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

Mixed Topic Worksheet Grades 6/7: Day 086

Grades 6/7Calculator

  1. Question 1. After a 15% increase, a salary is £34 500.
    Work out the salary before the increase.

    Show worked answerHide worked answer
    1. M1: 100 + 15 = 115%
    2. M1: 34500 ÷ 1.15
    3. A1: 30000
    Answer: £30 000
    Percentage Multipliers
    [3 marks]

  2. Question 2. Snails in a garden are marked with a dot of paint and returned to the garden.
    25 snails are marked.
    The next day, a sample of snails is caught from the same garden.
    The table shows the results.

    Show worked answerHide worked answer
    1. M1: total caught = 5 + 35 = 40
    2. M1: 25 × 40 ÷ 5
    3. A1: 200
    Answer: 200
    Capture-Recapture
    MarkedNot markedNumber of snails535
    [3 marks]

  3. Question 3. The daily sales, in pounds, of a stall are 40, 45, 48, 52, 55, 58, 61, 190. Work out the interquartile range and explain why it is better than the range here.

    Show worked answerHide worked answer
    1. M1: lower quartile is the mean of 45 and 48, upper quartile the mean of 58 and 61
    2. A1: IQR =13
    3. B1: range =150 is distorted by the extreme value 190
    Answer: IQR =13; the range (150) is distorted by the extreme value 190
    Benefits of IQR & Range
    [3 marks]

  4. Question 4. Here is an identity
    a(x + b) - 6 equiv 6x + 18
    Work out the values of a and b.

    Show worked answerHide worked answer
    1. M1: ab - 6 = 18 (constants compared), so 6b = 24
    2. A1: a = 6, b = 4
    Answer: a = 6, b = 4
    Equating Coefficients
    [2 marks]

  5. Question 5. Here is triangle KLM.
    Work out the size of angle LMK.
    Give your answer to 1 decimal place.

    Show worked answerHide worked answer
    1. M1: dfracsin LMK11.2 = dfracsin 75^°14.8
    2. M1: sin LMK = dfrac11.2 × sin 75^°14.8
    3. A1: 47.0
    Answer: 47.0
    Finding Angles Using the Sine Rule
    11.2 cm14.8 cm75°KLMNot drawn accurately
    [3 marks]
📅 Free lesson: Tue 17th NovSave your place →

Mixed Topic Worksheet Grades 6/7: Day 086

Grades 6/7Calculator

  1. Question 1. After a 15% increase, a salary is £34 500.
    Work out the salary before the increase.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: 100 + 15 = 115%
    2. M1: 34500 ÷ 1.15
    3. A1: 30000
    Answer: £30 000
    Percentage Multipliers

  2. Question 2. Snails in a garden are marked with a dot of paint and returned to the garden.
    25 snails are marked.
    The next day, a sample of snails is caught from the same garden.
    The table shows the results.

    [3 marks]
    MarkedNot markedNumber of snails535
    Show worked answerHide worked answer
    1. M1: total caught = 5 + 35 = 40
    2. M1: 25 × 40 ÷ 5
    3. A1: 200
    Answer: 200
    Capture-Recapture

  3. Question 3. The daily sales, in pounds, of a stall are 40, 45, 48, 52, 55, 58, 61, 190. Work out the interquartile range and explain why it is better than the range here.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: lower quartile is the mean of 45 and 48, upper quartile the mean of 58 and 61
    2. A1: IQR =13
    3. B1: range =150 is distorted by the extreme value 190
    Answer: IQR =13; the range (150) is distorted by the extreme value 190
    Benefits of IQR & Range

  4. Question 4. Here is an identity
    a(x + b) - 6 equiv 6x + 18
    Work out the values of a and b.

    [2 marks]
    Show worked answerHide worked answer
    1. M1: ab - 6 = 18 (constants compared), so 6b = 24
    2. A1: a = 6, b = 4
    Answer: a = 6, b = 4
    Equating Coefficients

  5. Question 5. Here is triangle KLM.
    Work out the size of angle LMK.
    Give your answer to 1 decimal place.

    [3 marks]
    11.2 cm14.8 cm75°KLMNot drawn accurately
    Show worked answerHide worked answer
    1. M1: dfracsin LMK11.2 = dfracsin 75^°14.8
    2. M1: sin LMK = dfrac11.2 × sin 75^°14.8
    3. A1: 47.0
    Answer: 47.0
    Finding Angles Using the Sine Rule
📅 Free live lesson: Tuesday 17th NovemberSave your free place →

Mixed Topic Worksheet Grades 6/7: Day 086

Grades 6/7Calculator

  1. Question 1. After a 15% increase, a salary is £34 500.
    Work out the salary before the increase.

    Show worked answerHide worked answer
    1. M1: 100 + 15 = 115%
    2. M1: 34500 ÷ 1.15
    3. A1: 30000
    Answer: £30 000
    Percentage Multipliers
    [3 marks]

  2. Question 2. Snails in a garden are marked with a dot of paint and returned to the garden.
    25 snails are marked.
    The next day, a sample of snails is caught from the same garden.
    The table shows the results.

    Show worked answerHide worked answer
    1. M1: total caught = 5 + 35 = 40
    2. M1: 25 × 40 ÷ 5
    3. A1: 200
    Answer: 200
    Capture-Recapture
    MarkedNot markedNumber of snails535
    [3 marks]

  3. Question 3. The daily sales, in pounds, of a stall are 40, 45, 48, 52, 55, 58, 61, 190. Work out the interquartile range and explain why it is better than the range here.

    Show worked answerHide worked answer
    1. M1: lower quartile is the mean of 45 and 48, upper quartile the mean of 58 and 61
    2. A1: IQR =13
    3. B1: range =150 is distorted by the extreme value 190
    Answer: IQR =13; the range (150) is distorted by the extreme value 190
    Benefits of IQR & Range
    [3 marks]

  4. Question 4. Here is an identity
    a(x + b) - 6 equiv 6x + 18
    Work out the values of a and b.

    Show worked answerHide worked answer
    1. M1: ab - 6 = 18 (constants compared), so 6b = 24
    2. A1: a = 6, b = 4
    Answer: a = 6, b = 4
    Equating Coefficients
    [2 marks]

  5. Question 5. Here is triangle KLM.
    Work out the size of angle LMK.
    Give your answer to 1 decimal place.

    Show worked answerHide worked answer
    1. M1: dfracsin LMK11.2 = dfracsin 75^°14.8
    2. M1: sin LMK = dfrac11.2 × sin 75^°14.8
    3. A1: 47.0
    Answer: 47.0
    Finding Angles Using the Sine Rule
    11.2 cm14.8 cm75°KLMNot drawn accurately
    [3 marks]