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

Mixed Topic Worksheet Grades 6/7: Day 013

Grades 6/7Non-calculator

  1. Question 1. The table shows the masses of 30 bags of potatoes. Work out the greatest possible range of the masses. Use the lower limit of the first class and the upper limit of the last class.

    Show worked answerHide worked answer
    1. M1: 60 - 10
    2. A1: 50 kg
    Answer: 50 kg
    Interpreting Grouped Frequency Tables
    Mass, m (kg)Frequency10 < m ≤ 20320 < m ≤ 30730 < m ≤ 401240 < m ≤ 50650 < m ≤ 602
    [2 marks]

  2. Question 2. An enlargement has centre (-2, 5) and scale factor 3
    Write down the invariant point and work out the image of the point (0, 6)

    Show worked answerHide worked answer
    1. B1: invariant point (-2, 5), the centre
    2. M1: from the centre to (0, 6) is 2 right and 1 up, so 6 right and 3 up after the enlargement
    3. A1: image (4, 8)
    Answer: invariant point (-2, 5); image (4, 8)
    Invariant Points
    [3 marks]

  3. Question 3. Work out an estimate for dfrac√4024.1
    Use a square number for the root and round 4.1 to 1 significant figure.
    Give your answer as an integer.

    Show worked answerHide worked answer
    1. M1: √400 = 20 and 4.1 to 4
    2. M1: 20 ÷ 4
    3. A1: 5
    Answer: 5
    Estimating Roots
    [3 marks]

  4. Question 4. f(x) = 5x - 1
    Jo's working for f⁻¹(5): f(5) = 5 × 5 - 1 = 24, so f⁻¹(5) = dfrac124
    Is Jo correct? You must show your working.

    Show worked answerHide worked answer
    1. M1: y = 5x - 1, so x = dfracy + 15
    2. A1: f⁻¹(5) = dfrac5 + 15 = dfrac65, so Jo is not correct
    Answer: No, f⁻¹(5) = dfrac65
    Inverse Functions
    [2 marks]

  5. Question 5. Here is triangle ABC.
    Work out the value of cos BAC.
    Give your answer as a fraction in its simplest form.

    Show worked answerHide worked answer
    1. M1: 7² = 5² + 6² - 2 × 5 × 6 × cos BAC
    2. M1: cos BAC = dfrac5² + 6² - 7²2 × 5 × 6 = dfrac1260
    3. A1: cos BAC = dfrac15
    Answer: dfrac15
    Fundamentals of the Cosine Rule
    5 cm7 cm6 cmABC
    [3 marks]
📅 Free lesson: Tue 17th NovSave your place →

Mixed Topic Worksheet Grades 6/7: Day 013

Grades 6/7Non-calculator

  1. Question 1. The table shows the masses of 30 bags of potatoes. Work out the greatest possible range of the masses. Use the lower limit of the first class and the upper limit of the last class.

    [2 marks]
    Mass, m (kg)Frequency10 < m ≤ 20320 < m ≤ 30730 < m ≤ 401240 < m ≤ 50650 < m ≤ 602
    Show worked answerHide worked answer
    1. M1: 60 - 10
    2. A1: 50 kg
    Answer: 50 kg
    Interpreting Grouped Frequency Tables

  2. Question 2. An enlargement has centre (-2, 5) and scale factor 3
    Write down the invariant point and work out the image of the point (0, 6)

    [3 marks]
    Show worked answerHide worked answer
    1. B1: invariant point (-2, 5), the centre
    2. M1: from the centre to (0, 6) is 2 right and 1 up, so 6 right and 3 up after the enlargement
    3. A1: image (4, 8)
    Answer: invariant point (-2, 5); image (4, 8)
    Invariant Points

  3. Question 3. Work out an estimate for dfrac√4024.1
    Use a square number for the root and round 4.1 to 1 significant figure.
    Give your answer as an integer.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: √400 = 20 and 4.1 to 4
    2. M1: 20 ÷ 4
    3. A1: 5
    Answer: 5
    Estimating Roots

  4. Question 4. f(x) = 5x - 1
    Jo's working for f⁻¹(5): f(5) = 5 × 5 - 1 = 24, so f⁻¹(5) = dfrac124
    Is Jo correct? You must show your working.

    [2 marks]
    Show worked answerHide worked answer
    1. M1: y = 5x - 1, so x = dfracy + 15
    2. A1: f⁻¹(5) = dfrac5 + 15 = dfrac65, so Jo is not correct
    Answer: No, f⁻¹(5) = dfrac65
    Inverse Functions

  5. Question 5. Here is triangle ABC.
    Work out the value of cos BAC.
    Give your answer as a fraction in its simplest form.

    [3 marks]
    5 cm7 cm6 cmABC
    Show worked answerHide worked answer
    1. M1: 7² = 5² + 6² - 2 × 5 × 6 × cos BAC
    2. M1: cos BAC = dfrac5² + 6² - 7²2 × 5 × 6 = dfrac1260
    3. A1: cos BAC = dfrac15
    Answer: dfrac15
    Fundamentals of the Cosine Rule
📅 Free live lesson: Tuesday 17th NovemberSave your free place →

Mixed Topic Worksheet Grades 6/7: Day 013

Grades 6/7Non-calculator

  1. Question 1. The table shows the masses of 30 bags of potatoes. Work out the greatest possible range of the masses. Use the lower limit of the first class and the upper limit of the last class.

    Show worked answerHide worked answer
    1. M1: 60 - 10
    2. A1: 50 kg
    Answer: 50 kg
    Interpreting Grouped Frequency Tables
    Mass, m (kg)Frequency10 < m ≤ 20320 < m ≤ 30730 < m ≤ 401240 < m ≤ 50650 < m ≤ 602
    [2 marks]

  2. Question 2. An enlargement has centre (-2, 5) and scale factor 3
    Write down the invariant point and work out the image of the point (0, 6)

    Show worked answerHide worked answer
    1. B1: invariant point (-2, 5), the centre
    2. M1: from the centre to (0, 6) is 2 right and 1 up, so 6 right and 3 up after the enlargement
    3. A1: image (4, 8)
    Answer: invariant point (-2, 5); image (4, 8)
    Invariant Points
    [3 marks]

  3. Question 3. Work out an estimate for dfrac√4024.1
    Use a square number for the root and round 4.1 to 1 significant figure.
    Give your answer as an integer.

    Show worked answerHide worked answer
    1. M1: √400 = 20 and 4.1 to 4
    2. M1: 20 ÷ 4
    3. A1: 5
    Answer: 5
    Estimating Roots
    [3 marks]

  4. Question 4. f(x) = 5x - 1
    Jo's working for f⁻¹(5): f(5) = 5 × 5 - 1 = 24, so f⁻¹(5) = dfrac124
    Is Jo correct? You must show your working.

    Show worked answerHide worked answer
    1. M1: y = 5x - 1, so x = dfracy + 15
    2. A1: f⁻¹(5) = dfrac5 + 15 = dfrac65, so Jo is not correct
    Answer: No, f⁻¹(5) = dfrac65
    Inverse Functions
    [2 marks]

  5. Question 5. Here is triangle ABC.
    Work out the value of cos BAC.
    Give your answer as a fraction in its simplest form.

    Show worked answerHide worked answer
    1. M1: 7² = 5² + 6² - 2 × 5 × 6 × cos BAC
    2. M1: cos BAC = dfrac5² + 6² - 7²2 × 5 × 6 = dfrac1260
    3. A1: cos BAC = dfrac15
    Answer: dfrac15
    Fundamentals of the Cosine Rule
    5 cm7 cm6 cmABC
    [3 marks]