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

Mixed Topic Worksheet Grades 8/9: Day 092

Grades 8/9Calculator

  1. Question 1. The graph of y = f(x + 2) - 5 passes through the point (6, 1). Work out the value of f(8).

    Show worked answerHide worked answer
    1. M1: f(6 + 2) - 5 = 1
    2. A1: f(8) = 6
    Answer: f(8) = 6
    Translations Along the x- & y-Axes
    [2 marks]

  2. Question 2. F is directly proportional to m and inversely proportional to the square of d.
    F = 12 when m = 6 and d = 2.
    Find the value of F when m = 9 and d = 6.

    Show worked answerHide worked answer
    1. M1: 12 = k × 6 ÷ 2²
    2. M1: F = 8 × 9 ÷ 6²
    3. A1: 2
    Answer: 2
    Direct & Inverse Proportion with Functions
    [3 marks]

  3. Question 3. a = 5.2 and b = 3.4, both correct to 1 decimal place. Work out the lower bound of a² - b. Give your answer to 3 significant figures.

    Show worked answerHide worked answer
    1. M1: (5.2 - 0.05)² - (3.4 + 0.05) (lower bound of a, upper bound of b)
    2. A1: 23.1
    Answer: 23.1
    Combining Upper & Lower Bounds
    [3 marks]

  4. Question 4. The table shows the frequency densities of a histogram. Estimate the interquartile range.

    Show worked answerHide worked answer
    1. M1: frequencies 4×10, 8×5, 4×15; quartiles are a quarter and three quarters of the total
    2. M1: dfrac3540×10=8.75 and 15+dfrac2560×15=21.25
    3. A1: 12.5
    Answer: 12.5
    Median from a Histogram
    ClassFrequency density0 < x ≤ 10410 < x ≤ 15815 < x ≤ 304
    [3 marks]

  5. Question 5. x is an integer. x²-4x-21 < 0 and x² ≥ 4. Work out how many values x can take.

    Show worked answerHide worked answer
    1. M1: (x-7)(x+3) < 0, so -3 < x < 7
    2. M1: x² ≥ 4 gives x ≤ -2 or x ≥ 2
    3. M1: the integers are -2, 2, 3, 4, 5, 6
    4. A1: 6
    Answer: 6
    Solving Quadratic Inequalities
    [4 marks]
📅 Free lesson: Tue 17th NovSave your place →

Mixed Topic Worksheet Grades 8/9: Day 092

Grades 8/9Calculator

  1. Question 1. The graph of y = f(x + 2) - 5 passes through the point (6, 1). Work out the value of f(8).

    [2 marks]
    Show worked answerHide worked answer
    1. M1: f(6 + 2) - 5 = 1
    2. A1: f(8) = 6
    Answer: f(8) = 6
    Translations Along the x- & y-Axes

  2. Question 2. F is directly proportional to m and inversely proportional to the square of d.
    F = 12 when m = 6 and d = 2.
    Find the value of F when m = 9 and d = 6.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: 12 = k × 6 ÷ 2²
    2. M1: F = 8 × 9 ÷ 6²
    3. A1: 2
    Answer: 2
    Direct & Inverse Proportion with Functions

  3. Question 3. a = 5.2 and b = 3.4, both correct to 1 decimal place. Work out the lower bound of a² - b. Give your answer to 3 significant figures.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: (5.2 - 0.05)² - (3.4 + 0.05) (lower bound of a, upper bound of b)
    2. A1: 23.1
    Answer: 23.1
    Combining Upper & Lower Bounds

  4. Question 4. The table shows the frequency densities of a histogram. Estimate the interquartile range.

    [3 marks]
    ClassFrequency density0 < x ≤ 10410 < x ≤ 15815 < x ≤ 304
    Show worked answerHide worked answer
    1. M1: frequencies 4×10, 8×5, 4×15; quartiles are a quarter and three quarters of the total
    2. M1: dfrac3540×10=8.75 and 15+dfrac2560×15=21.25
    3. A1: 12.5
    Answer: 12.5
    Median from a Histogram

  5. Question 5. x is an integer. x²-4x-21 < 0 and x² ≥ 4. Work out how many values x can take.

    [4 marks]
    Show worked answerHide worked answer
    1. M1: (x-7)(x+3) < 0, so -3 < x < 7
    2. M1: x² ≥ 4 gives x ≤ -2 or x ≥ 2
    3. M1: the integers are -2, 2, 3, 4, 5, 6
    4. A1: 6
    Answer: 6
    Solving Quadratic Inequalities
📅 Free live lesson: Tuesday 17th NovemberSave your free place →

Mixed Topic Worksheet Grades 8/9: Day 092

Grades 8/9Calculator

  1. Question 1. The graph of y = f(x + 2) - 5 passes through the point (6, 1). Work out the value of f(8).

    Show worked answerHide worked answer
    1. M1: f(6 + 2) - 5 = 1
    2. A1: f(8) = 6
    Answer: f(8) = 6
    Translations Along the x- & y-Axes
    [2 marks]

  2. Question 2. F is directly proportional to m and inversely proportional to the square of d.
    F = 12 when m = 6 and d = 2.
    Find the value of F when m = 9 and d = 6.

    Show worked answerHide worked answer
    1. M1: 12 = k × 6 ÷ 2²
    2. M1: F = 8 × 9 ÷ 6²
    3. A1: 2
    Answer: 2
    Direct & Inverse Proportion with Functions
    [3 marks]

  3. Question 3. a = 5.2 and b = 3.4, both correct to 1 decimal place. Work out the lower bound of a² - b. Give your answer to 3 significant figures.

    Show worked answerHide worked answer
    1. M1: (5.2 - 0.05)² - (3.4 + 0.05) (lower bound of a, upper bound of b)
    2. A1: 23.1
    Answer: 23.1
    Combining Upper & Lower Bounds
    [3 marks]

  4. Question 4. The table shows the frequency densities of a histogram. Estimate the interquartile range.

    Show worked answerHide worked answer
    1. M1: frequencies 4×10, 8×5, 4×15; quartiles are a quarter and three quarters of the total
    2. M1: dfrac3540×10=8.75 and 15+dfrac2560×15=21.25
    3. A1: 12.5
    Answer: 12.5
    Median from a Histogram
    ClassFrequency density0 < x ≤ 10410 < x ≤ 15815 < x ≤ 304
    [3 marks]

  5. Question 5. x is an integer. x²-4x-21 < 0 and x² ≥ 4. Work out how many values x can take.

    Show worked answerHide worked answer
    1. M1: (x-7)(x+3) < 0, so -3 < x < 7
    2. M1: x² ≥ 4 gives x ≤ -2 or x ≥ 2
    3. M1: the integers are -2, 2, 3, 4, 5, 6
    4. A1: 6
    Answer: 6
    Solving Quadratic Inequalities
    [4 marks]