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

Mixed Topic Worksheet Grades 6/7: Day 043

Grades 6/7Non-calculator

  1. Question 1. Here is triangle ABC.
    Work out the length of BC.

    Show worked answerHide worked answer
    1. M1: BC = 9 × tan 45^°
    2. A1: 9
    Answer: 9
    SOH, CAH, TOA with Exact Trig Values
    9 cm45°ABC
    [2 marks]

  2. Question 2. Prove that (n + 6)² - (n + 2)² is a multiple of 8 for all integer values of n.

    Show worked answerHide worked answer
    1. M1: n² + 12n + 36 - (n² + 4n + 4)
    2. M1: 8n + 32
    3. C1: 8(n + 4), which is a multiple of 8
    Answer: 8(n + 4)
    Proof with Multiples
    [3 marks]

  3. Question 3. An enlargement has scale factor 3 and centre (-2, 5).
    Write down the coordinates of the invariant point of this enlargement.

    Show worked answerHide worked answer
    1. B1: (-2, 5), the centre of enlargement
    Answer: (-2, 5)
    Invariant Points
    [1 mark]

  4. Question 4. A rope is 5.6 m long, correct to 1 decimal place.
    A piece of length 1.9 m, correct to 1 decimal place, is cut from the rope.
    Work out the upper bound of the length of rope that is left.

    Show worked answerHide worked answer
    1. M1: 5.6 + 0.05 and 1.9 - 0.05
    2. M1: 5.65 - 1.85
    3. A1: 3.8
    Answer: 3.8 m
    Bounds & Error Intervals Involving Calculations
    [3 marks]

  5. Question 5. A solid cone has radius 12 cm and height 18 cm.
    A cone of height 6 cm is cut from the top, leaving a frustum.
    Work out the volume of the frustum in terms of π
    (Volume of a cone = dfrac13π r²h)

    Show worked answerHide worked answer
    1. M1: small cone radius = 12 × dfrac618 = 4
    2. M1: 1/3 × π × 12² × 18 = 864π and 1/3 × π × 4² × 6 = 32π
    3. M1: 864π - 32π
    4. A1: 832π
    Answer: 832π cm³
    Volume of Frustums
    [4 marks]
📅 Free lesson: Tue 17th NovSave your place →

Mixed Topic Worksheet Grades 6/7: Day 043

Grades 6/7Non-calculator

  1. Question 1. Here is triangle ABC.
    Work out the length of BC.

    [2 marks]
    9 cm45°ABC
    Show worked answerHide worked answer
    1. M1: BC = 9 × tan 45^°
    2. A1: 9
    Answer: 9
    SOH, CAH, TOA with Exact Trig Values

  2. Question 2. Prove that (n + 6)² - (n + 2)² is a multiple of 8 for all integer values of n.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: n² + 12n + 36 - (n² + 4n + 4)
    2. M1: 8n + 32
    3. C1: 8(n + 4), which is a multiple of 8
    Answer: 8(n + 4)
    Proof with Multiples

  3. Question 3. An enlargement has scale factor 3 and centre (-2, 5).
    Write down the coordinates of the invariant point of this enlargement.

    [1 mark]
    Show worked answerHide worked answer
    1. B1: (-2, 5), the centre of enlargement
    Answer: (-2, 5)
    Invariant Points

  4. Question 4. A rope is 5.6 m long, correct to 1 decimal place.
    A piece of length 1.9 m, correct to 1 decimal place, is cut from the rope.
    Work out the upper bound of the length of rope that is left.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: 5.6 + 0.05 and 1.9 - 0.05
    2. M1: 5.65 - 1.85
    3. A1: 3.8
    Answer: 3.8 m
    Bounds & Error Intervals Involving Calculations

  5. Question 5. A solid cone has radius 12 cm and height 18 cm.
    A cone of height 6 cm is cut from the top, leaving a frustum.
    Work out the volume of the frustum in terms of π
    (Volume of a cone = dfrac13π r²h)

    [4 marks]
    Show worked answerHide worked answer
    1. M1: small cone radius = 12 × dfrac618 = 4
    2. M1: 1/3 × π × 12² × 18 = 864π and 1/3 × π × 4² × 6 = 32π
    3. M1: 864π - 32π
    4. A1: 832π
    Answer: 832π cm³
    Volume of Frustums
📅 Free live lesson: Tuesday 17th NovemberSave your free place →

Mixed Topic Worksheet Grades 6/7: Day 043

Grades 6/7Non-calculator

  1. Question 1. Here is triangle ABC.
    Work out the length of BC.

    Show worked answerHide worked answer
    1. M1: BC = 9 × tan 45^°
    2. A1: 9
    Answer: 9
    SOH, CAH, TOA with Exact Trig Values
    9 cm45°ABC
    [2 marks]

  2. Question 2. Prove that (n + 6)² - (n + 2)² is a multiple of 8 for all integer values of n.

    Show worked answerHide worked answer
    1. M1: n² + 12n + 36 - (n² + 4n + 4)
    2. M1: 8n + 32
    3. C1: 8(n + 4), which is a multiple of 8
    Answer: 8(n + 4)
    Proof with Multiples
    [3 marks]

  3. Question 3. An enlargement has scale factor 3 and centre (-2, 5).
    Write down the coordinates of the invariant point of this enlargement.

    Show worked answerHide worked answer
    1. B1: (-2, 5), the centre of enlargement
    Answer: (-2, 5)
    Invariant Points
    [1 mark]

  4. Question 4. A rope is 5.6 m long, correct to 1 decimal place.
    A piece of length 1.9 m, correct to 1 decimal place, is cut from the rope.
    Work out the upper bound of the length of rope that is left.

    Show worked answerHide worked answer
    1. M1: 5.6 + 0.05 and 1.9 - 0.05
    2. M1: 5.65 - 1.85
    3. A1: 3.8
    Answer: 3.8 m
    Bounds & Error Intervals Involving Calculations
    [3 marks]

  5. Question 5. A solid cone has radius 12 cm and height 18 cm.
    A cone of height 6 cm is cut from the top, leaving a frustum.
    Work out the volume of the frustum in terms of π
    (Volume of a cone = dfrac13π r²h)

    Show worked answerHide worked answer
    1. M1: small cone radius = 12 × dfrac618 = 4
    2. M1: 1/3 × π × 12² × 18 = 864π and 1/3 × π × 4² × 6 = 32π
    3. M1: 864π - 32π
    4. A1: 832π
    Answer: 832π cm³
    Volume of Frustums
    [4 marks]