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Mixed Topic Worksheet Grades 8/9: Day 036

Grades 8/9Calculator

  1. Question 1. Solve sin x = -0.35 for -180^° ≤ x ≤ 180^°. Give your answers correct to 1 decimal place

    Show worked answerHide worked answer
    1. M1: x = sin⁻¹(-0.35)
    2. M1: second solution is -180^° minus the first
    3. A1: -20.5^° and -159.5^°
    Answer: x = -20.5^° and x = -159.5^°
    Solving Trigonometric Equations Using a Graph
    [3 marks]

  2. Question 2. PT is a tangent to a circle with centre O, touching it at T. OT = 5 cm and PT = 12 cm. Work out the size of angle TPO. Give your answer correct to 1 decimal place.

    Show worked answerHide worked answer
    1. B1: angle OTP = 90° (tangent meets radius at right angle)
    2. M1: tan TPO = dfrac512
    3. A1: 22.6°
    Answer: 22.6°
    Circle Theorems
    [3 marks]

  3. Question 3. Use a change of sign to show that sqrt[3]20 is 2.7 correct to 1 decimal place

    Show worked answerHide worked answer
    1. M1: f(x) = x³ - 20, work out f(x) at the ends of the range
    2. M1: f(2.65) = -1.39... and f(2.75) = 0.797...
    3. C1: sign change so sqrt[3]20 is between 2.65 and 2.75, which is 2.7
    Answer: Shown: between 2.65 and 2.75
    Change of Signs
    [3 marks]

  4. Question 4. The graph of y = x² - 6x + 5 is translated by the vector beginpmatrix 2 -3 endpmatrix
    Work out the coordinates of the turning point of the translated graph.

    Show worked answerHide worked answer
    1. M1: x² - 6x + 5 = (x - 3)² - 4
    2. A1: turning point of the original graph (3, -4)
    3. M1: add 2 to x and subtract 3 from y
    4. A1: (5, -7)
    Answer: (5, -7)
    Translations Along the x- & y-Axes
    [4 marks]

  5. Question 5. Write dfrac√3√3 - 2 in the form a + b√3 where a and b are integers.

    Show worked answerHide worked answer
    1. M1: multiply top and bottom by √3 + 2
    2. M1: dfrac3 + 2√33 - 4
    3. A1: -3 - 2√3
    Answer: -3 - 2√3
    Rationalising Denominators of the Form a ± √b
    [3 marks]
📅 Free lesson: Tue 17th NovSave your place →

Mixed Topic Worksheet Grades 8/9: Day 036

Grades 8/9Calculator

  1. Question 1. Solve sin x = -0.35 for -180^° ≤ x ≤ 180^°. Give your answers correct to 1 decimal place

    [3 marks]
    Show worked answerHide worked answer
    1. M1: x = sin⁻¹(-0.35)
    2. M1: second solution is -180^° minus the first
    3. A1: -20.5^° and -159.5^°
    Answer: x = -20.5^° and x = -159.5^°
    Solving Trigonometric Equations Using a Graph

  2. Question 2. PT is a tangent to a circle with centre O, touching it at T. OT = 5 cm and PT = 12 cm. Work out the size of angle TPO. Give your answer correct to 1 decimal place.

    [3 marks]
    Show worked answerHide worked answer
    1. B1: angle OTP = 90° (tangent meets radius at right angle)
    2. M1: tan TPO = dfrac512
    3. A1: 22.6°
    Answer: 22.6°
    Circle Theorems

  3. Question 3. Use a change of sign to show that sqrt[3]20 is 2.7 correct to 1 decimal place

    [3 marks]
    Show worked answerHide worked answer
    1. M1: f(x) = x³ - 20, work out f(x) at the ends of the range
    2. M1: f(2.65) = -1.39... and f(2.75) = 0.797...
    3. C1: sign change so sqrt[3]20 is between 2.65 and 2.75, which is 2.7
    Answer: Shown: between 2.65 and 2.75
    Change of Signs

  4. Question 4. The graph of y = x² - 6x + 5 is translated by the vector beginpmatrix 2 -3 endpmatrix
    Work out the coordinates of the turning point of the translated graph.

    [4 marks]
    Show worked answerHide worked answer
    1. M1: x² - 6x + 5 = (x - 3)² - 4
    2. A1: turning point of the original graph (3, -4)
    3. M1: add 2 to x and subtract 3 from y
    4. A1: (5, -7)
    Answer: (5, -7)
    Translations Along the x- & y-Axes

  5. Question 5. Write dfrac√3√3 - 2 in the form a + b√3 where a and b are integers.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: multiply top and bottom by √3 + 2
    2. M1: dfrac3 + 2√33 - 4
    3. A1: -3 - 2√3
    Answer: -3 - 2√3
    Rationalising Denominators of the Form a ± √b
📅 Free live lesson: Tuesday 17th NovemberSave your free place →

Mixed Topic Worksheet Grades 8/9: Day 036

Grades 8/9Calculator

  1. Question 1. Solve sin x = -0.35 for -180^° ≤ x ≤ 180^°. Give your answers correct to 1 decimal place

    Show worked answerHide worked answer
    1. M1: x = sin⁻¹(-0.35)
    2. M1: second solution is -180^° minus the first
    3. A1: -20.5^° and -159.5^°
    Answer: x = -20.5^° and x = -159.5^°
    Solving Trigonometric Equations Using a Graph
    [3 marks]

  2. Question 2. PT is a tangent to a circle with centre O, touching it at T. OT = 5 cm and PT = 12 cm. Work out the size of angle TPO. Give your answer correct to 1 decimal place.

    Show worked answerHide worked answer
    1. B1: angle OTP = 90° (tangent meets radius at right angle)
    2. M1: tan TPO = dfrac512
    3. A1: 22.6°
    Answer: 22.6°
    Circle Theorems
    [3 marks]

  3. Question 3. Use a change of sign to show that sqrt[3]20 is 2.7 correct to 1 decimal place

    Show worked answerHide worked answer
    1. M1: f(x) = x³ - 20, work out f(x) at the ends of the range
    2. M1: f(2.65) = -1.39... and f(2.75) = 0.797...
    3. C1: sign change so sqrt[3]20 is between 2.65 and 2.75, which is 2.7
    Answer: Shown: between 2.65 and 2.75
    Change of Signs
    [3 marks]

  4. Question 4. The graph of y = x² - 6x + 5 is translated by the vector beginpmatrix 2 -3 endpmatrix
    Work out the coordinates of the turning point of the translated graph.

    Show worked answerHide worked answer
    1. M1: x² - 6x + 5 = (x - 3)² - 4
    2. A1: turning point of the original graph (3, -4)
    3. M1: add 2 to x and subtract 3 from y
    4. A1: (5, -7)
    Answer: (5, -7)
    Translations Along the x- & y-Axes
    [4 marks]

  5. Question 5. Write dfrac√3√3 - 2 in the form a + b√3 where a and b are integers.

    Show worked answerHide worked answer
    1. M1: multiply top and bottom by √3 + 2
    2. M1: dfrac3 + 2√33 - 4
    3. A1: -3 - 2√3
    Answer: -3 - 2√3
    Rationalising Denominators of the Form a ± √b
    [3 marks]