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

Mixed Topic Worksheet Grades 6/7: Day 055

Grades 6/7Non-calculator

  1. Question 1. The diagram shows the graph of y = -x² + 2x + 3
    Write down the greatest value of y.

    Show worked answerHide worked answer
    1. M1: the highest point of the graph, at x = 1
    2. A1: 4
    Answer: 4
    General Shape of a Quadratic
    xy−6−4−224−2−11234
    [2 marks]

  2. Question 2. n is an integer.
    Prove that 5(n + 4) - 2(n - 2) is a multiple of 3.

    Show worked answerHide worked answer
    1. M1: 5n + 20 - 2n + 4
    2. C1: 3n + 24 = 3(n + 8), which is a multiple of 3
    Answer: 3(n + 8)
    Proof with Multiples
    [2 marks]

  3. Question 3. Here are seven numbers.
    3 5 6 8 9 11 60
    The lower quartile is 5 and the upper quartile is 11
    Work out the interquartile range and give a reason why it is better than the range here.

    Show worked answerHide worked answer
    1. M1: 11 - 5
    2. A1: 6
    3. B1: 60 is an outlier; the range, 60 - 3 = 57, uses it but the interquartile range does not
    Answer: 6; 60 is an outlier, which affects the range but not the interquartile range
    Benefits of IQR & Range
    [3 marks]

  4. Question 4. p is directly proportional to the cube of q.
    p = 54 when q = 3.
    Find the value of p when q = 5.

    Show worked answerHide worked answer
    1. M1: 54 = k × 3³
    2. M1: p = 2 × 5³
    3. A1: 250
    Answer: 250
    Algebraic Direct Proportion
    [3 marks]

  5. Question 5. A code is 2 letters followed by 3 digits.
    The letters are chosen from A, B, C, D, E and F.
    The digits are chosen from 1, 2, 3 and 4
    Letters and digits can be used more than once.
    Work out the number of different codes.

    Show worked answerHide worked answer
    1. M1: 6 × 6 = 36 or 4 × 4 × 4 = 64
    2. M1: 6² × 4³
    3. A1: 2 304
    Answer: 2 304
    Combinations Problem Solving
    [3 marks]
📅 Free lesson: Tue 17th NovSave your place →

Mixed Topic Worksheet Grades 6/7: Day 055

Grades 6/7Non-calculator

  1. Question 1. The diagram shows the graph of y = -x² + 2x + 3
    Write down the greatest value of y.

    [2 marks]
    xy−6−4−224−2−11234
    Show worked answerHide worked answer
    1. M1: the highest point of the graph, at x = 1
    2. A1: 4
    Answer: 4
    General Shape of a Quadratic

  2. Question 2. n is an integer.
    Prove that 5(n + 4) - 2(n - 2) is a multiple of 3.

    [2 marks]
    Show worked answerHide worked answer
    1. M1: 5n + 20 - 2n + 4
    2. C1: 3n + 24 = 3(n + 8), which is a multiple of 3
    Answer: 3(n + 8)
    Proof with Multiples

  3. Question 3. Here are seven numbers.
    3 5 6 8 9 11 60
    The lower quartile is 5 and the upper quartile is 11
    Work out the interquartile range and give a reason why it is better than the range here.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: 11 - 5
    2. A1: 6
    3. B1: 60 is an outlier; the range, 60 - 3 = 57, uses it but the interquartile range does not
    Answer: 6; 60 is an outlier, which affects the range but not the interquartile range
    Benefits of IQR & Range

  4. Question 4. p is directly proportional to the cube of q.
    p = 54 when q = 3.
    Find the value of p when q = 5.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: 54 = k × 3³
    2. M1: p = 2 × 5³
    3. A1: 250
    Answer: 250
    Algebraic Direct Proportion

  5. Question 5. A code is 2 letters followed by 3 digits.
    The letters are chosen from A, B, C, D, E and F.
    The digits are chosen from 1, 2, 3 and 4
    Letters and digits can be used more than once.
    Work out the number of different codes.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: 6 × 6 = 36 or 4 × 4 × 4 = 64
    2. M1: 6² × 4³
    3. A1: 2 304
    Answer: 2 304
    Combinations Problem Solving
📅 Free live lesson: Tuesday 17th NovemberSave your free place →

Mixed Topic Worksheet Grades 6/7: Day 055

Grades 6/7Non-calculator

  1. Question 1. The diagram shows the graph of y = -x² + 2x + 3
    Write down the greatest value of y.

    Show worked answerHide worked answer
    1. M1: the highest point of the graph, at x = 1
    2. A1: 4
    Answer: 4
    General Shape of a Quadratic
    xy−6−4−224−2−11234
    [2 marks]

  2. Question 2. n is an integer.
    Prove that 5(n + 4) - 2(n - 2) is a multiple of 3.

    Show worked answerHide worked answer
    1. M1: 5n + 20 - 2n + 4
    2. C1: 3n + 24 = 3(n + 8), which is a multiple of 3
    Answer: 3(n + 8)
    Proof with Multiples
    [2 marks]

  3. Question 3. Here are seven numbers.
    3 5 6 8 9 11 60
    The lower quartile is 5 and the upper quartile is 11
    Work out the interquartile range and give a reason why it is better than the range here.

    Show worked answerHide worked answer
    1. M1: 11 - 5
    2. A1: 6
    3. B1: 60 is an outlier; the range, 60 - 3 = 57, uses it but the interquartile range does not
    Answer: 6; 60 is an outlier, which affects the range but not the interquartile range
    Benefits of IQR & Range
    [3 marks]

  4. Question 4. p is directly proportional to the cube of q.
    p = 54 when q = 3.
    Find the value of p when q = 5.

    Show worked answerHide worked answer
    1. M1: 54 = k × 3³
    2. M1: p = 2 × 5³
    3. A1: 250
    Answer: 250
    Algebraic Direct Proportion
    [3 marks]

  5. Question 5. A code is 2 letters followed by 3 digits.
    The letters are chosen from A, B, C, D, E and F.
    The digits are chosen from 1, 2, 3 and 4
    Letters and digits can be used more than once.
    Work out the number of different codes.

    Show worked answerHide worked answer
    1. M1: 6 × 6 = 36 or 4 × 4 × 4 = 64
    2. M1: 6² × 4³
    3. A1: 2 304
    Answer: 2 304
    Combinations Problem Solving
    [3 marks]