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Mixed Topic Worksheet Grades 6/7: Day 018

Grades 6/7Calculator

  1. Question 1. Tom says that the points A(1, -1), B(2, -1), C(4, 5) and D(-1, 4) all lie on the graph of y = x² - 3x + 1
    Is Tom correct? You must show your working.

    Show worked answerHide worked answer
    1. M1: substitutes the x-coordinates of at least two of the points
    2. M1: finds that y = 5 when x = -1
    3. A1: No, with D identified
    Answer: No: D does not lie on the graph, since when x = -1, y = 5 and not 4
    Plotting Quadratics
    [3 marks]

  2. Question 2. The diagram shows triangle FKL. Work out the area of triangle FKL. Give your answer to 1 decimal place.

    Show worked answerHide worked answer
    1. M1: 1/2 × 6.8 × 9.3 × sin 124^°
    2. A1: 26.2
    Answer: 26.2
    Area of Triangles Using ½ab sin C
    6.8 cm9.3 cm124°KFLNot drawn accurately
    [2 marks]

  3. Question 3. An enlargement has scale factor -3 and centre (0, 0).
    The point (2, -1) is mapped onto the point Q.
    Write down the coordinates of Q.

    Show worked answerHide worked answer
    1. B1: Q = (-6, 3) as each coordinate is multiplied by -3
    Answer: (-6, 3)
    Enlargements with Negative Integer Scale Factors
    [1 mark]

  4. Question 4. A runner travels 120 m, correct to the nearest 10 m.
    The time taken is 14.5 seconds, correct to 1 decimal place.
    Calculate the upper bound of the runner's average speed in metres per second.
    Give your answer correct to 3 significant figures.

    Show worked answerHide worked answer
    1. M1: 120 + 5 and 14.5 - 0.05
    2. M1: 125 ÷ 14.45
    3. A1: 8.65
    Answer: 8.65 m/s
    Bounds & Error Intervals Involving Calculations
    [3 marks]

  5. Question 5. Here is a frustum of a cone. Work out the volume of the frustum.
    Give your answer to 1 decimal place.

    Show worked answerHide worked answer
    1. M1: complete cone height = 6 × 8 ÷ (8 - 4) = 12
    2. M1: 1/3 × π × 8² × 12 and 1/3 × π × 4² × 6
    3. M1: 256π - 32π
    4. A1: 703.7
    Answer: 703.7
    Volume of Frustums
    6 cm4 cm8 cm
    [4 marks]
📅 Free lesson: Tue 17th NovSave your place →

Mixed Topic Worksheet Grades 6/7: Day 018

Grades 6/7Calculator

  1. Question 1. Tom says that the points A(1, -1), B(2, -1), C(4, 5) and D(-1, 4) all lie on the graph of y = x² - 3x + 1
    Is Tom correct? You must show your working.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: substitutes the x-coordinates of at least two of the points
    2. M1: finds that y = 5 when x = -1
    3. A1: No, with D identified
    Answer: No: D does not lie on the graph, since when x = -1, y = 5 and not 4
    Plotting Quadratics

  2. Question 2. The diagram shows triangle FKL. Work out the area of triangle FKL. Give your answer to 1 decimal place.

    [2 marks]
    6.8 cm9.3 cm124°KFLNot drawn accurately
    Show worked answerHide worked answer
    1. M1: 1/2 × 6.8 × 9.3 × sin 124^°
    2. A1: 26.2
    Answer: 26.2
    Area of Triangles Using ½ab sin C

  3. Question 3. An enlargement has scale factor -3 and centre (0, 0).
    The point (2, -1) is mapped onto the point Q.
    Write down the coordinates of Q.

    [1 mark]
    Show worked answerHide worked answer
    1. B1: Q = (-6, 3) as each coordinate is multiplied by -3
    Answer: (-6, 3)
    Enlargements with Negative Integer Scale Factors

  4. Question 4. A runner travels 120 m, correct to the nearest 10 m.
    The time taken is 14.5 seconds, correct to 1 decimal place.
    Calculate the upper bound of the runner's average speed in metres per second.
    Give your answer correct to 3 significant figures.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: 120 + 5 and 14.5 - 0.05
    2. M1: 125 ÷ 14.45
    3. A1: 8.65
    Answer: 8.65 m/s
    Bounds & Error Intervals Involving Calculations

  5. Question 5. Here is a frustum of a cone. Work out the volume of the frustum.
    Give your answer to 1 decimal place.

    [4 marks]
    6 cm4 cm8 cm
    Show worked answerHide worked answer
    1. M1: complete cone height = 6 × 8 ÷ (8 - 4) = 12
    2. M1: 1/3 × π × 8² × 12 and 1/3 × π × 4² × 6
    3. M1: 256π - 32π
    4. A1: 703.7
    Answer: 703.7
    Volume of Frustums
📅 Free live lesson: Tuesday 17th NovemberSave your free place →

Mixed Topic Worksheet Grades 6/7: Day 018

Grades 6/7Calculator

  1. Question 1. Tom says that the points A(1, -1), B(2, -1), C(4, 5) and D(-1, 4) all lie on the graph of y = x² - 3x + 1
    Is Tom correct? You must show your working.

    Show worked answerHide worked answer
    1. M1: substitutes the x-coordinates of at least two of the points
    2. M1: finds that y = 5 when x = -1
    3. A1: No, with D identified
    Answer: No: D does not lie on the graph, since when x = -1, y = 5 and not 4
    Plotting Quadratics
    [3 marks]

  2. Question 2. The diagram shows triangle FKL. Work out the area of triangle FKL. Give your answer to 1 decimal place.

    Show worked answerHide worked answer
    1. M1: 1/2 × 6.8 × 9.3 × sin 124^°
    2. A1: 26.2
    Answer: 26.2
    Area of Triangles Using ½ab sin C
    6.8 cm9.3 cm124°KFLNot drawn accurately
    [2 marks]

  3. Question 3. An enlargement has scale factor -3 and centre (0, 0).
    The point (2, -1) is mapped onto the point Q.
    Write down the coordinates of Q.

    Show worked answerHide worked answer
    1. B1: Q = (-6, 3) as each coordinate is multiplied by -3
    Answer: (-6, 3)
    Enlargements with Negative Integer Scale Factors
    [1 mark]

  4. Question 4. A runner travels 120 m, correct to the nearest 10 m.
    The time taken is 14.5 seconds, correct to 1 decimal place.
    Calculate the upper bound of the runner's average speed in metres per second.
    Give your answer correct to 3 significant figures.

    Show worked answerHide worked answer
    1. M1: 120 + 5 and 14.5 - 0.05
    2. M1: 125 ÷ 14.45
    3. A1: 8.65
    Answer: 8.65 m/s
    Bounds & Error Intervals Involving Calculations
    [3 marks]

  5. Question 5. Here is a frustum of a cone. Work out the volume of the frustum.
    Give your answer to 1 decimal place.

    Show worked answerHide worked answer
    1. M1: complete cone height = 6 × 8 ÷ (8 - 4) = 12
    2. M1: 1/3 × π × 8² × 12 and 1/3 × π × 4² × 6
    3. M1: 256π - 32π
    4. A1: 703.7
    Answer: 703.7
    Volume of Frustums
    6 cm4 cm8 cm
    [4 marks]