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

Mixed Topic Worksheet Grades 6/7: Day 035

Grades 6/7Non-calculator

  1. Question 1. Is 3⁻² greater than 2⁻³? You must show your working.

    Show worked answerHide worked answer
    1. M1: 3⁻² = dfrac19 and 2⁻³ = dfrac18
    2. A1: No, dfrac18 is greater
    Answer: No. 3⁻² = dfrac19 and 2⁻³ = dfrac18, and dfrac18 > dfrac19
    Negative Powers
    [2 marks]

  2. Question 2. Make x the subject of y = dfrac5x - 2

    Show worked answerHide worked answer
    1. M1: y(x - 2) = 5
    2. M1: x - 2 = dfrac5y
    3. A1: x = dfrac5y + 2
    Answer: x = dfrac5y + 2
    Rearranging Harder Equations
    [3 marks]

  3. Question 3. A nature reserve is given protected status for a butterfly if there are at least 300 of them.
    A team marks 45 butterflies in a first catch and releases them.
    In a second catch, the team catches 36 butterflies.
    6 of these 36 butterflies are marked.
    Does the team's estimate show that the butterfly has protected status? You must show your working.

    Show worked answerHide worked answer
    1. M1: 45 × 36 ÷ 6
    2. A1: 270
    3. C1: 270 < 300, so no
    Answer: No: estimate is 270, which is less than 300
    Capture-Recapture
    [3 marks]

  4. Question 4. A code has 2 letters followed by 3 digits.
    The letters are chosen from A, B, C, D and E.
    The digits are chosen from 0 to 9.
    Letters and digits can be used more than once.
    Work out the number of different codes.

    Show worked answerHide worked answer
    1. M1: 5 × 5 × 10 × 10 × 10
    2. A1: 25000
    Answer: 25000
    Combinations Problem Solving
    [2 marks]

  5. Question 5. Triangle ABC has AB = 8 cm, AC = 10 cm and area 20√2 cm². Angle A is acute. Without using a calculator, work out the size of angle A.

    Show worked answerHide worked answer
    1. M1: 1/2 × 8 × 10 × sin A = 20√2
    2. M1: sin A = frac√22
    3. A1: A = 45°
    Answer: 45°
    Calculating Side Lengths Using ½ab sin C
    [3 marks]
📅 Free lesson: Tue 17th NovSave your place →

Mixed Topic Worksheet Grades 6/7: Day 035

Grades 6/7Non-calculator

  1. Question 1. Is 3⁻² greater than 2⁻³? You must show your working.

    [2 marks]
    Show worked answerHide worked answer
    1. M1: 3⁻² = dfrac19 and 2⁻³ = dfrac18
    2. A1: No, dfrac18 is greater
    Answer: No. 3⁻² = dfrac19 and 2⁻³ = dfrac18, and dfrac18 > dfrac19
    Negative Powers

  2. Question 2. Make x the subject of y = dfrac5x - 2

    [3 marks]
    Show worked answerHide worked answer
    1. M1: y(x - 2) = 5
    2. M1: x - 2 = dfrac5y
    3. A1: x = dfrac5y + 2
    Answer: x = dfrac5y + 2
    Rearranging Harder Equations

  3. Question 3. A nature reserve is given protected status for a butterfly if there are at least 300 of them.
    A team marks 45 butterflies in a first catch and releases them.
    In a second catch, the team catches 36 butterflies.
    6 of these 36 butterflies are marked.
    Does the team's estimate show that the butterfly has protected status? You must show your working.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: 45 × 36 ÷ 6
    2. A1: 270
    3. C1: 270 < 300, so no
    Answer: No: estimate is 270, which is less than 300
    Capture-Recapture

  4. Question 4. A code has 2 letters followed by 3 digits.
    The letters are chosen from A, B, C, D and E.
    The digits are chosen from 0 to 9.
    Letters and digits can be used more than once.
    Work out the number of different codes.

    [2 marks]
    Show worked answerHide worked answer
    1. M1: 5 × 5 × 10 × 10 × 10
    2. A1: 25000
    Answer: 25000
    Combinations Problem Solving

  5. Question 5. Triangle ABC has AB = 8 cm, AC = 10 cm and area 20√2 cm². Angle A is acute. Without using a calculator, work out the size of angle A.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: 1/2 × 8 × 10 × sin A = 20√2
    2. M1: sin A = frac√22
    3. A1: A = 45°
    Answer: 45°
    Calculating Side Lengths Using ½ab sin C
📅 Free live lesson: Tuesday 17th NovemberSave your free place →

Mixed Topic Worksheet Grades 6/7: Day 035

Grades 6/7Non-calculator

  1. Question 1. Is 3⁻² greater than 2⁻³? You must show your working.

    Show worked answerHide worked answer
    1. M1: 3⁻² = dfrac19 and 2⁻³ = dfrac18
    2. A1: No, dfrac18 is greater
    Answer: No. 3⁻² = dfrac19 and 2⁻³ = dfrac18, and dfrac18 > dfrac19
    Negative Powers
    [2 marks]

  2. Question 2. Make x the subject of y = dfrac5x - 2

    Show worked answerHide worked answer
    1. M1: y(x - 2) = 5
    2. M1: x - 2 = dfrac5y
    3. A1: x = dfrac5y + 2
    Answer: x = dfrac5y + 2
    Rearranging Harder Equations
    [3 marks]

  3. Question 3. A nature reserve is given protected status for a butterfly if there are at least 300 of them.
    A team marks 45 butterflies in a first catch and releases them.
    In a second catch, the team catches 36 butterflies.
    6 of these 36 butterflies are marked.
    Does the team's estimate show that the butterfly has protected status? You must show your working.

    Show worked answerHide worked answer
    1. M1: 45 × 36 ÷ 6
    2. A1: 270
    3. C1: 270 < 300, so no
    Answer: No: estimate is 270, which is less than 300
    Capture-Recapture
    [3 marks]

  4. Question 4. A code has 2 letters followed by 3 digits.
    The letters are chosen from A, B, C, D and E.
    The digits are chosen from 0 to 9.
    Letters and digits can be used more than once.
    Work out the number of different codes.

    Show worked answerHide worked answer
    1. M1: 5 × 5 × 10 × 10 × 10
    2. A1: 25000
    Answer: 25000
    Combinations Problem Solving
    [2 marks]

  5. Question 5. Triangle ABC has AB = 8 cm, AC = 10 cm and area 20√2 cm². Angle A is acute. Without using a calculator, work out the size of angle A.

    Show worked answerHide worked answer
    1. M1: 1/2 × 8 × 10 × sin A = 20√2
    2. M1: sin A = frac√22
    3. A1: A = 45°
    Answer: 45°
    Calculating Side Lengths Using ½ab sin C
    [3 marks]