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

Mixed Topic Worksheet Grades 6/7: Day 017

Grades 6/7Non-calculator

  1. Question 1. 50 students are in a club.
    28 students play chess.
    19 students play draughts.
    8 students play neither chess nor draughts.
    Draw a Venn diagram to show this information.

    Show worked answerHide worked answer
    1. M1: 50 - 8 = 42 play at least one game
    2. M1: 28 + 19 - 42 = 5 play both
    3. A1: chess only 23 and draughts only 14
    4. A1: fully correct Venn diagram with 5 in the middle and 8 outside
    ξChessDraughts235148
    Answer: Chess only: 23. Both: 5. Draughts only: 14. Neither: 8
    Constructing Venn Diagrams
    [4 marks]

  2. Question 2. The diagram shows triangle DEF.
    Work out the area of triangle DEF.

    Show worked answerHide worked answer
    1. M1: 1/2 × 10 × 8 × sin 30^°
    2. A1: 20
    Answer: 20 cm²
    Area of Triangles Using ½ab sin C
    10 cm8 cm30°DEF
    [2 marks]

  3. Question 3. Box plot A: minimum 10, lower quartile 18, median 24, upper quartile 40, maximum 52. Box plot B: minimum 14, lower quartile 20, median 30, upper quartile 38, maximum 48. Work out the difference between the medians and between the interquartile ranges.

    Show worked answerHide worked answer
    1. M1: medians: 30 - 24 = 6
    2. M1: IQRs: A 22, B 18
    3. A1: 6 and 4
    Answer: Medians differ by 6; IQRs differ by 4
    Comparing Data Using Box Plots
    [3 marks]

  4. Question 4. Solve 2x² + 5x - 3 = 0 [3]

    Show worked answerHide worked answer
    1. M1: (2x - 1)(x + 3) = 0
    2. A1: x = dfrac12
    3. A1: x = -3
    Answer: x = dfrac12 or x = -3
    Solving Quadratics by Factorising (a > 1)
    [3 marks]

  5. Question 5. The graph of y = ax, where a is a positive number, passes through the point ≤ft(3, dfrac6427)
    Work out the value of y when x = -2

    Show worked answerHide worked answer
    1. M1: a³ = dfrac6427
    2. A1: a = 4/3
    3. A1: y = 9/16
    Answer: 9/16
    Sketching Exponential Graphs
    [3 marks]
📅 Free lesson: Tue 17th NovSave your place →

Mixed Topic Worksheet Grades 6/7: Day 017

Grades 6/7Non-calculator

  1. Question 1. 50 students are in a club.
    28 students play chess.
    19 students play draughts.
    8 students play neither chess nor draughts.
    Draw a Venn diagram to show this information.

    [4 marks]
    Show worked answerHide worked answer
    1. M1: 50 - 8 = 42 play at least one game
    2. M1: 28 + 19 - 42 = 5 play both
    3. A1: chess only 23 and draughts only 14
    4. A1: fully correct Venn diagram with 5 in the middle and 8 outside
    ξChessDraughts235148
    Answer: Chess only: 23. Both: 5. Draughts only: 14. Neither: 8
    Constructing Venn Diagrams

  2. Question 2. The diagram shows triangle DEF.
    Work out the area of triangle DEF.

    [2 marks]
    10 cm8 cm30°DEF
    Show worked answerHide worked answer
    1. M1: 1/2 × 10 × 8 × sin 30^°
    2. A1: 20
    Answer: 20 cm²
    Area of Triangles Using ½ab sin C

  3. Question 3. Box plot A: minimum 10, lower quartile 18, median 24, upper quartile 40, maximum 52. Box plot B: minimum 14, lower quartile 20, median 30, upper quartile 38, maximum 48. Work out the difference between the medians and between the interquartile ranges.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: medians: 30 - 24 = 6
    2. M1: IQRs: A 22, B 18
    3. A1: 6 and 4
    Answer: Medians differ by 6; IQRs differ by 4
    Comparing Data Using Box Plots

  4. Question 4. Solve 2x² + 5x - 3 = 0 [3]

    [3 marks]
    Show worked answerHide worked answer
    1. M1: (2x - 1)(x + 3) = 0
    2. A1: x = dfrac12
    3. A1: x = -3
    Answer: x = dfrac12 or x = -3
    Solving Quadratics by Factorising (a > 1)

  5. Question 5. The graph of y = ax, where a is a positive number, passes through the point ≤ft(3, dfrac6427)
    Work out the value of y when x = -2

    [3 marks]
    Show worked answerHide worked answer
    1. M1: a³ = dfrac6427
    2. A1: a = 4/3
    3. A1: y = 9/16
    Answer: 9/16
    Sketching Exponential Graphs
📅 Free live lesson: Tuesday 17th NovemberSave your free place →

Mixed Topic Worksheet Grades 6/7: Day 017

Grades 6/7Non-calculator

  1. Question 1. 50 students are in a club.
    28 students play chess.
    19 students play draughts.
    8 students play neither chess nor draughts.
    Draw a Venn diagram to show this information.

    Show worked answerHide worked answer
    1. M1: 50 - 8 = 42 play at least one game
    2. M1: 28 + 19 - 42 = 5 play both
    3. A1: chess only 23 and draughts only 14
    4. A1: fully correct Venn diagram with 5 in the middle and 8 outside
    ξChessDraughts235148
    Answer: Chess only: 23. Both: 5. Draughts only: 14. Neither: 8
    Constructing Venn Diagrams
    [4 marks]

  2. Question 2. The diagram shows triangle DEF.
    Work out the area of triangle DEF.

    Show worked answerHide worked answer
    1. M1: 1/2 × 10 × 8 × sin 30^°
    2. A1: 20
    Answer: 20 cm²
    Area of Triangles Using ½ab sin C
    10 cm8 cm30°DEF
    [2 marks]

  3. Question 3. Box plot A: minimum 10, lower quartile 18, median 24, upper quartile 40, maximum 52. Box plot B: minimum 14, lower quartile 20, median 30, upper quartile 38, maximum 48. Work out the difference between the medians and between the interquartile ranges.

    Show worked answerHide worked answer
    1. M1: medians: 30 - 24 = 6
    2. M1: IQRs: A 22, B 18
    3. A1: 6 and 4
    Answer: Medians differ by 6; IQRs differ by 4
    Comparing Data Using Box Plots
    [3 marks]

  4. Question 4. Solve 2x² + 5x - 3 = 0 [3]

    Show worked answerHide worked answer
    1. M1: (2x - 1)(x + 3) = 0
    2. A1: x = dfrac12
    3. A1: x = -3
    Answer: x = dfrac12 or x = -3
    Solving Quadratics by Factorising (a > 1)
    [3 marks]

  5. Question 5. The graph of y = ax, where a is a positive number, passes through the point ≤ft(3, dfrac6427)
    Work out the value of y when x = -2

    Show worked answerHide worked answer
    1. M1: a³ = dfrac6427
    2. A1: a = 4/3
    3. A1: y = 9/16
    Answer: 9/16
    Sketching Exponential Graphs
    [3 marks]