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

Mixed Topic Worksheet Grades 6/7: Day 085

Grades 6/7Non-calculator

  1. Question 1. Event A and event B are independent.
    The probability of event A is 0.4
    The probability that both A and B happen is 0.12
    Work out the probability of event B.

    Show worked answerHide worked answer
    1. M1: 0.12 ÷ 0.4
    2. A1: 0.3
    Answer: 0.3
    And/Or Rules
    [2 marks]

  2. Question 2. An enlargement has scale factor 3.
    It maps the point (2, 5) onto the point (8, 5).
    Work out the x-coordinate of the centre.

    Show worked answerHide worked answer
    1. M1: c + 3(2 - c) = 8
    2. A1: c = -1
    Answer: -1
    Invariant Points
    [2 marks]

  3. Question 3. Work out an estimate for sqrtdfrac19.7 × 8.20.41 by rounding each number inside the square root to 1 significant figure.

    Show worked answerHide worked answer
    1. M1: rounds each number to 1 s.f.: 20, 8 and 0.4
    2. M1: dfrac20 × 80.4 = 400
    3. A1: √400 = 20
    Answer: 20
    Estimating Roots
    [3 marks]

  4. Question 4. Prove algebraically that the difference between the squares of two consecutive even integers is a multiple of 4.
    The smaller square is subtracted from the larger.

    Show worked answerHide worked answer
    1. M1: (2n + 2)² - (2n)² = 4n² + 8n + 4 - 4n²
    2. A1: 8n + 4
    3. C1: 8n + 4 = 4(2n + 1), which is a multiple of 4
    Answer: 4(2n + 1), a multiple of 4
    Proof with Square Numbers
    [3 marks]

  5. Question 5. A sketch is to be drawn of the graph of y = x² + 6x + 8
    Work out the coordinates of the turning point and of the point where the graph crosses the y-axis.

    Show worked answerHide worked answer
    1. M1: (x + 3)² - 9 + 8
    2. A1: turning point (-3, -1)
    3. B1: (0, 8)
    Answer: (-3, -1) and (0, 8)
    Full Process for Sketching Quadratics
    [3 marks]
📅 Free lesson: Tue 17th NovSave your place →

Mixed Topic Worksheet Grades 6/7: Day 085

Grades 6/7Non-calculator

  1. Question 1. Event A and event B are independent.
    The probability of event A is 0.4
    The probability that both A and B happen is 0.12
    Work out the probability of event B.

    [2 marks]
    Show worked answerHide worked answer
    1. M1: 0.12 ÷ 0.4
    2. A1: 0.3
    Answer: 0.3
    And/Or Rules

  2. Question 2. An enlargement has scale factor 3.
    It maps the point (2, 5) onto the point (8, 5).
    Work out the x-coordinate of the centre.

    [2 marks]
    Show worked answerHide worked answer
    1. M1: c + 3(2 - c) = 8
    2. A1: c = -1
    Answer: -1
    Invariant Points

  3. Question 3. Work out an estimate for sqrtdfrac19.7 × 8.20.41 by rounding each number inside the square root to 1 significant figure.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: rounds each number to 1 s.f.: 20, 8 and 0.4
    2. M1: dfrac20 × 80.4 = 400
    3. A1: √400 = 20
    Answer: 20
    Estimating Roots

  4. Question 4. Prove algebraically that the difference between the squares of two consecutive even integers is a multiple of 4.
    The smaller square is subtracted from the larger.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: (2n + 2)² - (2n)² = 4n² + 8n + 4 - 4n²
    2. A1: 8n + 4
    3. C1: 8n + 4 = 4(2n + 1), which is a multiple of 4
    Answer: 4(2n + 1), a multiple of 4
    Proof with Square Numbers

  5. Question 5. A sketch is to be drawn of the graph of y = x² + 6x + 8
    Work out the coordinates of the turning point and of the point where the graph crosses the y-axis.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: (x + 3)² - 9 + 8
    2. A1: turning point (-3, -1)
    3. B1: (0, 8)
    Answer: (-3, -1) and (0, 8)
    Full Process for Sketching Quadratics
📅 Free live lesson: Tuesday 17th NovemberSave your free place →

Mixed Topic Worksheet Grades 6/7: Day 085

Grades 6/7Non-calculator

  1. Question 1. Event A and event B are independent.
    The probability of event A is 0.4
    The probability that both A and B happen is 0.12
    Work out the probability of event B.

    Show worked answerHide worked answer
    1. M1: 0.12 ÷ 0.4
    2. A1: 0.3
    Answer: 0.3
    And/Or Rules
    [2 marks]

  2. Question 2. An enlargement has scale factor 3.
    It maps the point (2, 5) onto the point (8, 5).
    Work out the x-coordinate of the centre.

    Show worked answerHide worked answer
    1. M1: c + 3(2 - c) = 8
    2. A1: c = -1
    Answer: -1
    Invariant Points
    [2 marks]

  3. Question 3. Work out an estimate for sqrtdfrac19.7 × 8.20.41 by rounding each number inside the square root to 1 significant figure.

    Show worked answerHide worked answer
    1. M1: rounds each number to 1 s.f.: 20, 8 and 0.4
    2. M1: dfrac20 × 80.4 = 400
    3. A1: √400 = 20
    Answer: 20
    Estimating Roots
    [3 marks]

  4. Question 4. Prove algebraically that the difference between the squares of two consecutive even integers is a multiple of 4.
    The smaller square is subtracted from the larger.

    Show worked answerHide worked answer
    1. M1: (2n + 2)² - (2n)² = 4n² + 8n + 4 - 4n²
    2. A1: 8n + 4
    3. C1: 8n + 4 = 4(2n + 1), which is a multiple of 4
    Answer: 4(2n + 1), a multiple of 4
    Proof with Square Numbers
    [3 marks]

  5. Question 5. A sketch is to be drawn of the graph of y = x² + 6x + 8
    Work out the coordinates of the turning point and of the point where the graph crosses the y-axis.

    Show worked answerHide worked answer
    1. M1: (x + 3)² - 9 + 8
    2. A1: turning point (-3, -1)
    3. B1: (0, 8)
    Answer: (-3, -1) and (0, 8)
    Full Process for Sketching Quadratics
    [3 marks]