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

Mixed Topic Worksheet Grades 6/7: Day 051

Grades 6/7Non-calculator

  1. Question 1. A Venn diagram shows 40 elements. There are x in A only, 7 in both, 2x in B only and 9 in neither. Work out the probability that a chosen element is in B only.

    Show worked answerHide worked answer
    1. M1: x+7+2x+9=40, so 3x=24, x=8
    2. M1: B only =16
    3. A1: 16/40=2/5
    Answer: 2/5
    Finding Probabilities with Venn Diagrams
    [3 marks]

  2. Question 2. A reflection has mirror line x = 3.
    One of the points (5, 3), (0, 3) and (3, 5) is an invariant point under this reflection.
    Write down that point.

    Show worked answerHide worked answer
    1. B1: (3, 5) as it lies on the mirror line
    Answer: (3, 5)
    Invariant Points
    [1 mark]

  3. Question 3. f(x) = x² + bx + c, where b and c are integers.
    f(2) = -1
    f(5) = 14
    Work out the value of b and the value of c

    Show worked answerHide worked answer
    1. M1: 4 + 2b + c = -1
    2. M1: 25 + 5b + c = 14
    3. M1: eliminates c to get 21 + 3b = 15
    4. A1: b = -2
    5. A1: c = -1
    Answer: b = -2, c = -1
    Fundamentals of Functions
    [5 marks]

  4. Question 4. n is a positive integer. √n × √18 = 12. Work out the value of n.

    Show worked answerHide worked answer
    1. M1: √18n = 12 so 18n = 144
    2. A1: n = 8
    Answer: 8
    Six Laws of Surds
    [2 marks]

  5. Question 5. The graph of y = 3 × 4x is drawn for positive and negative values of x.
    (a) Work out the value of y when x = 2 [1]
    (b) Work out the value of y when x = -1 [1]

    Show worked answerHide worked answer
    1. (a) B1: 48
    2. (b) B1: 3/4
    Answer: (a) 48; (b) 3/4
    Sketching Exponential Graphs
    [2 marks]
📅 Free lesson: Tue 17th NovSave your place →

Mixed Topic Worksheet Grades 6/7: Day 051

Grades 6/7Non-calculator

  1. Question 1. A Venn diagram shows 40 elements. There are x in A only, 7 in both, 2x in B only and 9 in neither. Work out the probability that a chosen element is in B only.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: x+7+2x+9=40, so 3x=24, x=8
    2. M1: B only =16
    3. A1: 16/40=2/5
    Answer: 2/5
    Finding Probabilities with Venn Diagrams

  2. Question 2. A reflection has mirror line x = 3.
    One of the points (5, 3), (0, 3) and (3, 5) is an invariant point under this reflection.
    Write down that point.

    [1 mark]
    Show worked answerHide worked answer
    1. B1: (3, 5) as it lies on the mirror line
    Answer: (3, 5)
    Invariant Points

  3. Question 3. f(x) = x² + bx + c, where b and c are integers.
    f(2) = -1
    f(5) = 14
    Work out the value of b and the value of c

    [5 marks]
    Show worked answerHide worked answer
    1. M1: 4 + 2b + c = -1
    2. M1: 25 + 5b + c = 14
    3. M1: eliminates c to get 21 + 3b = 15
    4. A1: b = -2
    5. A1: c = -1
    Answer: b = -2, c = -1
    Fundamentals of Functions

  4. Question 4. n is a positive integer. √n × √18 = 12. Work out the value of n.

    [2 marks]
    Show worked answerHide worked answer
    1. M1: √18n = 12 so 18n = 144
    2. A1: n = 8
    Answer: 8
    Six Laws of Surds

  5. Question 5. The graph of y = 3 × 4x is drawn for positive and negative values of x.
    (a) Work out the value of y when x = 2 [1]
    (b) Work out the value of y when x = -1 [1]

    [2 marks]
    Show worked answerHide worked answer
    1. (a) B1: 48
    2. (b) B1: 3/4
    Answer: (a) 48; (b) 3/4
    Sketching Exponential Graphs
📅 Free live lesson: Tuesday 17th NovemberSave your free place →

Mixed Topic Worksheet Grades 6/7: Day 051

Grades 6/7Non-calculator

  1. Question 1. A Venn diagram shows 40 elements. There are x in A only, 7 in both, 2x in B only and 9 in neither. Work out the probability that a chosen element is in B only.

    Show worked answerHide worked answer
    1. M1: x+7+2x+9=40, so 3x=24, x=8
    2. M1: B only =16
    3. A1: 16/40=2/5
    Answer: 2/5
    Finding Probabilities with Venn Diagrams
    [3 marks]

  2. Question 2. A reflection has mirror line x = 3.
    One of the points (5, 3), (0, 3) and (3, 5) is an invariant point under this reflection.
    Write down that point.

    Show worked answerHide worked answer
    1. B1: (3, 5) as it lies on the mirror line
    Answer: (3, 5)
    Invariant Points
    [1 mark]

  3. Question 3. f(x) = x² + bx + c, where b and c are integers.
    f(2) = -1
    f(5) = 14
    Work out the value of b and the value of c

    Show worked answerHide worked answer
    1. M1: 4 + 2b + c = -1
    2. M1: 25 + 5b + c = 14
    3. M1: eliminates c to get 21 + 3b = 15
    4. A1: b = -2
    5. A1: c = -1
    Answer: b = -2, c = -1
    Fundamentals of Functions
    [5 marks]

  4. Question 4. n is a positive integer. √n × √18 = 12. Work out the value of n.

    Show worked answerHide worked answer
    1. M1: √18n = 12 so 18n = 144
    2. A1: n = 8
    Answer: 8
    Six Laws of Surds
    [2 marks]

  5. Question 5. The graph of y = 3 × 4x is drawn for positive and negative values of x.
    (a) Work out the value of y when x = 2 [1]
    (b) Work out the value of y when x = -1 [1]

    Show worked answerHide worked answer
    1. (a) B1: 48
    2. (b) B1: 3/4
    Answer: (a) 48; (b) 3/4
    Sketching Exponential Graphs
    [2 marks]