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

Mixed Topic Worksheet Grades 6/7: Day 083

Grades 6/7Non-calculator

  1. Question 1. The difference between two numbers is 4.5 × 10⁴
    The larger number is 6 × 10⁵
    Work out the smaller number.
    Give your answer in standard form.

    Show worked answerHide worked answer
    1. M1: Writes 6 × 10⁵ and 4.5 × 10⁴ as ordinary numbers
    2. M1: Subtracts the difference from the larger number: 600 000 - 45 000
    3. A1: 5.55 × 10⁵
    Answer: 5.55 × 10⁵
    Adding & Subtracting in Standard Form
    [3 marks]

  2. Question 2. Set A has minimum 25, lower quartile 31, median 36, upper quartile 40 and maximum 62. Explain why the interquartile range is better than the range for describing how spread out the middle of set A is.

    Show worked answerHide worked answer
    1. B1: the maximum 62 is far from the rest, so the range is large; the interquartile range uses only the middle 50% so is not affected
    Answer: The range is affected by the extreme maximum of 62; the interquartile range uses the middle half of the data only.
    Comparing Data Using Box Plots
    [1 mark]

  3. Question 3. The point P(3, -2) is enlarged by scale factor -2, centre (0, 0).
    Write down the coordinates of the image of P.

    Show worked answerHide worked answer
    1. M1: -2 × 3 and -2 × (-2)
    2. A1: (-6, 4)
    Answer: (-6, 4)
    Enlargements with Negative Integer Scale Factors
    [2 marks]

  4. Question 4. Lena says that the graph of y = x² + 6x + 14 does not cross the x-axis.
    Is Lena correct? You must show your working.

    Show worked answerHide worked answer
    1. M1: (x + 3)² + 5
    2. M1: turning point (-3, 5) has a positive y-coordinate, on a graph that opens upwards
    3. A1: Yes, with the reason
    Answer: Yes: y = (x + 3)² + 5, so the turning point is (-3, 5), above the x-axis, and the graph never reaches y = 0
    Turning Points of Quadratics
    [3 marks]

  5. Question 5. Solve 2x² + 3x - 4 = 0
    Give the solutions in the form dfraca ± √bc where a, b and c are integers.

    Show worked answerHide worked answer
    1. M1: substitute a = 2, b = 3, c = -4 into the quadratic formula
    2. M1: simplify the discriminant: 3² - 4 × 2 × (-4) = 41
    3. M1: x = dfrac-3 ± √414
    4. A1: a = -3, b = 41, c = 4
    Answer: x = (-3 ± √41)/4
    Solving Quadratics with the Quadratic Formula
    [4 marks]
📅 Free lesson: Tue 17th NovSave your place →

Mixed Topic Worksheet Grades 6/7: Day 083

Grades 6/7Non-calculator

  1. Question 1. The difference between two numbers is 4.5 × 10⁴
    The larger number is 6 × 10⁵
    Work out the smaller number.
    Give your answer in standard form.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: Writes 6 × 10⁵ and 4.5 × 10⁴ as ordinary numbers
    2. M1: Subtracts the difference from the larger number: 600 000 - 45 000
    3. A1: 5.55 × 10⁵
    Answer: 5.55 × 10⁵
    Adding & Subtracting in Standard Form

  2. Question 2. Set A has minimum 25, lower quartile 31, median 36, upper quartile 40 and maximum 62. Explain why the interquartile range is better than the range for describing how spread out the middle of set A is.

    [1 mark]
    Show worked answerHide worked answer
    1. B1: the maximum 62 is far from the rest, so the range is large; the interquartile range uses only the middle 50% so is not affected
    Answer: The range is affected by the extreme maximum of 62; the interquartile range uses the middle half of the data only.
    Comparing Data Using Box Plots

  3. Question 3. The point P(3, -2) is enlarged by scale factor -2, centre (0, 0).
    Write down the coordinates of the image of P.

