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Mixed Topic Worksheet Grades 8/9: Day 028

Grades 8/9Calculator

  1. Question 1. The graph of y = cos x is reflected in the x-axis and then translated 2 units up. Write down the equation of the new graph.

    Show worked answerHide worked answer
    1. M1: reflection gives y = -cos x
    2. A1: y = 2 - cos x
    Answer: y = 2 - cos x
    Transforming Trigonometric Graphs
    [2 marks]

  2. Question 2. The equation x³ + 2x = 9 has a solution between x = 1.7 and x = 1.8. Find this solution to 1 decimal place. Show your working.

    Show worked answerHide worked answer
    1. M1: work out f(1.7) and f(1.8) for f(x) = x³ + 2x - 9
    2. M1 A1: -0.687 and 0.432; f(1.75) = -0.141 < 0, so the solution is 1.8
    Answer: 1.8
    Change of Signs
    [3 marks]

  3. Question 3. The table shows the frequency densities for the masses, m kg, of 90 suitcases. Work out the value of k.

    Show worked answerHide worked answer
    1. M1: 1.8 × 10 and 2.4 × 20, then 90 - (18 + 48)
    2. M1: 24 ÷ 0.6 (width 40)
    3. M1: 30 + 40
    4. A1: 70
    Answer: 70
    Sketching Histograms
    Mass, m (kg)Frequency density0 < m ≤ 101.810 < m ≤ 302.430 < m ≤ k0.6
    [4 marks]

  4. Question 4. Of 250 drivers, 40% are under 30. 15% of the drivers under 30 and 6% of the other drivers have had an accident. Given that a driver has had an accident, work out the probability that this driver is under 30.

    Show worked answerHide worked answer
    1. M1: under 30: 0.15 × 100 = 15
    2. M1: others: 0.06 × 150 = 9
    3. M1: 15/15 + 9 A1: 5/8
    Answer: 5/8
    Conditional Probability with Two-Way Tables
    [4 marks]

  5. Question 5. Rationalise the denominator of dfrac3 + √33 - √3
    Give your answer in the form a + b√3, where a and b are integers.

    Show worked answerHide worked answer
    1. M1: multiply the numerator and the denominator by 3 + √3
    2. M1: dfrac9 + 6√3 + 39 - 3 = dfrac12 + 6√36
    3. A1: 2 + √3
    Answer: 2 + √3
    Rationalising Denominators of the Form a ± √b
    [3 marks]
📅 Free lesson: Tue 17th NovSave your place →

Mixed Topic Worksheet Grades 8/9: Day 028

Grades 8/9Calculator

  1. Question 1. The graph of y = cos x is reflected in the x-axis and then translated 2 units up. Write down the equation of the new graph.

    [2 marks]
    Show worked answerHide worked answer
    1. M1: reflection gives y = -cos x
    2. A1: y = 2 - cos x
    Answer: y = 2 - cos x
    Transforming Trigonometric Graphs

  2. Question 2. The equation x³ + 2x = 9 has a solution between x = 1.7 and x = 1.8. Find this solution to 1 decimal place. Show your working.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: work out f(1.7) and f(1.8) for f(x) = x³ + 2x - 9
    2. M1 A1: -0.687 and 0.432; f(1.75) = -0.141 < 0, so the solution is 1.8
    Answer: 1.8
    Change of Signs

  3. Question 3. The table shows the frequency densities for the masses, m kg, of 90 suitcases. Work out the value of k.

    [4 marks]
    Mass, m (kg)Frequency density0 < m ≤ 101.810 < m ≤ 302.430 < m ≤ k0.6
    Show worked answerHide worked answer
    1. M1: 1.8 × 10 and 2.4 × 20, then 90 - (18 + 48)
    2. M1: 24 ÷ 0.6 (width 40)
    3. M1: 30 + 40
    4. A1: 70
    Answer: 70
    Sketching Histograms

  4. Question 4. Of 250 drivers, 40% are under 30. 15% of the drivers under 30 and 6% of the other drivers have had an accident. Given that a driver has had an accident, work out the probability that this driver is under 30.

    [4 marks]
    Show worked answerHide worked answer
    1. M1: under 30: 0.15 × 100 = 15
    2. M1: others: 0.06 × 150 = 9
    3. M1: 15/15 + 9 A1: 5/8
    Answer: 5/8
    Conditional Probability with Two-Way Tables

  5. Question 5. Rationalise the denominator of dfrac3 + √33 - √3
    Give your answer in the form a + b√3, where a and b are integers.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: multiply the numerator and the denominator by 3 + √3
    2. M1: dfrac9 + 6√3 + 39 - 3 = dfrac12 + 6√36
    3. A1: 2 + √3
    Answer: 2 + √3
    Rationalising Denominators of the Form a ± √b
📅 Free live lesson: Tuesday 17th NovemberSave your free place →

Mixed Topic Worksheet Grades 8/9: Day 028

Grades 8/9Calculator

  1. Question 1. The graph of y = cos x is reflected in the x-axis and then translated 2 units up. Write down the equation of the new graph.

    Show worked answerHide worked answer
    1. M1: reflection gives y = -cos x
    2. A1: y = 2 - cos x
    Answer: y = 2 - cos x
    Transforming Trigonometric Graphs
    [2 marks]

  2. Question 2. The equation x³ + 2x = 9 has a solution between x = 1.7 and x = 1.8. Find this solution to 1 decimal place. Show your working.

    Show worked answerHide worked answer
    1. M1: work out f(1.7) and f(1.8) for f(x) = x³ + 2x - 9
    2. M1 A1: -0.687 and 0.432; f(1.75) = -0.141 < 0, so the solution is 1.8
    Answer: 1.8
    Change of Signs
    [3 marks]

  3. Question 3. The table shows the frequency densities for the masses, m kg, of 90 suitcases. Work out the value of k.

    Show worked answerHide worked answer
    1. M1: 1.8 × 10 and 2.4 × 20, then 90 - (18 + 48)
    2. M1: 24 ÷ 0.6 (width 40)
    3. M1: 30 + 40
    4. A1: 70
    Answer: 70
    Sketching Histograms
    Mass, m (kg)Frequency density0 < m ≤ 101.810 < m ≤ 302.430 < m ≤ k0.6
    [4 marks]

  4. Question 4. Of 250 drivers, 40% are under 30. 15% of the drivers under 30 and 6% of the other drivers have had an accident. Given that a driver has had an accident, work out the probability that this driver is under 30.

    Show worked answerHide worked answer
    1. M1: under 30: 0.15 × 100 = 15
    2. M1: others: 0.06 × 150 = 9
    3. M1: 15/15 + 9 A1: 5/8
    Answer: 5/8
    Conditional Probability with Two-Way Tables
    [4 marks]

  5. Question 5. Rationalise the denominator of dfrac3 + √33 - √3
    Give your answer in the form a + b√3, where a and b are integers.

    Show worked answerHide worked answer
    1. M1: multiply the numerator and the denominator by 3 + √3
    2. M1: dfrac9 + 6√3 + 39 - 3 = dfrac12 + 6√36
    3. A1: 2 + √3
    Answer: 2 + √3
    Rationalising Denominators of the Form a ± √b
    [3 marks]