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

Mixed Topic Worksheet Grades 6/7: Day 067

Grades 6/7Non-calculator

  1. Question 1. The diagram shows a shape. All the angles are right angles.
    The perimeter of the shape is 74 cm.
    Work out the length of the side marked x.

    Show worked answerHide worked answer
    1. M1: the right-hand side is x - 6
    2. M1: 20 + 12 + 8 + 6 + x + (x - 6) = 74
    3. A1: 17
    Answer: 17 cm
    Finding Side Lengths of Compound Shapes
    12 cm6 cm8 cm20 cmxNot drawn accurately
    [3 marks]

  2. Question 2. Prove that (2n + 7)² - (2n + 1)² is a multiple of 24 for all integer values of n.

    Show worked answerHide worked answer
    1. M1: 4n² + 28n + 49 - (4n² + 4n + 1)
    2. M1: 24n + 48
    3. C1: 24(n + 2), which is a multiple of 24
    Answer: 24(n + 2)
    Proof with Multiples
    [3 marks]

  3. Question 3. The temperatures, in °C, at midday on 9 days are -3, 2, 4, 5, 5, 6, 8, 9, 12. Work out the range and the interquartile range.

    Show worked answerHide worked answer
    1. M1: lower quartile dfrac2+42, upper quartile dfrac8+92
    2. A1: range =15
    3. A1: IQR =5.5
    Answer: Range 15 °C, interquartile range 5.5 °C
    Benefits of IQR & Range
    [3 marks]

  4. Question 4. Simplify (3√2)³
    Give your answer in the form a√2, where a is an integer.

    Show worked answerHide worked answer
    1. M1: 3³ = 27
    2. M1: (√2)³ = 2√2
    3. A1: 54√2
    Answer: 54√2
    Six Laws of Surds
    [3 marks]

  5. Question 5. The curve y = 16 - dfracx²4 is a model of an arch of a bridge.
    x and y are in metres and the river is along the line y = 0
    Work out the width of the arch at a height of 7 m above the river.

    Show worked answerHide worked answer
    1. M1: 16 - dfracx²4 = 7
    2. M1: x² = 36, so x = 6 and x = -6
    3. A1: 12 metres
    Answer: 12
    Full Process for Sketching Quadratics
    [3 marks]
📅 Free lesson: Tue 17th NovSave your place →

Mixed Topic Worksheet Grades 6/7: Day 067

Grades 6/7Non-calculator

  1. Question 1. The diagram shows a shape. All the angles are right angles.
    The perimeter of the shape is 74 cm.
    Work out the length of the side marked x.

    [3 marks]
    12 cm6 cm8 cm20 cmxNot drawn accurately
    Show worked answerHide worked answer
    1. M1: the right-hand side is x - 6
    2. M1: 20 + 12 + 8 + 6 + x + (x - 6) = 74
    3. A1: 17
    Answer: 17 cm
    Finding Side Lengths of Compound Shapes

  2. Question 2. Prove that (2n + 7)² - (2n + 1)² is a multiple of 24 for all integer values of n.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: 4n² + 28n + 49 - (4n² + 4n + 1)
    2. M1: 24n + 48
    3. C1: 24(n + 2), which is a multiple of 24
    Answer: 24(n + 2)
    Proof with Multiples

  3. Question 3. The temperatures, in °C, at midday on 9 days are -3, 2, 4, 5, 5, 6, 8, 9, 12. Work out the range and the interquartile range.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: lower quartile dfrac2+42, upper quartile dfrac8+92
    2. A1: range =15
    3. A1: IQR =5.5
    Answer: Range 15 °C, interquartile range 5.5 °C
    Benefits of IQR & Range

  4. Question 4. Simplify (3√2)³
    Give your answer in the form a√2, where a is an integer.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: 3³ = 27
    2. M1: (√2)³ = 2√2
    3. A1: 54√2
    Answer: 54√2
    Six Laws of Surds

  5. Question 5. The curve y = 16 - dfracx²4 is a model of an arch of a bridge.
    x and y are in metres and the river is along the line y = 0
    Work out the width of the arch at a height of 7 m above the river.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: 16 - dfracx²4 = 7
    2. M1: x² = 36, so x = 6 and x = -6
    3. A1: 12 metres
    Answer: 12
    Full Process for Sketching Quadratics
📅 Free live lesson: Tuesday 17th NovemberSave your free place →

Mixed Topic Worksheet Grades 6/7: Day 067

Grades 6/7Non-calculator

  1. Question 1. The diagram shows a shape. All the angles are right angles.
    The perimeter of the shape is 74 cm.
    Work out the length of the side marked x.

    Show worked answerHide worked answer
    1. M1: the right-hand side is x - 6
    2. M1: 20 + 12 + 8 + 6 + x + (x - 6) = 74
    3. A1: 17
    Answer: 17 cm
    Finding Side Lengths of Compound Shapes
    12 cm6 cm8 cm20 cmxNot drawn accurately
    [3 marks]

  2. Question 2. Prove that (2n + 7)² - (2n + 1)² is a multiple of 24 for all integer values of n.

    Show worked answerHide worked answer
    1. M1: 4n² + 28n + 49 - (4n² + 4n + 1)
    2. M1: 24n + 48
    3. C1: 24(n + 2), which is a multiple of 24
    Answer: 24(n + 2)
    Proof with Multiples
    [3 marks]

  3. Question 3. The temperatures, in °C, at midday on 9 days are -3, 2, 4, 5, 5, 6, 8, 9, 12. Work out the range and the interquartile range.

    Show worked answerHide worked answer
    1. M1: lower quartile dfrac2+42, upper quartile dfrac8+92
    2. A1: range =15
    3. A1: IQR =5.5
    Answer: Range 15 °C, interquartile range 5.5 °C
    Benefits of IQR & Range
    [3 marks]

  4. Question 4. Simplify (3√2)³
    Give your answer in the form a√2, where a is an integer.

    Show worked answerHide worked answer
    1. M1: 3³ = 27
    2. M1: (√2)³ = 2√2
    3. A1: 54√2
    Answer: 54√2
    Six Laws of Surds
    [3 marks]

  5. Question 5. The curve y = 16 - dfracx²4 is a model of an arch of a bridge.
    x and y are in metres and the river is along the line y = 0
    Work out the width of the arch at a height of 7 m above the river.

    Show worked answerHide worked answer
    1. M1: 16 - dfracx²4 = 7
    2. M1: x² = 36, so x = 6 and x = -6
    3. A1: 12 metres
    Answer: 12
    Full Process for Sketching Quadratics
    [3 marks]