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

Mixed Topic Worksheet Grades 8/9: Day 067

Grades 8/9Non-calculator

  1. Question 1. After a reflection in the y-axis, the image of the graph of y = f(x) is the graph of y = 2x³ - 7x² + x + 4.
    Write down f(x).

    Show worked answerHide worked answer
    1. M1: replace x with -x: 2(-x)³ - 7(-x)² + (-x) + 4
    2. A1: y = -2x³ - 7x² - x + 4
    Answer: y = -2x³ - 7x² - x + 4
    Reflections in the x- & y-Axes
    [2 marks]

  2. Question 2. The graph of y = sin x is translated by the vector beginpmatrix 40 -2 endpmatrix. Write down the coordinates of the first maximum point of the new graph.

    Show worked answerHide worked answer
    1. M1: maximum of sin x is (90^°, 1)
    2. A1: add the vector: (130^°, -1)
    Answer: (130^°, -1)
    Transforming Trigonometric Graphs
    [2 marks]

  3. Question 3. Simplify √75 - √12 giving your answer in the form a√3 where a is an integer.

    Show worked answerHide worked answer
    1. M1: √75 = 5√3
    2. M1: √12 = 2√3
    3. A1: 3√3
    Answer: 3√3
    Simplifying Surds
    [3 marks]

  4. Question 4. y is inversely proportional to the square root of x.
    y = 5 when x = 16.
    Find the value of y when x = 64.

    Show worked answerHide worked answer
    1. M1: 5 = k ÷ √16
    2. M1: y = 20 ÷ √64
    3. A1: 2.5
    Answer: 2.5
    Direct & Inverse Proportion with Functions
    [3 marks]

  5. Question 5. Solve 2x² - x - 6 > 0 [3]

    Show worked answerHide worked answer
    1. M1: (2x + 3)(x - 2) = 0 so critical values -dfrac32 and 2
    2. M1: sketch or sign test for > 0
    3. A1: x < -dfrac32 or x > 2
    Answer: x < -dfrac32 or x > 2
    Solving Quadratic Inequalities
    [3 marks]
📅 Free lesson: Tue 17th NovSave your place →

Mixed Topic Worksheet Grades 8/9: Day 067

Grades 8/9Non-calculator

  1. Question 1. After a reflection in the y-axis, the image of the graph of y = f(x) is the graph of y = 2x³ - 7x² + x + 4.
    Write down f(x).

    [2 marks]
    Show worked answerHide worked answer
    1. M1: replace x with -x: 2(-x)³ - 7(-x)² + (-x) + 4
    2. A1: y = -2x³ - 7x² - x + 4
    Answer: y = -2x³ - 7x² - x + 4
    Reflections in the x- & y-Axes

  2. Question 2. The graph of y = sin x is translated by the vector beginpmatrix 40 -2 endpmatrix. Write down the coordinates of the first maximum point of the new graph.

    [2 marks]
    Show worked answerHide worked answer
    1. M1: maximum of sin x is (90^°, 1)
    2. A1: add the vector: (130^°, -1)
    Answer: (130^°, -1)
    Transforming Trigonometric Graphs

  3. Question 3. Simplify √75 - √12 giving your answer in the form a√3 where a is an integer.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: √75 = 5√3
    2. M1: √12 = 2√3
    3. A1: 3√3
    Answer: 3√3
    Simplifying Surds

  4. Question 4. y is inversely proportional to the square root of x.
    y = 5 when x = 16.
    Find the value of y when x = 64.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: 5 = k ÷ √16
    2. M1: y = 20 ÷ √64
    3. A1: 2.5
    Answer: 2.5
    Direct & Inverse Proportion with Functions

  5. Question 5. Solve 2x² - x - 6 > 0 [3]

    [3 marks]
    Show worked answerHide worked answer
    1. M1: (2x + 3)(x - 2) = 0 so critical values -dfrac32 and 2
    2. M1: sketch or sign test for > 0
    3. A1: x < -dfrac32 or x > 2
    Answer: x < -dfrac32 or x > 2
    Solving Quadratic Inequalities
📅 Free live lesson: Tuesday 17th NovemberSave your free place →

Mixed Topic Worksheet Grades 8/9: Day 067

Grades 8/9Non-calculator

  1. Question 1. After a reflection in the y-axis, the image of the graph of y = f(x) is the graph of y = 2x³ - 7x² + x + 4.
    Write down f(x).

    Show worked answerHide worked answer
    1. M1: replace x with -x: 2(-x)³ - 7(-x)² + (-x) + 4
    2. A1: y = -2x³ - 7x² - x + 4
    Answer: y = -2x³ - 7x² - x + 4
    Reflections in the x- & y-Axes
    [2 marks]

  2. Question 2. The graph of y = sin x is translated by the vector beginpmatrix 40 -2 endpmatrix. Write down the coordinates of the first maximum point of the new graph.

    Show worked answerHide worked answer
    1. M1: maximum of sin x is (90^°, 1)
    2. A1: add the vector: (130^°, -1)
    Answer: (130^°, -1)
    Transforming Trigonometric Graphs
    [2 marks]

  3. Question 3. Simplify √75 - √12 giving your answer in the form a√3 where a is an integer.

    Show worked answerHide worked answer
    1. M1: √75 = 5√3
    2. M1: √12 = 2√3
    3. A1: 3√3
    Answer: 3√3
    Simplifying Surds
    [3 marks]

  4. Question 4. y is inversely proportional to the square root of x.
    y = 5 when x = 16.
    Find the value of y when x = 64.

    Show worked answerHide worked answer
    1. M1: 5 = k ÷ √16
    2. M1: y = 20 ÷ √64
    3. A1: 2.5
    Answer: 2.5
    Direct & Inverse Proportion with Functions
    [3 marks]

  5. Question 5. Solve 2x² - x - 6 > 0 [3]

    Show worked answerHide worked answer
    1. M1: (2x + 3)(x - 2) = 0 so critical values -dfrac32 and 2
    2. M1: sketch or sign test for > 0
    3. A1: x < -dfrac32 or x > 2
    Answer: x < -dfrac32 or x > 2
    Solving Quadratic Inequalities
    [3 marks]