    [2 marks]
    Show worked answerHide worked answer
    1. M1: -2 × 3 and -2 × (-2)
    2. A1: (-6, 4)
    Answer: (-6, 4)
    Enlargements with Negative Integer Scale Factors

  4. Question 4. Lena says that the graph of y = x² + 6x + 14 does not cross the x-axis.
    Is Lena correct? You must show your working.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: (x + 3)² + 5
    2. M1: turning point (-3, 5) has a positive y-coordinate, on a graph that opens upwards
    3. A1: Yes, with the reason
    Answer: Yes: y = (x + 3)² + 5, so the turning point is (-3, 5), above the x-axis, and the graph never reaches y = 0
    Turning Points of Quadratics

  5. Question 5. Solve 2x² + 3x - 4 = 0
    Give the solutions in the form dfraca ± √bc where a, b and c are integers.

    [4 marks]
    Show worked answerHide worked answer
    1. M1: substitute a = 2, b = 3, c = -4 into the quadratic formula
    2. M1: simplify the discriminant: 3² - 4 × 2 × (-4) = 41
    3. M1: x = dfrac-3 ± √414
    4. A1: a = -3, b = 41, c = 4
    Answer: x = (-3 ± √41)/4
    Solving Quadratics with the Quadratic Formula
📅 Free live lesson: Tuesday 17th NovemberSave your free place →

Mixed Topic Worksheet Grades 6/7: Day 083

Grades 6/7Non-calculator

  1. Question 1. The difference between two numbers is 4.5 × 10⁴
    The larger number is 6 × 10⁵
    Work out the smaller number.
    Give your answer in standard form.

    Show worked answerHide worked answer
    1. M1: Writes 6 × 10⁵ and 4.5 × 10⁴ as ordinary numbers
    2. M1: Subtracts the difference from the larger number: 600 000 - 45 000
    3. A1: 5.55 × 10⁵
    Answer: 5.55 × 10⁵
    Adding & Subtracting in Standard Form
    [3 marks]

  2. Question 2. Set A has minimum 25, lower quartile 31, median 36, upper quartile 40 and maximum 62. Explain why the interquartile range is better than the range for describing how spread out the middle of set A is.

    Show worked answerHide worked answer
    1. B1: the maximum 62 is far from the rest, so the range is large; the interquartile range uses only the middle 50% so is not affected
    Answer: The range is affected by the extreme maximum of 62; the interquartile range uses the middle half of the data only.
    Comparing Data Using Box Plots
    [1 mark]

  3. Question 3. The point P(3, -2) is enlarged by scale factor -2, centre (0, 0).
    Write down the coordinates of the image of P.

    Show worked answerHide worked answer
    1. M1: -2 × 3 and -2 × (-2)
    2. A1: (-6, 4)
    Answer: (-6, 4)
    Enlargements with Negative Integer Scale Factors
    [2 marks]

  4. Question 4. Lena says that the graph of y = x² + 6x + 14 does not cross the x-axis.
    Is Lena correct? You must show your working.

    Show worked answerHide worked answer
    1. M1: (x + 3)² + 5
    2. M1: turning point (-3, 5) has a positive y-coordinate, on a graph that opens upwards
    3. A1: Yes, with the reason
    Answer: Yes: y = (x + 3)² + 5, so the turning point is (-3, 5), above the x-axis, and the graph never reaches y = 0
    Turning Points of Quadratics
    [3 marks]

  5. Question 5. Solve 2x² + 3x - 4 = 0
    Give the solutions in the form dfraca ± √bc where a, b and c are integers.

    Show worked answerHide worked answer
    1. M1: substitute a = 2, b = 3, c = -4 into the quadratic formula
    2. M1: simplify the discriminant: 3² - 4 × 2 × (-4) = 41
    3. M1: x = dfrac-3 ± √414
    4. A1: a = -3, b = 41, c = 4
    Answer: x = (-3 ± √41)/4
    Solving Quadratics with the Quadratic Formula
    [4 marks]