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

Mixed Topic Worksheet Grades 6/7: Day 026

Grades 6/7Calculator

  1. Question 1. The table shows information about the favourite fruit of 36 pupils. Each pupil chose one fruit.
    Draw an accurate pie chart for this information. Label each sector.

    Show worked answerHide worked answer
    1. M1: 360 ÷ 36 = 10
    2. A1: at least two correct angles (120° and 150° or any two)
    3. A1: all angles correct, sectors labelled, pie chart drawn to within 2°
    Apple120°Banana150°Cherry 60°Grape 30°
    Answer: Sectors: Apple 120°; Banana 150°; Cherry 60°; Grape 30°
    Drawing Pie Charts
    FruitFrequencyApple12Banana15Cherry6Grape3
    [3 marks]

  2. Question 2. Make x the subject of y = 3x² - 4, where x is positive.

    Show worked answerHide worked answer
    1. M1: x² = dfracy + 43
    2. A1: x = sqrtdfracy + 43
    Answer: x = sqrtdfracy + 43
    Rearranging Harder Equations
    [2 marks]

  3. Question 3. ABCD is a rhombus. AB = 12 cm. Angle DAB = 64^° Work out the area of the rhombus. Give your answer to 1 decimal place.

    Show worked answerHide worked answer
    1. M1: area of triangle ABD = 1/2 × 12 × 12 × sin 64^°
    2. M1: area of rhombus = 2 × area of triangle ABD
    3. A1: 129.4
    Answer: 129.4
    Area of Triangles Using ½ab sin C
    12 cm64°ABDCNot drawn accurately
    [3 marks]

  4. Question 4. The graph of y = x² + x - 6 is shown. A straight line crosses it where x = -1 and x = 2.
    (a) Write down the coordinates of the two points where the line crosses the curve. [2]
    (b) Work out the equation of the line. [2]

    Show worked answerHide worked answer
    1. (a) B1: (-1, -6)
    2. (a) B1: (2, 0)
    3. (b) M1: gradient = (0 - (-6)) ÷ (2 - (-1)) = 2
    4. (b) A1: y = 2x - 4
    Answer: (a) (-1, -6) and (2, 0); (b) y = 2x - 4
    Solving Quadratic Simultaneous Equations Graphically
    xy−6−4−224−4−22
    [4 marks]

  5. Question 5. Here is triangle ABC.
    Work out the length of BC.
    Give your answer to 1 decimal place.

    Show worked answerHide worked answer
    1. M1: BC² = 8.6² + 12.4² - 2 × 8.6 × 12.4 × cos 64^°
    2. M1: BC² = 227.72 - 93.50 = 134.22
    3. A1: BC = 11.6
    Answer: 11.6 cm
    Fundamentals of the Cosine Rule
    12.4 cm8.6 cm64°ABC
    [3 marks]
📅 Free lesson: Tue 17th NovSave your place →

Mixed Topic Worksheet Grades 6/7: Day 026

Grades 6/7Calculator

  1. Question 1. The table shows information about the favourite fruit of 36 pupils. Each pupil chose one fruit.
    Draw an accurate pie chart for this information. Label each sector.

    [3 marks]
    FruitFrequencyApple12Banana15Cherry6Grape3
    Show worked answerHide worked answer
    1. M1: 360 ÷ 36 = 10
    2. A1: at least two correct angles (120° and 150° or any two)
    3. A1: all angles correct, sectors labelled, pie chart drawn to within 2°
    Apple120°Banana150°Cherry 60°Grape 30°
    Answer: Sectors: Apple 120°; Banana 150°; Cherry 60°; Grape 30°
    Drawing Pie Charts

  2. Question 2. Make x the subject of y = 3x² - 4, where x is positive.

    [2 marks]
    Show worked answerHide worked answer
    1. M1: x² = dfracy + 43
    2. A1: x = sqrtdfracy + 43
    Answer: x = sqrtdfracy + 43
    Rearranging Harder Equations

  3. Question 3. ABCD is a rhombus. AB = 12 cm. Angle DAB = 64^° Work out the area of the rhombus. Give your answer to 1 decimal place.

