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

Mixed Topic Worksheet Grades 6/7: Day 100

Grades 6/7Calculator

  1. Question 1. P(A)=0.6, P(B)=0.3 and P(Acap B)=0.2. Work out P(Acup B).

    Show worked answerHide worked answer
    1. M1: 0.6+0.3-0.2
    2. A1: 0.7
    Answer: 0.7
    Finding Probabilities with Venn Diagrams
    [2 marks]

  2. Question 2. Ruth and Sam each estimate the number of rabbits on the same field.
    The table shows their results.
    Work out each estimate.
    Whose estimate is likely to be more reliable?
    Give a reason for your answer.

    Show worked answerHide worked answer
    1. M1: 50 × 40 ÷ 8
    2. M1: 50 × 120 ÷ 20
    3. A1: 250 for Ruth, 300 for Sam
    4. C1: Sam's, because his second catch is larger
    Answer: Ruth 250, Sam 300; Sam's, because his second catch is larger
    Capture-Recapture
    RuthSamRabbits marked and released5050Rabbits in the second catch40120Marked rabbits in the second catch820
    [4 marks]

  3. Question 3. 6.4² = 40.96 and 6.5² = 42.25
    Use these to write down the value of √41
    Give your answer correct to 1 decimal place.

    Show worked answerHide worked answer
    1. M1: 41 - 40.96 = 0.04 and 42.25 - 41 = 1.25
    2. A1: 6.4
    Answer: 6.4
    Estimating Roots
    [2 marks]

  4. Question 4. Isosceles triangle ABC: AB = AC = x cm, angle BAC = 50^°, area = 40 cm²
    Work out x to 1 decimal place.

    Show worked answerHide worked answer
    1. M1: 40 = 1/2 x² sin 50^°
    2. M1: x² = 80/sin 50^° = 104.4
    3. A1: 10.2
    Answer: 10.2 cm
    Using the Area Rule with Isosceles Triangles
    x cmx cm50°BCANot drawn accurately
    [3 marks]

  5. Question 5. The product of two consecutive positive odd numbers is 63.
    Use algebra to work out the two numbers.

    Show worked answerHide worked answer
    1. M1: (2n + 1)(2n + 3) = 4n² + 8n + 3
    2. M1: 4n² + 8n + 3 = 63 so n² + 2n - 15 = 0
    3. M1: (n + 5)(n - 3) = 0
    4. A1: n = 3 so the numbers are 7 and 9
    Answer: 7 and 9
    Proof with Odd Numbers
    [4 marks]
📅 Free lesson: Tue 17th NovSave your place →

Mixed Topic Worksheet Grades 6/7: Day 100

Grades 6/7Calculator

  1. Question 1. P(A)=0.6, P(B)=0.3 and P(Acap B)=0.2. Work out P(Acup B).

    [2 marks]
    Show worked answerHide worked answer
    1. M1: 0.6+0.3-0.2
    2. A1: 0.7
    Answer: 0.7
    Finding Probabilities with Venn Diagrams

  2. Question 2. Ruth and Sam each estimate the number of rabbits on the same field.
    The table shows their results.
    Work out each estimate.
    Whose estimate is likely to be more reliable?
    Give a reason for your answer.

    [4 marks]
    RuthSamRabbits marked and released5050Rabbits in the second catch40120Marked rabbits in the second catch820
    Show worked answerHide worked answer
    1. M1: 50 × 40 ÷ 8
    2. M1: 50 × 120 ÷ 20
    3. A1: 250 for Ruth, 300 for Sam
    4. C1: Sam's, because his second catch is larger
    Answer: Ruth 250, Sam 300; Sam's, because his second catch is larger
    Capture-Recapture

  3. Question 3. 6.4² = 40.96 and 6.5² = 42.25
    Use these to write down the value of √41
    Give your answer correct to 1 decimal place.

    [2 marks]
    Show worked answerHide worked answer
    1. M1: 41 - 40.96 = 0.04 and 42.25 - 41 = 1.25
    2. A1: 6.4
    Answer: 6.4
    Estimating Roots

  4. Question 4. Isosceles triangle ABC: AB = AC = x cm, angle BAC = 50^°, area = 40 cm²
    Work out x to 1 decimal place.

    [3 marks]
    x cmx cm50°BCANot drawn accurately
    Show worked answerHide worked answer
    1. M1: 40 = 1/2 x² sin 50^°
    2. M1: x² = 80/sin 50^° = 104.4
    3. A1: 10.2
    Answer: 10.2 cm
    Using the Area Rule with Isosceles Triangles

  5. Question 5. The product of two consecutive positive odd numbers is 63.
    Use algebra to work out the two numbers.

    [4 marks]
    Show worked answerHide worked answer
    1. M1: (2n + 1)(2n + 3) = 4n² + 8n + 3
    2. M1: 4n² + 8n + 3 = 63 so n² + 2n - 15 = 0
    3. M1: (n + 5)(n - 3) = 0
    4. A1: n = 3 so the numbers are 7 and 9
    Answer: 7 and 9
    Proof with Odd Numbers
📅 Free live lesson: Tuesday 17th NovemberSave your free place →

Mixed Topic Worksheet Grades 6/7: Day 100

Grades 6/7Calculator

  1. Question 1. P(A)=0.6, P(B)=0.3 and P(Acap B)=0.2. Work out P(Acup B).

    Show worked answerHide worked answer
    1. M1: 0.6+0.3-0.2
    2. A1: 0.7
    Answer: 0.7
    Finding Probabilities with Venn Diagrams
    [2 marks]

  2. Question 2. Ruth and Sam each estimate the number of rabbits on the same field.
    The table shows their results.
    Work out each estimate.
    Whose estimate is likely to be more reliable?
    Give a reason for your answer.

    Show worked answerHide worked answer
    1. M1: 50 × 40 ÷ 8
    2. M1: 50 × 120 ÷ 20
    3. A1: 250 for Ruth, 300 for Sam
    4. C1: Sam's, because his second catch is larger
    Answer: Ruth 250, Sam 300; Sam's, because his second catch is larger
    Capture-Recapture
    RuthSamRabbits marked and released5050Rabbits in the second catch40120Marked rabbits in the second catch820
    [4 marks]

  3. Question 3. 6.4² = 40.96 and 6.5² = 42.25
    Use these to write down the value of √41
    Give your answer correct to 1 decimal place.

    Show worked answerHide worked answer
    1. M1: 41 - 40.96 = 0.04 and 42.25 - 41 = 1.25
    2. A1: 6.4
    Answer: 6.4
    Estimating Roots
    [2 marks]

  4. Question 4. Isosceles triangle ABC: AB = AC = x cm, angle BAC = 50^°, area = 40 cm²
    Work out x to 1 decimal place.

    Show worked answerHide worked answer
    1. M1: 40 = 1/2 x² sin 50^°
    2. M1: x² = 80/sin 50^° = 104.4
    3. A1: 10.2
    Answer: 10.2 cm
    Using the Area Rule with Isosceles Triangles
    x cmx cm50°BCANot drawn accurately
    [3 marks]

  5. Question 5. The product of two consecutive positive odd numbers is 63.
    Use algebra to work out the two numbers.

    Show worked answerHide worked answer
    1. M1: (2n + 1)(2n + 3) = 4n² + 8n + 3
    2. M1: 4n² + 8n + 3 = 63 so n² + 2n - 15 = 0
    3. M1: (n + 5)(n - 3) = 0
    4. A1: n = 3 so the numbers are 7 and 9
    Answer: 7 and 9
    Proof with Odd Numbers
    [4 marks]