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

Mixed Topic Worksheet Grades 8/9: Day 035

Grades 8/9Non-calculator

  1. Question 1. sin 25^° = 0.423 correct to 3 decimal places. Find the two values of x, between 0^° and 360^°, for which sin x = -0.423

    Show worked answerHide worked answer
    1. M1: x = 180^° + 25^° or 360^° - 25^°
    2. A1: x = 205^° and x = 335^°
    Answer: x = 205^° and x = 335^°
    Calculating Values of Trig Functions Using Graphs
    [2 marks]

  2. Question 2. p = 15.4 and q = 8.2, each correct to 1 decimal place.
    Ravi's lower bound of p - q is 15.35 - 8.15 = 7.2, which is not correct.
    Work out the lower bound of p - q.

    Show worked answerHide worked answer
    1. M1: 15.4 - 0.05 and 8.2 + 0.05
    2. M1: 15.35 - 8.25
    3. A1: 7.1
    Answer: 7.1
    Combining Upper & Lower Bounds
    [3 marks]

  3. Question 3. Simplify fully dfracx²-365÷dfracx-615

    Show worked answerHide worked answer
    1. M1: dfracx²-365×dfrac15x-6
    2. M1: dfrac(x-6)(x+6)×155(x-6)
    3. A1: 3(x+6)
    Answer: 3(x+6)
    Multiplying & Dividing Algebraic Fractions
    [3 marks]

  4. Question 4. A bag has 5 red counters and 4 blue counters.
    Two counters are taken at random from the bag without replacement.
    Work out the probability that the two counters are different colours.

    Show worked answerHide worked answer
    1. M1: red then blue = 5/9 × 4/8 = 20/72
    2. M1 M1: blue then red is also 20/72; add
    3. A1: 40/72 = 5/9
    Answer: 5/9
    Conditional Probability with Tree Diagrams
    [4 marks]

  5. Question 5. GHJ is a triangle. overrightarrowGH = 3mathbfa and overrightarrowGJ = mathbfb
    M is on HJ with HM : MJ = 1 : 2
    Find overrightarrowGM in terms of mathbfa and mathbfb.

    Show worked answerHide worked answer
    1. M1: overrightarrowHJ = mathbfb - 3mathbfa
    2. M1 M1: 3mathbfa + 1/3(mathbfb - 3mathbfa)
    3. A1: 2mathbfa + 1/3mathbfb
    Answer: 2mathbfa + 1/3mathbfb
    Vector Ratio Problems
    3abGHJMNot drawn accurately
    [4 marks]
📅 Free lesson: Tue 17th NovSave your place →

Mixed Topic Worksheet Grades 8/9: Day 035

Grades 8/9Non-calculator

  1. Question 1. sin 25^° = 0.423 correct to 3 decimal places. Find the two values of x, between 0^° and 360^°, for which sin x = -0.423

    [2 marks]
    Show worked answerHide worked answer
    1. M1: x = 180^° + 25^° or 360^° - 25^°
    2. A1: x = 205^° and x = 335^°
    Answer: x = 205^° and x = 335^°
    Calculating Values of Trig Functions Using Graphs

  2. Question 2. p = 15.4 and q = 8.2, each correct to 1 decimal place.
    Ravi's lower bound of p - q is 15.35 - 8.15 = 7.2, which is not correct.
    Work out the lower bound of p - q.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: 15.4 - 0.05 and 8.2 + 0.05
    2. M1: 15.35 - 8.25
    3. A1: 7.1
    Answer: 7.1
    Combining Upper & Lower Bounds

  3. Question 3. Simplify fully dfracx²-365÷dfracx-615

    [3 marks]
    Show worked answerHide worked answer
    1. M1: dfracx²-365×dfrac15x-6
    2. M1: dfrac(x-6)(x+6)×155(x-6)
    3. A1: 3(x+6)
    Answer: 3(x+6)
    Multiplying & Dividing Algebraic Fractions

  4. Question 4. A bag has 5 red counters and 4 blue counters.
    Two counters are taken at random from the bag without replacement.
    Work out the probability that the two counters are different colours.

    [4 marks]
    Show worked answerHide worked answer
    1. M1: red then blue = 5/9 × 4/8 = 20/72
    2. M1 M1: blue then red is also 20/72; add
    3. A1: 40/72 = 5/9
    Answer: 5/9
    Conditional Probability with Tree Diagrams

  5. Question 5. GHJ is a triangle. overrightarrowGH = 3mathbfa and overrightarrowGJ = mathbfb
    M is on HJ with HM : MJ = 1 : 2
    Find overrightarrowGM in terms of mathbfa and mathbfb.

    [4 marks]
    3abGHJMNot drawn accurately
    Show worked answerHide worked answer
    1. M1: overrightarrowHJ = mathbfb - 3mathbfa
    2. M1 M1: 3mathbfa + 1/3(mathbfb - 3mathbfa)
    3. A1: 2mathbfa + 1/3mathbfb
    Answer: 2mathbfa + 1/3mathbfb
    Vector Ratio Problems
📅 Free live lesson: Tuesday 17th NovemberSave your free place →

Mixed Topic Worksheet Grades 8/9: Day 035

Grades 8/9Non-calculator

  1. Question 1. sin 25^° = 0.423 correct to 3 decimal places. Find the two values of x, between 0^° and 360^°, for which sin x = -0.423

    Show worked answerHide worked answer
    1. M1: x = 180^° + 25^° or 360^° - 25^°
    2. A1: x = 205^° and x = 335^°
    Answer: x = 205^° and x = 335^°
    Calculating Values of Trig Functions Using Graphs
    [2 marks]

  2. Question 2. p = 15.4 and q = 8.2, each correct to 1 decimal place.
    Ravi's lower bound of p - q is 15.35 - 8.15 = 7.2, which is not correct.
    Work out the lower bound of p - q.

    Show worked answerHide worked answer
    1. M1: 15.4 - 0.05 and 8.2 + 0.05
    2. M1: 15.35 - 8.25
    3. A1: 7.1
    Answer: 7.1
    Combining Upper & Lower Bounds
    [3 marks]

  3. Question 3. Simplify fully dfracx²-365÷dfracx-615

    Show worked answerHide worked answer
    1. M1: dfracx²-365×dfrac15x-6
    2. M1: dfrac(x-6)(x+6)×155(x-6)
    3. A1: 3(x+6)
    Answer: 3(x+6)
    Multiplying & Dividing Algebraic Fractions
    [3 marks]

  4. Question 4. A bag has 5 red counters and 4 blue counters.
    Two counters are taken at random from the bag without replacement.
    Work out the probability that the two counters are different colours.

    Show worked answerHide worked answer
    1. M1: red then blue = 5/9 × 4/8 = 20/72
    2. M1 M1: blue then red is also 20/72; add
    3. A1: 40/72 = 5/9
    Answer: 5/9
    Conditional Probability with Tree Diagrams
    [4 marks]

  5. Question 5. GHJ is a triangle. overrightarrowGH = 3mathbfa and overrightarrowGJ = mathbfb
    M is on HJ with HM : MJ = 1 : 2
    Find overrightarrowGM in terms of mathbfa and mathbfb.

    Show worked answerHide worked answer
    1. M1: overrightarrowHJ = mathbfb - 3mathbfa
    2. M1 M1: 3mathbfa + 1/3(mathbfb - 3mathbfa)
    3. A1: 2mathbfa + 1/3mathbfb
    Answer: 2mathbfa + 1/3mathbfb
    Vector Ratio Problems
    3abGHJMNot drawn accurately
    [4 marks]