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

Mixed Topic Worksheet Grades 8/9: Day 087

Grades 8/9Non-calculator

  1. Question 1. The curve y = f(x) has a minimum at (2, -5). Write down the minimum point of y = f(x + 3) - 1.

    Show worked answerHide worked answer
    1. M1: 3 left and 1 down
    2. A1: (-1, -6)
    Answer: (-1, -6)
    Translations Along the x- & y-Axes
    [2 marks]

  2. Question 2. Raj says that the sum of the squares of any three consecutive integers is always 2 more than a multiple of 3.
    Is Raj correct?
    You must show your working.

    Show worked answerHide worked answer
    1. M1: (n - 1)² + n² + (n + 1)² = n² - 2n + 1 + n² + n² + 2n + 1
    2. A1: 3n² + 2
    3. C1: 3n² is a multiple of 3, so Raj is correct
    Answer: Raj is correct
    Proof with Consecutive Numbers
    [3 marks]

  3. Question 3. The class 10 < x ≤ 30 has a frequency of 60.
    The class 30 < x ≤ 35 has a frequency of 22.
    Work out the frequency density of each class.

    Show worked answerHide worked answer
    1. M1: 60 ÷ 20 or 22 ÷ 5
    2. A1: 3
    3. A1: 4.4
    Answer: 3 and 4.4
    Sketching Histograms
    [3 marks]

  4. Question 4. Solve x² + 6x - 2 = 0 by completing the square. Give your solutions in the form a ± √b.

    Show worked answerHide worked answer
    1. M1: (x + 3)² - 9 - 2 = 0
    2. M1: (x + 3)² = 11
    3. A1: x = -3 ± √11
    Answer: x = -3 ± √11
    Solving Quadratics by Completing the Square (a = 1)
    [3 marks]

  5. Question 5. A stall's daily profit, pounds P, when each drink costs pounds x, is

    P = 60x - 5x² - 100

    Work out the values of x for which the profit is more than pounds 75

    Show worked answerHide worked answer
    1. M1: 60x - 5x² - 100 > 75
    2. M1: x²-12x+35 < 0
    3. M1: (x - 5)(x - 7) < 0
    4. A1: 5 < x < 7
    Answer: 5 < x < 7
    Solving Quadratic Inequalities
    [4 marks]
📅 Free lesson: Tue 17th NovSave your place →

Mixed Topic Worksheet Grades 8/9: Day 087

Grades 8/9Non-calculator

  1. Question 1. The curve y = f(x) has a minimum at (2, -5). Write down the minimum point of y = f(x + 3) - 1.

    [2 marks]
    Show worked answerHide worked answer
    1. M1: 3 left and 1 down
    2. A1: (-1, -6)
    Answer: (-1, -6)
    Translations Along the x- & y-Axes

  2. Question 2. Raj says that the sum of the squares of any three consecutive integers is always 2 more than a multiple of 3.
    Is Raj correct?
    You must show your working.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: (n - 1)² + n² + (n + 1)² = n² - 2n + 1 + n² + n² + 2n + 1
    2. A1: 3n² + 2
    3. C1: 3n² is a multiple of 3, so Raj is correct
    Answer: Raj is correct
    Proof with Consecutive Numbers

  3. Question 3. The class 10 < x ≤ 30 has a frequency of 60.
    The class 30 < x ≤ 35 has a frequency of 22.
    Work out the frequency density of each class.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: 60 ÷ 20 or 22 ÷ 5
    2. A1: 3
    3. A1: 4.4
    Answer: 3 and 4.4
    Sketching Histograms

  4. Question 4. Solve x² + 6x - 2 = 0 by completing the square. Give your solutions in the form a ± √b.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: (x + 3)² - 9 - 2 = 0
    2. M1: (x + 3)² = 11
    3. A1: x = -3 ± √11
    Answer: x = -3 ± √11
    Solving Quadratics by Completing the Square (a = 1)

  5. Question 5. A stall's daily profit, pounds P, when each drink costs pounds x, is

    P = 60x - 5x² - 100

    Work out the values of x for which the profit is more than pounds 75

    [4 marks]
    Show worked answerHide worked answer
    1. M1: 60x - 5x² - 100 > 75
    2. M1: x²-12x+35 < 0
    3. M1: (x - 5)(x - 7) < 0
    4. A1: 5 < x < 7
    Answer: 5 < x < 7
    Solving Quadratic Inequalities
📅 Free live lesson: Tuesday 17th NovemberSave your free place →

Mixed Topic Worksheet Grades 8/9: Day 087

Grades 8/9Non-calculator

  1. Question 1. The curve y = f(x) has a minimum at (2, -5). Write down the minimum point of y = f(x + 3) - 1.

    Show worked answerHide worked answer
    1. M1: 3 left and 1 down
    2. A1: (-1, -6)
    Answer: (-1, -6)
    Translations Along the x- & y-Axes
    [2 marks]

  2. Question 2. Raj says that the sum of the squares of any three consecutive integers is always 2 more than a multiple of 3.
    Is Raj correct?
    You must show your working.

    Show worked answerHide worked answer
    1. M1: (n - 1)² + n² + (n + 1)² = n² - 2n + 1 + n² + n² + 2n + 1
    2. A1: 3n² + 2
    3. C1: 3n² is a multiple of 3, so Raj is correct
    Answer: Raj is correct
    Proof with Consecutive Numbers
    [3 marks]

  3. Question 3. The class 10 < x ≤ 30 has a frequency of 60.
    The class 30 < x ≤ 35 has a frequency of 22.
    Work out the frequency density of each class.

    Show worked answerHide worked answer
    1. M1: 60 ÷ 20 or 22 ÷ 5
    2. A1: 3
    3. A1: 4.4
    Answer: 3 and 4.4
    Sketching Histograms
    [3 marks]

  4. Question 4. Solve x² + 6x - 2 = 0 by completing the square. Give your solutions in the form a ± √b.

    Show worked answerHide worked answer
    1. M1: (x + 3)² - 9 - 2 = 0
    2. M1: (x + 3)² = 11
    3. A1: x = -3 ± √11
    Answer: x = -3 ± √11
    Solving Quadratics by Completing the Square (a = 1)
    [3 marks]

  5. Question 5. A stall's daily profit, pounds P, when each drink costs pounds x, is

    P = 60x - 5x² - 100

    Work out the values of x for which the profit is more than pounds 75

    Show worked answerHide worked answer
    1. M1: 60x - 5x² - 100 > 75
    2. M1: x²-12x+35 < 0
    3. M1: (x - 5)(x - 7) < 0
    4. A1: 5 < x < 7
    Answer: 5 < x < 7
    Solving Quadratic Inequalities
    [4 marks]