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

Mixed Topic Worksheet Grades 8/9: Day 045

Grades 8/9Non-calculator

  1. Question 1. The graph of y = 3cos x + 1 is drawn for 0° ≤ x ≤ 360°. Write down the minimum value of y.

    Show worked answerHide worked answer
    1. M1: minimum of cos x is -1
    2. A1: 3 × (-1) + 1 = -2
    Answer: -2
    Transforming Trigonometric Graphs
    [2 marks]

  2. Question 2. a is a positive integer.
    √75 + √a = 8√3
    Work out the value of a.

    Show worked answerHide worked answer
    1. M1: √75 = 5√3
    2. M1: √a = 3√3
    3. A1: a = 27
    Answer: 27
    Simplifying Surds
    [3 marks]

  3. Question 3. Simplify fully dfracx + 2x - 1 × dfracx² - 1x² + 2x

    Show worked answerHide worked answer
    1. M1: factorises (x-1)(x+1) and x(x+2)
    2. M1: cancels common factors
    3. A1: dfracx + 1x
    Answer: dfracx + 1x
    Multiplying & Dividing Algebraic Fractions
    [3 marks]

  4. Question 4. The table shows the waiting times, t minutes, of 114 passengers.
    (a) Work out k. [2]
    (b) Work out the frequency density for 20 < t ≤ 40. [2]

    Show worked answerHide worked answer
    1. (a) M1: k + 2k + 36 + (k + 6) = 114
    2. (a) A1: 18
    3. (b) M1: 36 ÷ (40 - 20)
    4. (b) A1: 1.8
    Answer: (a) 18; (b) 1.8
    Sketching Histograms
    Time, t (minutes)Frequency0 < t ≤ 10k10 < t ≤ 202k20 < t ≤ 403640 < t ≤ 50k + 6
    [4 marks]

  5. Question 5. overrightarrowOA = mathbfa + 2mathbfb, overrightarrowOB = 3mathbfa + 4mathbfb and overrightarrowOC = 7mathbfa + 8mathbfb
    Prove that A, B and C lie on a straight line.

    Show worked answerHide worked answer
    1. M1: overrightarrowAB = 2mathbfa + 2mathbfb
    2. M1: overrightarrowBC = 4mathbfa + 4mathbfb
    3. A1: overrightarrowBC = 2overrightarrowAB
    4. C1: parallel, with B common
    Answer: overrightarrowBC = 2overrightarrowAB and B is common
    Vectors Along a Straight Line
    [4 marks]
📅 Free lesson: Tue 17th NovSave your place →

Mixed Topic Worksheet Grades 8/9: Day 045

Grades 8/9Non-calculator

  1. Question 1. The graph of y = 3cos x + 1 is drawn for 0° ≤ x ≤ 360°. Write down the minimum value of y.

    [2 marks]
    Show worked answerHide worked answer
    1. M1: minimum of cos x is -1
    2. A1: 3 × (-1) + 1 = -2
    Answer: -2
    Transforming Trigonometric Graphs

  2. Question 2. a is a positive integer.
    √75 + √a = 8√3
    Work out the value of a.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: √75 = 5√3
    2. M1: √a = 3√3
    3. A1: a = 27
    Answer: 27
    Simplifying Surds

  3. Question 3. Simplify fully dfracx + 2x - 1 × dfracx² - 1x² + 2x

    [3 marks]
    Show worked answerHide worked answer
    1. M1: factorises (x-1)(x+1) and x(x+2)
    2. M1: cancels common factors
    3. A1: dfracx + 1x
    Answer: dfracx + 1x
    Multiplying & Dividing Algebraic Fractions

  4. Question 4. The table shows the waiting times, t minutes, of 114 passengers.
    (a) Work out k. [2]
    (b) Work out the frequency density for 20 < t ≤ 40. [2]

    [4 marks]
    Time, t (minutes)Frequency0 < t ≤ 10k10 < t ≤ 202k20 < t ≤ 403640 < t ≤ 50k + 6
    Show worked answerHide worked answer
    1. (a) M1: k + 2k + 36 + (k + 6) = 114
    2. (a) A1: 18
    3. (b) M1: 36 ÷ (40 - 20)
    4. (b) A1: 1.8
    Answer: (a) 18; (b) 1.8
    Sketching Histograms

  5. Question 5. overrightarrowOA = mathbfa + 2mathbfb, overrightarrowOB = 3mathbfa + 4mathbfb and overrightarrowOC = 7mathbfa + 8mathbfb
    Prove that A, B and C lie on a straight line.

    [4 marks]
    Show worked answerHide worked answer
    1. M1: overrightarrowAB = 2mathbfa + 2mathbfb
    2. M1: overrightarrowBC = 4mathbfa + 4mathbfb
    3. A1: overrightarrowBC = 2overrightarrowAB
    4. C1: parallel, with B common
    Answer: overrightarrowBC = 2overrightarrowAB and B is common
    Vectors Along a Straight Line
📅 Free live lesson: Tuesday 17th NovemberSave your free place →

Mixed Topic Worksheet Grades 8/9: Day 045

Grades 8/9Non-calculator

  1. Question 1. The graph of y = 3cos x + 1 is drawn for 0° ≤ x ≤ 360°. Write down the minimum value of y.

    Show worked answerHide worked answer
    1. M1: minimum of cos x is -1
    2. A1: 3 × (-1) + 1 = -2
    Answer: -2
    Transforming Trigonometric Graphs
    [2 marks]

  2. Question 2. a is a positive integer.
    √75 + √a = 8√3
    Work out the value of a.

    Show worked answerHide worked answer
    1. M1: √75 = 5√3
    2. M1: √a = 3√3
    3. A1: a = 27
    Answer: 27
    Simplifying Surds
    [3 marks]

  3. Question 3. Simplify fully dfracx + 2x - 1 × dfracx² - 1x² + 2x

    Show worked answerHide worked answer
    1. M1: factorises (x-1)(x+1) and x(x+2)
    2. M1: cancels common factors
    3. A1: dfracx + 1x
    Answer: dfracx + 1x
    Multiplying & Dividing Algebraic Fractions
    [3 marks]

  4. Question 4. The table shows the waiting times, t minutes, of 114 passengers.
    (a) Work out k. [2]
    (b) Work out the frequency density for 20 < t ≤ 40. [2]

    Show worked answerHide worked answer
    1. (a) M1: k + 2k + 36 + (k + 6) = 114
    2. (a) A1: 18
    3. (b) M1: 36 ÷ (40 - 20)
    4. (b) A1: 1.8
    Answer: (a) 18; (b) 1.8
    Sketching Histograms
    Time, t (minutes)Frequency0 < t ≤ 10k10 < t ≤ 202k20 < t ≤ 403640 < t ≤ 50k + 6
    [4 marks]

  5. Question 5. overrightarrowOA = mathbfa + 2mathbfb, overrightarrowOB = 3mathbfa + 4mathbfb and overrightarrowOC = 7mathbfa + 8mathbfb
    Prove that A, B and C lie on a straight line.

    Show worked answerHide worked answer
    1. M1: overrightarrowAB = 2mathbfa + 2mathbfb
    2. M1: overrightarrowBC = 4mathbfa + 4mathbfb
    3. A1: overrightarrowBC = 2overrightarrowAB
    4. C1: parallel, with B common
    Answer: overrightarrowBC = 2overrightarrowAB and B is common
    Vectors Along a Straight Line
    [4 marks]