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

Mixed Topic Worksheet Grades 6/7: Day 042

Grades 6/7Calculator

  1. Question 1. A coat costs £50.
    It is reduced by 30%.
    Then the new price is reduced by a further 10%.

    Ed says,
    "That is the same as taking 40% off the £50."

    Is Ed correct?
    You must show your working.

    Show worked answerHide worked answer
    1. M1: 50 - 15 = 35 (30% of 50 is 15)
    2. M1: 10% of 35 = 3.5, so the price is 31.5
    3. M1: 50 - 20 = 30 (40% of 50 is 20)
    4. C1: 31.5 is not equal to 30, so Ed is not correct
    Answer: No: £31.50 is not £30
    Applied Best Buys
    [4 marks]

  2. Question 2. f(x) = x² - 2x
    Ravi works out f(-3).
    Ravi's working is f(-3) = -9 + 6 = -3
    Ravi says f(-3) = -3
    Is Ravi correct? You must show your working.

    Show worked answerHide worked answer
    1. M1: (-3)² = 9
    2. A1: 9 - 2 × (-3) = 15, so Ravi is not correct
    Answer: No, f(-3) = 15
    Fundamentals of Functions
    [2 marks]

  3. Question 3. Triangle ABC has vertices A(1, 1), B(5, 1) and C(3, 4).
    Triangle ABC is reflected in the line x = 1.
    Write down the number of vertices of triangle ABC that are invariant.

    Show worked answerHide worked answer
    1. M1: an invariant vertex has x-coordinate 1, the same as the mirror line: only A
    2. A1: 1
    Answer: 1
    Invariant Points
    [2 marks]

  4. Question 4. A circle has centre (0, 0) and passes through the point (6, -8)
    Write down the equation of the circle.

    Show worked answerHide worked answer
    1. M1: r² = 6² + (-8)² = 36 + 64 = 100
    2. A1: x² + y² = 100
    Answer: x² + y² = 100
    Sketching Circles
    [2 marks]

  5. Question 5. In triangle ABC, dfrac6sin A = 8.5 and A is acute.
    Work out angle A. Give your answer to 1 decimal place.

    Show worked answerHide worked answer
    1. M1: sin A = dfrac68.5
    2. M1: A = sin⁻¹≤ft(dfrac68.5)
    3. A1: 44.9
    Answer: 44.9
    Fundamentals of the Sine Rule
    [3 marks]
📅 Free lesson: Tue 17th NovSave your place →

Mixed Topic Worksheet Grades 6/7: Day 042

Grades 6/7Calculator

  1. Question 1. A coat costs £50.
    It is reduced by 30%.
    Then the new price is reduced by a further 10%.

    Ed says,
    "That is the same as taking 40% off the £50."

    Is Ed correct?
    You must show your working.

    [4 marks]
    Show worked answerHide worked answer
    1. M1: 50 - 15 = 35 (30% of 50 is 15)
    2. M1: 10% of 35 = 3.5, so the price is 31.5
    3. M1: 50 - 20 = 30 (40% of 50 is 20)
    4. C1: 31.5 is not equal to 30, so Ed is not correct
    Answer: No: £31.50 is not £30
    Applied Best Buys

  2. Question 2. f(x) = x² - 2x
    Ravi works out f(-3).
    Ravi's working is f(-3) = -9 + 6 = -3
    Ravi says f(-3) = -3
    Is Ravi correct? You must show your working.

    [2 marks]
    Show worked answerHide worked answer
    1. M1: (-3)² = 9
    2. A1: 9 - 2 × (-3) = 15, so Ravi is not correct
    Answer: No, f(-3) = 15
    Fundamentals of Functions

  3. Question 3. Triangle ABC has vertices A(1, 1), B(5, 1) and C(3, 4).
    Triangle ABC is reflected in the line x = 1.
    Write down the number of vertices of triangle ABC that are invariant.

    [2 marks]
    Show worked answerHide worked answer
    1. M1: an invariant vertex has x-coordinate 1, the same as the mirror line: only A
    2. A1: 1
    Answer: 1
    Invariant Points

  4. Question 4. A circle has centre (0, 0) and passes through the point (6, -8)
    Write down the equation of the circle.

    [2 marks]
    Show worked answerHide worked answer
    1. M1: r² = 6² + (-8)² = 36 + 64 = 100
    2. A1: x² + y² = 100
    Answer: x² + y² = 100
    Sketching Circles

  5. Question 5. In triangle ABC, dfrac6sin A = 8.5 and A is acute.
    Work out angle A. Give your answer to 1 decimal place.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: sin A = dfrac68.5
    2. M1: A = sin⁻¹≤ft(dfrac68.5)
    3. A1: 44.9
    Answer: 44.9
    Fundamentals of the Sine Rule
📅 Free live lesson: Tuesday 17th NovemberSave your free place →

Mixed Topic Worksheet Grades 6/7: Day 042

Grades 6/7Calculator

  1. Question 1. A coat costs £50.
    It is reduced by 30%.
    Then the new price is reduced by a further 10%.

    Ed says,
    "That is the same as taking 40% off the £50."

    Is Ed correct?
    You must show your working.

    Show worked answerHide worked answer
    1. M1: 50 - 15 = 35 (30% of 50 is 15)
    2. M1: 10% of 35 = 3.5, so the price is 31.5
    3. M1: 50 - 20 = 30 (40% of 50 is 20)
    4. C1: 31.5 is not equal to 30, so Ed is not correct
    Answer: No: £31.50 is not £30
    Applied Best Buys
    [4 marks]

  2. Question 2. f(x) = x² - 2x
    Ravi works out f(-3).
    Ravi's working is f(-3) = -9 + 6 = -3
    Ravi says f(-3) = -3
    Is Ravi correct? You must show your working.

    Show worked answerHide worked answer
    1. M1: (-3)² = 9
    2. A1: 9 - 2 × (-3) = 15, so Ravi is not correct
    Answer: No, f(-3) = 15
    Fundamentals of Functions
    [2 marks]

  3. Question 3. Triangle ABC has vertices A(1, 1), B(5, 1) and C(3, 4).
    Triangle ABC is reflected in the line x = 1.
    Write down the number of vertices of triangle ABC that are invariant.

    Show worked answerHide worked answer
    1. M1: an invariant vertex has x-coordinate 1, the same as the mirror line: only A
    2. A1: 1
    Answer: 1
    Invariant Points
    [2 marks]

  4. Question 4. A circle has centre (0, 0) and passes through the point (6, -8)
    Write down the equation of the circle.

    Show worked answerHide worked answer
    1. M1: r² = 6² + (-8)² = 36 + 64 = 100
    2. A1: x² + y² = 100
    Answer: x² + y² = 100
    Sketching Circles
    [2 marks]

  5. Question 5. In triangle ABC, dfrac6sin A = 8.5 and A is acute.
    Work out angle A. Give your answer to 1 decimal place.

    Show worked answerHide worked answer
    1. M1: sin A = dfrac68.5
    2. M1: A = sin⁻¹≤ft(dfrac68.5)
    3. A1: 44.9
    Answer: 44.9
    Fundamentals of the Sine Rule
    [3 marks]