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

Mixed Topic Worksheet Grades 6/7: Day 064

Grades 6/7Calculator

  1. Question 1. Kai invests £800 in an account.
    The account pays 5% compound interest per year.
    Work out the total in the account after 3 years.

    Show worked answerHide worked answer
    1. M1: 100 + 5 = 105%
    2. M1: 800 × 1.05 × 1.05 × 1.05
    3. A1: 926.10
    Answer: £926.10
    Compound Interest
    [3 marks]

  2. Question 2. Shape B is the image of shape A under a single reflection.
    Describe fully all the invariant points of this reflection.

    Show worked answerHide worked answer
    1. M1: matching points of A and B are the same distance from the mirror line, with (1, 3) matching (3, 1)
    2. A1: every point on the line y = x
    Answer: Every point on the line y = x
    Invariant Points
    xy0246AB0246
    [2 marks]

  3. Question 3. Class P test marks: median 62, interquartile range 14.
    Class Q test marks: median 55, interquartile range 20.
    Compare the marks of the two classes. [2]

    Show worked answerHide worked answer
    1. B1: P has the higher median, so P did better on average
    2. B1: P has the smaller IQR, so its marks are more consistent
    Answer: Class P did better on average (higher median) and was more consistent (smaller IQR)
    Comparing Data Using Box Plots
    [2 marks]

  4. Question 4. Here is triangle ABC.
    Work out the length of BC.
    Give your answer to 1 decimal place.

    Show worked answerHide worked answer
    1. M1: BC² = 16.2² + 17.2² - 2 × 16.2 × 17.2 × cos 13^°
    2. M1: BC² = 558.28 - 543.00 = 15.28
    3. A1: BC = 3.9
    Answer: 3.9 cm
    Finding Side Lengths Using the Cosine Rule
    17.2 cm16.2 cm13°ABC
    [3 marks]

  5. Question 5. f(x) = 11 - x
    g(x) = x - 11
    One of these functions is the same as its own inverse.
    Which one? You must show your working.

    Show worked answerHide worked answer
    1. M1: f(f(x)) = 11 - (11 - x)
    2. M1: g⁻¹(x) = x + 11, which is not g(x)
    3. A1: f, since f(f(x)) = x
    Answer: f
    Inverse Functions
    [3 marks]
📅 Free lesson: Tue 17th NovSave your place →

Mixed Topic Worksheet Grades 6/7: Day 064

Grades 6/7Calculator

  1. Question 1. Kai invests £800 in an account.
    The account pays 5% compound interest per year.
    Work out the total in the account after 3 years.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: 100 + 5 = 105%
    2. M1: 800 × 1.05 × 1.05 × 1.05
    3. A1: 926.10
    Answer: £926.10
    Compound Interest

  2. Question 2. Shape B is the image of shape A under a single reflection.
    Describe fully all the invariant points of this reflection.

    [2 marks]
    xy0246AB0246
    Show worked answerHide worked answer
    1. M1: matching points of A and B are the same distance from the mirror line, with (1, 3) matching (3, 1)
    2. A1: every point on the line y = x
    Answer: Every point on the line y = x
    Invariant Points

  3. Question 3. Class P test marks: median 62, interquartile range 14.
    Class Q test marks: median 55, interquartile range 20.
    Compare the marks of the two classes. [2]

    [2 marks]
    Show worked answerHide worked answer
    1. B1: P has the higher median, so P did better on average
    2. B1: P has the smaller IQR, so its marks are more consistent
    Answer: Class P did better on average (higher median) and was more consistent (smaller IQR)
    Comparing Data Using Box Plots

  4. Question 4. Here is triangle ABC.
    Work out the length of BC.
    Give your answer to 1 decimal place.

    [3 marks]
    17.2 cm16.2 cm13°ABC
    Show worked answerHide worked answer
    1. M1: BC² = 16.2² + 17.2² - 2 × 16.2 × 17.2 × cos 13^°
    2. M1: BC² = 558.28 - 543.00 = 15.28
    3. A1: BC = 3.9
    Answer: 3.9 cm
    Finding Side Lengths Using the Cosine Rule

  5. Question 5. f(x) = 11 - x
    g(x) = x - 11
    One of these functions is the same as its own inverse.
    Which one? You must show your working.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: f(f(x)) = 11 - (11 - x)
    2. M1: g⁻¹(x) = x + 11, which is not g(x)
    3. A1: f, since f(f(x)) = x
    Answer: f
    Inverse Functions
📅 Free live lesson: Tuesday 17th NovemberSave your free place →

Mixed Topic Worksheet Grades 6/7: Day 064

Grades 6/7Calculator

  1. Question 1. Kai invests £800 in an account.
    The account pays 5% compound interest per year.
    Work out the total in the account after 3 years.

    Show worked answerHide worked answer
    1. M1: 100 + 5 = 105%
    2. M1: 800 × 1.05 × 1.05 × 1.05
    3. A1: 926.10
    Answer: £926.10
    Compound Interest
    [3 marks]

  2. Question 2. Shape B is the image of shape A under a single reflection.
    Describe fully all the invariant points of this reflection.

    Show worked answerHide worked answer
    1. M1: matching points of A and B are the same distance from the mirror line, with (1, 3) matching (3, 1)
    2. A1: every point on the line y = x
    Answer: Every point on the line y = x
    Invariant Points
    xy0246AB0246
    [2 marks]

  3. Question 3. Class P test marks: median 62, interquartile range 14.
    Class Q test marks: median 55, interquartile range 20.
    Compare the marks of the two classes. [2]

    Show worked answerHide worked answer
    1. B1: P has the higher median, so P did better on average
    2. B1: P has the smaller IQR, so its marks are more consistent
    Answer: Class P did better on average (higher median) and was more consistent (smaller IQR)
    Comparing Data Using Box Plots
    [2 marks]

  4. Question 4. Here is triangle ABC.
    Work out the length of BC.
    Give your answer to 1 decimal place.

    Show worked answerHide worked answer
    1. M1: BC² = 16.2² + 17.2² - 2 × 16.2 × 17.2 × cos 13^°
    2. M1: BC² = 558.28 - 543.00 = 15.28
    3. A1: BC = 3.9
    Answer: 3.9 cm
    Finding Side Lengths Using the Cosine Rule
    17.2 cm16.2 cm13°ABC
    [3 marks]

  5. Question 5. f(x) = 11 - x
    g(x) = x - 11
    One of these functions is the same as its own inverse.
    Which one? You must show your working.

    Show worked answerHide worked answer
    1. M1: f(f(x)) = 11 - (11 - x)
    2. M1: g⁻¹(x) = x + 11, which is not g(x)
    3. A1: f, since f(f(x)) = x
    Answer: f
    Inverse Functions
    [3 marks]