and simplify 5(2 - √7)

    Show worked answerHide worked answer
    1. M1: 5 × 2 and 5 × √7
    2. A1: 10 - 5√7
    Answer: 10 - 5√7
    Expanding Brackets with Surds
    [2 marks]

  5. Question 5. Equation A is 2x² - 15x - 8 = 0
    Equation B is 4x² - 35x - 9 = 0
    Which equation has the larger positive solution? Show how you know.

    Show worked answerHide worked answer
    1. M1: A: (2x + 1)(x - 8) = 0
    2. M1: B: (4x + 1)(x - 9) = 0
    3. A1: A has x = 8 and B has x = 9
    4. B1: Equation B
    Answer: Equation B (x = 9 compared with x = 8)
    Solving Quadratics by Factorising (a > 1)
    [4 marks]
📅 Free lesson: Tue 17th NovSave your place →

Mixed Topic Worksheet Grades 6/7: Day 069

Grades 6/7Non-calculator

  1. Question 1. The graph shows the cost of hiring a bike for different numbers of hours.
    (a) Write down the cost of hiring the bike for 0 hours. [1]
    (b) Work out the extra cost for each hour of hire. [2]

    [3 marks]
    Time (hours)Cost (£)010203040500123456
    Show worked answerHide worked answer
    1. (a) B1: Read the value where the line meets the vertical axis: 20
    2. (b) M1: (50 − 20) ÷ 5
    3. (b) A1: 6
    Answer: (a) 20; (b) 6
    Gradient as a Rate of Change

  2. Question 2. A reflection maps the point (2, 9) onto the point (2, 1).
    Write down the equation of the line of invariant points of this reflection.

    [2 marks]
    Show worked answerHide worked answer
    1. M1: the mirror line is halfway between the y-coordinates, (9 + 1) ÷ 2
    2. A1: y = 5
    Answer: y = 5
    Invariant Points

  3. Question 3. The number of hedgehogs in a park is estimated to be 540.
    The estimate was found by marking 60 hedgehogs in a first catch.
    In a second catch, 45 hedgehogs were caught.
    Some of these 45 hedgehogs were marked.
    Work out how many of the 45 hedgehogs were marked.

    [2 marks]
    Show worked answerHide worked answer
    1. M1: dfracm45 = dfrac60540 or 60 × 45 ÷ 540
    2. A1: 5
    Answer: 5
    Capture-Recapture

  4. Question 4. Expand and simplify 5(2 - √7)

    [2 marks]
    Show worked answerHide worked answer
    1. M1: 5 × 2 and 5 × √7
    2. A1: 10 - 5√7
    Answer: 10 - 5√7
    Expanding Brackets with Surds

  5. Question 5. Equation A is 2x² - 15x - 8 = 0
    Equation B is 4x² - 35x - 9 = 0
    Which equation has the larger positive solution? Show how you know.

    [4 marks]
    Show worked answerHide worked answer
    1. M1: A: (2x + 1)(x - 8) = 0
    2. M1: B: (4x + 1)(x - 9) = 0
    3. A1: A has x = 8 and B has x = 9
    4. B1: Equation B
    Answer: Equation B (x = 9 compared with x = 8)
    Solving Quadratics by Factorising (a > 1)
📅 Free live lesson: Tuesday 17th NovemberSave your free place →

Mixed Topic Worksheet Grades 6/7: Day 069

Grades 6/7Non-calculator

  1. Question 1. The graph shows the cost of hiring a bike for different numbers of hours.
    (a) Write down the cost of hiring the bike for 0 hours. [1]
    (b) Work out the extra cost for each hour of hire. [2]

    Show worked answerHide worked answer
    1. (a) B1: Read the value where the line meets the vertical axis: 20
    2. (b) M1: (50 − 20) ÷ 5
    3. (b) A1: 6
    Answer: (a) 20; (b) 6
    Gradient as a Rate of Change
    Time (hours)Cost (£)010203040500123456
    [3 marks]

  2. Question 2. A reflection maps the point (2, 9) onto the point (2, 1).
    Write down the equation of the line of invariant points of this reflection.

    Show worked answerHide worked answer
    1. M1: the mirror line is halfway between the y-coordinates, (9 + 1) ÷ 2
    2. A1: y = 5
    Answer: y = 5
    Invariant Points
    [2 marks]

  3. Question 3. The number of hedgehogs in a park is estimated to be 540.
    The estimate was found by marking 60 hedgehogs in a first catch.
    In a second catch, 45 hedgehogs were caught.
    Some of these 45 hedgehogs were marked.
    Work out how many of the 45 hedgehogs were marked.

    Show worked answerHide worked answer
    1. M1: dfracm45 = dfrac60540 or 60 × 45 ÷ 540
    2. A1: 5
    Answer: 5
    Capture-Recapture
    [2 marks]

  4. Question 4. Expand and simplify 5(2 - √7)

    Show worked answerHide worked answer
    1. M1: 5 × 2 and 5 × √7
    2. A1: 10 - 5√7
    Answer: 10 - 5√7
    Expanding Brackets with Surds
    [2 marks]

  5. Question 5. Equation A is 2x² - 15x - 8 = 0
    Equation B is 4x² - 35x - 9 = 0
    Which equation has the larger positive solution? Show how you know.

    Show worked answerHide worked answer
    1. M1: A: (2x + 1)(x - 8) = 0
    2. M1: B: (4x + 1)(x - 9) = 0
    3. A1: A has x = 8 and B has x = 9
    4. B1: Equation B
    Answer: Equation B (x = 9 compared with x = 8)
    Solving Quadratics by Factorising (a > 1)
    [4 marks]