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

Mixed Topic Worksheet Grades 8/9: Day 003

Grades 8/9Non-calculator

  1. Question 1. The class 14 < x ≤ 24 has a frequency of 45.
    The class 24 < x ≤ 30 has a frequency of 33.
    Work out the frequency density of each class.

    Show worked answerHide worked answer
    1. M1: 45 ÷ 10 or 33 ÷ 6
    2. A1: 4.5
    3. A1: 5.5
    Answer: 4.5 and 5.5
    Sketching Histograms
    [3 marks]

  2. Question 2. Solve tan(x - 20^°) = 1 for 0^° ≤ x ≤ 360^°

    Show worked answerHide worked answer
    1. M1: x - 20^° = tan⁻¹1 and +180^°
    2. M1: add 20^°
    3. A1: 65^° and 245^°
    Answer: x = 65^° and x = 245^°
    Solving Trigonometric Equations Using a Graph
    [3 marks]

  3. Question 3. y is directly proportional to x and inversely proportional to the square of z. When x=8 and z=2, y=6. Work out the value of x when y=3 and z=4.

    Show worked answerHide worked answer
    1. M1: y=dfrackxz², 6=dfrac8k4, k=3
    2. M1: 3=dfrac3x16
    3. A1: x=16
    Answer: x=16
    Direct & Inverse Proportion with Functions
    [3 marks]

  4. Question 4. Write y = x² + 10x + 30 in the form y = (x + a)² + b and write down the coordinates of its turning point.

    Show worked answerHide worked answer
    1. M1: (x + 5)² + 5
    2. M1 A1: turning point (-5, 5)
    Answer: y = (x + 5)² + 5, turning point (-5, 5)
    Solving Quadratics by Completing the Square (a = 1)
    [3 marks]

  5. Question 5. A car brakes. Its speed, v m/s, is measured every 4 seconds
    beginarrayc|cccc t & 0 & 4 & 8 & 12 hline v & 20 & 14 & 8 & 2 endarray
    Use 3 trapezia to estimate the distance travelled in the 12 seconds

    Show worked answerHide worked answer
    1. M1: area = dfrac12 × 4 × (20 + 2 + 2(14 + 8))
    2. M1: 2 × 66
    3. A1: 132 m
    Answer: 132 m
    Estimating Areas Under Curves
    [3 marks]
📅 Free lesson: Tue 17th NovSave your place →

Mixed Topic Worksheet Grades 8/9: Day 003

Grades 8/9Non-calculator

  1. Question 1. The class 14 < x ≤ 24 has a frequency of 45.
    The class 24 < x ≤ 30 has a frequency of 33.
    Work out the frequency density of each class.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: 45 ÷ 10 or 33 ÷ 6
    2. A1: 4.5
    3. A1: 5.5
    Answer: 4.5 and 5.5
    Sketching Histograms

  2. Question 2. Solve tan(x - 20^°) = 1 for 0^° ≤ x ≤ 360^°

    [3 marks]
    Show worked answerHide worked answer
    1. M1: x - 20^° = tan⁻¹1 and +180^°
    2. M1: add 20^°
    3. A1: 65^° and 245^°
    Answer: x = 65^° and x = 245^°
    Solving Trigonometric Equations Using a Graph

  3. Question 3. y is directly proportional to x and inversely proportional to the square of z. When x=8 and z=2, y=6. Work out the value of x when y=3 and z=4.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: y=dfrackxz², 6=dfrac8k4, k=3
    2. M1: 3=dfrac3x16
    3. A1: x=16
    Answer: x=16
    Direct & Inverse Proportion with Functions

  4. Question 4. Write y = x² + 10x + 30 in the form y = (x + a)² + b and write down the coordinates of its turning point.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: (x + 5)² + 5
    2. M1 A1: turning point (-5, 5)
    Answer: y = (x + 5)² + 5, turning point (-5, 5)
    Solving Quadratics by Completing the Square (a = 1)

  5. Question 5. A car brakes. Its speed, v m/s, is measured every 4 seconds
    beginarrayc|cccc t & 0 & 4 & 8 & 12 hline v & 20 & 14 & 8 & 2 endarray
    Use 3 trapezia to estimate the distance travelled in the 12 seconds

    [3 marks]
    Show worked answerHide worked answer
    1. M1: area = dfrac12 × 4 × (20 + 2 + 2(14 + 8))
    2. M1: 2 × 66
    3. A1: 132 m
    Answer: 132 m
    Estimating Areas Under Curves
📅 Free live lesson: Tuesday 17th NovemberSave your free place →

Mixed Topic Worksheet Grades 8/9: Day 003

Grades 8/9Non-calculator

  1. Question 1. The class 14 < x ≤ 24 has a frequency of 45.
    The class 24 < x ≤ 30 has a frequency of 33.
    Work out the frequency density of each class.

    Show worked answerHide worked answer
    1. M1: 45 ÷ 10 or 33 ÷ 6
    2. A1: 4.5
    3. A1: 5.5
    Answer: 4.5 and 5.5
    Sketching Histograms
    [3 marks]

  2. Question 2. Solve tan(x - 20^°) = 1 for 0^° ≤ x ≤ 360^°

    Show worked answerHide worked answer
    1. M1: x - 20^° = tan⁻¹1 and +180^°
    2. M1: add 20^°
    3. A1: 65^° and 245^°
    Answer: x = 65^° and x = 245^°
    Solving Trigonometric Equations Using a Graph
    [3 marks]

  3. Question 3. y is directly proportional to x and inversely proportional to the square of z. When x=8 and z=2, y=6. Work out the value of x when y=3 and z=4.

    Show worked answerHide worked answer
    1. M1: y=dfrackxz², 6=dfrac8k4, k=3
    2. M1: 3=dfrac3x16
    3. A1: x=16
    Answer: x=16
    Direct & Inverse Proportion with Functions
    [3 marks]

  4. Question 4. Write y = x² + 10x + 30 in the form y = (x + a)² + b and write down the coordinates of its turning point.

    Show worked answerHide worked answer
    1. M1: (x + 5)² + 5
    2. M1 A1: turning point (-5, 5)
    Answer: y = (x + 5)² + 5, turning point (-5, 5)
    Solving Quadratics by Completing the Square (a = 1)
    [3 marks]

  5. Question 5. A car brakes. Its speed, v m/s, is measured every 4 seconds
    beginarrayc|cccc t & 0 & 4 & 8 & 12 hline v & 20 & 14 & 8 & 2 endarray
    Use 3 trapezia to estimate the distance travelled in the 12 seconds

    Show worked answerHide worked answer
    1. M1: area = dfrac12 × 4 × (20 + 2 + 2(14 + 8))
    2. M1: 2 × 66
    3. A1: 132 m
    Answer: 132 m
    Estimating Areas Under Curves
    [3 marks]