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

Mixed Topic Worksheet Grades 6/7: Day 062

Grades 6/7Calculator

  1. Question 1. The diagram shows a circular pizza with a diameter of 34 cm.
    The pizza is cut into 8 equal slices.
    Work out the area of one slice.
    Give your answer to 1 decimal place.

    Show worked answerHide worked answer
    1. M1: π × 17²
    2. M1: 907.9... ÷ 8
    3. A1: 113.5
    Answer: 113.5
    Area of a Circle Sector
    34 cm
    [3 marks]

  2. Question 2. n is an integer. Prove that 8(n + 3) - 3(n - 2) is a multiple of 5.

    Show worked answerHide worked answer
    1. M1: 8n + 24 - 3n + 6
    2. C1: 5n + 30 = 5(n + 6), which is a multiple of 5 for every integer n
    Answer: 5(n + 6), a multiple of 5
    Proof with Multiples
    [2 marks]

  3. Question 3. Here are the times, in minutes, taken by 9 students to complete a puzzle, in order.
    30 32 34 35 36 37 38 40 91
    Mia wants to describe how spread out the times are.
    She can use the range or the interquartile range.
    Which measure should Mia use?
    Give a reason for your answer.

    Show worked answerHide worked answer
    1. B1: the interquartile range
    2. C1: the range, 91 − 30 = 61, is affected by the one very high time
    3. C1: the interquartile range, 39 − 33 = 6, is not affected by it
    Answer: the interquartile range
    Benefits of IQR & Range
    [3 marks]

  4. Question 4. Rationalise the denominator of dfrac10√5

    Show worked answerHide worked answer
    1. M1: multiplies top and bottom by √5
    2. A1: 2√5
    Answer: 2√5
    Rationalising Denominators of the Form √a
    [2 marks]

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

    Show worked answerHide worked answer
    1. M1: 25² = 17.3² + 22.5² - 2 × 17.3 × 22.5 × cos BAC
    2. M1: cos BAC = dfrac17.3² + 22.5² - 25²2 × 17.3 × 22.5 = 0.2319
    3. A1: BAC = 76.6^°
    Answer: 76.6^°
    Finding Angles Using the Cosine Rule
    17.3 cm25 cm22.5 cmABC
    [3 marks]
📅 Free lesson: Tue 17th NovSave your place →

Mixed Topic Worksheet Grades 6/7: Day 062

Grades 6/7Calculator

  1. Question 1. The diagram shows a circular pizza with a diameter of 34 cm.
    The pizza is cut into 8 equal slices.
    Work out the area of one slice.
    Give your answer to 1 decimal place.

    [3 marks]
    34 cm
    Show worked answerHide worked answer
    1. M1: π × 17²
    2. M1: 907.9... ÷ 8
    3. A1: 113.5
    Answer: 113.5
    Area of a Circle Sector

  2. Question 2. n is an integer. Prove that 8(n + 3) - 3(n - 2) is a multiple of 5.

    [2 marks]
    Show worked answerHide worked answer
    1. M1: 8n + 24 - 3n + 6
    2. C1: 5n + 30 = 5(n + 6), which is a multiple of 5 for every integer n
    Answer: 5(n + 6), a multiple of 5
    Proof with Multiples

  3. Question 3. Here are the times, in minutes, taken by 9 students to complete a puzzle, in order.
    30 32 34 35 36 37 38 40 91
    Mia wants to describe how spread out the times are.
    She can use the range or the interquartile range.
    Which measure should Mia use?
    Give a reason for your answer.

    [3 marks]
    Show worked answerHide worked answer
    1. B1: the interquartile range
    2. C1: the range, 91 − 30 = 61, is affected by the one very high time
    3. C1: the interquartile range, 39 − 33 = 6, is not affected by it
    Answer: the interquartile range
    Benefits of IQR & Range

  4. Question 4. Rationalise the denominator of dfrac10√5

    [2 marks]
    Show worked answerHide worked answer
    1. M1: multiplies top and bottom by √5
    2. A1: 2√5
    Answer: 2√5
    Rationalising Denominators of the Form √a

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

    [3 marks]
    17.3 cm25 cm22.5 cmABC
    Show worked answerHide worked answer
    1. M1: 25² = 17.3² + 22.5² - 2 × 17.3 × 22.5 × cos BAC
    2. M1: cos BAC = dfrac17.3² + 22.5² - 25²2 × 17.3 × 22.5 = 0.2319
    3. A1: BAC = 76.6^°
    Answer: 76.6^°
    Finding Angles Using the Cosine Rule
📅 Free live lesson: Tuesday 17th NovemberSave your free place →

Mixed Topic Worksheet Grades 6/7: Day 062

Grades 6/7Calculator

  1. Question 1. The diagram shows a circular pizza with a diameter of 34 cm.
    The pizza is cut into 8 equal slices.
    Work out the area of one slice.
    Give your answer to 1 decimal place.

    Show worked answerHide worked answer
    1. M1: π × 17²
    2. M1: 907.9... ÷ 8
    3. A1: 113.5
    Answer: 113.5
    Area of a Circle Sector
    34 cm
    [3 marks]

  2. Question 2. n is an integer. Prove that 8(n + 3) - 3(n - 2) is a multiple of 5.

    Show worked answerHide worked answer
    1. M1: 8n + 24 - 3n + 6
    2. C1: 5n + 30 = 5(n + 6), which is a multiple of 5 for every integer n
    Answer: 5(n + 6), a multiple of 5
    Proof with Multiples
    [2 marks]

  3. Question 3. Here are the times, in minutes, taken by 9 students to complete a puzzle, in order.
    30 32 34 35 36 37 38 40 91
    Mia wants to describe how spread out the times are.
    She can use the range or the interquartile range.
    Which measure should Mia use?
    Give a reason for your answer.

    Show worked answerHide worked answer
    1. B1: the interquartile range
    2. C1: the range, 91 − 30 = 61, is affected by the one very high time
    3. C1: the interquartile range, 39 − 33 = 6, is not affected by it
    Answer: the interquartile range
    Benefits of IQR & Range
    [3 marks]

  4. Question 4. Rationalise the denominator of dfrac10√5

    Show worked answerHide worked answer
    1. M1: multiplies top and bottom by √5
    2. A1: 2√5
    Answer: 2√5
    Rationalising Denominators of the Form √a
    [2 marks]

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

    Show worked answerHide worked answer
    1. M1: 25² = 17.3² + 22.5² - 2 × 17.3 × 22.5 × cos BAC
    2. M1: cos BAC = dfrac17.3² + 22.5² - 25²2 × 17.3 × 22.5 = 0.2319
    3. A1: BAC = 76.6^°
    Answer: 76.6^°
    Finding Angles Using the Cosine Rule
    17.3 cm25 cm22.5 cmABC
    [3 marks]