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

Mixed Topic Worksheet Grades 6/7: Day 094

Grades 6/7Calculator

  1. Question 1. The mean mass of 6 bags is 12 kg.
    A seventh bag is added and the mean mass of the 7 bags is 13 kg.
    Work out the mass of the seventh bag.

    Show worked answerHide worked answer
    1. M1: total of 7 bags 7 x 13 = 91, total of 6 bags 6 x 12 = 72
    2. M1: 91 - 72
    3. A1: 19 kg
    Answer: 19 kg
    Reverse Mean from a List
    [3 marks]

  2. Question 2. A field is in the shape of a triangle.
    Two sides of the field are 120 m and 85 m long.
    The angle between these two sides is 58^°.
    One bag of grass seed covers 600 m².
    Work out the number of bags of grass seed needed to cover the field.

    Show worked answerHide worked answer
    1. M1: area = 1/2 × 120 × 85 × sin 58^°
    2. M1: area ÷ 600 = 7.2
    3. A1: 8 bags (rounded up)
    Answer: 8 bags
    Area of Triangles Using ½ab sin C
    [3 marks]

  3. Question 3. Sam thinks of an integer n. He adds 2 to the number and cubes the result. He then subtracts n³ and subtracts 8. Prove that Sam's final answer is a multiple of 6.

    Show worked answerHide worked answer
    1. M1: (n + 2)³ = n³ + 6n² + 12n + 8
    2. M1: (n + 2)³ - n³ - 8 = 6n² + 12n
    3. M1: 6n(n + 2)
    4. C1: a multiple of 6 for every integer n
    Answer: 6n(n + 2), a multiple of 6
    Proof with Multiples
    [4 marks]

  4. Question 4. Work out 125¹/³

    Show worked answerHide worked answer
    1. B1: 5
    Answer: 5
    Fractional Powers
    [1 mark]

  5. Question 5. In triangle PQR, angle PRQ = 29^° and dfracPQsin 29^° = 13.6
    Work out PQ. Give your answer to 1 decimal place.

    Show worked answerHide worked answer
    1. M1: PQ = 13.6 × sin 29^°
    2. A1: 6.6
    Answer: 6.6
    Fundamentals of the Sine Rule
    [2 marks]
📅 Free lesson: Tue 17th NovSave your place →

Mixed Topic Worksheet Grades 6/7: Day 094

Grades 6/7Calculator

  1. Question 1. The mean mass of 6 bags is 12 kg.
    A seventh bag is added and the mean mass of the 7 bags is 13 kg.
    Work out the mass of the seventh bag.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: total of 7 bags 7 x 13 = 91, total of 6 bags 6 x 12 = 72
    2. M1: 91 - 72
    3. A1: 19 kg
    Answer: 19 kg
    Reverse Mean from a List

  2. Question 2. A field is in the shape of a triangle.
    Two sides of the field are 120 m and 85 m long.
    The angle between these two sides is 58^°.
    One bag of grass seed covers 600 m².
    Work out the number of bags of grass seed needed to cover the field.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: area = 1/2 × 120 × 85 × sin 58^°
    2. M1: area ÷ 600 = 7.2
    3. A1: 8 bags (rounded up)
    Answer: 8 bags
    Area of Triangles Using ½ab sin C

  3. Question 3. Sam thinks of an integer n. He adds 2 to the number and cubes the result. He then subtracts n³ and subtracts 8. Prove that Sam's final answer is a multiple of 6.

    [4 marks]
    Show worked answerHide worked answer
    1. M1: (n + 2)³ = n³ + 6n² + 12n + 8
    2. M1: (n + 2)³ - n³ - 8 = 6n² + 12n
    3. M1: 6n(n + 2)
    4. C1: a multiple of 6 for every integer n
    Answer: 6n(n + 2), a multiple of 6
    Proof with Multiples

  4. Question 4. Work out 125¹/³

    [1 mark]
    Show worked answerHide worked answer
    1. B1: 5
    Answer: 5
    Fractional Powers

  5. Question 5. In triangle PQR, angle PRQ = 29^° and dfracPQsin 29^° = 13.6
    Work out PQ. Give your answer to 1 decimal place.

    [2 marks]
    Show worked answerHide worked answer
    1. M1: PQ = 13.6 × sin 29^°
    2. A1: 6.6
    Answer: 6.6
    Fundamentals of the Sine Rule
📅 Free live lesson: Tuesday 17th NovemberSave your free place →

Mixed Topic Worksheet Grades 6/7: Day 094

Grades 6/7Calculator

  1. Question 1. The mean mass of 6 bags is 12 kg.
    A seventh bag is added and the mean mass of the 7 bags is 13 kg.
    Work out the mass of the seventh bag.

    Show worked answerHide worked answer
    1. M1: total of 7 bags 7 x 13 = 91, total of 6 bags 6 x 12 = 72
    2. M1: 91 - 72
    3. A1: 19 kg
    Answer: 19 kg
    Reverse Mean from a List
    [3 marks]

  2. Question 2. A field is in the shape of a triangle.
    Two sides of the field are 120 m and 85 m long.
    The angle between these two sides is 58^°.
    One bag of grass seed covers 600 m².
    Work out the number of bags of grass seed needed to cover the field.

    Show worked answerHide worked answer
    1. M1: area = 1/2 × 120 × 85 × sin 58^°
    2. M1: area ÷ 600 = 7.2
    3. A1: 8 bags (rounded up)
    Answer: 8 bags
    Area of Triangles Using ½ab sin C
    [3 marks]

  3. Question 3. Sam thinks of an integer n. He adds 2 to the number and cubes the result. He then subtracts n³ and subtracts 8. Prove that Sam's final answer is a multiple of 6.

    Show worked answerHide worked answer
    1. M1: (n + 2)³ = n³ + 6n² + 12n + 8
    2. M1: (n + 2)³ - n³ - 8 = 6n² + 12n
    3. M1: 6n(n + 2)
    4. C1: a multiple of 6 for every integer n
    Answer: 6n(n + 2), a multiple of 6
    Proof with Multiples
    [4 marks]

  4. Question 4. Work out 125¹/³

    Show worked answerHide worked answer
    1. B1: 5
    Answer: 5
    Fractional Powers
    [1 mark]

  5. Question 5. In triangle PQR, angle PRQ = 29^° and dfracPQsin 29^° = 13.6
    Work out PQ. Give your answer to 1 decimal place.

    Show worked answerHide worked answer
    1. M1: PQ = 13.6 × sin 29^°
    2. A1: 6.6
    Answer: 6.6
    Fundamentals of the Sine Rule
    [2 marks]