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

Mixed Topic Worksheet Grades 6/7: Day 076

Grades 6/7Calculator

  1. Question 1. A jacket costs £85 in the UK.
    The same jacket costs €96 in France.
    £1 = €1.20

    Where is the jacket cheaper, and by how much in pounds? You must show working.

    Show worked answerHide worked answer
    1. M1: 96 ÷ 1.20 = 80
    2. M1: 85 − 80
    3. A1: France, cheaper by £5
    Answer: France, by £5. €96 = £80
    Currency Conversions
    [3 marks]

  2. Question 2. The diagram shows triangle PQR.
    Work out the area of triangle PQR.
    Give your answer to 1 decimal place.

    Show worked answerHide worked answer
    1. M1: 1/2 × 12 × 7 × sin 125^°
    2. A1: 34.4
    Answer: 34.4 cm²
    Area of Triangles Using ½ab sin C
    12 cm7 cm125°QRP
    [2 marks]

  3. Question 3. Anna and Ben simplify dfracx²-25x²-5x.
    Anna's answer is dfracx+5x.
    Ben's answer is dfracx-5x.
    Work out who is correct.
    You must show your working.

    Show worked answerHide worked answer
    1. M1: (x+5)(x-5) or x(x-5)
    2. M1: cancels (x-5)
    3. A1: dfracx+5x, so Anna
    Answer: Anna is correct; the simplified fraction is dfracx+5x
    Simplifying Algebraic Fractions
    [3 marks]

  4. Question 4. Cumulative frequency graphs for test marks give these values. Boys: lower quartile 41, median 52, upper quartile 63. Girls: lower quartile 50, median 58, upper quartile 64. Compare the marks of the boys and the girls.

    Show worked answerHide worked answer
    1. B1: girls have the higher median (58 > 52)
    2. B1: girls have the smaller interquartile range (14 < 22), so are more consistent
    Answer: The girls' median is higher (58 > 52) and their interquartile range is smaller (14 < 22), so the girls did better and were more consistent.
    Cumulative Frequency Median & IQR
    [2 marks]

  5. Question 5. A triangular field ABC has AB = 48 m, BC = 63 m and angle ABC = 82^°
    Grass seed costs £1.35 per square metre for the whole field.
    Work out the total cost of the seed, to the nearest pound.

    Show worked answerHide worked answer
    1. M1: 1/2 × 48 × 63 × sin 82^°
    2. A1: area = 1497.3 m²
    3. M1: 1497.3 × 1.35
    4. A1: 2021
    Answer: £2021
    Calculating Area Using ½ab sin C
    [4 marks]
📅 Free lesson: Tue 17th NovSave your place →

Mixed Topic Worksheet Grades 6/7: Day 076

Grades 6/7Calculator

  1. Question 1. A jacket costs £85 in the UK.
    The same jacket costs €96 in France.
    £1 = €1.20

    Where is the jacket cheaper, and by how much in pounds? You must show working.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: 96 ÷ 1.20 = 80
    2. M1: 85 − 80
    3. A1: France, cheaper by £5
    Answer: France, by £5. €96 = £80
    Currency Conversions

  2. Question 2. The diagram shows triangle PQR.
    Work out the area of triangle PQR.
    Give your answer to 1 decimal place.

    [2 marks]
    12 cm7 cm125°QRP
    Show worked answerHide worked answer
    1. M1: 1/2 × 12 × 7 × sin 125^°
    2. A1: 34.4
    Answer: 34.4 cm²
    Area of Triangles Using ½ab sin C

  3. Question 3. Anna and Ben simplify dfracx²-25x²-5x.
    Anna's answer is dfracx+5x.
    Ben's answer is dfracx-5x.
    Work out who is correct.
    You must show your working.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: (x+5)(x-5) or x(x-5)
    2. M1: cancels (x-5)
    3. A1: dfracx+5x, so Anna
    Answer: Anna is correct; the simplified fraction is dfracx+5x
    Simplifying Algebraic Fractions

  4. Question 4. Cumulative frequency graphs for test marks give these values. Boys: lower quartile 41, median 52, upper quartile 63. Girls: lower quartile 50, median 58, upper quartile 64. Compare the marks of the boys and the girls.

