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

Mixed Topic Worksheet Grades 8/9: Day 070

Grades 8/9Calculator

  1. Question 1. Solve 7sin x + 2 = 0 for 0^° ≤ x ≤ 360^°. Give your answers correct to 1 decimal place.

    Show worked answerHide worked answer
    1. M1: sin x = -2/7, so the acute angle is sin⁻¹2/7
    2. A1: x = 196.6^° and x = 343.4^°
    Answer: x = 196.6^° and x = 343.4^°
    Solving Trigonometric Equations Using a Graph
    [2 marks]

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

    Show worked answerHide worked answer
    1. M1: (x + 6)²
    2. A1: (x + 6)² - 41
    Answer: (x + 6)² - 41
    Solving Quadratics by Completing the Square (a = 1)
    [2 marks]

  3. Question 3. Show that the equation 2x + x = 10 has a solution between x = 2.8 and x = 2.9

    Show worked answerHide worked answer
    1. M1: f(x) = 2x + x - 10, work out f(2.8) and f(2.9)
    2. M1: f(2.8) = -0.236 < 0 and f(2.9) = 0.364 > 0, sign change
    Answer: Shown
    Change of Signs
    [2 marks]

  4. Question 4. PT is a tangent to a circle, centre O, at T.
    Angle OPT = 24^°.
    Work out angle POT. Give reasons. [3]

    Show worked answerHide worked answer
    1. B1: angle OTP = 90^° (tangent is perpendicular to the radius)
    2. M1: angles in a triangle sum to 180^°: 180 - 90 - 24
    3. A1: 66^°
    Answer: 66^°
    Combining Circle Theorems
    [3 marks]

  5. Question 5. The circle C, centre O, has equation x² + y² = 80
    The tangent to C at the point P has gradient -2
    P lies in the first quadrant.
    Work out the coordinates of P.

    Show worked answerHide worked answer
    1. M1: m_OP = dfrac12, so P lies on y = dfrac12x
    2. M1: x² + ≤ft(dfracx2)² = 80, giving x² = 64
    3. A1: (8, 4)
    Answer: (8, 4)
    Finding Equations of Tangents to Circles
    [3 marks]
📅 Free lesson: Tue 17th NovSave your place →

Mixed Topic Worksheet Grades 8/9: Day 070

Grades 8/9Calculator

  1. Question 1. Solve 7sin x + 2 = 0 for 0^° ≤ x ≤ 360^°. Give your answers correct to 1 decimal place.

    [2 marks]
    Show worked answerHide worked answer
    1. M1: sin x = -2/7, so the acute angle is sin⁻¹2/7
    2. A1: x = 196.6^° and x = 343.4^°
    Answer: x = 196.6^° and x = 343.4^°
    Solving Trigonometric Equations Using a Graph

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

    [2 marks]
    Show worked answerHide worked answer
    1. M1: (x + 6)²
    2. A1: (x + 6)² - 41
    Answer: (x + 6)² - 41
    Solving Quadratics by Completing the Square (a = 1)

  3. Question 3. Show that the equation 2x + x = 10 has a solution between x = 2.8 and x = 2.9

    [2 marks]
    Show worked answerHide worked answer
    1. M1: f(x) = 2x + x - 10, work out f(2.8) and f(2.9)
    2. M1: f(2.8) = -0.236 < 0 and f(2.9) = 0.364 > 0, sign change
    Answer: Shown
    Change of Signs

  4. Question 4. PT is a tangent to a circle, centre O, at T.
    Angle OPT = 24^°.
    Work out angle POT. Give reasons. [3]

    [3 marks]
    Show worked answerHide worked answer
    1. B1: angle OTP = 90^° (tangent is perpendicular to the radius)
    2. M1: angles in a triangle sum to 180^°: 180 - 90 - 24
    3. A1: 66^°
    Answer: 66^°
    Combining Circle Theorems

  5. Question 5. The circle C, centre O, has equation x² + y² = 80
    The tangent to C at the point P has gradient -2
    P lies in the first quadrant.
    Work out the coordinates of P.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: m_OP = dfrac12, so P lies on y = dfrac12x
    2. M1: x² + ≤ft(dfracx2)² = 80, giving x² = 64
    3. A1: (8, 4)
    Answer: (8, 4)
    Finding Equations of Tangents to Circles
📅 Free live lesson: Tuesday 17th NovemberSave your free place →

Mixed Topic Worksheet Grades 8/9: Day 070

Grades 8/9Calculator

  1. Question 1. Solve 7sin x + 2 = 0 for 0^° ≤ x ≤ 360^°. Give your answers correct to 1 decimal place.

    Show worked answerHide worked answer
    1. M1: sin x = -2/7, so the acute angle is sin⁻¹2/7
    2. A1: x = 196.6^° and x = 343.4^°
    Answer: x = 196.6^° and x = 343.4^°
    Solving Trigonometric Equations Using a Graph
    [2 marks]

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

    Show worked answerHide worked answer
    1. M1: (x + 6)²
    2. A1: (x + 6)² - 41
    Answer: (x + 6)² - 41
    Solving Quadratics by Completing the Square (a = 1)
    [2 marks]

  3. Question 3. Show that the equation 2x + x = 10 has a solution between x = 2.8 and x = 2.9

    Show worked answerHide worked answer
    1. M1: f(x) = 2x + x - 10, work out f(2.8) and f(2.9)
    2. M1: f(2.8) = -0.236 < 0 and f(2.9) = 0.364 > 0, sign change
    Answer: Shown
    Change of Signs
    [2 marks]

  4. Question 4. PT is a tangent to a circle, centre O, at T.
    Angle OPT = 24^°.
    Work out angle POT. Give reasons. [3]

    Show worked answerHide worked answer
    1. B1: angle OTP = 90^° (tangent is perpendicular to the radius)
    2. M1: angles in a triangle sum to 180^°: 180 - 90 - 24
    3. A1: 66^°
    Answer: 66^°
    Combining Circle Theorems
    [3 marks]

  5. Question 5. The circle C, centre O, has equation x² + y² = 80
    The tangent to C at the point P has gradient -2
    P lies in the first quadrant.
    Work out the coordinates of P.

    Show worked answerHide worked answer
    1. M1: m_OP = dfrac12, so P lies on y = dfrac12x
    2. M1: x² + ≤ft(dfracx2)² = 80, giving x² = 64
    3. A1: (8, 4)
    Answer: (8, 4)
    Finding Equations of Tangents to Circles
    [3 marks]