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

Mixed Topic Worksheet Grades 6/7: Day 012

Grades 6/7Calculator

  1. Question 1. The population of a town is 40 000.
    The population falls by 5% each year.
    Work out the population of the town after 2 years.

    Show worked answerHide worked answer
    1. M1: 100 - 5 = 95%
    2. M1: 40000 × 0.95 × 0.95
    3. A1: 36100
    Answer: 36 100
    Compound Decay
    [3 marks]

  2. Question 2. A shop sells one type of T-shirt.
    It comes in 3 colours and 4 designs.
    Each colour and design comes in the same number of sizes.
    There are 96 different T-shirts in total.
    Work out the number of sizes.

    Show worked answerHide worked answer
    1. M1: 3 × 4 = 12 combinations of colour and design
    2. M1: 96 ÷ 12
    3. A1: 8
    Answer: 8
    Calculating Combinations
    [3 marks]

  3. Question 3. Make x the subject of y = dfrac15x - 4

    Show worked answerHide worked answer
    1. M1: y(x - 4) = 15
    2. M1: x - 4 = dfrac15y
    3. A1: x = dfrac15y + 4
    Answer: x = dfrac15y + 4
    Rearranging Harder Equations
    [3 marks]

  4. Question 4. Here is a speed-time graph for a car.
    Nina says, "The distance is 12 × 40 = 480 metres."
    Is Nina correct?
    Give a reason for your answer.

    Show worked answerHide worked answer
    1. M1: ½ × (40 + 20) × 12 = 360
    2. C1: No, 480 is greater than 360 because the speed was not 12 throughout
    Answer: No: the distance is 360 m
    Calculating Total Distance Travelled Using Speed-Time Graphs
    Time (seconds)Speed (m/s)04812010203040
    [2 marks]

  5. Question 5. Here is triangle ABC.
    Work out the length of BC.
    Give your answer to 1 decimal place.

    Show worked answerHide worked answer
    1. M1: BC² = 8² + 13² - 2 × 8 × 13 × cos 38^°
    2. M1: BC² = 233.00 - 163.91 = 69.09
    3. A1: BC = 8.3
    Answer: 8.3 cm
    Finding Side Lengths Using the Cosine Rule
    13 cm8 cm38°ABC
    [3 marks]
📅 Free lesson: Tue 17th NovSave your place →

Mixed Topic Worksheet Grades 6/7: Day 012

Grades 6/7Calculator

  1. Question 1. The population of a town is 40 000.
    The population falls by 5% each year.
    Work out the population of the town after 2 years.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: 100 - 5 = 95%
    2. M1: 40000 × 0.95 × 0.95
    3. A1: 36100
    Answer: 36 100
    Compound Decay

  2. Question 2. A shop sells one type of T-shirt.
    It comes in 3 colours and 4 designs.
    Each colour and design comes in the same number of sizes.
    There are 96 different T-shirts in total.
    Work out the number of sizes.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: 3 × 4 = 12 combinations of colour and design
    2. M1: 96 ÷ 12
    3. A1: 8
    Answer: 8
    Calculating Combinations

  3. Question 3. Make x the subject of y = dfrac15x - 4

    [3 marks]
    Show worked answerHide worked answer
    1. M1: y(x - 4) = 15
    2. M1: x - 4 = dfrac15y
    3. A1: x = dfrac15y + 4
    Answer: x = dfrac15y + 4
    Rearranging Harder Equations

  4. Question 4. Here is a speed-time graph for a car.
    Nina says, "The distance is 12 × 40 = 480 metres."
    Is Nina correct?
    Give a reason for your answer.

    [2 marks]
    Time (seconds)Speed (m/s)04812010203040
    Show worked answerHide worked answer
    1. M1: ½ × (40 + 20) × 12 = 360
    2. C1: No, 480 is greater than 360 because the speed was not 12 throughout
    Answer: No: the distance is 360 m
    Calculating Total Distance Travelled Using Speed-Time Graphs

  5. Question 5. Here is triangle ABC.
    Work out the length of BC.
    Give your answer to 1 decimal place.

    [3 marks]
    13 cm8 cm38°ABC
    Show worked answerHide worked answer
    1. M1: BC² = 8² + 13² - 2 × 8 × 13 × cos 38^°
    2. M1: BC² = 233.00 - 163.91 = 69.09
    3. A1: BC = 8.3
    Answer: 8.3 cm
    Finding Side Lengths Using the Cosine Rule
📅 Free live lesson: Tuesday 17th NovemberSave your free place →

Mixed Topic Worksheet Grades 6/7: Day 012

Grades 6/7Calculator

  1. Question 1. The population of a town is 40 000.
    The population falls by 5% each year.
    Work out the population of the town after 2 years.

    Show worked answerHide worked answer
    1. M1: 100 - 5 = 95%
    2. M1: 40000 × 0.95 × 0.95
    3. A1: 36100
    Answer: 36 100
    Compound Decay
    [3 marks]

  2. Question 2. A shop sells one type of T-shirt.
    It comes in 3 colours and 4 designs.
    Each colour and design comes in the same number of sizes.
    There are 96 different T-shirts in total.
    Work out the number of sizes.

    Show worked answerHide worked answer
    1. M1: 3 × 4 = 12 combinations of colour and design
    2. M1: 96 ÷ 12
    3. A1: 8
    Answer: 8
    Calculating Combinations
    [3 marks]

  3. Question 3. Make x the subject of y = dfrac15x - 4

    Show worked answerHide worked answer
    1. M1: y(x - 4) = 15
    2. M1: x - 4 = dfrac15y
    3. A1: x = dfrac15y + 4
    Answer: x = dfrac15y + 4
    Rearranging Harder Equations
    [3 marks]

  4. Question 4. Here is a speed-time graph for a car.
    Nina says, "The distance is 12 × 40 = 480 metres."
    Is Nina correct?
    Give a reason for your answer.

    Show worked answerHide worked answer
    1. M1: ½ × (40 + 20) × 12 = 360
    2. C1: No, 480 is greater than 360 because the speed was not 12 throughout
    Answer: No: the distance is 360 m
    Calculating Total Distance Travelled Using Speed-Time Graphs
    Time (seconds)Speed (m/s)04812010203040
    [2 marks]

  5. Question 5. Here is triangle ABC.
    Work out the length of BC.
    Give your answer to 1 decimal place.

    Show worked answerHide worked answer
    1. M1: BC² = 8² + 13² - 2 × 8 × 13 × cos 38^°
    2. M1: BC² = 233.00 - 163.91 = 69.09
    3. A1: BC = 8.3
    Answer: 8.3 cm
    Finding Side Lengths Using the Cosine Rule
    13 cm8 cm38°ABC
    [3 marks]