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

Mixed Topic Worksheet Grades 8/9: Day 066

Grades 8/9Calculator

  1. Question 1. y = x³ - 4x is translated 2 units right and 5 units up to give y = f(x).
    Work out f(x) in the form y = x³ + ax² + bx + c where a, b, c are integers.

    Show worked answerHide worked answer
    1. M1: (x - 2)³ - 4(x - 2) + 5
    2. M1: x³ - 6x² + 12x - 8 - 4x + 8 + 5
    3. A1: x³ - 6x² + 8x + 5
    Answer: f(x) = x³ - 6x² + 8x + 5
    Translations Along the x- & y-Axes
    [3 marks]

  2. Question 2. Solve 4sin x - 1 = 2 for 0^° ≤ x ≤ 360^°. Give your answers correct to 1 decimal place

    Show worked answerHide worked answer
    1. M1: 4sin x = 3, so x = sin⁻¹dfrac34
    2. M1: 180^° - 48.6^°
    3. A1: 48.6^° and 131.4^°
    Answer: x = 48.6^° and x = 131.4^°
    Solving Trigonometric Equations Using a Graph
    [3 marks]

  3. Question 3. A car travels 120 m, correct to the nearest 10 m, in 8.0 s, correct to the nearest 0.1 s. Work out the lower bound of its speed in m/s. Give your answer to 1 decimal place.

    Show worked answerHide worked answer
    1. M1: 120 - 5/8.0 + 0.05 (lower distance over upper time)
    2. A1: 14.3 m/s
    Answer: 14.3 m/s
    Combining Upper & Lower Bounds
    [3 marks]

  4. Question 4. A, B, C and D are points on a circle with centre O. ABCD is a cyclic quadrilateral and B is on the major arc AC. Angle AOC = 140°. Work out the size of angle ADC. Give reasons.

    Show worked answerHide worked answer
    1. B1: angle ABC = 140 ÷ 2 = 70° (angle at the centre is twice the angle at the circumference)
    2. M1: 180 - 70
    3. A1: 110° (opposite angles of a cyclic quadrilateral add to 180°)
    Answer: 110°
    Circle Theorems
    [3 marks]

  5. Question 5. Solve 6x² + x - 2 ≤ 0

    Show worked answerHide worked answer
    1. M1: (3x + 2)(2x - 1) ≤ 0
    2. M1: critical values -dfrac23 and dfrac12
    3. A1: -dfrac23 ≤ x ≤ dfrac12
    Answer: -dfrac23 ≤ x ≤ dfrac12
    Solving Quadratic Inequalities
    [3 marks]
📅 Free lesson: Tue 17th NovSave your place →

Mixed Topic Worksheet Grades 8/9: Day 066

Grades 8/9Calculator

  1. Question 1. y = x³ - 4x is translated 2 units right and 5 units up to give y = f(x).
    Work out f(x) in the form y = x³ + ax² + bx + c where a, b, c are integers.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: (x - 2)³ - 4(x - 2) + 5
    2. M1: x³ - 6x² + 12x - 8 - 4x + 8 + 5
    3. A1: x³ - 6x² + 8x + 5
    Answer: f(x) = x³ - 6x² + 8x + 5
    Translations Along the x- & y-Axes

  2. Question 2. Solve 4sin x - 1 = 2 for 0^° ≤ x ≤ 360^°. Give your answers correct to 1 decimal place

    [3 marks]
    Show worked answerHide worked answer
    1. M1: 4sin x = 3, so x = sin⁻¹dfrac34
    2. M1: 180^° - 48.6^°
    3. A1: 48.6^° and 131.4^°
    Answer: x = 48.6^° and x = 131.4^°
    Solving Trigonometric Equations Using a Graph

  3. Question 3. A car travels 120 m, correct to the nearest 10 m, in 8.0 s, correct to the nearest 0.1 s. Work out the lower bound of its speed in m/s. Give your answer to 1 decimal place.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: 120 - 5/8.0 + 0.05 (lower distance over upper time)
    2. A1: 14.3 m/s
    Answer: 14.3 m/s
    Combining Upper & Lower Bounds

  4. Question 4. A, B, C and D are points on a circle with centre O. ABCD is a cyclic quadrilateral and B is on the major arc AC. Angle AOC = 140°. Work out the size of angle ADC. Give reasons.

    [3 marks]
    Show worked answerHide worked answer
    1. B1: angle ABC = 140 ÷ 2 = 70° (angle at the centre is twice the angle at the circumference)
    2. M1: 180 - 70
    3. A1: 110° (opposite angles of a cyclic quadrilateral add to 180°)
    Answer: 110°
    Circle Theorems

  5. Question 5. Solve 6x² + x - 2 ≤ 0

    [3 marks]
    Show worked answerHide worked answer
    1. M1: (3x + 2)(2x - 1) ≤ 0
    2. M1: critical values -dfrac23 and dfrac12
    3. A1: -dfrac23 ≤ x ≤ dfrac12
    Answer: -dfrac23 ≤ x ≤ dfrac12
    Solving Quadratic Inequalities
📅 Free live lesson: Tuesday 17th NovemberSave your free place →

Mixed Topic Worksheet Grades 8/9: Day 066

Grades 8/9Calculator

  1. Question 1. y = x³ - 4x is translated 2 units right and 5 units up to give y = f(x).
    Work out f(x) in the form y = x³ + ax² + bx + c where a, b, c are integers.

    Show worked answerHide worked answer
    1. M1: (x - 2)³ - 4(x - 2) + 5
    2. M1: x³ - 6x² + 12x - 8 - 4x + 8 + 5
    3. A1: x³ - 6x² + 8x + 5
    Answer: f(x) = x³ - 6x² + 8x + 5
    Translations Along the x- & y-Axes
    [3 marks]

  2. Question 2. Solve 4sin x - 1 = 2 for 0^° ≤ x ≤ 360^°. Give your answers correct to 1 decimal place

    Show worked answerHide worked answer
    1. M1: 4sin x = 3, so x = sin⁻¹dfrac34
    2. M1: 180^° - 48.6^°
    3. A1: 48.6^° and 131.4^°
    Answer: x = 48.6^° and x = 131.4^°
    Solving Trigonometric Equations Using a Graph
    [3 marks]

  3. Question 3. A car travels 120 m, correct to the nearest 10 m, in 8.0 s, correct to the nearest 0.1 s. Work out the lower bound of its speed in m/s. Give your answer to 1 decimal place.

    Show worked answerHide worked answer
    1. M1: 120 - 5/8.0 + 0.05 (lower distance over upper time)
    2. A1: 14.3 m/s
    Answer: 14.3 m/s
    Combining Upper & Lower Bounds
    [3 marks]

  4. Question 4. A, B, C and D are points on a circle with centre O. ABCD is a cyclic quadrilateral and B is on the major arc AC. Angle AOC = 140°. Work out the size of angle ADC. Give reasons.

    Show worked answerHide worked answer
    1. B1: angle ABC = 140 ÷ 2 = 70° (angle at the centre is twice the angle at the circumference)
    2. M1: 180 - 70
    3. A1: 110° (opposite angles of a cyclic quadrilateral add to 180°)
    Answer: 110°
    Circle Theorems
    [3 marks]

  5. Question 5. Solve 6x² + x - 2 ≤ 0

    Show worked answerHide worked answer
    1. M1: (3x + 2)(2x - 1) ≤ 0
    2. M1: critical values -dfrac23 and dfrac12
    3. A1: -dfrac23 ≤ x ≤ dfrac12
    Answer: -dfrac23 ≤ x ≤ dfrac12
    Solving Quadratic Inequalities
    [3 marks]