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

Mixed Topic Worksheet Grades 8/9: Day 022

Grades 8/9Calculator

  1. Question 1. The graph of y = cos x is drawn for 0° ≤ x ≤ 360°. The line y = -0.8 meets the graph at x = 143.1° and at x = b. Work out the value of b.

    Show worked answerHide worked answer
    1. M1: the graph is symmetrical about x = 180°
    2. A1: b = 360° - 143.1° = 216.9°
    Answer: b = 216.9°
    Sketching sin, cos & tan
    [2 marks]

  2. Question 2. p = 3.7, correct to 1 decimal place.
    q = 15, correct to the nearest integer.
    Work out the upper bound of p × q

    Show worked answerHide worked answer
    1. M1: upper bound of p is 3.75
    2. M1: upper bound of q is 15.5, and 3.75 × 15.5
    3. A1: 58.125
    Answer: 58.125
    Combining Upper & Lower Bounds
    [3 marks]

  3. Question 3. Solve dfracx² - x - 6x² - 4 = dfrac1x
    Give your solutions correct to 2 decimal places

    Show worked answerHide worked answer
    1. M1: dfrac(x - 3)(x + 2)(x - 2)(x + 2) = dfracx - 3x - 2 and x(x - 3) = x - 2
    2. M1: x² - 4x + 2 = 0
    3. A1: x = 3.41 or x = 0.59
    Answer: x = 3.41 or x = 0.59
    Algebraic Fractions Involving Factorising
    [3 marks]

  4. Question 4. The graph of y = x² + 2x - 3 is translated by the vector beginpmatrix 3 -2 endpmatrix
    Find the equation of the translated graph.
    Give your answer in the form y = x² + bx + c

    Show worked answerHide worked answer
    1. M1: replace x with x - 3: (x - 3)² + 2(x - 3) - 3
    2. M1: subtract 2: y = (x - 3)² + 2(x - 3) - 5
    3. M1: x² - 6x + 9 + 2x - 6 - 5
    4. A1: y = x² - 4x - 2
    Answer: y = x² - 4x - 2
    Translations Along the x- & y-Axes
    [4 marks]

  5. Question 5. overrightarrowWX = 2mathbfa + 3mathbfb
    overrightarrowWY = 5mathbfa + 5mathbfb
    overrightarrowWZ = 14mathbfa + 11mathbfb
    Prove, using vectors, that X, Y and Z lie on a straight line.

    Show worked answerHide worked answer
    1. M1: overrightarrowXY = overrightarrowWY - overrightarrowWX = 3mathbfa + 2mathbfb or overrightarrowYZ = overrightarrowWZ - overrightarrowWY
    2. M1: overrightarrowYZ = 9mathbfa + 6mathbfb = 3overrightarrowXY
    3. C1: parallel vectors with the point Y in common, so X, Y, Z lie on a straight line
    Answer: proof: overrightarrowYZ = 3overrightarrowXY
    Vectors Along a Straight Line
    [3 marks]
📅 Free lesson: Tue 17th NovSave your place →

Mixed Topic Worksheet Grades 8/9: Day 022

Grades 8/9Calculator

  1. Question 1. The graph of y = cos x is drawn for 0° ≤ x ≤ 360°. The line y = -0.8 meets the graph at x = 143.1° and at x = b. Work out the value of b.

    [2 marks]
    Show worked answerHide worked answer
    1. M1: the graph is symmetrical about x = 180°
    2. A1: b = 360° - 143.1° = 216.9°
    Answer: b = 216.9°
    Sketching sin, cos & tan

  2. Question 2. p = 3.7, correct to 1 decimal place.
    q = 15, correct to the nearest integer.
    Work out the upper bound of p × q

    [3 marks]
    Show worked answerHide worked answer
    1. M1: upper bound of p is 3.75
    2. M1: upper bound of q is 15.5, and 3.75 × 15.5
    3. A1: 58.125
    Answer: 58.125
    Combining Upper & Lower Bounds

  3. Question 3. Solve dfracx² - x - 6x² - 4 = dfrac1x
    Give your solutions correct to 2 decimal places

    [3 marks]
    Show worked answerHide worked answer
    1. M1: dfrac(x - 3)(x + 2)(x - 2)(x + 2) = dfracx - 3x - 2 and x(x - 3) = x - 2
    2. M1: x² - 4x + 2 = 0
    3. A1: x = 3.41 or x = 0.59
    Answer: x = 3.41 or x = 0.59
    Algebraic Fractions Involving Factorising

