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

Mixed Topic Worksheet Grades 6/7: Day 080

Grades 6/7Calculator

  1. Question 1. Work out the distance between the points E(-2, -3) and F(6, 12).

    Show worked answerHide worked answer
    1. M1: √8² + 15²
    2. A1: 17
    Answer: 17
    Finding the Distance Between Two Points
    [2 marks]

  2. Question 2. A data set has lower quartile 24 and upper quartile 36
    Work out the interquartile range.

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    1. M1: 36 - 24
    2. A1: 12
    Answer: 12
    Benefits of IQR & Range
    [2 marks]

  3. Question 3. Prove that 4(n + 5)² - (2n - 3)² is a multiple of 13 for all integer values of n.

    Show worked answerHide worked answer
    1. M1: 4n² + 40n + 100 - (4n² - 12n + 9)
    2. A1: 52n + 91
    3. C1: 13(4n + 7), which is a multiple of 13
    Answer: 13(4n + 7)
    Proof with Multiples
    [3 marks]

  4. Question 4. Here is triangle ABC.
    Work out the size of the largest angle in triangle ABC.
    Give your answer to 1 decimal place.

    Show worked answerHide worked answer
    1. M1: 11² = 9² + 8² - 2 × 9 × 8 × cos BAC
    2. M1: cos BAC = dfrac9² + 8² - 11²2 × 9 × 8 = 0.1667
    3. A1: BAC = 80.4^°
    Answer: 80.4^°
    Finding Angles Using the Cosine Rule
    9 cm11 cm8 cmABC
    [3 marks]

  5. Question 5. a = 9.4 and b = 2.1, both correct to 1 decimal place.
    Lina works out the lower bound of a ÷ b.
    Lina's working: 9.35 ÷ 2.05 = 4.56
    Lina's answer is not correct.
    Work out the lower bound of a ÷ b.
    Give your answer correct to 3 significant figures.

    Show worked answerHide worked answer
    1. M1: 9.4 - 0.05 and 2.1 + 0.05
    2. M1: 9.35 ÷ 2.15
    3. A1: 4.35
    Answer: 4.35
    Bounds & Error Intervals Involving Calculations
    [3 marks]
📅 Free lesson: Tue 17th NovSave your place →

Mixed Topic Worksheet Grades 6/7: Day 080

Grades 6/7Calculator

  1. Question 1. Work out the distance between the points E(-2, -3) and F(6, 12).

    [2 marks]
    Show worked answerHide worked answer
    1. M1: √8² + 15²
    2. A1: 17
    Answer: 17
    Finding the Distance Between Two Points

  2. Question 2. A data set has lower quartile 24 and upper quartile 36
    Work out the interquartile range.

    [2 marks]
    Show worked answerHide worked answer
    1. M1: 36 - 24
    2. A1: 12
    Answer: 12
    Benefits of IQR & Range

  3. Question 3. Prove that 4(n + 5)² - (2n - 3)² is a multiple of 13 for all integer values of n.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: 4n² + 40n + 100 - (4n² - 12n + 9)
    2. A1: 52n + 91
    3. C1: 13(4n + 7), which is a multiple of 13
    Answer: 13(4n + 7)
    Proof with Multiples

  4. Question 4. Here is triangle ABC.
    Work out the size of the largest angle in triangle ABC.
    Give your answer to 1 decimal place.

    [3 marks]
    9 cm11 cm8 cmABC
    Show worked answerHide worked answer
    1. M1: 11² = 9² + 8² - 2 × 9 × 8 × cos BAC
    2. M1: cos BAC = dfrac9² + 8² - 11²2 × 9 × 8 = 0.1667
    3. A1: BAC = 80.4^°
    Answer: 80.4^°
    Finding Angles Using the Cosine Rule

  5. Question 5. a = 9.4 and b = 2.1, both correct to 1 decimal place.
    Lina works out the lower bound of a ÷ b.
    Lina's working: 9.35 ÷ 2.05 = 4.56
    Lina's answer is not correct.
    Work out the lower bound of a ÷ b.
    Give your answer correct to 3 significant figures.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: 9.4 - 0.05 and 2.1 + 0.05
    2. M1: 9.35 ÷ 2.15
    3. A1: 4.35
    Answer: 4.35
    Bounds & Error Intervals Involving Calculations
📅 Free live lesson: Tuesday 17th NovemberSave your free place →

Mixed Topic Worksheet Grades 6/7: Day 080

Grades 6/7Calculator

  1. Question 1. Work out the distance between the points E(-2, -3) and F(6, 12).

    Show worked answerHide worked answer
    1. M1: √8² + 15²
    2. A1: 17
    Answer: 17
    Finding the Distance Between Two Points
    [2 marks]

  2. Question 2. A data set has lower quartile 24 and upper quartile 36
    Work out the interquartile range.

    Show worked answerHide worked answer
    1. M1: 36 - 24
    2. A1: 12
    Answer: 12
    Benefits of IQR & Range
    [2 marks]

  3. Question 3. Prove that 4(n + 5)² - (2n - 3)² is a multiple of 13 for all integer values of n.

    Show worked answerHide worked answer
    1. M1: 4n² + 40n + 100 - (4n² - 12n + 9)
    2. A1: 52n + 91
    3. C1: 13(4n + 7), which is a multiple of 13
    Answer: 13(4n + 7)
    Proof with Multiples
    [3 marks]

  4. Question 4. Here is triangle ABC.
    Work out the size of the largest angle in triangle ABC.
    Give your answer to 1 decimal place.

    Show worked answerHide worked answer
    1. M1: 11² = 9² + 8² - 2 × 9 × 8 × cos BAC
    2. M1: cos BAC = dfrac9² + 8² - 11²2 × 9 × 8 = 0.1667
    3. A1: BAC = 80.4^°
    Answer: 80.4^°
    Finding Angles Using the Cosine Rule
    9 cm11 cm8 cmABC
    [3 marks]

  5. Question 5. a = 9.4 and b = 2.1, both correct to 1 decimal place.
    Lina works out the lower bound of a ÷ b.
    Lina's working: 9.35 ÷ 2.05 = 4.56
    Lina's answer is not correct.
    Work out the lower bound of a ÷ b.
    Give your answer correct to 3 significant figures.

    Show worked answerHide worked answer
    1. M1: 9.4 - 0.05 and 2.1 + 0.05
    2. M1: 9.35 ÷ 2.15
    3. A1: 4.35
    Answer: 4.35
    Bounds & Error Intervals Involving Calculations
    [3 marks]