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

Mixed Topic Worksheet Grades 8/9: Day 048

Grades 8/9Calculator

  1. Question 1. Find all the values of x between 0° and 360° for which tan x = -1.

    Show worked answerHide worked answer
    1. M1: tan⁻¹(-1) = -45°, then add 180° and 360°
    2. A1: 135° and 315°
    Answer: 135° and 315°
    Sketching sin, cos & tan
    [2 marks]

  2. Question 2. Frequency densities: 0 < w ≤ 20 is 1.5 and 20 < w ≤ 40 is 3.5. Work out an estimate for the median. Give your answer to 1 decimal place.

    Show worked answerHide worked answer
    1. M1: frequencies 30 and 70; the 50th value is 20 into the second class
    2. A1: 20 + 20/70 × 20 = 25.7
    Answer: 25.7
    Median from a Histogram
    [2 marks]

  3. Question 3. The graph of y = sin x is translated by the vector beginpmatrix 90 2 endpmatrix
    Write down the equation of the translated graph.

    Show worked answerHide worked answer
    1. B1: x replaced with x - 90
    2. B1: + 2 for the move up
    3. B1: y = sin(x - 90) + 2
    Answer: y = sin(x - 90) + 2
    Translations Along the x- & y-Axes
    [3 marks]

  4. Question 4. Solve the simultaneous equations
    x² + y² = 25
    y = x - 1

    Show worked answerHide worked answer
    1. M1: x² + (x - 1)² = 25 so x² - x - 12 = 0
    2. M1: (x - 4)(x + 3) = 0
    3. A2: x = 4, y = 3 and x = -3, y = -4
    Answer: x = 4, y = 3 or x = -3, y = -4
    Solving Quadratic Simultaneous Equations
    [4 marks]

  5. Question 5. The circle C has equation x² + y² = 40 The point P lies on C. P has x-coordinate -6 and a positive y-coordinate. Find an equation of the tangent to C at P.

    Show worked answerHide worked answer
    1. M1: y² = 40 - 6² so y = 2 and P = (-6, 2)
    2. M1: gradient of the tangent = 3 and y - 2 = 3(x + 6)
    3. A1: y = 3x + 20
    Answer: y = 3x + 20
    Finding Equations of Tangents to Circles
    [3 marks]
📅 Free lesson: Tue 17th NovSave your place →

Mixed Topic Worksheet Grades 8/9: Day 048

Grades 8/9Calculator

  1. Question 1. Find all the values of x between 0° and 360° for which tan x = -1.

    [2 marks]
    Show worked answerHide worked answer
    1. M1: tan⁻¹(-1) = -45°, then add 180° and 360°
    2. A1: 135° and 315°
    Answer: 135° and 315°
    Sketching sin, cos & tan

  2. Question 2. Frequency densities: 0 < w ≤ 20 is 1.5 and 20 < w ≤ 40 is 3.5. Work out an estimate for the median. Give your answer to 1 decimal place.

    [2 marks]
    Show worked answerHide worked answer
    1. M1: frequencies 30 and 70; the 50th value is 20 into the second class
    2. A1: 20 + 20/70 × 20 = 25.7
    Answer: 25.7
    Median from a Histogram

  3. Question 3. The graph of y = sin x is translated by the vector beginpmatrix 90 2 endpmatrix
    Write down the equation of the translated graph.

    [3 marks]
    Show worked answerHide worked answer
    1. B1: x replaced with x - 90
    2. B1: + 2 for the move up
    3. B1: y = sin(x - 90) + 2
    Answer: y = sin(x - 90) + 2
    Translations Along the x- & y-Axes

  4. Question 4. Solve the simultaneous equations
    x² + y² = 25
    y = x - 1

    [4 marks]
    Show worked answerHide worked answer
    1. M1: x² + (x - 1)² = 25 so x² - x - 12 = 0
    2. M1: (x - 4)(x + 3) = 0
    3. A2: x = 4, y = 3 and x = -3, y = -4
    Answer: x = 4, y = 3 or x = -3, y = -4
    Solving Quadratic Simultaneous Equations

  5. Question 5. The circle C has equation x² + y² = 40 The point P lies on C. P has x-coordinate -6 and a positive y-coordinate. Find an equation of the tangent to C at P.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: y² = 40 - 6² so y = 2 and P = (-6, 2)
    2. M1: gradient of the tangent = 3 and y - 2 = 3(x + 6)
    3. A1: y = 3x + 20
    Answer: y = 3x + 20
    Finding Equations of Tangents to Circles
📅 Free live lesson: Tuesday 17th NovemberSave your free place →

Mixed Topic Worksheet Grades 8/9: Day 048

Grades 8/9Calculator

  1. Question 1. Find all the values of x between 0° and 360° for which tan x = -1.

    Show worked answerHide worked answer
    1. M1: tan⁻¹(-1) = -45°, then add 180° and 360°
    2. A1: 135° and 315°
    Answer: 135° and 315°
    Sketching sin, cos & tan
    [2 marks]

  2. Question 2. Frequency densities: 0 < w ≤ 20 is 1.5 and 20 < w ≤ 40 is 3.5. Work out an estimate for the median. Give your answer to 1 decimal place.

    Show worked answerHide worked answer
    1. M1: frequencies 30 and 70; the 50th value is 20 into the second class
    2. A1: 20 + 20/70 × 20 = 25.7
    Answer: 25.7
    Median from a Histogram
    [2 marks]

  3. Question 3. The graph of y = sin x is translated by the vector beginpmatrix 90 2 endpmatrix
    Write down the equation of the translated graph.

    Show worked answerHide worked answer
    1. B1: x replaced with x - 90
    2. B1: + 2 for the move up
    3. B1: y = sin(x - 90) + 2
    Answer: y = sin(x - 90) + 2
    Translations Along the x- & y-Axes
    [3 marks]

  4. Question 4. Solve the simultaneous equations
    x² + y² = 25
    y = x - 1

    Show worked answerHide worked answer
    1. M1: x² + (x - 1)² = 25 so x² - x - 12 = 0
    2. M1: (x - 4)(x + 3) = 0
    3. A2: x = 4, y = 3 and x = -3, y = -4
    Answer: x = 4, y = 3 or x = -3, y = -4
    Solving Quadratic Simultaneous Equations
    [4 marks]

  5. Question 5. The circle C has equation x² + y² = 40 The point P lies on C. P has x-coordinate -6 and a positive y-coordinate. Find an equation of the tangent to C at P.

    Show worked answerHide worked answer
    1. M1: y² = 40 - 6² so y = 2 and P = (-6, 2)
    2. M1: gradient of the tangent = 3 and y - 2 = 3(x + 6)
    3. A1: y = 3x + 20
    Answer: y = 3x + 20
    Finding Equations of Tangents to Circles
    [3 marks]