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

Mixed Topic Worksheet Grades 6/7: Day 031

Grades 6/7Non-calculator

  1. Question 1. A car travels at 90 kilometres per hour.

    Work out the speed of the car in kilometres per minute.

    Show worked answerHide worked answer
    1. M1: 90 ÷ 60
    2. A1: 1.5
    Answer: 1.5 km per minute
    Converting Compound Measures
    [2 marks]

  2. Question 2. Triangle T has vertices P(2, 2), Q(5, 2) and R(2, 6).
    T is reflected in the line y = 2.
    Write down the image of R and the two vertices that are invariant.

    Show worked answerHide worked answer
    1. B1: R is 4 above y = 2, so its image is (2, -2)
    2. B1: one of P or Q
    3. B1: P and Q, as they lie on y = 2
    Answer: image of R: (2, -2); P and Q are invariant
    Invariant Points
    [3 marks]

  3. Question 3. The cost, in pounds, of a journey of d miles is given by a rule for each of two taxi companies.
    Company A: A(d) = 3 + 2d
    Company B: B(d) = 5 + 1.5d
    Which taxi company is cheaper for a journey of 9 miles?
    You must show your working.

    Show worked answerHide worked answer
    1. M1: A(9) = 3 + 2 × 9
    2. M1: B(9) = 5 + 1.5 × 9
    3. C1: £21 and £18.50, so Company B is cheaper
    Answer: Company B (£18.50 against £21)
    Fundamentals of Functions
    [3 marks]

  4. Question 4. Write dfrac37 as a recurring decimal.
    You must show all your working.

    Show worked answerHide worked answer
    1. M1: 3 ÷ 7 = 0.428571428571...
    2. M1: the block 428571 repeats
    3. A1: 0.dot42857dot1 (dots on the first and last digit of the block)
    Answer: 0.dot42857dot1
    Writing Fractions as Recurring Decimals
    [3 marks]

  5. Question 5. A curve has equation y = 5 × 2x
    Work out the value of y when x = 3 and the value of y when x = -2

    Show worked answerHide worked answer
    1. M1: 2³ = 8
    2. A1: y = 40
    3. B1: y = 5 × dfrac14 = dfrac54
    Answer: y = 40 and y = dfrac54
    Sketching Exponential Graphs
    [3 marks]
📅 Free lesson: Tue 17th NovSave your place →

Mixed Topic Worksheet Grades 6/7: Day 031

Grades 6/7Non-calculator

  1. Question 1. A car travels at 90 kilometres per hour.

    Work out the speed of the car in kilometres per minute.

    [2 marks]
    Show worked answerHide worked answer
    1. M1: 90 ÷ 60
    2. A1: 1.5
    Answer: 1.5 km per minute
    Converting Compound Measures

  2. Question 2. Triangle T has vertices P(2, 2), Q(5, 2) and R(2, 6).
    T is reflected in the line y = 2.
    Write down the image of R and the two vertices that are invariant.

    [3 marks]
    Show worked answerHide worked answer
    1. B1: R is 4 above y = 2, so its image is (2, -2)
    2. B1: one of P or Q
    3. B1: P and Q, as they lie on y = 2
    Answer: image of R: (2, -2); P and Q are invariant
    Invariant Points

  3. Question 3. The cost, in pounds, of a journey of d miles is given by a rule for each of two taxi companies.
    Company A: A(d) = 3 + 2d
    Company B: B(d) = 5 + 1.5d
    Which taxi company is cheaper for a journey of 9 miles?
    You must show your working.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: A(9) = 3 + 2 × 9
    2. M1: B(9) = 5 + 1.5 × 9
    3. C1: £21 and £18.50, so Company B is cheaper
    Answer: Company B (£18.50 against £21)
    Fundamentals of Functions

  4. Question 4. Write dfrac37 as a recurring decimal.
    You must show all your working.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: 3 ÷ 7 = 0.428571428571...
    2. M1: the block 428571 repeats
    3. A1: 0.dot42857dot1 (dots on the first and last digit of the block)
    Answer: 0.dot42857dot1
    Writing Fractions as Recurring Decimals

  5. Question 5. A curve has equation y = 5 × 2x
    Work out the value of y when x = 3 and the value of y when x = -2

    [3 marks]
    Show worked answerHide worked answer
    1. M1: 2³ = 8
    2. A1: y = 40
    3. B1: y = 5 × dfrac14 = dfrac54
    Answer: y = 40 and y = dfrac54
    Sketching Exponential Graphs
📅 Free live lesson: Tuesday 17th NovemberSave your free place →

Mixed Topic Worksheet Grades 6/7: Day 031

Grades 6/7Non-calculator

  1. Question 1. A car travels at 90 kilometres per hour.

    Work out the speed of the car in kilometres per minute.

    Show worked answerHide worked answer
    1. M1: 90 ÷ 60
    2. A1: 1.5
    Answer: 1.5 km per minute
    Converting Compound Measures
    [2 marks]

  2. Question 2. Triangle T has vertices P(2, 2), Q(5, 2) and R(2, 6).
    T is reflected in the line y = 2.
    Write down the image of R and the two vertices that are invariant.

    Show worked answerHide worked answer
    1. B1: R is 4 above y = 2, so its image is (2, -2)
    2. B1: one of P or Q
    3. B1: P and Q, as they lie on y = 2
    Answer: image of R: (2, -2); P and Q are invariant
    Invariant Points
    [3 marks]

  3. Question 3. The cost, in pounds, of a journey of d miles is given by a rule for each of two taxi companies.
    Company A: A(d) = 3 + 2d
    Company B: B(d) = 5 + 1.5d
    Which taxi company is cheaper for a journey of 9 miles?
    You must show your working.

    Show worked answerHide worked answer
    1. M1: A(9) = 3 + 2 × 9
    2. M1: B(9) = 5 + 1.5 × 9
    3. C1: £21 and £18.50, so Company B is cheaper
    Answer: Company B (£18.50 against £21)
    Fundamentals of Functions
    [3 marks]

  4. Question 4. Write dfrac37 as a recurring decimal.
    You must show all your working.

    Show worked answerHide worked answer
    1. M1: 3 ÷ 7 = 0.428571428571...
    2. M1: the block 428571 repeats
    3. A1: 0.dot42857dot1 (dots on the first and last digit of the block)
    Answer: 0.dot42857dot1
    Writing Fractions as Recurring Decimals
    [3 marks]

  5. Question 5. A curve has equation y = 5 × 2x
    Work out the value of y when x = 3 and the value of y when x = -2

    Show worked answerHide worked answer
    1. M1: 2³ = 8
    2. A1: y = 40
    3. B1: y = 5 × dfrac14 = dfrac54
    Answer: y = 40 and y = dfrac54
    Sketching Exponential Graphs
    [3 marks]