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

Mixed Topic Worksheet Grades 6/7: Day 052

Grades 6/7Calculator

  1. Question 1. A clock has a minute hand of length 12 cm.
    The minute hand turns for 20 minutes.
    Work out the distance moved by the tip of the minute hand.
    Give your answer to 1 decimal place.

    Show worked answerHide worked answer
    1. M1: 20/60 × 360 = 120
    2. M1: 120/360 × 2 × π × 12
    3. A1: 25.1
    Answer: 25.1
    Length of a Circle Arc
    12 cm
    [3 marks]

  2. Question 2. For a set of data the lowest value is 3, the lower quartile is 12, the median is 15, the upper quartile is 20 and the highest value is 41. Work out the range and the interquartile range.

    Show worked answerHide worked answer
    1. M1: 41-3 or 20-12
    2. A1: range =38 and IQR =8
    Answer: Range 38, interquartile range 8
    Benefits of IQR & Range
    [2 marks]

  3. Question 3. Prove that (n + 9)(n + 8) - (n - 3)(n - 2) is a multiple of 11 for all integer values of n.

    Show worked answerHide worked answer
    1. M1: n² + 17n + 72 and n² - 5n + 6
    2. M1: 22n + 66
    3. C1: 22n + 66 = 22(n + 3), which is 11 × 2(n + 3), a multiple of 11
    Answer: 22(n + 3), which is 11 × 2(n + 3), a multiple of 11
    Proof with Multiples
    [3 marks]

  4. Question 4. Here is triangle PQR.
    Angle QPR = 47°.
    Work out the length of QR.
    Give your answer to 1 decimal place.

    Show worked answerHide worked answer
    1. M1: QR² = 7² + 13² - 2 × 7 × 13 × cos 47^°
    2. M1: QR² = 218 - 124.12ldots = 93.87ldots
    3. A1: QR = 9.7 cm
    Answer: 9.7 cm
    Fundamentals of the Cosine Rule
    13 cm7 cm47°PQRNot drawn accurately
    [3 marks]

  5. Question 5. y is inversely proportional to the square of x.
    y = 2 when x = 6.
    Find the positive value of x when y = 8.

    Show worked answerHide worked answer
    1. M1: 2 = k ÷ 6²
    2. M1: 8 = 72 ÷ x²
    3. A1: 3
    Answer: 3
    Algebraic Inverse Proportion
    [3 marks]
📅 Free lesson: Tue 17th NovSave your place →

Mixed Topic Worksheet Grades 6/7: Day 052

Grades 6/7Calculator

  1. Question 1. A clock has a minute hand of length 12 cm.
    The minute hand turns for 20 minutes.
    Work out the distance moved by the tip of the minute hand.
    Give your answer to 1 decimal place.

    [3 marks]
    12 cm
    Show worked answerHide worked answer
    1. M1: 20/60 × 360 = 120
    2. M1: 120/360 × 2 × π × 12
    3. A1: 25.1
    Answer: 25.1
    Length of a Circle Arc

  2. Question 2. For a set of data the lowest value is 3, the lower quartile is 12, the median is 15, the upper quartile is 20 and the highest value is 41. Work out the range and the interquartile range.

    [2 marks]
    Show worked answerHide worked answer
    1. M1: 41-3 or 20-12
    2. A1: range =38 and IQR =8
    Answer: Range 38, interquartile range 8
    Benefits of IQR & Range

  3. Question 3. Prove that (n + 9)(n + 8) - (n - 3)(n - 2) is a multiple of 11 for all integer values of n.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: n² + 17n + 72 and n² - 5n + 6
    2. M1: 22n + 66
    3. C1: 22n + 66 = 22(n + 3), which is 11 × 2(n + 3), a multiple of 11
    Answer: 22(n + 3), which is 11 × 2(n + 3), a multiple of 11
    Proof with Multiples

  4. Question 4. Here is triangle PQR.
    Angle QPR = 47°.
    Work out the length of QR.
    Give your answer to 1 decimal place.

    [3 marks]
    13 cm7 cm47°PQRNot drawn accurately
    Show worked answerHide worked answer
    1. M1: QR² = 7² + 13² - 2 × 7 × 13 × cos 47^°
    2. M1: QR² = 218 - 124.12ldots = 93.87ldots
    3. A1: QR = 9.7 cm
    Answer: 9.7 cm
    Fundamentals of the Cosine Rule

  5. Question 5. y is inversely proportional to the square of x.
    y = 2 when x = 6.
    Find the positive value of x when y = 8.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: 2 = k ÷ 6²
    2. M1: 8 = 72 ÷ x²
    3. A1: 3
    Answer: 3
    Algebraic Inverse Proportion
📅 Free live lesson: Tuesday 17th NovemberSave your free place →

Mixed Topic Worksheet Grades 6/7: Day 052

Grades 6/7Calculator

  1. Question 1. A clock has a minute hand of length 12 cm.
    The minute hand turns for 20 minutes.
    Work out the distance moved by the tip of the minute hand.
    Give your answer to 1 decimal place.

    Show worked answerHide worked answer
    1. M1: 20/60 × 360 = 120
    2. M1: 120/360 × 2 × π × 12
    3. A1: 25.1
    Answer: 25.1
    Length of a Circle Arc
    12 cm
    [3 marks]

  2. Question 2. For a set of data the lowest value is 3, the lower quartile is 12, the median is 15, the upper quartile is 20 and the highest value is 41. Work out the range and the interquartile range.

    Show worked answerHide worked answer
    1. M1: 41-3 or 20-12
    2. A1: range =38 and IQR =8
    Answer: Range 38, interquartile range 8
    Benefits of IQR & Range
    [2 marks]

  3. Question 3. Prove that (n + 9)(n + 8) - (n - 3)(n - 2) is a multiple of 11 for all integer values of n.

    Show worked answerHide worked answer
    1. M1: n² + 17n + 72 and n² - 5n + 6
    2. M1: 22n + 66
    3. C1: 22n + 66 = 22(n + 3), which is 11 × 2(n + 3), a multiple of 11
    Answer: 22(n + 3), which is 11 × 2(n + 3), a multiple of 11
    Proof with Multiples
    [3 marks]

  4. Question 4. Here is triangle PQR.
    Angle QPR = 47°.
    Work out the length of QR.
    Give your answer to 1 decimal place.

    Show worked answerHide worked answer
    1. M1: QR² = 7² + 13² - 2 × 7 × 13 × cos 47^°
    2. M1: QR² = 218 - 124.12ldots = 93.87ldots
    3. A1: QR = 9.7 cm
    Answer: 9.7 cm
    Fundamentals of the Cosine Rule
    13 cm7 cm47°PQRNot drawn accurately
    [3 marks]

  5. Question 5. y is inversely proportional to the square of x.
    y = 2 when x = 6.
    Find the positive value of x when y = 8.

    Show worked answerHide worked answer
    1. M1: 2 = k ÷ 6²
    2. M1: 8 = 72 ÷ x²
    3. A1: 3
    Answer: 3
    Algebraic Inverse Proportion
    [3 marks]