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

Mixed Topic Worksheet Grades 8/9: Day 072

Grades 8/9Calculator

  1. Question 1. Frequency densities: 0 < t ≤ 10 is 3, 10 < t ≤ 30 is 2.5, 30 < t ≤ 40 is 2. Work out an estimate for the median.

    Show worked answerHide worked answer
    1. M1: frequencies 30, 50, 20; the 50th value is 20 into the second class
    2. A1: 10 + 20/50 × 20 = 18
    Answer: 18
    Median from a Histogram
    [2 marks]

  2. Question 2. A cone has a base radius of 5 cm and a slant height of 13 cm. Work out the angle between the slant height and the base. Give your answer correct to 1 decimal place.

    Show worked answerHide worked answer
    1. M1: cosθ = 5/13
    2. A1: 67.4°
    Answer: 67.4°
    3D Trigonometry
    [2 marks]

  3. Question 3. Simplify fully dfracx² - 9x + 2 × dfracx² - 4x + 3

    Show worked answerHide worked answer
    1. M1: dfrac(x - 3)(x + 3)x + 2 × dfrac(x - 2)(x + 2)x + 3
    2. M1: cancel (x + 3) and (x + 2)
    3. A1: (x - 3)(x - 2)
    Answer: (x - 3)(x - 2)
    Multiplying & Dividing Algebraic Fractions
    [3 marks]

  4. Question 4. A rectangle has width x cm and length (x + 6) cm
    The area of the rectangle is 25 cm²
    Use completing the square to work out the value of x
    Give your answer correct to 3 significant figures.

    Show worked answerHide worked answer
    1. M1: x(x + 6) = 25 so x² + 6x - 25 = 0
    2. M1: (x + 3)² - 9 - 25 = 0
    3. M1: (x + 3)² = 34
    4. M1: x + 3 = ±√34
    5. A1: x = 2.83 (x = -8.83 rejected as a width cannot be negative)
    Answer: x = 2.83
    Solving Quadratics by Completing the Square (a = 1)
    [5 marks]

  5. Question 5. Write 3 - 12x - 2x² in the form a(x + p)² + q

    Show worked answerHide worked answer
    1. M1: -2(x² + 6x) + 3
    2. M1: -2≤ft((x + 3)² - 9) + 3
    3. A1: -2(x + 3)² + 21
    Answer: -2(x + 3)² + 21
    Solving Quadratics by Completing the Square (a > 1)
    [3 marks]
📅 Free lesson: Tue 17th NovSave your place →

Mixed Topic Worksheet Grades 8/9: Day 072

Grades 8/9Calculator

  1. Question 1. Frequency densities: 0 < t ≤ 10 is 3, 10 < t ≤ 30 is 2.5, 30 < t ≤ 40 is 2. Work out an estimate for the median.

    [2 marks]
    Show worked answerHide worked answer
    1. M1: frequencies 30, 50, 20; the 50th value is 20 into the second class
    2. A1: 10 + 20/50 × 20 = 18
    Answer: 18
    Median from a Histogram

  2. Question 2. A cone has a base radius of 5 cm and a slant height of 13 cm. Work out the angle between the slant height and the base. Give your answer correct to 1 decimal place.

    [2 marks]
    Show worked answerHide worked answer
    1. M1: cosθ = 5/13
    2. A1: 67.4°
    Answer: 67.4°
    3D Trigonometry

  3. Question 3. Simplify fully dfracx² - 9x + 2 × dfracx² - 4x + 3

    [3 marks]
    Show worked answerHide worked answer
    1. M1: dfrac(x - 3)(x + 3)x + 2 × dfrac(x - 2)(x + 2)x + 3
    2. M1: cancel (x + 3) and (x + 2)
    3. A1: (x - 3)(x - 2)
    Answer: (x - 3)(x - 2)
    Multiplying & Dividing Algebraic Fractions

  4. Question 4. A rectangle has width x cm and length (x + 6) cm
    The area of the rectangle is 25 cm²
    Use completing the square to work out the value of x
    Give your answer correct to 3 significant figures.

    [5 marks]
    Show worked answerHide worked answer
    1. M1: x(x + 6) = 25 so x² + 6x - 25 = 0
    2. M1: (x + 3)² - 9 - 25 = 0
    3. M1: (x + 3)² = 34
    4. M1: x + 3 = ±√34
    5. A1: x = 2.83 (x = -8.83 rejected as a width cannot be negative)
    Answer: x = 2.83
    Solving Quadratics by Completing the Square (a = 1)

  5. Question 5. Write 3 - 12x - 2x² in the form a(x + p)² + q

    [3 marks]
    Show worked answerHide worked answer
    1. M1: -2(x² + 6x) + 3
    2. M1: -2≤ft((x + 3)² - 9) + 3
    3. A1: -2(x + 3)² + 21
    Answer: -2(x + 3)² + 21
    Solving Quadratics by Completing the Square (a > 1)
📅 Free live lesson: Tuesday 17th NovemberSave your free place →

Mixed Topic Worksheet Grades 8/9: Day 072

Grades 8/9Calculator

  1. Question 1. Frequency densities: 0 < t ≤ 10 is 3, 10 < t ≤ 30 is 2.5, 30 < t ≤ 40 is 2. Work out an estimate for the median.

    Show worked answerHide worked answer
    1. M1: frequencies 30, 50, 20; the 50th value is 20 into the second class
    2. A1: 10 + 20/50 × 20 = 18
    Answer: 18
    Median from a Histogram
    [2 marks]

  2. Question 2. A cone has a base radius of 5 cm and a slant height of 13 cm. Work out the angle between the slant height and the base. Give your answer correct to 1 decimal place.

    Show worked answerHide worked answer
    1. M1: cosθ = 5/13
    2. A1: 67.4°
    Answer: 67.4°
    3D Trigonometry
    [2 marks]

  3. Question 3. Simplify fully dfracx² - 9x + 2 × dfracx² - 4x + 3

    Show worked answerHide worked answer
    1. M1: dfrac(x - 3)(x + 3)x + 2 × dfrac(x - 2)(x + 2)x + 3
    2. M1: cancel (x + 3) and (x + 2)
    3. A1: (x - 3)(x - 2)
    Answer: (x - 3)(x - 2)
    Multiplying & Dividing Algebraic Fractions
    [3 marks]

  4. Question 4. A rectangle has width x cm and length (x + 6) cm
    The area of the rectangle is 25 cm²
    Use completing the square to work out the value of x
    Give your answer correct to 3 significant figures.

    Show worked answerHide worked answer
    1. M1: x(x + 6) = 25 so x² + 6x - 25 = 0
    2. M1: (x + 3)² - 9 - 25 = 0
    3. M1: (x + 3)² = 34
    4. M1: x + 3 = ±√34
    5. A1: x = 2.83 (x = -8.83 rejected as a width cannot be negative)
    Answer: x = 2.83
    Solving Quadratics by Completing the Square (a = 1)
    [5 marks]

  5. Question 5. Write 3 - 12x - 2x² in the form a(x + p)² + q

    Show worked answerHide worked answer
    1. M1: -2(x² + 6x) + 3
    2. M1: -2≤ft((x + 3)² - 9) + 3
    3. A1: -2(x + 3)² + 21
    Answer: -2(x + 3)² + 21
    Solving Quadratics by Completing the Square (a > 1)
    [3 marks]