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

Mixed Topic Worksheet Grades 6/7: Day 070

Grades 6/7Calculator

  1. Question 1. Two sails are similar right-angled triangles.
    The small sail has a base of 2.4 m and a height of 3.6 m.
    The large sail has a base of 5.4 m.
    Work out the height of the large sail.

    Show worked answerHide worked answer
    1. M1: 5.4 ÷ 2.4 = 2.25
    2. M1: 2.25 × 3.6
    3. A1: 8.1
    Answer: 8.1 m
    Similar Side Lengths
    2.4 m3.6 m5.4 mhABCDEFNot drawn accurately
    [3 marks]

  2. Question 2. Boys: median 54 kg, interquartile range 8 kg. Girls: median 49 kg, interquartile range 12 kg. Make two comparisons.

    Show worked answerHide worked answer
    1. B1: boys heavier on average (median 54 > 49)
    2. B1: boys' masses more consistent (IQR 8 < 12)
    Answer: Boys are heavier on average (54 > 49) and more consistent (8 < 12)
    Comparing Data Using Box Plots
    [2 marks]

  3. Question 3. A square patio has side (5n + 2) metres, where n is a positive integer.
    A square pond with side (2n - 1) metres is built on the patio.
    Prove that the area of the patio not covered by the pond is a multiple of 3 square metres.

    Show worked answerHide worked answer
    1. M1: (5n + 2)² = 25n² + 20n + 4
    2. M1: (2n - 1)² = 4n² - 4n + 1
    3. A1: 25n² + 20n + 4 - (4n² - 4n + 1) = 21n² + 24n + 3
    4. C1: 3(7n² + 8n + 1), which is a multiple of 3
    Answer: 3(7n² + 8n + 1)
    Proof with Multiples
    [4 marks]

  4. Question 4. Here is triangle XYZ.
    Work out the length of YZ.
    Give your answer to 1 decimal place.

    Show worked answerHide worked answer
    1. M1: dfracYZsin 41^° = dfrac11.5sin 63^°
    2. M1: YZ = dfrac11.5 × sin 41^°sin 63^°
    3. A1: 8.5
    Answer: 8.5
    Finding Side Lengths Using the Sine Rule
    11.5 cm41°63°XYZNot drawn accurately
    [3 marks]

  5. Question 5. x_n+1 = dfrac5x_n + 2
    x_0 = 1
    Work out x_1, x_2 and x_3
    Give your answers correct to 3 decimal places

    Show worked answerHide worked answer
    1. M1: x_1 = dfrac51 + 2
    2. M1: x_1 = 1.667 and x_2 = dfrac51.6667 + 2
    3. A1: x_2 = 1.364 and x_3 = 1.486
    Answer: x_1 = 1.667, x_2 = 1.364, x_3 = 1.486
    Iteration Equations
    [3 marks]
📅 Free lesson: Tue 17th NovSave your place →

Mixed Topic Worksheet Grades 6/7: Day 070

Grades 6/7Calculator

  1. Question 1. Two sails are similar right-angled triangles.
    The small sail has a base of 2.4 m and a height of 3.6 m.
    The large sail has a base of 5.4 m.
    Work out the height of the large sail.

    [3 marks]
    2.4 m3.6 m5.4 mhABCDEFNot drawn accurately
    Show worked answerHide worked answer
    1. M1: 5.4 ÷ 2.4 = 2.25
    2. M1: 2.25 × 3.6
    3. A1: 8.1
    Answer: 8.1 m
    Similar Side Lengths

  2. Question 2. Boys: median 54 kg, interquartile range 8 kg. Girls: median 49 kg, interquartile range 12 kg. Make two comparisons.

    [2 marks]
    Show worked answerHide worked answer
    1. B1: boys heavier on average (median 54 > 49)
    2. B1: boys' masses more consistent (IQR 8 < 12)
    Answer: Boys are heavier on average (54 > 49) and more consistent (8 < 12)
    Comparing Data Using Box Plots

  3. Question 3. A square patio has side (5n + 2) metres, where n is a positive integer.
    A square pond with side (2n - 1) metres is built on the patio.
    Prove that the area of the patio not covered by the pond is a multiple of 3 square metres.

