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

Mixed Topic Worksheet Grades 6/7: Day 048

Grades 6/7Calculator

  1. Question 1. The table shows the times taken by 30 students to complete a puzzle. Write down the modal class.

    Show worked answerHide worked answer
    1. B1: the class with the highest frequency, 20 < t ≤ 30
    Answer: 20 < t ≤ 30
    Interpreting Grouped Frequency Tables
    Time, t (minutes)Frequency0 < t ≤ 10410 < t ≤ 20920 < t ≤ 301230 < t ≤ 405
    [1 mark]

  2. Question 2. Simplify fully dfrac3x²+6x9x

    Show worked answerHide worked answer
    1. M1: dfrac3x(x+2)9x
    2. A1: dfracx+23
    Answer: dfracx+23
    Simplifying Algebraic Fractions
    [2 marks]

  3. Question 3. The area of triangle CDE is 31.5 cm². Angle y is obtuse. Work out the size of angle y. Give your answer to 1 decimal place.

    Show worked answerHide worked answer
    1. M1: 1/2 × 9 × 10 × sin y = 31.5
    2. M1: y = 180^° - sin⁻¹(0.7)
    3. A1: 135.6
    Answer: 135.6
    Area of Triangles Using ½ab sin C
    9 cm10 cmyCDENot drawn accurately
    [3 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 = 7² + 10² - 2 × 7 × 10 × cos 112^°
    2. M1: BC² = 149.00 + 52.44 = 201.44
    3. A1: BC = 14.2
    Answer: 14.2 cm
    Finding Side Lengths Using the Cosine Rule
    10 cm7 cm112°ABC
    [3 marks]

  5. Question 5. The graph of y = -(x - p)² + q has its maximum point at (3, 16).
    Work out the y-coordinate of the point where the graph crosses the y-axis.

    Show worked answerHide worked answer
    1. M1: p = 3 and q = 16
    2. M1: y = -(0 - 3)² + 16
    3. A1: 7
    Answer: 7
    Full Process for Sketching Quadratics
    [3 marks]
📅 Free lesson: Tue 17th NovSave your place →

Mixed Topic Worksheet Grades 6/7: Day 048

Grades 6/7Calculator

  1. Question 1. The table shows the times taken by 30 students to complete a puzzle. Write down the modal class.

    [1 mark]
    Time, t (minutes)Frequency0 < t ≤ 10410 < t ≤ 20920 < t ≤ 301230 < t ≤ 405
    Show worked answerHide worked answer
    1. B1: the class with the highest frequency, 20 < t ≤ 30
    Answer: 20 < t ≤ 30
    Interpreting Grouped Frequency Tables

  2. Question 2. Simplify fully dfrac3x²+6x9x

    [2 marks]
    Show worked answerHide worked answer
    1. M1: dfrac3x(x+2)9x
    2. A1: dfracx+23
    Answer: dfracx+23
    Simplifying Algebraic Fractions

  3. Question 3. The area of triangle CDE is 31.5 cm². Angle y is obtuse. Work out the size of angle y. Give your answer to 1 decimal place.

    [3 marks]
    9 cm10 cmyCDENot drawn accurately
    Show worked answerHide worked answer
    1. M1: 1/2 × 9 × 10 × sin y = 31.5
    2. M1: y = 180^° - sin⁻¹(0.7)
    3. A1: 135.6
    Answer: 135.6
    Area of Triangles Using ½ab sin C

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

    [3 marks]
    10 cm7 cm112°ABC
    Show worked answerHide worked answer
    1. M1: BC² = 7² + 10² - 2 × 7 × 10 × cos 112^°
    2. M1: BC² = 149.00 + 52.44 = 201.44
    3. A1: BC = 14.2
    Answer: 14.2 cm
    Finding Side Lengths Using the Cosine Rule

  5. Question 5. The graph of y = -(x - p)² + q has its maximum point at (3, 16).
    Work out the y-coordinate of the point where the graph crosses the y-axis.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: p = 3 and q = 16
    2. M1: y = -(0 - 3)² + 16
    3. A1: 7
    Answer: 7
    Full Process for Sketching Quadratics
📅 Free live lesson: Tuesday 17th NovemberSave your free place →

Mixed Topic Worksheet Grades 6/7: Day 048

Grades 6/7Calculator

  1. Question 1. The table shows the times taken by 30 students to complete a puzzle. Write down the modal class.

    Show worked answerHide worked answer
    1. B1: the class with the highest frequency, 20 < t ≤ 30
    Answer: 20 < t ≤ 30
    Interpreting Grouped Frequency Tables
    Time, t (minutes)Frequency0 < t ≤ 10410 < t ≤ 20920 < t ≤ 301230 < t ≤ 405
    [1 mark]

  2. Question 2. Simplify fully dfrac3x²+6x9x

    Show worked answerHide worked answer
    1. M1: dfrac3x(x+2)9x
    2. A1: dfracx+23
    Answer: dfracx+23
    Simplifying Algebraic Fractions
    [2 marks]

  3. Question 3. The area of triangle CDE is 31.5 cm². Angle y is obtuse. Work out the size of angle y. Give your answer to 1 decimal place.

    Show worked answerHide worked answer
    1. M1: 1/2 × 9 × 10 × sin y = 31.5
    2. M1: y = 180^° - sin⁻¹(0.7)
    3. A1: 135.6
    Answer: 135.6
    Area of Triangles Using ½ab sin C
    9 cm10 cmyCDENot drawn accurately
    [3 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 = 7² + 10² - 2 × 7 × 10 × cos 112^°
    2. M1: BC² = 149.00 + 52.44 = 201.44
    3. A1: BC = 14.2
    Answer: 14.2 cm
    Finding Side Lengths Using the Cosine Rule
    10 cm7 cm112°ABC
    [3 marks]

  5. Question 5. The graph of y = -(x - p)² + q has its maximum point at (3, 16).
    Work out the y-coordinate of the point where the graph crosses the y-axis.

    Show worked answerHide worked answer
    1. M1: p = 3 and q = 16
    2. M1: y = -(0 - 3)² + 16
    3. A1: 7
    Answer: 7
    Full Process for Sketching Quadratics
    [3 marks]