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Mixed Topic Worksheet Grades 8/9: Day 084

Grades 8/9Calculator

  1. Question 1. Describe fully the single transformation that maps the graph of y = x² onto the graph of y = (x + 5)²

    Show worked answerHide worked answer
    1. B1: translation
    2. B1: by the vector beginpmatrix -5 0 endpmatrix
    Answer: Translation by beginpmatrix -5 0 endpmatrix
    Translations Along the x- & y-Axes
    [2 marks]

  2. Question 2. A cuboid has a 3 cm by 4 cm base. A space diagonal makes 60° with the base. Work out the height to 1 decimal place.

    Show worked answerHide worked answer
    1. M1: base diagonal 5, h = 5tan 60°
    2. A1: 8.7 cm
    Answer: 8.7 cm
    3D Trigonometry
    [2 marks]

  3. Question 3. The class 10 < m ≤ 25 has a frequency of 54.
    The class 25 < m ≤ 40 has a frequency of 36.
    Work out the frequency density of each class.

    Show worked answerHide worked answer
    1. M1: 54 ÷ 15 or 36 ÷ 15
    2. A1: 3.6
    3. A1: 2.4
    Answer: 3.6 and 2.4
    Sketching Histograms
    [3 marks]

  4. Question 4. A solid sphere has radius 3.5 cm, correct to 1 decimal place.
    The mass of the sphere is 750 g, correct to the nearest 10 g.
    Work out the upper bound of the density of the sphere in grams per cubic centimetre.
    density = dfracmassvolume
    volume of a sphere = dfrac43π r³
    Give your answer correct to 3 significant figures.

    Show worked answerHide worked answer
    1. M1: 750 + 5 and 3.5 - 0.05
    2. M1: (4/3) × π × 3.45³
    3. M1: 755 ÷ ((4/3) × π × 3.45³)
    4. A1: 4.39
    Answer: 4.39
    Combining Upper & Lower Bounds
    [4 marks]

  5. Question 5. The line y = 5 touches the curve with equation y = 3x² - 18x + c at one point
    Work out the value of c

    Show worked answerHide worked answer
    1. M1: 3≤ft((x - 3)² - 9) + c
    2. M1: 3(x - 3)² + c - 27
    3. M1: minimum value c - 27 = 5
    4. A1: c = 32
    Answer: c = 32
    Solving Quadratics by Completing the Square (a > 1)
    [4 marks]
📅 Free lesson: Tue 17th NovSave your place →

Mixed Topic Worksheet Grades 8/9: Day 084

Grades 8/9Calculator

  1. Question 1. Describe fully the single transformation that maps the graph of y = x² onto the graph of y = (x + 5)²

    [2 marks]
    Show worked answerHide worked answer
    1. B1: translation
    2. B1: by the vector beginpmatrix -5 0 endpmatrix
    Answer: Translation by beginpmatrix -5 0 endpmatrix
    Translations Along the x- & y-Axes

  2. Question 2. A cuboid has a 3 cm by 4 cm base. A space diagonal makes 60° with the base. Work out the height to 1 decimal place.

    [2 marks]
    Show worked answerHide worked answer
    1. M1: base diagonal 5, h = 5tan 60°
    2. A1: 8.7 cm
    Answer: 8.7 cm
    3D Trigonometry

  3. Question 3. The class 10 < m ≤ 25 has a frequency of 54.
    The class 25 < m ≤ 40 has a frequency of 36.
    Work out the frequency density of each class.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: 54 ÷ 15 or 36 ÷ 15
    2. A1: 3.6
    3. A1: 2.4
    Answer: 3.6 and 2.4
    Sketching Histograms

  4. Question 4. A solid sphere has radius 3.5 cm, correct to 1 decimal place.
    The mass of the sphere is 750 g, correct to the nearest 10 g.
    Work out the upper bound of the density of the sphere in grams per cubic centimetre.
    density = dfracmassvolume
    volume of a sphere = dfrac43π r³
    Give your answer correct to 3 significant figures.

    [4 marks]
    Show worked answerHide worked answer
    1. M1: 750 + 5 and 3.5 - 0.05
    2. M1: (4/3) × π × 3.45³
    3. M1: 755 ÷ ((4/3) × π × 3.45³)
    4. A1: 4.39
    Answer: 4.39
    Combining Upper & Lower Bounds

  5. Question 5. The line y = 5 touches the curve with equation y = 3x² - 18x + c at one point
    Work out the value of c

    [4 marks]
    Show worked answerHide worked answer
    1. M1: 3≤ft((x - 3)² - 9) + c
    2. M1: 3(x - 3)² + c - 27
    3. M1: minimum value c - 27 = 5
    4. A1: c = 32
    Answer: c = 32
    Solving Quadratics by Completing the Square (a > 1)
📅 Free live lesson: Tuesday 17th NovemberSave your free place →

Mixed Topic Worksheet Grades 8/9: Day 084

Grades 8/9Calculator

  1. Question 1. Describe fully the single transformation that maps the graph of y = x² onto the graph of y = (x + 5)²

    Show worked answerHide worked answer
    1. B1: translation
    2. B1: by the vector beginpmatrix -5 0 endpmatrix
    Answer: Translation by beginpmatrix -5 0 endpmatrix
    Translations Along the x- & y-Axes
    [2 marks]

  2. Question 2. A cuboid has a 3 cm by 4 cm base. A space diagonal makes 60° with the base. Work out the height to 1 decimal place.

    Show worked answerHide worked answer
    1. M1: base diagonal 5, h = 5tan 60°
    2. A1: 8.7 cm
    Answer: 8.7 cm
    3D Trigonometry
    [2 marks]

  3. Question 3. The class 10 < m ≤ 25 has a frequency of 54.
    The class 25 < m ≤ 40 has a frequency of 36.
    Work out the frequency density of each class.

    Show worked answerHide worked answer
    1. M1: 54 ÷ 15 or 36 ÷ 15
    2. A1: 3.6
    3. A1: 2.4
    Answer: 3.6 and 2.4
    Sketching Histograms
    [3 marks]

  4. Question 4. A solid sphere has radius 3.5 cm, correct to 1 decimal place.
    The mass of the sphere is 750 g, correct to the nearest 10 g.
    Work out the upper bound of the density of the sphere in grams per cubic centimetre.
    density = dfracmassvolume
    volume of a sphere = dfrac43π r³
    Give your answer correct to 3 significant figures.

    Show worked answerHide worked answer
    1. M1: 750 + 5 and 3.5 - 0.05
    2. M1: (4/3) × π × 3.45³
    3. M1: 755 ÷ ((4/3) × π × 3.45³)
    4. A1: 4.39
    Answer: 4.39
    Combining Upper & Lower Bounds
    [4 marks]

  5. Question 5. The line y = 5 touches the curve with equation y = 3x² - 18x + c at one point
    Work out the value of c

    Show worked answerHide worked answer
    1. M1: 3≤ft((x - 3)² - 9) + c
    2. M1: 3(x - 3)² + c - 27
    3. M1: minimum value c - 27 = 5
    4. A1: c = 32
    Answer: c = 32
    Solving Quadratics by Completing the Square (a > 1)
    [4 marks]