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

Mixed Topic Worksheet Grades 6/7: Day 050

Grades 6/7Calculator

  1. Question 1. A is the point (2, 3).
    B is the point (6, 8).
    Work out the distance between A and B.
    Round your answer to one decimal place.

    Show worked answerHide worked answer
    1. M1: (6 - 2)² + (8 - 3)²
    2. M1: √41 = 6.4031ldots
    3. A1: 6.4
    Answer: 6.4
    Distance Between Two Points
    xy02468AB02468
    [3 marks]

  2. Question 2. Group P: median 61, interquartile range 14. Group Q: median 55, interquartile range 14. Compare the two groups.

    Show worked answerHide worked answer
    1. B1: P higher on average (median 61 > 55)
    2. B1: same consistency (IQR 14 = 14)
    Answer: P has the higher average (61 > 55); the spread is the same (14 = 14)
    Comparing Data Using Box Plots
    [2 marks]

  3. Question 3. A code has 3 digits.
    Each digit is chosen from 1 to 9.
    No digit may be used more than once in the code.
    Work out the number of different codes.

    Show worked answerHide worked answer
    1. M1: 9 × 8 × 7
    2. A1: 504
    Answer: 504
    Calculating Combinations
    [2 marks]

  4. Question 4. x_n+1 = sqrt[3]2x_n + 9
    x_0 = 2
    Work out x_1, x_2 and x_3
    Give your answers correct to 3 decimal places.

    Show worked answerHide worked answer
    1. M1: x_1 = sqrt[3]2 × 2 + 9
    2. A1: x_1 = 2.351 and x_2 = 2.393
    3. A1: x_3 = 2.398
    Answer: x_1 = 2.351, x_2 = 2.393, x_3 = 2.398
    Iteration Equations
    [3 marks]

  5. Question 5. A right-angled triangle has a base of (4 + √2) cm and a height of (4 - √2) cm. Work out the area of the triangle.

    Show worked answerHide worked answer
    1. M1: dfrac12 × (4 + √2)(4 - √2)
    2. M1: dfrac12 × (16 - 2)
    3. A1: 7 cm²
    Answer: 7 cm²
    Expanding Brackets with Surds
    [3 marks]
📅 Free lesson: Tue 17th NovSave your place →

Mixed Topic Worksheet Grades 6/7: Day 050

Grades 6/7Calculator

  1. Question 1. A is the point (2, 3).
    B is the point (6, 8).
    Work out the distance between A and B.
    Round your answer to one decimal place.

    [3 marks]
    xy02468AB02468
    Show worked answerHide worked answer
    1. M1: (6 - 2)² + (8 - 3)²
    2. M1: √41 = 6.4031ldots
    3. A1: 6.4
    Answer: 6.4
    Distance Between Two Points

  2. Question 2. Group P: median 61, interquartile range 14. Group Q: median 55, interquartile range 14. Compare the two groups.

    [2 marks]
    Show worked answerHide worked answer
    1. B1: P higher on average (median 61 > 55)
    2. B1: same consistency (IQR 14 = 14)
    Answer: P has the higher average (61 > 55); the spread is the same (14 = 14)
    Comparing Data Using Box Plots

  3. Question 3. A code has 3 digits.
    Each digit is chosen from 1 to 9.
    No digit may be used more than once in the code.
    Work out the number of different codes.

    [2 marks]
    Show worked answerHide worked answer
    1. M1: 9 × 8 × 7
    2. A1: 504
    Answer: 504
    Calculating Combinations

  4. Question 4. x_n+1 = sqrt[3]2x_n + 9
    x_0 = 2
    Work out x_1, x_2 and x_3
    Give your answers correct to 3 decimal places.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: x_1 = sqrt[3]2 × 2 + 9
    2. A1: x_1 = 2.351 and x_2 = 2.393
    3. A1: x_3 = 2.398
    Answer: x_1 = 2.351, x_2 = 2.393, x_3 = 2.398
    Iteration Equations

  5. Question 5. A right-angled triangle has a base of (4 + √2) cm and a height of (4 - √2) cm. Work out the area of the triangle.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: dfrac12 × (4 + √2)(4 - √2)
    2. M1: dfrac12 × (16 - 2)
    3. A1: 7 cm²
    Answer: 7 cm²
    Expanding Brackets with Surds
📅 Free live lesson: Tuesday 17th NovemberSave your free place →

Mixed Topic Worksheet Grades 6/7: Day 050

Grades 6/7Calculator

  1. Question 1. A is the point (2, 3).
    B is the point (6, 8).
    Work out the distance between A and B.
    Round your answer to one decimal place.

    Show worked answerHide worked answer
    1. M1: (6 - 2)² + (8 - 3)²
    2. M1: √41 = 6.4031ldots
    3. A1: 6.4
    Answer: 6.4
    Distance Between Two Points
    xy02468AB02468
    [3 marks]

  2. Question 2. Group P: median 61, interquartile range 14. Group Q: median 55, interquartile range 14. Compare the two groups.

    Show worked answerHide worked answer
    1. B1: P higher on average (median 61 > 55)
    2. B1: same consistency (IQR 14 = 14)
    Answer: P has the higher average (61 > 55); the spread is the same (14 = 14)
    Comparing Data Using Box Plots
    [2 marks]

  3. Question 3. A code has 3 digits.
    Each digit is chosen from 1 to 9.
    No digit may be used more than once in the code.
    Work out the number of different codes.

    Show worked answerHide worked answer
    1. M1: 9 × 8 × 7
    2. A1: 504
    Answer: 504
    Calculating Combinations
    [2 marks]

  4. Question 4. x_n+1 = sqrt[3]2x_n + 9
    x_0 = 2
    Work out x_1, x_2 and x_3
    Give your answers correct to 3 decimal places.

    Show worked answerHide worked answer
    1. M1: x_1 = sqrt[3]2 × 2 + 9
    2. A1: x_1 = 2.351 and x_2 = 2.393
    3. A1: x_3 = 2.398
    Answer: x_1 = 2.351, x_2 = 2.393, x_3 = 2.398
    Iteration Equations
    [3 marks]

  5. Question 5. A right-angled triangle has a base of (4 + √2) cm and a height of (4 - √2) cm. Work out the area of the triangle.

    Show worked answerHide worked answer
    1. M1: dfrac12 × (4 + √2)(4 - √2)
    2. M1: dfrac12 × (16 - 2)
    3. A1: 7 cm²
    Answer: 7 cm²
    Expanding Brackets with Surds
    [3 marks]