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

Mixed Topic Worksheet Grades 8/9: Day 037

Grades 8/9Non-calculator

  1. Question 1. Work out the number of times the graph of y = sin 2x meets the x-axis for 0° ≤ x ≤ 360°.

    Show worked answerHide worked answer
    1. M1: sin 2x = 0 when 2x = 0°, 180°, 360°, 540°, 720°
    2. A1: 5
    Answer: 5
    Transforming Trigonometric Graphs
    [2 marks]

  2. Question 2. A, B, C, D lie on a circle, centre O. AC is a diameter. Angle DCA = 29^°
    Work out angle DBC. Give reasons for each stage.

    Show worked answerHide worked answer
    1. M1: 90 - 29
    2. A1: angle DBC = 61^°
    3. C1: reasons: angle in a semicircle (ABC = 90^°), angles in the same segment (ABD = ACD)
    Answer: 61^°
    Circle Theorems
    29°OACBDNot drawn accurately
    [3 marks]

  3. Question 3. y is directly proportional to x and inversely proportional to the square root of z.
    y = 15 when x = 5 and z = 4.
    Find the value of y when x = 8 and z = 25.

    Show worked answerHide worked answer
    1. M1: y = dfrackx√z
    2. M1: 15 = dfrac5k2, so k = 6
    3. A1: y = dfrac6 × 85 = 9.6
    Answer: 9.6
    Direct & Inverse Proportion with Functions
    [3 marks]

  4. Question 4. The circle has equation x² + y² = 50
    The line x + 2y = 10 meets the circle at the points A and B
    Work out the coordinates of the midpoint of AB

    Show worked answerHide worked answer
    1. M1: (10 - 2y)² + y² = 50
    2. M1: y² - 8y + 10 = 0
    3. M1: mean of the roots = 8 ÷ 2 = 4
    4. A1: (2, 4)
    Answer: (2, 4)
    Solving Quadratic Simultaneous Equations
    [4 marks]

  5. Question 5. Find the values of x for which both x² ≤ 25 and x² - 2x - 3 > 0

    Show worked answerHide worked answer
    1. M1: x² ≤ 25 gives -5 ≤ x ≤ 5
    2. M1: (x - 3)(x + 1) > 0 gives x < -1 or x > 3
    3. A2: -5 ≤ x < -1 or 3 < x ≤ 5
    Answer: -5 ≤ x < -1 or 3 < x ≤ 5
    Sketching Quadratic Inequalities
    [4 marks]
📅 Free lesson: Tue 17th NovSave your place →

Mixed Topic Worksheet Grades 8/9: Day 037

Grades 8/9Non-calculator

  1. Question 1. Work out the number of times the graph of y = sin 2x meets the x-axis for 0° ≤ x ≤ 360°.

    [2 marks]
    Show worked answerHide worked answer
    1. M1: sin 2x = 0 when 2x = 0°, 180°, 360°, 540°, 720°
    2. A1: 5
    Answer: 5
    Transforming Trigonometric Graphs

  2. Question 2. A, B, C, D lie on a circle, centre O. AC is a diameter. Angle DCA = 29^°
    Work out angle DBC. Give reasons for each stage.

    [3 marks]
    29°OACBDNot drawn accurately
    Show worked answerHide worked answer
    1. M1: 90 - 29
    2. A1: angle DBC = 61^°
    3. C1: reasons: angle in a semicircle (ABC = 90^°), angles in the same segment (ABD = ACD)
    Answer: 61^°
    Circle Theorems

  3. Question 3. y is directly proportional to x and inversely proportional to the square root of z.
    y = 15 when x = 5 and z = 4.
    Find the value of y when x = 8 and z = 25.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: y = dfrackx√z
    2. M1: 15 = dfrac5k2, so k = 6
    3. A1: y = dfrac6 × 85 = 9.6
    Answer: 9.6
    Direct & Inverse Proportion with Functions

  4. Question 4. The circle has equation x² + y² = 50
    The line x + 2y = 10 meets the circle at the points A and B
    Work out the coordinates of the midpoint of AB

    [4 marks]
    Show worked answerHide worked answer
    1. M1: (10 - 2y)² + y² = 50
    2. M1: y² - 8y + 10 = 0
    3. M1: mean of the roots = 8 ÷ 2 = 4
    4. A1: (2, 4)
    Answer: (2, 4)
    Solving Quadratic Simultaneous Equations

  5. Question 5. Find the values of x for which both x² ≤ 25 and x² - 2x - 3 > 0

    [4 marks]
    Show worked answerHide worked answer
    1. M1: x² ≤ 25 gives -5 ≤ x ≤ 5
    2. M1: (x - 3)(x + 1) > 0 gives x < -1 or x > 3
    3. A2: -5 ≤ x < -1 or 3 < x ≤ 5
    Answer: -5 ≤ x < -1 or 3 < x ≤ 5
    Sketching Quadratic Inequalities
📅 Free live lesson: Tuesday 17th NovemberSave your free place →

Mixed Topic Worksheet Grades 8/9: Day 037

Grades 8/9Non-calculator

  1. Question 1. Work out the number of times the graph of y = sin 2x meets the x-axis for 0° ≤ x ≤ 360°.

    Show worked answerHide worked answer
    1. M1: sin 2x = 0 when 2x = 0°, 180°, 360°, 540°, 720°
    2. A1: 5
    Answer: 5
    Transforming Trigonometric Graphs
    [2 marks]

  2. Question 2. A, B, C, D lie on a circle, centre O. AC is a diameter. Angle DCA = 29^°
    Work out angle DBC. Give reasons for each stage.

    Show worked answerHide worked answer
    1. M1: 90 - 29
    2. A1: angle DBC = 61^°
    3. C1: reasons: angle in a semicircle (ABC = 90^°), angles in the same segment (ABD = ACD)
    Answer: 61^°
    Circle Theorems
    29°OACBDNot drawn accurately
    [3 marks]

  3. Question 3. y is directly proportional to x and inversely proportional to the square root of z.
    y = 15 when x = 5 and z = 4.
    Find the value of y when x = 8 and z = 25.

    Show worked answerHide worked answer
    1. M1: y = dfrackx√z
    2. M1: 15 = dfrac5k2, so k = 6
    3. A1: y = dfrac6 × 85 = 9.6
    Answer: 9.6
    Direct & Inverse Proportion with Functions
    [3 marks]

  4. Question 4. The circle has equation x² + y² = 50
    The line x + 2y = 10 meets the circle at the points A and B
    Work out the coordinates of the midpoint of AB

    Show worked answerHide worked answer
    1. M1: (10 - 2y)² + y² = 50
    2. M1: y² - 8y + 10 = 0
    3. M1: mean of the roots = 8 ÷ 2 = 4
    4. A1: (2, 4)
    Answer: (2, 4)
    Solving Quadratic Simultaneous Equations
    [4 marks]

  5. Question 5. Find the values of x for which both x² ≤ 25 and x² - 2x - 3 > 0

    Show worked answerHide worked answer
    1. M1: x² ≤ 25 gives -5 ≤ x ≤ 5
    2. M1: (x - 3)(x + 1) > 0 gives x < -1 or x > 3
    3. A2: -5 ≤ x < -1 or 3 < x ≤ 5
    Answer: -5 ≤ x < -1 or 3 < x ≤ 5
    Sketching Quadratic Inequalities
    [4 marks]