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

Mixed Topic Worksheet Grades 8/9: Day 082

Grades 8/9Calculator

  1. Question 1. A histogram bar for 10 < t ≤ 30 has frequency density 2.5. Work out the frequency.

    Show worked answerHide worked answer
    1. M1: 2.5 × 20
    2. A1: 50
    Answer: 50
    Interpreting Histograms
    [2 marks]

  2. Question 2. A rectangle has area 30 cm², correct to the nearest cm².
    The width of the rectangle is 4.2 cm, correct to 1 decimal place.
    Work out the greatest possible length of the rectangle.
    Give your answer correct to 3 significant figures.

    Show worked answerHide worked answer
    1. M1: 30 + 0.5 and 4.2 - 0.05
    2. M1: 30.5 ÷ 4.15
    3. A1: 7.35
    Answer: 7.35 cm
    Combining Upper & Lower Bounds
    [3 marks]

  3. Question 3. a is an integer.
    dfracax-4+dfrac2x=dfrac6x-8x≤ft(x-4)
    Work out the value of a.

    Show worked answerHide worked answer
    1. M1: dfracax+2(x-4)x≤ft(x-4)
    2. M1: (a+2)x-8 = 6x-8
    3. A1: a=4
    Answer: a=4
    Algebraic Fractions Involving Factorising
    [3 marks]

  4. Question 4. A box is a cuboid. Carol says a straight 110 cm pole will fit inside it.
    Is Carol correct? Compare 110 cm with the longest straight line that fits in the box. Show your working.

    Show worked answerHide worked answer
    1. M1: base diagonal² = 85² + 60²
    2. M1: longest² = base diagonal² + 50²
    3. A1: longest = 115.4 cm
    4. B1: Yes, because 115.4 > 110
    Answer: Yes: the longest line is 115.4 cm, which is more than 110 cm
    3D Pythagoras
    85 cm50 cmADBCFGEH60 cm
    [4 marks]

  5. Question 5. Solve 4 - x² ≥ 3x

    Show worked answerHide worked answer
    1. M1: x² + 3x - 4 ≤ 0
    2. M1: (x + 4)(x - 1) ≤ 0
    3. A1: -4 ≤ x ≤ 1
    Answer: -4 ≤ x ≤ 1
    Solving Quadratic Inequalities
    [3 marks]
📅 Free lesson: Tue 17th NovSave your place →

Mixed Topic Worksheet Grades 8/9: Day 082

Grades 8/9Calculator

  1. Question 1. A histogram bar for 10 < t ≤ 30 has frequency density 2.5. Work out the frequency.

    [2 marks]
    Show worked answerHide worked answer
    1. M1: 2.5 × 20
    2. A1: 50
    Answer: 50
    Interpreting Histograms

  2. Question 2. A rectangle has area 30 cm², correct to the nearest cm².
    The width of the rectangle is 4.2 cm, correct to 1 decimal place.
    Work out the greatest possible length of the rectangle.
    Give your answer correct to 3 significant figures.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: 30 + 0.5 and 4.2 - 0.05
    2. M1: 30.5 ÷ 4.15
    3. A1: 7.35
    Answer: 7.35 cm
    Combining Upper & Lower Bounds

  3. Question 3. a is an integer.
    dfracax-4+dfrac2x=dfrac6x-8x≤ft(x-4)
    Work out the value of a.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: dfracax+2(x-4)x≤ft(x-4)
    2. M1: (a+2)x-8 = 6x-8
    3. A1: a=4
    Answer: a=4
    Algebraic Fractions Involving Factorising

  4. Question 4. A box is a cuboid. Carol says a straight 110 cm pole will fit inside it.
    Is Carol correct? Compare 110 cm with the longest straight line that fits in the box. Show your working.

    [4 marks]
    85 cm50 cmADBCFGEH60 cm
    Show worked answerHide worked answer
    1. M1: base diagonal² = 85² + 60²
    2. M1: longest² = base diagonal² + 50²
    3. A1: longest = 115.4 cm
    4. B1: Yes, because 115.4 > 110
    Answer: Yes: the longest line is 115.4 cm, which is more than 110 cm
    3D Pythagoras

  5. Question 5. Solve 4 - x² ≥ 3x

    [3 marks]
    Show worked answerHide worked answer
    1. M1: x² + 3x - 4 ≤ 0
    2. M1: (x + 4)(x - 1) ≤ 0
    3. A1: -4 ≤ x ≤ 1
    Answer: -4 ≤ x ≤ 1
    Solving Quadratic Inequalities
📅 Free live lesson: Tuesday 17th NovemberSave your free place →

Mixed Topic Worksheet Grades 8/9: Day 082

Grades 8/9Calculator

  1. Question 1. A histogram bar for 10 < t ≤ 30 has frequency density 2.5. Work out the frequency.

    Show worked answerHide worked answer
    1. M1: 2.5 × 20
    2. A1: 50
    Answer: 50
    Interpreting Histograms
    [2 marks]

  2. Question 2. A rectangle has area 30 cm², correct to the nearest cm².
    The width of the rectangle is 4.2 cm, correct to 1 decimal place.
    Work out the greatest possible length of the rectangle.
    Give your answer correct to 3 significant figures.

    Show worked answerHide worked answer
    1. M1: 30 + 0.5 and 4.2 - 0.05
    2. M1: 30.5 ÷ 4.15
    3. A1: 7.35
    Answer: 7.35 cm
    Combining Upper & Lower Bounds
    [3 marks]

  3. Question 3. a is an integer.
    dfracax-4+dfrac2x=dfrac6x-8x≤ft(x-4)
    Work out the value of a.

    Show worked answerHide worked answer
    1. M1: dfracax+2(x-4)x≤ft(x-4)
    2. M1: (a+2)x-8 = 6x-8
    3. A1: a=4
    Answer: a=4
    Algebraic Fractions Involving Factorising
    [3 marks]

  4. Question 4. A box is a cuboid. Carol says a straight 110 cm pole will fit inside it.
    Is Carol correct? Compare 110 cm with the longest straight line that fits in the box. Show your working.

    Show worked answerHide worked answer
    1. M1: base diagonal² = 85² + 60²
    2. M1: longest² = base diagonal² + 50²
    3. A1: longest = 115.4 cm
    4. B1: Yes, because 115.4 > 110
    Answer: Yes: the longest line is 115.4 cm, which is more than 110 cm
    3D Pythagoras
    85 cm50 cmADBCFGEH60 cm
    [4 marks]

  5. Question 5. Solve 4 - x² ≥ 3x

    Show worked answerHide worked answer
    1. M1: x² + 3x - 4 ≤ 0
    2. M1: (x + 4)(x - 1) ≤ 0
    3. A1: -4 ≤ x ≤ 1
    Answer: -4 ≤ x ≤ 1
    Solving Quadratic Inequalities
    [3 marks]