    [2 marks]
    Show worked answerHide worked answer
    1. B1: girls have the higher median (58 > 52)
    2. B1: girls have the smaller interquartile range (14 < 22), so are more consistent
    Answer: The girls' median is higher (58 > 52) and their interquartile range is smaller (14 < 22), so the girls did better and were more consistent.
    Cumulative Frequency Median & IQR

  5. Question 5. A triangular field ABC has AB = 48 m, BC = 63 m and angle ABC = 82^°
    Grass seed costs £1.35 per square metre for the whole field.
    Work out the total cost of the seed, to the nearest pound.

    [4 marks]
    Show worked answerHide worked answer
    1. M1: 1/2 × 48 × 63 × sin 82^°
    2. A1: area = 1497.3 m²
    3. M1: 1497.3 × 1.35
    4. A1: 2021
    Answer: £2021
    Calculating Area Using ½ab sin C
📅 Free live lesson: Tuesday 17th NovemberSave your free place →

Mixed Topic Worksheet Grades 6/7: Day 076

Grades 6/7Calculator

  1. Question 1. A jacket costs £85 in the UK.
    The same jacket costs €96 in France.
    £1 = €1.20

    Where is the jacket cheaper, and by how much in pounds? You must show working.

    Show worked answerHide worked answer
    1. M1: 96 ÷ 1.20 = 80
    2. M1: 85 − 80
    3. A1: France, cheaper by £5
    Answer: France, by £5. €96 = £80
    Currency Conversions
    [3 marks]

  2. Question 2. The diagram shows triangle PQR.
    Work out the area of triangle PQR.
    Give your answer to 1 decimal place.

    Show worked answerHide worked answer
    1. M1: 1/2 × 12 × 7 × sin 125^°
    2. A1: 34.4
    Answer: 34.4 cm²
    Area of Triangles Using ½ab sin C
    12 cm7 cm125°QRP
    [2 marks]

  3. Question 3. Anna and Ben simplify dfracx²-25x²-5x.
    Anna's answer is dfracx+5x.
    Ben's answer is dfracx-5x.
    Work out who is correct.
    You must show your working.

    Show worked answerHide worked answer
    1. M1: (x+5)(x-5) or x(x-5)
    2. M1: cancels (x-5)
    3. A1: dfracx+5x, so Anna
    Answer: Anna is correct; the simplified fraction is dfracx+5x
    Simplifying Algebraic Fractions
    [3 marks]

  4. Question 4. Cumulative frequency graphs for test marks give these values. Boys: lower quartile 41, median 52, upper quartile 63. Girls: lower quartile 50, median 58, upper quartile 64. Compare the marks of the boys and the girls.

    Show worked answerHide worked answer
    1. B1: girls have the higher median (58 > 52)
    2. B1: girls have the smaller interquartile range (14 < 22), so are more consistent
    Answer: The girls' median is higher (58 > 52) and their interquartile range is smaller (14 < 22), so the girls did better and were more consistent.
    Cumulative Frequency Median & IQR
    [2 marks]

  5. Question 5. A triangular field ABC has AB = 48 m, BC = 63 m and angle ABC = 82^°
    Grass seed costs £1.35 per square metre for the whole field.
    Work out the total cost of the seed, to the nearest pound.

    Show worked answerHide worked answer
    1. M1: 1/2 × 48 × 63 × sin 82^°
    2. A1: area = 1497.3 m²
    3. M1: 1497.3 × 1.35
    4. A1: 2021
    Answer: £2021
    Calculating Area Using ½ab sin C
    [4 marks]