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

Mixed Topic Worksheet Grades 6/7: Day 075

Grades 6/7Non-calculator

  1. Question 1. Here is a prism.
    The cross-section is a rectangle with an isosceles triangle on top.
    The perpendicular height of the triangle is 2 cm.
    Work out the volume of the prism.

    Show worked answerHide worked answer
    1. M1: 6 × 4 = 24 and 1/2 × 6 × 2 = 6
    2. M1: 24 + 6
    3. M1: 30 × 10
    4. A1: 300
    Answer: 300
    Volume of Composite Shapes
    6 cm4 cm4 cm10 cm
    [4 marks]

  2. Question 2. Prove that (4n + 5)² - (4n - 5)² is a multiple of 16 for all integer values of n.

    Show worked answerHide worked answer
    1. M1: (4n + 5)² = 16n² + 40n + 25 and (4n - 5)² = 16n² - 40n + 25
    2. M1: 80n
    3. C1: 80n = 16 × 5n, which is a multiple of 16
    Answer: 16 × 5n, a multiple of 16
    Proof with Multiples
    [3 marks]

  3. Question 3. Values: 3, 5, 6, 8, 9, 11, 40. Work out the range and the interquartile range.

    Show worked answerHide worked answer
    1. B1: range = 40 - 3 = 37
    2. M1: lower quartile 5, upper quartile 11
    3. A1: IQR = 6
    Answer: Range 37, IQR 6
    Benefits of IQR & Range
    [3 marks]

  4. Question 4. The time T seconds a pendulum takes to swing is directly proportional to the square root of its length L metres.
    T = 3 when L = 2.25.
    Work out the value of T when L = 6.25.

    Show worked answerHide worked answer
    1. M1: 3 = k√2.25
    2. M1: T = 2 × √6.25
    3. A1: 5
    Answer: 5
    Algebraic Direct Proportion
    [3 marks]

  5. Question 5. Here is a speed-time graph for a lorry.
    Work out the distance travelled between 10 seconds and 60 seconds.

    Show worked answerHide worked answer
    1. M1: the speed is 10 m/s at 10 seconds and at 60 seconds
    2. M1: ½ × (10 + 20) × 10 = 150 for each end section
    3. M1: 20 × (50 - 20) = 600
    4. A1: 150 + 150 + 600 = 900 m
    Answer: 900 m
    Calculating Total Distance Travelled Using Speed-Time Graphs
    Time (seconds)Speed (m/s)05101520250204060
    [4 marks]
📅 Free lesson: Tue 17th NovSave your place →

Mixed Topic Worksheet Grades 6/7: Day 075

Grades 6/7Non-calculator

  1. Question 1. Here is a prism.
    The cross-section is a rectangle with an isosceles triangle on top.
    The perpendicular height of the triangle is 2 cm.
    Work out the volume of the prism.

    [4 marks]
    6 cm4 cm4 cm10 cm
    Show worked answerHide worked answer
    1. M1: 6 × 4 = 24 and 1/2 × 6 × 2 = 6
    2. M1: 24 + 6
    3. M1: 30 × 10
    4. A1: 300
    Answer: 300
    Volume of Composite Shapes

  2. Question 2. Prove that (4n + 5)² - (4n - 5)² is a multiple of 16 for all integer values of n.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: (4n + 5)² = 16n² + 40n + 25 and (4n - 5)² = 16n² - 40n + 25
    2. M1: 80n
    3. C1: 80n = 16 × 5n, which is a multiple of 16
    Answer: 16 × 5n, a multiple of 16
    Proof with Multiples

  3. Question 3. Values: 3, 5, 6, 8, 9, 11, 40. Work out the range and the interquartile range.

    [3 marks]
    Show worked answerHide worked answer
    1. B1: range = 40 - 3 = 37
    2. M1: lower quartile 5, upper quartile 11
    3. A1: IQR = 6
    Answer: Range 37, IQR 6
    Benefits of IQR & Range

  4. Question 4. The time T seconds a pendulum takes to swing is directly proportional to the square root of its length L metres.
    T = 3 when L = 2.25.
    Work out the value of T when L = 6.25.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: 3 = k√2.25
    2. M1: T = 2 × √6.25
    3. A1: 5
    Answer: 5
    Algebraic Direct Proportion

  5. Question 5. Here is a speed-time graph for a lorry.
    Work out the distance travelled between 10 seconds and 60 seconds.

    [4 marks]
    Time (seconds)Speed (m/s)05101520250204060
    Show worked answerHide worked answer
    1. M1: the speed is 10 m/s at 10 seconds and at 60 seconds
    2. M1: ½ × (10 + 20) × 10 = 150 for each end section
    3. M1: 20 × (50 - 20) = 600
    4. A1: 150 + 150 + 600 = 900 m
    Answer: 900 m
    Calculating Total Distance Travelled Using Speed-Time Graphs
📅 Free live lesson: Tuesday 17th NovemberSave your free place →

Mixed Topic Worksheet Grades 6/7: Day 075

Grades 6/7Non-calculator

  1. Question 1. Here is a prism.
    The cross-section is a rectangle with an isosceles triangle on top.
    The perpendicular height of the triangle is 2 cm.
    Work out the volume of the prism.

    Show worked answerHide worked answer
    1. M1: 6 × 4 = 24 and 1/2 × 6 × 2 = 6
    2. M1: 24 + 6
    3. M1: 30 × 10
    4. A1: 300
    Answer: 300
    Volume of Composite Shapes
    6 cm4 cm4 cm10 cm
    [4 marks]

  2. Question 2. Prove that (4n + 5)² - (4n - 5)² is a multiple of 16 for all integer values of n.

    Show worked answerHide worked answer
    1. M1: (4n + 5)² = 16n² + 40n + 25 and (4n - 5)² = 16n² - 40n + 25
    2. M1: 80n
    3. C1: 80n = 16 × 5n, which is a multiple of 16
    Answer: 16 × 5n, a multiple of 16
    Proof with Multiples
    [3 marks]

  3. Question 3. Values: 3, 5, 6, 8, 9, 11, 40. Work out the range and the interquartile range.

    Show worked answerHide worked answer
    1. B1: range = 40 - 3 = 37
    2. M1: lower quartile 5, upper quartile 11
    3. A1: IQR = 6
    Answer: Range 37, IQR 6
    Benefits of IQR & Range
    [3 marks]

  4. Question 4. The time T seconds a pendulum takes to swing is directly proportional to the square root of its length L metres.
    T = 3 when L = 2.25.
    Work out the value of T when L = 6.25.

    Show worked answerHide worked answer
    1. M1: 3 = k√2.25
    2. M1: T = 2 × √6.25
    3. A1: 5
    Answer: 5
    Algebraic Direct Proportion
    [3 marks]

  5. Question 5. Here is a speed-time graph for a lorry.
    Work out the distance travelled between 10 seconds and 60 seconds.

    Show worked answerHide worked answer
    1. M1: the speed is 10 m/s at 10 seconds and at 60 seconds
    2. M1: ½ × (10 + 20) × 10 = 150 for each end section
    3. M1: 20 × (50 - 20) = 600
    4. A1: 150 + 150 + 600 = 900 m
    Answer: 900 m
    Calculating Total Distance Travelled Using Speed-Time Graphs
    Time (seconds)Speed (m/s)05101520250204060
    [4 marks]