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

Mixed Topic Worksheet Grades 8/9: Day 001

Grades 8/9Non-calculator

  1. Question 1. The graph of y = asin x + b has a maximum point at (90^°, 5) and a minimum point at (270^°, -1). Work out the value of a and the value of b.

    Show worked answerHide worked answer
    1. M1: a = (5 - (-1)) ÷ 2
    2. A1: a = 3
    3. A1: b = 2
    Answer: a = 3 and b = 2
    Transforming Trigonometric Graphs
    [3 marks]

  2. Question 2. A right-angled triangle has shorter sides 4√3 cm and 3√3 cm. Work out the length of the hypotenuse. Give your answer in the form a√b.

    Show worked answerHide worked answer
    1. M1: square and add the two shorter sides: 48 + 27
    2. M1: √75
    3. A1: 5√3 cm
    Answer: 5√3 cm
    Simplifying Surds
    [3 marks]

  3. Question 3. The graph of y = x² is translated by the vector beginpmatrix 3 -4 endpmatrix Work out the x-coordinates of the points where the new graph crosses the x-axis

    Show worked answerHide worked answer
    1. M1: new equation is y = (x - 3)² - 4
    2. M1: (x - 3)² = 4
    3. A1: x = 1 and x = 5
    Answer: x = 1 and x = 5
    Translations Along the x- & y-Axes
    [3 marks]

  4. Question 4. The table shows the lengths, x metres, of some bridges. Assume values are spread evenly in each class and the median is the n/2th value. Work out an estimate for the median length.

    Show worked answerHide worked answer
    1. M1: 2 × 4, 3 × 6, 5 × 10, 1 × 20
    2. M1: 96 ÷ 2 = 48 and 48 - 26
    3. M1: 10 + 22 ÷ 5
    4. A1: 14.4
    Answer: 14.4
    Median from a Histogram
    Length, x (m)Frequency density0 < x ≤ 424 < x ≤ 10310 < x ≤ 20520 < x ≤ 401
    [4 marks]

  5. Question 5. Write 2x² - 12x + 5 in the form a(x + b)² + c

    Show worked answerHide worked answer
    1. M1: 2(x² - 6x) and 2(x-3)²
    2. M1: -18 seen
    3. A1: 2(x - 3)² - 13
    Answer: 2(x - 3)² - 13
    Solving Quadratics by Completing the Square (a > 1)
    [3 marks]
📅 Free lesson: Tue 17th NovSave your place →

Mixed Topic Worksheet Grades 8/9: Day 001

Grades 8/9Non-calculator

  1. Question 1. The graph of y = asin x + b has a maximum point at (90^°, 5) and a minimum point at (270^°, -1). Work out the value of a and the value of b.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: a = (5 - (-1)) ÷ 2
    2. A1: a = 3
    3. A1: b = 2
    Answer: a = 3 and b = 2
    Transforming Trigonometric Graphs

  2. Question 2. A right-angled triangle has shorter sides 4√3 cm and 3√3 cm. Work out the length of the hypotenuse. Give your answer in the form a√b.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: square and add the two shorter sides: 48 + 27
    2. M1: √75
    3. A1: 5√3 cm
    Answer: 5√3 cm
    Simplifying Surds

  3. Question 3. The graph of y = x² is translated by the vector beginpmatrix 3 -4 endpmatrix Work out the x-coordinates of the points where the new graph crosses the x-axis

    [3 marks]
    Show worked answerHide worked answer
    1. M1: new equation is y = (x - 3)² - 4
    2. M1: (x - 3)² = 4
    3. A1: x = 1 and x = 5
    Answer: x = 1 and x = 5
    Translations Along the x- & y-Axes

  4. Question 4. The table shows the lengths, x metres, of some bridges. Assume values are spread evenly in each class and the median is the n/2th value. Work out an estimate for the median length.

    [4 marks]
    Length, x (m)Frequency density0 < x ≤ 424 < x ≤ 10310 < x ≤ 20520 < x ≤ 401
    Show worked answerHide worked answer
    1. M1: 2 × 4, 3 × 6, 5 × 10, 1 × 20
    2. M1: 96 ÷ 2 = 48 and 48 - 26
    3. M1: 10 + 22 ÷ 5
    4. A1: 14.4
    Answer: 14.4
    Median from a Histogram

  5. Question 5. Write 2x² - 12x + 5 in the form a(x + b)² + c

    [3 marks]
    Show worked answerHide worked answer
    1. M1: 2(x² - 6x) and 2(x-3)²
    2. M1: -18 seen
    3. A1: 2(x - 3)² - 13
    Answer: 2(x - 3)² - 13
    Solving Quadratics by Completing the Square (a > 1)
📅 Free live lesson: Tuesday 17th NovemberSave your free place →

Mixed Topic Worksheet Grades 8/9: Day 001

Grades 8/9Non-calculator

  1. Question 1. The graph of y = asin x + b has a maximum point at (90^°, 5) and a minimum point at (270^°, -1). Work out the value of a and the value of b.

    Show worked answerHide worked answer
    1. M1: a = (5 - (-1)) ÷ 2
    2. A1: a = 3
    3. A1: b = 2
    Answer: a = 3 and b = 2
    Transforming Trigonometric Graphs
    [3 marks]

  2. Question 2. A right-angled triangle has shorter sides 4√3 cm and 3√3 cm. Work out the length of the hypotenuse. Give your answer in the form a√b.

    Show worked answerHide worked answer
    1. M1: square and add the two shorter sides: 48 + 27
    2. M1: √75
    3. A1: 5√3 cm
    Answer: 5√3 cm
    Simplifying Surds
    [3 marks]

  3. Question 3. The graph of y = x² is translated by the vector beginpmatrix 3 -4 endpmatrix Work out the x-coordinates of the points where the new graph crosses the x-axis

    Show worked answerHide worked answer
    1. M1: new equation is y = (x - 3)² - 4
    2. M1: (x - 3)² = 4
    3. A1: x = 1 and x = 5
    Answer: x = 1 and x = 5
    Translations Along the x- & y-Axes
    [3 marks]

  4. Question 4. The table shows the lengths, x metres, of some bridges. Assume values are spread evenly in each class and the median is the n/2th value. Work out an estimate for the median length.

    Show worked answerHide worked answer
    1. M1: 2 × 4, 3 × 6, 5 × 10, 1 × 20
    2. M1: 96 ÷ 2 = 48 and 48 - 26
    3. M1: 10 + 22 ÷ 5
    4. A1: 14.4
    Answer: 14.4
    Median from a Histogram
    Length, x (m)Frequency density0 < x ≤ 424 < x ≤ 10310 < x ≤ 20520 < x ≤ 401
    [4 marks]

  5. Question 5. Write 2x² - 12x + 5 in the form a(x + b)² + c

    Show worked answerHide worked answer
    1. M1: 2(x² - 6x) and 2(x-3)²
    2. M1: -18 seen
    3. A1: 2(x - 3)² - 13
    Answer: 2(x - 3)² - 13
    Solving Quadratics by Completing the Square (a > 1)
    [3 marks]