    [4 marks]
    Show worked answerHide worked answer
    1. M1: (5n + 2)² = 25n² + 20n + 4
    2. M1: (2n - 1)² = 4n² - 4n + 1
    3. A1: 25n² + 20n + 4 - (4n² - 4n + 1) = 21n² + 24n + 3
    4. C1: 3(7n² + 8n + 1), which is a multiple of 3
    Answer: 3(7n² + 8n + 1)
    Proof with Multiples

  4. Question 4. Here is triangle XYZ.
    Work out the length of YZ.
    Give your answer to 1 decimal place.

    [3 marks]
    11.5 cm41°63°XYZNot drawn accurately
    Show worked answerHide worked answer
    1. M1: dfracYZsin 41^° = dfrac11.5sin 63^°
    2. M1: YZ = dfrac11.5 × sin 41^°sin 63^°
    3. A1: 8.5
    Answer: 8.5
    Finding Side Lengths Using the Sine Rule

  5. Question 5. x_n+1 = dfrac5x_n + 2
    x_0 = 1
    Work out x_1, x_2 and x_3
    Give your answers correct to 3 decimal places

    [3 marks]
    Show worked answerHide worked answer
    1. M1: x_1 = dfrac51 + 2
    2. M1: x_1 = 1.667 and x_2 = dfrac51.6667 + 2
    3. A1: x_2 = 1.364 and x_3 = 1.486
    Answer: x_1 = 1.667, x_2 = 1.364, x_3 = 1.486
    Iteration Equations
📅 Free live lesson: Tuesday 17th NovemberSave your free place →

Mixed Topic Worksheet Grades 6/7: Day 070

Grades 6/7Calculator

  1. Question 1. Two sails are similar right-angled triangles.
    The small sail has a base of 2.4 m and a height of 3.6 m.
    The large sail has a base of 5.4 m.
    Work out the height of the large sail.

    Show worked answerHide worked answer
    1. M1: 5.4 ÷ 2.4 = 2.25
    2. M1: 2.25 × 3.6
    3. A1: 8.1
    Answer: 8.1 m
    Similar Side Lengths
    2.4 m3.6 m5.4 mhABCDEFNot drawn accurately
    [3 marks]

  2. Question 2. Boys: median 54 kg, interquartile range 8 kg. Girls: median 49 kg, interquartile range 12 kg. Make two comparisons.

    Show worked answerHide worked answer
    1. B1: boys heavier on average (median 54 > 49)
    2. B1: boys' masses more consistent (IQR 8 < 12)
    Answer: Boys are heavier on average (54 > 49) and more consistent (8 < 12)
    Comparing Data Using Box Plots
    [2 marks]

  3. Question 3. A square patio has side (5n + 2) metres, where n is a positive integer.
    A square pond with side (2n - 1) metres is built on the patio.
    Prove that the area of the patio not covered by the pond is a multiple of 3 square metres.

    Show worked answerHide worked answer
    1. M1: (5n + 2)² = 25n² + 20n + 4
    2. M1: (2n - 1)² = 4n² - 4n + 1
    3. A1: 25n² + 20n + 4 - (4n² - 4n + 1) = 21n² + 24n + 3
    4. C1: 3(7n² + 8n + 1), which is a multiple of 3
    Answer: 3(7n² + 8n + 1)
    Proof with Multiples
    [4 marks]

  4. Question 4. Here is triangle XYZ.
    Work out the length of YZ.
    Give your answer to 1 decimal place.

    Show worked answerHide worked answer
    1. M1: dfracYZsin 41^° = dfrac11.5sin 63^°
    2. M1: YZ = dfrac11.5 × sin 41^°sin 63^°
    3. A1: 8.5
    Answer: 8.5
    Finding Side Lengths Using the Sine Rule
    11.5 cm41°63°XYZNot drawn accurately
    [3 marks]

  5. Question 5. x_n+1 = dfrac5x_n + 2
    x_0 = 1
    Work out x_1, x_2 and x_3
    Give your answers correct to 3 decimal places

    Show worked answerHide worked answer
    1. M1: x_1 = dfrac51 + 2
    2. M1: x_1 = 1.667 and x_2 = dfrac51.6667 + 2
    3. A1: x_2 = 1.364 and x_3 = 1.486
    Answer: x_1 = 1.667, x_2 = 1.364, x_3 = 1.486
    Iteration Equations
    [3 marks]