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

Mixed Topic Worksheet Grades 6/7: Day 056

Grades 6/7Calculator

  1. Question 1. Two phone plans last for 12 months.

    Plan A: £60 to join, then £12 each month
    Plan B: no joining fee, £16.50 each month

    Which plan costs less for the 12 months?
    You must show your working.

    Show worked answerHide worked answer
    1. M1: 12 × 12 + 60
    2. M1: 12 × 16.50 = 198
    3. C1: 198 is less than 204, so Plan B
    4. A1: 204 - 198 = £6
    Answer: Plan B, by £6
    Applied Best Buys
    [4 marks]

  2. Question 2. Write down the greatest integer that is less than √110

    Show worked answerHide worked answer
    1. M1: 10² = 100 < 110 and 11² = 121 > 110
    2. A1: 10
    Answer: 10
    Estimating Roots
    [2 marks]

  3. Question 3. A solid is enlarged to make a similar solid.
    The surface area of the solid increases by 44%.
    Work out the percentage increase in the volume of the solid.

    Show worked answerHide worked answer
    1. M1: 1 + dfrac44100
    2. M1: √1.44 = 1.2
    3. M1: 1.2³ = 1.728
    4. A1: 72.8
    Answer: 72.8%
    Similar Areas & Volumes
    [4 marks]

  4. Question 4. n is an integer.
    Prove that 5(2n + 3) - 7 is even.

    Show worked answerHide worked answer
    1. M1: 10n + 15 - 7
    2. A1: 10n + 8
    3. C1: 2(5n + 4), which is even
    Answer: 2(5n + 4)
    Proof with Even Numbers
    [3 marks]

  5. Question 5. Triangle P has sides 12 cm and 9 cm with an angle of 35^° between them.
    Triangle Q has sides 10 cm and 10 cm with an angle of 40^° between them.
    Which triangle has the larger area? You must show your working.

    Show worked answerHide worked answer
    1. M1: area of P = 1/2 × 12 × 9 × sin 35^°
    2. M1: area of Q = 1/2 × 10 × 10 × sin 40^°
    3. A1: Triangle Q with 32.1 cm² against 31.0 cm²
    Answer: Triangle Q (32.1 cm² against 31.0 cm²)
    Calculating Area Using ½ab sin C
    [3 marks]
📅 Free lesson: Tue 17th NovSave your place →

Mixed Topic Worksheet Grades 6/7: Day 056

Grades 6/7Calculator

  1. Question 1. Two phone plans last for 12 months.

    Plan A: £60 to join, then £12 each month
    Plan B: no joining fee, £16.50 each month

    Which plan costs less for the 12 months?
    You must show your working.

    [4 marks]
    Show worked answerHide worked answer
    1. M1: 12 × 12 + 60
    2. M1: 12 × 16.50 = 198
    3. C1: 198 is less than 204, so Plan B
    4. A1: 204 - 198 = £6
    Answer: Plan B, by £6
    Applied Best Buys

  2. Question 2. Write down the greatest integer that is less than √110

    [2 marks]
    Show worked answerHide worked answer
    1. M1: 10² = 100 < 110 and 11² = 121 > 110
    2. A1: 10
    Answer: 10
    Estimating Roots

  3. Question 3. A solid is enlarged to make a similar solid.
    The surface area of the solid increases by 44%.
    Work out the percentage increase in the volume of the solid.

    [4 marks]
    Show worked answerHide worked answer
    1. M1: 1 + dfrac44100
    2. M1: √1.44 = 1.2
    3. M1: 1.2³ = 1.728
    4. A1: 72.8
    Answer: 72.8%
    Similar Areas & Volumes

  4. Question 4. n is an integer.
    Prove that 5(2n + 3) - 7 is even.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: 10n + 15 - 7
    2. A1: 10n + 8
    3. C1: 2(5n + 4), which is even
    Answer: 2(5n + 4)
    Proof with Even Numbers

  5. Question 5. Triangle P has sides 12 cm and 9 cm with an angle of 35^° between them.
    Triangle Q has sides 10 cm and 10 cm with an angle of 40^° between them.
    Which triangle has the larger area? You must show your working.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: area of P = 1/2 × 12 × 9 × sin 35^°
    2. M1: area of Q = 1/2 × 10 × 10 × sin 40^°
    3. A1: Triangle Q with 32.1 cm² against 31.0 cm²
    Answer: Triangle Q (32.1 cm² against 31.0 cm²)
    Calculating Area Using ½ab sin C
📅 Free live lesson: Tuesday 17th NovemberSave your free place →

Mixed Topic Worksheet Grades 6/7: Day 056

Grades 6/7Calculator

  1. Question 1. Two phone plans last for 12 months.

    Plan A: £60 to join, then £12 each month
    Plan B: no joining fee, £16.50 each month

    Which plan costs less for the 12 months?
    You must show your working.

    Show worked answerHide worked answer
    1. M1: 12 × 12 + 60
    2. M1: 12 × 16.50 = 198
    3. C1: 198 is less than 204, so Plan B
    4. A1: 204 - 198 = £6
    Answer: Plan B, by £6
    Applied Best Buys
    [4 marks]

  2. Question 2. Write down the greatest integer that is less than √110

    Show worked answerHide worked answer
    1. M1: 10² = 100 < 110 and 11² = 121 > 110
    2. A1: 10
    Answer: 10
    Estimating Roots
    [2 marks]

  3. Question 3. A solid is enlarged to make a similar solid.
    The surface area of the solid increases by 44%.
    Work out the percentage increase in the volume of the solid.

    Show worked answerHide worked answer
    1. M1: 1 + dfrac44100
    2. M1: √1.44 = 1.2
    3. M1: 1.2³ = 1.728
    4. A1: 72.8
    Answer: 72.8%
    Similar Areas & Volumes
    [4 marks]

  4. Question 4. n is an integer.
    Prove that 5(2n + 3) - 7 is even.

    Show worked answerHide worked answer
    1. M1: 10n + 15 - 7
    2. A1: 10n + 8
    3. C1: 2(5n + 4), which is even
    Answer: 2(5n + 4)
    Proof with Even Numbers
    [3 marks]

  5. Question 5. Triangle P has sides 12 cm and 9 cm with an angle of 35^° between them.
    Triangle Q has sides 10 cm and 10 cm with an angle of 40^° between them.
    Which triangle has the larger area? You must show your working.

    Show worked answerHide worked answer
    1. M1: area of P = 1/2 × 12 × 9 × sin 35^°
    2. M1: area of Q = 1/2 × 10 × 10 × sin 40^°
    3. A1: Triangle Q with 32.1 cm² against 31.0 cm²
    Answer: Triangle Q (32.1 cm² against 31.0 cm²)
    Calculating Area Using ½ab sin C
    [3 marks]