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

Mixed Topic Worksheet Grades 8/9: Day 088

Grades 8/9Calculator

  1. Question 1. Write dfrac12√3 in the form a√3, where a is an integer.

    Show worked answerHide worked answer
    1. M1: dfrac12√33
    2. A1: 4√3
    Answer: 4√3
    Simplifying Surds
    [2 marks]

  2. Question 2. The table shows information about the lengths, x cm, of 115 fish.
    Work out the frequency density for the class 10 < x ≤ 25.

    Show worked answerHide worked answer
    1. M1: 45 ÷ (25 - 10)
    2. A1: 3
    Answer: 3
    Sketching Histograms
    Length, x (cm)Frequency0 < x ≤ 101410 < x ≤ 254525 < x ≤ 302030 < x ≤ 5036
    [2 marks]

  3. Question 3. Show that dfracx² + xx² - 4 ÷ dfracxx + 2 = dfracx + 1x - 2

    Show worked answerHide worked answer
    1. M1: dfracx(x + 1)(x - 2)(x + 2) × dfracx + 2x
    2. A1: cancel x and (x + 2) to give dfracx + 1x - 2
    Answer: Shown
    Multiplying & Dividing Algebraic Fractions
    [2 marks]

  4. Question 4. ABCDEFGH is a cuboid.
    Work out the perimeter of triangle ACG.
    Give your answer to 1 decimal place.

    Show worked answerHide worked answer
    1. M1: AC² = 9² + 6²
    2. M1: AG² = AC² + 5²
    3. M1: perimeter = AC + 5 + AG
    4. A1: perimeter = 10.8 + 5 + 11.9
    5. A1: 27.7
    Answer: 27.7
    3D Pythagoras
    9 cm5 cmADBCFGEH6 cm
    [5 marks]

  5. Question 5. Graph A is y = 3x² - 12x + 20
    Graph B is y = 2x² + 8x + 17
    Which graph has the greater minimum value? Show how you know.

    Show worked answerHide worked answer
    1. M1: A: 3≤ft((x - 2)² - 4) + 20
    2. M1: B: 2≤ft((x + 2)² - 4) + 17
    3. A1: A has minimum value 8
    4. A1: B has minimum value 9
    5. B1: Graph B
    Answer: Graph B (minimum value 9 compared with 8)
    Solving Quadratics by Completing the Square (a > 1)
    [5 marks]
📅 Free lesson: Tue 17th NovSave your place →

Mixed Topic Worksheet Grades 8/9: Day 088

Grades 8/9Calculator

  1. Question 1. Write dfrac12√3 in the form a√3, where a is an integer.

    [2 marks]
    Show worked answerHide worked answer
    1. M1: dfrac12√33
    2. A1: 4√3
    Answer: 4√3
    Simplifying Surds

  2. Question 2. The table shows information about the lengths, x cm, of 115 fish.
    Work out the frequency density for the class 10 < x ≤ 25.

    [2 marks]
    Length, x (cm)Frequency0 < x ≤ 101410 < x ≤ 254525 < x ≤ 302030 < x ≤ 5036
    Show worked answerHide worked answer
    1. M1: 45 ÷ (25 - 10)
    2. A1: 3
    Answer: 3
    Sketching Histograms

  3. Question 3. Show that dfracx² + xx² - 4 ÷ dfracxx + 2 = dfracx + 1x - 2

    [2 marks]
    Show worked answerHide worked answer
    1. M1: dfracx(x + 1)(x - 2)(x + 2) × dfracx + 2x
    2. A1: cancel x and (x + 2) to give dfracx + 1x - 2
    Answer: Shown
    Multiplying & Dividing Algebraic Fractions

  4. Question 4. ABCDEFGH is a cuboid.
    Work out the perimeter of triangle ACG.
    Give your answer to 1 decimal place.

    [5 marks]
    9 cm5 cmADBCFGEH6 cm
    Show worked answerHide worked answer
    1. M1: AC² = 9² + 6²
    2. M1: AG² = AC² + 5²
    3. M1: perimeter = AC + 5 + AG
    4. A1: perimeter = 10.8 + 5 + 11.9
    5. A1: 27.7
    Answer: 27.7
    3D Pythagoras

  5. Question 5. Graph A is y = 3x² - 12x + 20
    Graph B is y = 2x² + 8x + 17
    Which graph has the greater minimum value? Show how you know.

    [5 marks]
    Show worked answerHide worked answer
    1. M1: A: 3≤ft((x - 2)² - 4) + 20
    2. M1: B: 2≤ft((x + 2)² - 4) + 17
    3. A1: A has minimum value 8
    4. A1: B has minimum value 9
    5. B1: Graph B
    Answer: Graph B (minimum value 9 compared with 8)
    Solving Quadratics by Completing the Square (a > 1)
📅 Free live lesson: Tuesday 17th NovemberSave your free place →

Mixed Topic Worksheet Grades 8/9: Day 088

Grades 8/9Calculator

  1. Question 1. Write dfrac12√3 in the form a√3, where a is an integer.

    Show worked answerHide worked answer
    1. M1: dfrac12√33
    2. A1: 4√3
    Answer: 4√3
    Simplifying Surds
    [2 marks]

  2. Question 2. The table shows information about the lengths, x cm, of 115 fish.
    Work out the frequency density for the class 10 < x ≤ 25.

    Show worked answerHide worked answer
    1. M1: 45 ÷ (25 - 10)
    2. A1: 3
    Answer: 3
    Sketching Histograms
    Length, x (cm)Frequency0 < x ≤ 101410 < x ≤ 254525 < x ≤ 302030 < x ≤ 5036
    [2 marks]

  3. Question 3. Show that dfracx² + xx² - 4 ÷ dfracxx + 2 = dfracx + 1x - 2

    Show worked answerHide worked answer
    1. M1: dfracx(x + 1)(x - 2)(x + 2) × dfracx + 2x
    2. A1: cancel x and (x + 2) to give dfracx + 1x - 2
    Answer: Shown
    Multiplying & Dividing Algebraic Fractions
    [2 marks]

  4. Question 4. ABCDEFGH is a cuboid.
    Work out the perimeter of triangle ACG.
    Give your answer to 1 decimal place.

    Show worked answerHide worked answer
    1. M1: AC² = 9² + 6²
    2. M1: AG² = AC² + 5²
    3. M1: perimeter = AC + 5 + AG
    4. A1: perimeter = 10.8 + 5 + 11.9
    5. A1: 27.7
    Answer: 27.7
    3D Pythagoras
    9 cm5 cmADBCFGEH6 cm
    [5 marks]

  5. Question 5. Graph A is y = 3x² - 12x + 20
    Graph B is y = 2x² + 8x + 17
    Which graph has the greater minimum value? Show how you know.

    Show worked answerHide worked answer
    1. M1: A: 3≤ft((x - 2)² - 4) + 20
    2. M1: B: 2≤ft((x + 2)² - 4) + 17
    3. A1: A has minimum value 8
    4. A1: B has minimum value 9
    5. B1: Graph B
    Answer: Graph B (minimum value 9 compared with 8)
    Solving Quadratics by Completing the Square (a > 1)
    [5 marks]