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

Mixed Topic Worksheet Grades 8/9: Day 075

Grades 8/9Non-calculator

  1. Question 1. Write down the coordinates of the minimum point of the graph of y = 3sin x for 0° ≤ x ≤ 360°.

    Show worked answerHide worked answer
    1. B1: x = 270°
    2. B1: y = -3
    Answer: (270°, -3)
    Transforming Trigonometric Graphs
    [2 marks]

  2. Question 2. The graph of y = f(x + 2) - 1 has a minimum point at (0, 3). Write down the coordinates of the minimum point of the graph of y = f(x)

    Show worked answerHide worked answer
    1. M1: f(x + 2) moves the graph 2 left and -1 moves it 1 down, so y = f(x) is 2 right and 1 up
    2. A1: (2, 4)
    Answer: (2, 4)
    Translations Along the x- & y-Axes
    [2 marks]

  3. Question 3. Simplify dfrac√80 + √20√5.

    Show worked answerHide worked answer
    1. M1: √80 = 4√5 and √20 = 2√5
    2. M1: dfrac6√5√5
    3. A1: 6
    Answer: 6
    Simplifying Surds
    [3 marks]

  4. Question 4. PA and PB are tangents to a circle with centre O, touching it at A and B. Angle AOB = 124°. Work out the size of angle APB. Give reasons.

    Show worked answerHide worked answer
    1. B1: angles OAP and OBP are 90° (tangent and radius)
    2. M1: 360 - 90 - 90 - 124
    3. A1: 56° (angles in a quadrilateral)
    Answer: 56°
    Circle Theorems
    [3 marks]

  5. Question 5. 2x² + bx + 27 equiv 2(x + p)² - 5
    b is a positive number
    Work out the value of b and the value of p

    Show worked answerHide worked answer
    1. M1: expand: 2(x² + 2px + p²) - 5 = 2x² + 4px + 2p² - 5
    2. M1: 2p² - 5 = 27
    3. A1: p = 4
    4. A1: b = 16
    Answer: b = 16, p = 4
    Solving Quadratics by Completing the Square (a > 1)
    [4 marks]
📅 Free lesson: Tue 17th NovSave your place →

Mixed Topic Worksheet Grades 8/9: Day 075

Grades 8/9Non-calculator

  1. Question 1. Write down the coordinates of the minimum point of the graph of y = 3sin x for 0° ≤ x ≤ 360°.

    [2 marks]
    Show worked answerHide worked answer
    1. B1: x = 270°
    2. B1: y = -3
    Answer: (270°, -3)
    Transforming Trigonometric Graphs

  2. Question 2. The graph of y = f(x + 2) - 1 has a minimum point at (0, 3). Write down the coordinates of the minimum point of the graph of y = f(x)

    [2 marks]
    Show worked answerHide worked answer
    1. M1: f(x + 2) moves the graph 2 left and -1 moves it 1 down, so y = f(x) is 2 right and 1 up
    2. A1: (2, 4)
    Answer: (2, 4)
    Translations Along the x- & y-Axes

  3. Question 3. Simplify dfrac√80 + √20√5.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: √80 = 4√5 and √20 = 2√5
    2. M1: dfrac6√5√5
    3. A1: 6
    Answer: 6
    Simplifying Surds

  4. Question 4. PA and PB are tangents to a circle with centre O, touching it at A and B. Angle AOB = 124°. Work out the size of angle APB. Give reasons.

    [3 marks]
    Show worked answerHide worked answer
    1. B1: angles OAP and OBP are 90° (tangent and radius)
    2. M1: 360 - 90 - 90 - 124
    3. A1: 56° (angles in a quadrilateral)
    Answer: 56°
    Circle Theorems

  5. Question 5. 2x² + bx + 27 equiv 2(x + p)² - 5
    b is a positive number
    Work out the value of b and the value of p

    [4 marks]
    Show worked answerHide worked answer
    1. M1: expand: 2(x² + 2px + p²) - 5 = 2x² + 4px + 2p² - 5
    2. M1: 2p² - 5 = 27
    3. A1: p = 4
    4. A1: b = 16
    Answer: b = 16, p = 4
    Solving Quadratics by Completing the Square (a > 1)
📅 Free live lesson: Tuesday 17th NovemberSave your free place →

Mixed Topic Worksheet Grades 8/9: Day 075

Grades 8/9Non-calculator

  1. Question 1. Write down the coordinates of the minimum point of the graph of y = 3sin x for 0° ≤ x ≤ 360°.

    Show worked answerHide worked answer
    1. B1: x = 270°
    2. B1: y = -3
    Answer: (270°, -3)
    Transforming Trigonometric Graphs
    [2 marks]

  2. Question 2. The graph of y = f(x + 2) - 1 has a minimum point at (0, 3). Write down the coordinates of the minimum point of the graph of y = f(x)

    Show worked answerHide worked answer
    1. M1: f(x + 2) moves the graph 2 left and -1 moves it 1 down, so y = f(x) is 2 right and 1 up
    2. A1: (2, 4)
    Answer: (2, 4)
    Translations Along the x- & y-Axes
    [2 marks]

  3. Question 3. Simplify dfrac√80 + √20√5.

    Show worked answerHide worked answer
    1. M1: √80 = 4√5 and √20 = 2√5
    2. M1: dfrac6√5√5
    3. A1: 6
    Answer: 6
    Simplifying Surds
    [3 marks]

  4. Question 4. PA and PB are tangents to a circle with centre O, touching it at A and B. Angle AOB = 124°. Work out the size of angle APB. Give reasons.

    Show worked answerHide worked answer
    1. B1: angles OAP and OBP are 90° (tangent and radius)
    2. M1: 360 - 90 - 90 - 124
    3. A1: 56° (angles in a quadrilateral)
    Answer: 56°
    Circle Theorems
    [3 marks]

  5. Question 5. 2x² + bx + 27 equiv 2(x + p)² - 5
    b is a positive number
    Work out the value of b and the value of p

    Show worked answerHide worked answer
    1. M1: expand: 2(x² + 2px + p²) - 5 = 2x² + 4px + 2p² - 5
    2. M1: 2p² - 5 = 27
    3. A1: p = 4
    4. A1: b = 16
    Answer: b = 16, p = 4
    Solving Quadratics by Completing the Square (a > 1)
    [4 marks]