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

Mixed Topic Worksheet Grades 8/9: Day 040

Grades 8/9Calculator

  1. Question 1. P(A) = 0.5, P(B) = 0.4 and P(A cap B) = 0.2. Work out P(B mid A).

    Show worked answerHide worked answer
    1. M1: dfrac0.20.5
    2. A1: 0.4
    Answer: 0.4
    Conditional Probability with Venn Diagrams
    [2 marks]

  2. Question 2. The table shows the frequency densities of a histogram. Estimate the number of values greater than 25.

    Show worked answerHide worked answer
    1. M1: (30-25)×2.4=12
    2. M1: (50-30)×1.6=32
    3. A1: 44
    Answer: 44
    Interpreting Histograms
    ClassFrequency density0 < x ≤ 200.920 < x ≤ 302.430 < x ≤ 501.6
    [3 marks]

  3. Question 3. Simplify fully dfrac2x² + 7x - 152x² - 50

    Show worked answerHide worked answer
    1. M1: 2x² + 7x - 15 = (2x - 3)(x + 5)
    2. M1: 2x² - 50 = 2(x² - 25)
    3. M1: 2(x² - 25) = 2(x + 5)(x - 5)
    4. A1: dfrac2x - 32(x - 5)
    Answer: dfrac2x - 32(x - 5)
    Algebraic Fractions Involving Factorising
    [4 marks]

  4. Question 4. ABCDEFGH is a cuboid with AB = 7 cm, BC = 4 cm and CG = 5 cm. Work out the size of angle BAG. Give your answer correct to 1 decimal place.

    Show worked answerHide worked answer
    1. M1: BG is the diagonal of the face BCGF
    2. M1: AB is perpendicular to BG
    3. M1: tanangle BAG = frac√417
    4. A1: 42.5°
    Answer: 42.5°
    3D Trigonometry
    [4 marks]

  5. Question 5. The circle C, centre O, has equation x² + y² = 50
    P is the point (7, -1) on C.
    Find an equation of the tangent to C at P.

    Show worked answerHide worked answer
    1. M1: m_OP = dfrac-17, so the tangent has gradient 7
    2. M1: y + 1 = 7(x - 7)
    3. A1: y = 7x - 50 or an equivalent form
    Answer: y = 7x - 50
    Finding Equations of Tangents to Circles
    [3 marks]
📅 Free lesson: Tue 17th NovSave your place →

Mixed Topic Worksheet Grades 8/9: Day 040

Grades 8/9Calculator

  1. Question 1. P(A) = 0.5, P(B) = 0.4 and P(A cap B) = 0.2. Work out P(B mid A).

    [2 marks]
    Show worked answerHide worked answer
    1. M1: dfrac0.20.5
    2. A1: 0.4
    Answer: 0.4
    Conditional Probability with Venn Diagrams

  2. Question 2. The table shows the frequency densities of a histogram. Estimate the number of values greater than 25.

    [3 marks]
    ClassFrequency density0 < x ≤ 200.920 < x ≤ 302.430 < x ≤ 501.6
    Show worked answerHide worked answer
    1. M1: (30-25)×2.4=12
    2. M1: (50-30)×1.6=32
    3. A1: 44
    Answer: 44
    Interpreting Histograms

  3. Question 3. Simplify fully dfrac2x² + 7x - 152x² - 50

    [4 marks]
    Show worked answerHide worked answer
    1. M1: 2x² + 7x - 15 = (2x - 3)(x + 5)
    2. M1: 2x² - 50 = 2(x² - 25)
    3. M1: 2(x² - 25) = 2(x + 5)(x - 5)
    4. A1: dfrac2x - 32(x - 5)
    Answer: dfrac2x - 32(x - 5)
    Algebraic Fractions Involving Factorising

  4. Question 4. ABCDEFGH is a cuboid with AB = 7 cm, BC = 4 cm and CG = 5 cm. Work out the size of angle BAG. Give your answer correct to 1 decimal place.

    [4 marks]
    Show worked answerHide worked answer
    1. M1: BG is the diagonal of the face BCGF
    2. M1: AB is perpendicular to BG
    3. M1: tanangle BAG = frac√417
    4. A1: 42.5°
    Answer: 42.5°
    3D Trigonometry

  5. Question 5. The circle C, centre O, has equation x² + y² = 50
    P is the point (7, -1) on C.
    Find an equation of the tangent to C at P.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: m_OP = dfrac-17, so the tangent has gradient 7
    2. M1: y + 1 = 7(x - 7)
    3. A1: y = 7x - 50 or an equivalent form
    Answer: y = 7x - 50
    Finding Equations of Tangents to Circles
📅 Free live lesson: Tuesday 17th NovemberSave your free place →

Mixed Topic Worksheet Grades 8/9: Day 040

Grades 8/9Calculator

  1. Question 1. P(A) = 0.5, P(B) = 0.4 and P(A cap B) = 0.2. Work out P(B mid A).

    Show worked answerHide worked answer
    1. M1: dfrac0.20.5
    2. A1: 0.4
    Answer: 0.4
    Conditional Probability with Venn Diagrams
    [2 marks]

  2. Question 2. The table shows the frequency densities of a histogram. Estimate the number of values greater than 25.

    Show worked answerHide worked answer
    1. M1: (30-25)×2.4=12
    2. M1: (50-30)×1.6=32
    3. A1: 44
    Answer: 44
    Interpreting Histograms
    ClassFrequency density0 < x ≤ 200.920 < x ≤ 302.430 < x ≤ 501.6
    [3 marks]

  3. Question 3. Simplify fully dfrac2x² + 7x - 152x² - 50

    Show worked answerHide worked answer
    1. M1: 2x² + 7x - 15 = (2x - 3)(x + 5)
    2. M1: 2x² - 50 = 2(x² - 25)
    3. M1: 2(x² - 25) = 2(x + 5)(x - 5)
    4. A1: dfrac2x - 32(x - 5)
    Answer: dfrac2x - 32(x - 5)
    Algebraic Fractions Involving Factorising
    [4 marks]

  4. Question 4. ABCDEFGH is a cuboid with AB = 7 cm, BC = 4 cm and CG = 5 cm. Work out the size of angle BAG. Give your answer correct to 1 decimal place.

    Show worked answerHide worked answer
    1. M1: BG is the diagonal of the face BCGF
    2. M1: AB is perpendicular to BG
    3. M1: tanangle BAG = frac√417
    4. A1: 42.5°
    Answer: 42.5°
    3D Trigonometry
    [4 marks]

  5. Question 5. The circle C, centre O, has equation x² + y² = 50
    P is the point (7, -1) on C.
    Find an equation of the tangent to C at P.

    Show worked answerHide worked answer
    1. M1: m_OP = dfrac-17, so the tangent has gradient 7
    2. M1: y + 1 = 7(x - 7)
    3. A1: y = 7x - 50 or an equivalent form
    Answer: y = 7x - 50
    Finding Equations of Tangents to Circles
    [3 marks]