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

Mixed Topic Worksheet Grades 6/7: Day 014

Grades 6/7Calculator

  1. Question 1. Decrease 650 kg by 12%.

    Show worked answerHide worked answer
    1. M1: 100 - 12 = 88%
    2. M1: 650 × 0.88
    3. A1: 572
    Answer: 572 kg
    Percentage Multipliers
    [3 marks]

  2. Question 2. Prove that (n + 4)(n + 6) - n(n + 10) is a multiple of 6 for all integer values of n.

    Show worked answerHide worked answer
    1. M1: n² + 6n + 4n + 24 - (n² + 10n)
    2. M1: 24 after the terms in n cancel
    3. C1: 24 = 6 × 4, which is a multiple of 6
    Answer: 24 = 6 × 4
    Proof with Multiples
    [3 marks]

  3. Question 3. The table shows the number of pets owned by 20 pupils. Work out the range and the interquartile range.

    Show worked answerHide worked answer
    1. M1: lower quartile (5th to 6th value) =1; upper quartile (15th to 16th value) =2
    2. A1: range =4
    3. A1: IQR =1
    Answer: Range 4, interquartile range 1
    Benefits of IQR & Range
    Number of petsFrequency0417253341
    [3 marks]

  4. Question 4. Triangle XYZ has angle YZX = 72^°, XZ = 8.5 cm and YZ = 15 cm
    Work out its area.
    Give your answer to 1 decimal place.

    Show worked answerHide worked answer
    1. M1: 1/2 × 15 × 8.5 × sin 72^°
    2. A1: 60.6
    Answer: 60.6 cm²
    Calculating Area Using ½ab sin C
    [2 marks]

  5. Question 5. A ball is thrown upwards. Its height, h metres, above the ground after t seconds is given by h = 18t - 6t²
    Work out the greatest height of the ball above the ground.

    Show worked answerHide worked answer
    1. M1: the greatest height is at t = 18 / 12 = 1.5, halfway between the times at which h = 0
    2. M1: 18 × 1.5 - 6 × 1.5²
    3. A1: 13.5 metres
    Answer: 13.5
    Turning Points of Quadratics
    [3 marks]
📅 Free lesson: Tue 17th NovSave your place →

Mixed Topic Worksheet Grades 6/7: Day 014

Grades 6/7Calculator

  1. Question 1. Decrease 650 kg by 12%.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: 100 - 12 = 88%
    2. M1: 650 × 0.88
    3. A1: 572
    Answer: 572 kg
    Percentage Multipliers

  2. Question 2. Prove that (n + 4)(n + 6) - n(n + 10) is a multiple of 6 for all integer values of n.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: n² + 6n + 4n + 24 - (n² + 10n)
    2. M1: 24 after the terms in n cancel
    3. C1: 24 = 6 × 4, which is a multiple of 6
    Answer: 24 = 6 × 4
    Proof with Multiples

  3. Question 3. The table shows the number of pets owned by 20 pupils. Work out the range and the interquartile range.

    [3 marks]
    Number of petsFrequency0417253341
    Show worked answerHide worked answer
    1. M1: lower quartile (5th to 6th value) =1; upper quartile (15th to 16th value) =2
    2. A1: range =4
    3. A1: IQR =1
    Answer: Range 4, interquartile range 1
    Benefits of IQR & Range

  4. Question 4. Triangle XYZ has angle YZX = 72^°, XZ = 8.5 cm and YZ = 15 cm
    Work out its area.
    Give your answer to 1 decimal place.

    [2 marks]
    Show worked answerHide worked answer
    1. M1: 1/2 × 15 × 8.5 × sin 72^°
    2. A1: 60.6
    Answer: 60.6 cm²
    Calculating Area Using ½ab sin C

  5. Question 5. A ball is thrown upwards. Its height, h metres, above the ground after t seconds is given by h = 18t - 6t²
    Work out the greatest height of the ball above the ground.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: the greatest height is at t = 18 / 12 = 1.5, halfway between the times at which h = 0
    2. M1: 18 × 1.5 - 6 × 1.5²
    3. A1: 13.5 metres
    Answer: 13.5
    Turning Points of Quadratics
📅 Free live lesson: Tuesday 17th NovemberSave your free place →

Mixed Topic Worksheet Grades 6/7: Day 014

Grades 6/7Calculator

  1. Question 1. Decrease 650 kg by 12%.

    Show worked answerHide worked answer
    1. M1: 100 - 12 = 88%
    2. M1: 650 × 0.88
    3. A1: 572
    Answer: 572 kg
    Percentage Multipliers
    [3 marks]

  2. Question 2. Prove that (n + 4)(n + 6) - n(n + 10) is a multiple of 6 for all integer values of n.

    Show worked answerHide worked answer
    1. M1: n² + 6n + 4n + 24 - (n² + 10n)
    2. M1: 24 after the terms in n cancel
    3. C1: 24 = 6 × 4, which is a multiple of 6
    Answer: 24 = 6 × 4
    Proof with Multiples
    [3 marks]

  3. Question 3. The table shows the number of pets owned by 20 pupils. Work out the range and the interquartile range.

    Show worked answerHide worked answer
    1. M1: lower quartile (5th to 6th value) =1; upper quartile (15th to 16th value) =2
    2. A1: range =4
    3. A1: IQR =1
    Answer: Range 4, interquartile range 1
    Benefits of IQR & Range
    Number of petsFrequency0417253341
    [3 marks]

  4. Question 4. Triangle XYZ has angle YZX = 72^°, XZ = 8.5 cm and YZ = 15 cm
    Work out its area.
    Give your answer to 1 decimal place.

    Show worked answerHide worked answer
    1. M1: 1/2 × 15 × 8.5 × sin 72^°
    2. A1: 60.6
    Answer: 60.6 cm²
    Calculating Area Using ½ab sin C
    [2 marks]

  5. Question 5. A ball is thrown upwards. Its height, h metres, above the ground after t seconds is given by h = 18t - 6t²
    Work out the greatest height of the ball above the ground.

    Show worked answerHide worked answer
    1. M1: the greatest height is at t = 18 / 12 = 1.5, halfway between the times at which h = 0
    2. M1: 18 × 1.5 - 6 × 1.5²
    3. A1: 13.5 metres
    Answer: 13.5
    Turning Points of Quadratics
    [3 marks]