    [3 marks]
    12 cm64°ABDCNot drawn accurately
    Show worked answerHide worked answer
    1. M1: area of triangle ABD = 1/2 × 12 × 12 × sin 64^°
    2. M1: area of rhombus = 2 × area of triangle ABD
    3. A1: 129.4
    Answer: 129.4
    Area of Triangles Using ½ab sin C

  4. Question 4. The graph of y = x² + x - 6 is shown. A straight line crosses it where x = -1 and x = 2.
    (a) Write down the coordinates of the two points where the line crosses the curve. [2]
    (b) Work out the equation of the line. [2]

    [4 marks]
    xy−6−4−224−4−22
    Show worked answerHide worked answer
    1. (a) B1: (-1, -6)
    2. (a) B1: (2, 0)
    3. (b) M1: gradient = (0 - (-6)) ÷ (2 - (-1)) = 2
    4. (b) A1: y = 2x - 4
    Answer: (a) (-1, -6) and (2, 0); (b) y = 2x - 4
    Solving Quadratic Simultaneous Equations Graphically

  5. Question 5. Here is triangle ABC.
    Work out the length of BC.
    Give your answer to 1 decimal place.

    [3 marks]
    12.4 cm8.6 cm64°ABC
    Show worked answerHide worked answer
    1. M1: BC² = 8.6² + 12.4² - 2 × 8.6 × 12.4 × cos 64^°
    2. M1: BC² = 227.72 - 93.50 = 134.22
    3. A1: BC = 11.6
    Answer: 11.6 cm
    Fundamentals of the Cosine Rule
📅 Free live lesson: Tuesday 17th NovemberSave your free place →

Mixed Topic Worksheet Grades 6/7: Day 026

Grades 6/7Calculator

  1. Question 1. The table shows information about the favourite fruit of 36 pupils. Each pupil chose one fruit.
    Draw an accurate pie chart for this information. Label each sector.

    Show worked answerHide worked answer
    1. M1: 360 ÷ 36 = 10
    2. A1: at least two correct angles (120° and 150° or any two)
    3. A1: all angles correct, sectors labelled, pie chart drawn to within 2°
    Apple120°Banana150°Cherry 60°Grape 30°
    Answer: Sectors: Apple 120°; Banana 150°; Cherry 60°; Grape 30°
    Drawing Pie Charts
    FruitFrequencyApple12Banana15Cherry6Grape3
    [3 marks]

  2. Question 2. Make x the subject of y = 3x² - 4, where x is positive.

    Show worked answerHide worked answer
    1. M1: x² = dfracy + 43
    2. A1: x = sqrtdfracy + 43
    Answer: x = sqrtdfracy + 43
    Rearranging Harder Equations
    [2 marks]

  3. Question 3. ABCD is a rhombus. AB = 12 cm. Angle DAB = 64^° Work out the area of the rhombus. Give your answer to 1 decimal place.

    Show worked answerHide worked answer
    1. M1: area of triangle ABD = 1/2 × 12 × 12 × sin 64^°
    2. M1: area of rhombus = 2 × area of triangle ABD
    3. A1: 129.4
    Answer: 129.4
    Area of Triangles Using ½ab sin C
    12 cm64°ABDCNot drawn accurately
    [3 marks]

  4. Question 4. The graph of y = x² + x - 6 is shown. A straight line crosses it where x = -1 and x = 2.
    (a) Write down the coordinates of the two points where the line crosses the curve. [2]
    (b) Work out the equation of the line. [2]

    Show worked answerHide worked answer
    1. (a) B1: (-1, -6)
    2. (a) B1: (2, 0)
    3. (b) M1: gradient = (0 - (-6)) ÷ (2 - (-1)) = 2
    4. (b) A1: y = 2x - 4
    Answer: (a) (-1, -6) and (2, 0); (b) y = 2x - 4
    Solving Quadratic Simultaneous Equations Graphically
    xy−6−4−224−4−22
    [4 marks]

  5. Question 5. Here is triangle ABC.
    Work out the length of BC.
    Give your answer to 1 decimal place.

    Show worked answerHide worked answer
    1. M1: BC² = 8.6² + 12.4² - 2 × 8.6 × 12.4 × cos 64^°
    2. M1: BC² = 227.72 - 93.50 = 134.22
    3. A1: BC = 11.6
    Answer: 11.6 cm
    Fundamentals of the Cosine Rule
    12.4 cm8.6 cm64°ABC
    [3 marks]