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

Mixed Topic Worksheet Grades 6/7: Day 044

Grades 6/7Calculator

  1. Question 1. The cost per person, c pounds, of hiring a minibus is inversely proportional to the number of people, n, sharing it.
    When 4 people share the minibus, each person pays £15.
    Work out the percentage decrease in the cost per person when 5 people share the minibus.

    Show worked answerHide worked answer
    1. M1: 4 × 15 = 60
    2. M1: 60 ÷ 5 = 12
    3. M1: (15 − 12) ÷ 15 × 100
    4. A1: 20
    Answer: 20%
    Inverse Proportion Graphs
    [4 marks]

  2. Question 2. Make x the subject of y = dfrac6x + 1

    Show worked answerHide worked answer
    1. M1: y - 1 = dfrac6x
    2. M1: x(y - 1) = 6
    3. A1: x = dfrac6y - 1
    Answer: x = dfrac6y - 1
    Rearranging Harder Equations
    [3 marks]

  3. Question 3. Ravi says, "If I double the length, width and height of a cuboid, its volume doubles."
    Use a 2 cm by 3 cm by 4 cm cuboid to show that Ravi is wrong.

    Show worked answerHide worked answer
    1. M1: original volume 2 × 3 × 4 = 24
    2. M1: new volume 4 × 6 × 8 = 192
    3. A1: 192 ÷ 24 = 8, so the volume is 8 times as big
    Answer: 24 cm³ becomes 192 cm³, which is 8 times bigger
    Similar Areas & Volumes
    [3 marks]

  4. Question 4. Here is triangle DEF.
    Work out the length of DF.
    Give your answer to 1 decimal place.

    Show worked answerHide worked answer
    1. M1: dfracDFsin 112^° = dfrac9.4sin 35^°
    2. M1: DF = dfrac9.4 × sin 112^°sin 35^°
    3. A1: 15.2
    Answer: 15.2
    Finding Side Lengths Using the Sine Rule
    9.4 cm35°112°DEFNot drawn accurately
    [3 marks]

  5. Question 5. A shop increases the price of a jacket by 20%.
    It then reduces the new price by 25%.
    The final price of the jacket is £135.
    Work out the price of the jacket before the increase.

    Show worked answerHide worked answer
    1. M1: 100 + 20 = 120% and 100 - 25 = 75%
    2. M1: 1.2 × 0.75 = 0.9
    3. M1: 135 ÷ 0.9
    4. A1: 150
    Answer: £150
    Finding the Initial Amount
    [4 marks]
📅 Free lesson: Tue 17th NovSave your place →

Mixed Topic Worksheet Grades 6/7: Day 044

Grades 6/7Calculator

  1. Question 1. The cost per person, c pounds, of hiring a minibus is inversely proportional to the number of people, n, sharing it.
    When 4 people share the minibus, each person pays £15.
    Work out the percentage decrease in the cost per person when 5 people share the minibus.

    [4 marks]
    Show worked answerHide worked answer
    1. M1: 4 × 15 = 60
    2. M1: 60 ÷ 5 = 12
    3. M1: (15 − 12) ÷ 15 × 100
    4. A1: 20
    Answer: 20%
    Inverse Proportion Graphs

  2. Question 2. Make x the subject of y = dfrac6x + 1

    [3 marks]
    Show worked answerHide worked answer
    1. M1: y - 1 = dfrac6x
    2. M1: x(y - 1) = 6
    3. A1: x = dfrac6y - 1
    Answer: x = dfrac6y - 1
    Rearranging Harder Equations

  3. Question 3. Ravi says, "If I double the length, width and height of a cuboid, its volume doubles."
    Use a 2 cm by 3 cm by 4 cm cuboid to show that Ravi is wrong.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: original volume 2 × 3 × 4 = 24
    2. M1: new volume 4 × 6 × 8 = 192
    3. A1: 192 ÷ 24 = 8, so the volume is 8 times as big
    Answer: 24 cm³ becomes 192 cm³, which is 8 times bigger
    Similar Areas & Volumes

  4. Question 4. Here is triangle DEF.
    Work out the length of DF.
    Give your answer to 1 decimal place.

    [3 marks]
    9.4 cm35°112°DEFNot drawn accurately
    Show worked answerHide worked answer
    1. M1: dfracDFsin 112^° = dfrac9.4sin 35^°
    2. M1: DF = dfrac9.4 × sin 112^°sin 35^°
    3. A1: 15.2
    Answer: 15.2
    Finding Side Lengths Using the Sine Rule

  5. Question 5. A shop increases the price of a jacket by 20%.
    It then reduces the new price by 25%.
    The final price of the jacket is £135.
    Work out the price of the jacket before the increase.

    [4 marks]
    Show worked answerHide worked answer
    1. M1: 100 + 20 = 120% and 100 - 25 = 75%
    2. M1: 1.2 × 0.75 = 0.9
    3. M1: 135 ÷ 0.9
    4. A1: 150
    Answer: £150
    Finding the Initial Amount
📅 Free live lesson: Tuesday 17th NovemberSave your free place →

Mixed Topic Worksheet Grades 6/7: Day 044

Grades 6/7Calculator

  1. Question 1. The cost per person, c pounds, of hiring a minibus is inversely proportional to the number of people, n, sharing it.
    When 4 people share the minibus, each person pays £15.
    Work out the percentage decrease in the cost per person when 5 people share the minibus.

    Show worked answerHide worked answer
    1. M1: 4 × 15 = 60
    2. M1: 60 ÷ 5 = 12
    3. M1: (15 − 12) ÷ 15 × 100
    4. A1: 20
    Answer: 20%
    Inverse Proportion Graphs
    [4 marks]

  2. Question 2. Make x the subject of y = dfrac6x + 1

    Show worked answerHide worked answer
    1. M1: y - 1 = dfrac6x
    2. M1: x(y - 1) = 6
    3. A1: x = dfrac6y - 1
    Answer: x = dfrac6y - 1
    Rearranging Harder Equations
    [3 marks]

  3. Question 3. Ravi says, "If I double the length, width and height of a cuboid, its volume doubles."
    Use a 2 cm by 3 cm by 4 cm cuboid to show that Ravi is wrong.

    Show worked answerHide worked answer
    1. M1: original volume 2 × 3 × 4 = 24
    2. M1: new volume 4 × 6 × 8 = 192
    3. A1: 192 ÷ 24 = 8, so the volume is 8 times as big
    Answer: 24 cm³ becomes 192 cm³, which is 8 times bigger
    Similar Areas & Volumes
    [3 marks]

  4. Question 4. Here is triangle DEF.
    Work out the length of DF.
    Give your answer to 1 decimal place.

    Show worked answerHide worked answer
    1. M1: dfracDFsin 112^° = dfrac9.4sin 35^°
    2. M1: DF = dfrac9.4 × sin 112^°sin 35^°
    3. A1: 15.2
    Answer: 15.2
    Finding Side Lengths Using the Sine Rule
    9.4 cm35°112°DEFNot drawn accurately
    [3 marks]

  5. Question 5. A shop increases the price of a jacket by 20%.
    It then reduces the new price by 25%.
    The final price of the jacket is £135.
    Work out the price of the jacket before the increase.

    Show worked answerHide worked answer
    1. M1: 100 + 20 = 120% and 100 - 25 = 75%
    2. M1: 1.2 × 0.75 = 0.9
    3. M1: 135 ÷ 0.9
    4. A1: 150
    Answer: £150
    Finding the Initial Amount
    [4 marks]