  4. Question 4. The graph of y = x² + 2x - 3 is translated by the vector beginpmatrix 3 -2 endpmatrix
    Find the equation of the translated graph.
    Give your answer in the form y = x² + bx + c

    [4 marks]
    Show worked answerHide worked answer
    1. M1: replace x with x - 3: (x - 3)² + 2(x - 3) - 3
    2. M1: subtract 2: y = (x - 3)² + 2(x - 3) - 5
    3. M1: x² - 6x + 9 + 2x - 6 - 5
    4. A1: y = x² - 4x - 2
    Answer: y = x² - 4x - 2
    Translations Along the x- & y-Axes

  5. Question 5. overrightarrowWX = 2mathbfa + 3mathbfb
    overrightarrowWY = 5mathbfa + 5mathbfb
    overrightarrowWZ = 14mathbfa + 11mathbfb
    Prove, using vectors, that X, Y and Z lie on a straight line.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: overrightarrowXY = overrightarrowWY - overrightarrowWX = 3mathbfa + 2mathbfb or overrightarrowYZ = overrightarrowWZ - overrightarrowWY
    2. M1: overrightarrowYZ = 9mathbfa + 6mathbfb = 3overrightarrowXY
    3. C1: parallel vectors with the point Y in common, so X, Y, Z lie on a straight line
    Answer: proof: overrightarrowYZ = 3overrightarrowXY
    Vectors Along a Straight Line
📅 Free live lesson: Tuesday 17th NovemberSave your free place →

Mixed Topic Worksheet Grades 8/9: Day 022

Grades 8/9Calculator

  1. Question 1. The graph of y = cos x is drawn for 0° ≤ x ≤ 360°. The line y = -0.8 meets the graph at x = 143.1° and at x = b. Work out the value of b.

    Show worked answerHide worked answer
    1. M1: the graph is symmetrical about x = 180°
    2. A1: b = 360° - 143.1° = 216.9°
    Answer: b = 216.9°
    Sketching sin, cos & tan
    [2 marks]

  2. Question 2. p = 3.7, correct to 1 decimal place.
    q = 15, correct to the nearest integer.
    Work out the upper bound of p × q

    Show worked answerHide worked answer
    1. M1: upper bound of p is 3.75
    2. M1: upper bound of q is 15.5, and 3.75 × 15.5
    3. A1: 58.125
    Answer: 58.125
    Combining Upper & Lower Bounds
    [3 marks]

  3. Question 3. Solve dfracx² - x - 6x² - 4 = dfrac1x
    Give your solutions correct to 2 decimal places

    Show worked answerHide worked answer
    1. M1: dfrac(x - 3)(x + 2)(x - 2)(x + 2) = dfracx - 3x - 2 and x(x - 3) = x - 2
    2. M1: x² - 4x + 2 = 0
    3. A1: x = 3.41 or x = 0.59
    Answer: x = 3.41 or x = 0.59
    Algebraic Fractions Involving Factorising
    [3 marks]

  4. Question 4. The graph of y = x² + 2x - 3 is translated by the vector beginpmatrix 3 -2 endpmatrix
    Find the equation of the translated graph.
    Give your answer in the form y = x² + bx + c

    Show worked answerHide worked answer
    1. M1: replace x with x - 3: (x - 3)² + 2(x - 3) - 3
    2. M1: subtract 2: y = (x - 3)² + 2(x - 3) - 5
    3. M1: x² - 6x + 9 + 2x - 6 - 5
    4. A1: y = x² - 4x - 2
    Answer: y = x² - 4x - 2
    Translations Along the x- & y-Axes
    [4 marks]

  5. Question 5. overrightarrowWX = 2mathbfa + 3mathbfb
    overrightarrowWY = 5mathbfa + 5mathbfb
    overrightarrowWZ = 14mathbfa + 11mathbfb
    Prove, using vectors, that X, Y and Z lie on a straight line.

    Show worked answerHide worked answer
    1. M1: overrightarrowXY = overrightarrowWY - overrightarrowWX = 3mathbfa + 2mathbfb or overrightarrowYZ = overrightarrowWZ - overrightarrowWY
    2. M1: overrightarrowYZ = 9mathbfa + 6mathbfb = 3overrightarrowXY
    3. C1: parallel vectors with the point Y in common, so X, Y, Z lie on a straight line
    Answer: proof: overrightarrowYZ = 3overrightarrowXY
    Vectors Along a Straight Line
    [3 marks]