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

Mixed Topic Worksheet Grades 8/9: Day 056

Grades 8/9Calculator

  1. Question 1. In a group of 40 people, 15 like tea, 12 like coffee and 5 like both. Given that a person likes coffee, find the probability that they like tea.

    Show worked answerHide worked answer
    1. M1: P(T mid C) = dfrac512
    2. A1: dfrac512
    Answer: dfrac512
    Conditional Probability with Venn Diagrams
    [2 marks]

  2. Question 2. y = f(x) where f(x) = x² - 4x is translated 3 units right to give y = g(x).
    Ben says g crosses the x-axis at x = -3 and x = 1.
    Cara says it crosses at x = 3 and x = 7.
    Who is correct? Show your working.

    Show worked answerHide worked answer
    1. M1: g(x) = f(x - 3) = (x - 3)² - 4(x - 3)
    2. M1: (x - 3)(x - 7) = 0
    3. C1: Cara is correct
    Answer: Cara is correct
    Translations Along the x- & y-Axes
    [3 marks]

  3. Question 3. x = 7.4 and y = 2.5, both correct to 1 decimal place. Work out the upper bound of x/y. Give your answer to 3 significant figures.

    Show worked answerHide worked answer
    1. M1: 7.4 + 0.05/2.5 - 0.05 (upper bound of x over lower bound of y)
    2. A1: 3.04
    Answer: 3.04
    Combining Upper & Lower Bounds
    [3 marks]

  4. Question 4. A vertical mast CM is 25 m tall and stands at corner C of a horizontal rectangular field ABCD. AB = 60 m and BC = 80 m. Work out the angle of elevation of M from A. Give your answer correct to 1 decimal place.

    Show worked answerHide worked answer
    1. M1: AC = √60² + 80² = 100
    2. M1: tanθ = 25/100
    3. A1: 14.0°
    Answer: 14.0°
    3D Trigonometry
    [3 marks]

  5. Question 5. One solution of 2x² - 8x + k = 0 is x = 2 + √3
    Use completing the square to work out the value of k

    Show worked answerHide worked answer
    1. M1: 2(x - 2)² - 8 + k = 0
    2. M1: (x - 2)² = dfrac8 - k2 and dfrac8 - k2 = 3
    3. A1: k = 2
    Answer: k = 2
    Solving Quadratics by Completing the Square (a > 1)
    [3 marks]
📅 Free lesson: Tue 17th NovSave your place →

Mixed Topic Worksheet Grades 8/9: Day 056

Grades 8/9Calculator

  1. Question 1. In a group of 40 people, 15 like tea, 12 like coffee and 5 like both. Given that a person likes coffee, find the probability that they like tea.

    [2 marks]
    Show worked answerHide worked answer
    1. M1: P(T mid C) = dfrac512
    2. A1: dfrac512
    Answer: dfrac512
    Conditional Probability with Venn Diagrams

  2. Question 2. y = f(x) where f(x) = x² - 4x is translated 3 units right to give y = g(x).
    Ben says g crosses the x-axis at x = -3 and x = 1.
    Cara says it crosses at x = 3 and x = 7.
    Who is correct? Show your working.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: g(x) = f(x - 3) = (x - 3)² - 4(x - 3)
    2. M1: (x - 3)(x - 7) = 0
    3. C1: Cara is correct
    Answer: Cara is correct
    Translations Along the x- & y-Axes

  3. Question 3. x = 7.4 and y = 2.5, both correct to 1 decimal place. Work out the upper bound of x/y. Give your answer to 3 significant figures.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: 7.4 + 0.05/2.5 - 0.05 (upper bound of x over lower bound of y)
    2. A1: 3.04
    Answer: 3.04
    Combining Upper & Lower Bounds

  4. Question 4. A vertical mast CM is 25 m tall and stands at corner C of a horizontal rectangular field ABCD. AB = 60 m and BC = 80 m. Work out the angle of elevation of M from A. Give your answer correct to 1 decimal place.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: AC = √60² + 80² = 100
    2. M1: tanθ = 25/100
    3. A1: 14.0°
    Answer: 14.0°
    3D Trigonometry

  5. Question 5. One solution of 2x² - 8x + k = 0 is x = 2 + √3
    Use completing the square to work out the value of k

    [3 marks]
    Show worked answerHide worked answer
    1. M1: 2(x - 2)² - 8 + k = 0
    2. M1: (x - 2)² = dfrac8 - k2 and dfrac8 - k2 = 3
    3. A1: k = 2
    Answer: k = 2
    Solving Quadratics by Completing the Square (a > 1)
📅 Free live lesson: Tuesday 17th NovemberSave your free place →

Mixed Topic Worksheet Grades 8/9: Day 056

Grades 8/9Calculator

  1. Question 1. In a group of 40 people, 15 like tea, 12 like coffee and 5 like both. Given that a person likes coffee, find the probability that they like tea.

    Show worked answerHide worked answer
    1. M1: P(T mid C) = dfrac512
    2. A1: dfrac512
    Answer: dfrac512
    Conditional Probability with Venn Diagrams
    [2 marks]

  2. Question 2. y = f(x) where f(x) = x² - 4x is translated 3 units right to give y = g(x).
    Ben says g crosses the x-axis at x = -3 and x = 1.
    Cara says it crosses at x = 3 and x = 7.
    Who is correct? Show your working.

    Show worked answerHide worked answer
    1. M1: g(x) = f(x - 3) = (x - 3)² - 4(x - 3)
    2. M1: (x - 3)(x - 7) = 0
    3. C1: Cara is correct
    Answer: Cara is correct
    Translations Along the x- & y-Axes
    [3 marks]

  3. Question 3. x = 7.4 and y = 2.5, both correct to 1 decimal place. Work out the upper bound of x/y. Give your answer to 3 significant figures.

    Show worked answerHide worked answer
    1. M1: 7.4 + 0.05/2.5 - 0.05 (upper bound of x over lower bound of y)
    2. A1: 3.04
    Answer: 3.04
    Combining Upper & Lower Bounds
    [3 marks]

  4. Question 4. A vertical mast CM is 25 m tall and stands at corner C of a horizontal rectangular field ABCD. AB = 60 m and BC = 80 m. Work out the angle of elevation of M from A. Give your answer correct to 1 decimal place.

    Show worked answerHide worked answer
    1. M1: AC = √60² + 80² = 100
    2. M1: tanθ = 25/100
    3. A1: 14.0°
    Answer: 14.0°
    3D Trigonometry
    [3 marks]

  5. Question 5. One solution of 2x² - 8x + k = 0 is x = 2 + √3
    Use completing the square to work out the value of k

    Show worked answerHide worked answer
    1. M1: 2(x - 2)² - 8 + k = 0
    2. M1: (x - 2)² = dfrac8 - k2 and dfrac8 - k2 = 3
    3. A1: k = 2
    Answer: k = 2
    Solving Quadratics by Completing the Square (a > 1)
    [3 marks]