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

Mixed Topic Worksheet Grades 8/9: Day 006

Grades 8/9Calculator

  1. Question 1. A cuboid measures 12 cm by 4 cm by 3 cm.
    Work out the length of a diagonal of the cuboid that joins two opposite corners.

    Show worked answerHide worked answer
    1. M1: 12² + 4² = 160 (the diagonal of the base)
    2. M1: 160 + 3² = 169
    3. A1: √169 = 13 cm
    Answer: 13 cm
    3D Pythagoras
    [3 marks]

  2. Question 2. The histogram shows information about the times, t minutes, that some people waited at a clinic.
    Work out the frequency for the class 10 < t ≤ 20.

    Show worked answerHide worked answer
    1. M1: 2.5 × (20 - 10)
    2. A1: 25
    Answer: 25
    Interpreting Histograms
    Time, t (minutes)Frequency density0123401020304050
    [2 marks]

  3. Question 3. AB is a diameter of a circle and C is on the circle. Angle ABC=3x^° and angle BAC=(2x+10)^°. Work out x.

    Show worked answerHide worked answer
    1. M2: angle ACB=90^° (semicircle), so 3x+2x+10+90=180
    2. A1: x=16
    Answer: x=16
    Combining Circle Theorems
    [3 marks]

  4. Question 4. Solve y = x² - 2x and y = 3 - x Give each answer correct to 2 decimal places

    Show worked answerHide worked answer
    1. M1: x² - 2x = 3 - x so x² - x - 3 = 0
    2. M1: x = dfrac1 ± √132
    3. A2: x = 2.30, y = 0.70 and x = -1.30, y = 4.30
    Answer: x = 2.30, y = 0.70 or x = -1.30, y = 4.30
    Solving Quadratic Simultaneous Equations
    [4 marks]

  5. Question 5. overrightarrowWX = (k + 2)mathbfa + 9mathbfb overrightarrowYZ = 8mathbfa + 6mathbfb
    WX is parallel to YZ.
    Work out the value of k.

    Show worked answerHide worked answer
    1. M1: (k + 2) = 8 × dfrac96
    2. M1: k + 2 = 12
    3. A1: 10
    Answer: 10
    Vectors Along a Straight Line
    [3 marks]
📅 Free lesson: Tue 17th NovSave your place →

Mixed Topic Worksheet Grades 8/9: Day 006

Grades 8/9Calculator

  1. Question 1. A cuboid measures 12 cm by 4 cm by 3 cm.
    Work out the length of a diagonal of the cuboid that joins two opposite corners.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: 12² + 4² = 160 (the diagonal of the base)
    2. M1: 160 + 3² = 169
    3. A1: √169 = 13 cm
    Answer: 13 cm
    3D Pythagoras

  2. Question 2. The histogram shows information about the times, t minutes, that some people waited at a clinic.
    Work out the frequency for the class 10 < t ≤ 20.

    [2 marks]
    Time, t (minutes)Frequency density0123401020304050
    Show worked answerHide worked answer
    1. M1: 2.5 × (20 - 10)
    2. A1: 25
    Answer: 25
    Interpreting Histograms

  3. Question 3. AB is a diameter of a circle and C is on the circle. Angle ABC=3x^° and angle BAC=(2x+10)^°. Work out x.

    [3 marks]
    Show worked answerHide worked answer
    1. M2: angle ACB=90^° (semicircle), so 3x+2x+10+90=180
    2. A1: x=16
    Answer: x=16
    Combining Circle Theorems

  4. Question 4. Solve y = x² - 2x and y = 3 - x Give each answer correct to 2 decimal places

    [4 marks]
    Show worked answerHide worked answer
    1. M1: x² - 2x = 3 - x so x² - x - 3 = 0
    2. M1: x = dfrac1 ± √132
    3. A2: x = 2.30, y = 0.70 and x = -1.30, y = 4.30
    Answer: x = 2.30, y = 0.70 or x = -1.30, y = 4.30
    Solving Quadratic Simultaneous Equations

  5. Question 5. overrightarrowWX = (k + 2)mathbfa + 9mathbfb overrightarrowYZ = 8mathbfa + 6mathbfb
    WX is parallel to YZ.
    Work out the value of k.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: (k + 2) = 8 × dfrac96
    2. M1: k + 2 = 12
    3. A1: 10
    Answer: 10
    Vectors Along a Straight Line
📅 Free live lesson: Tuesday 17th NovemberSave your free place →

Mixed Topic Worksheet Grades 8/9: Day 006

Grades 8/9Calculator

  1. Question 1. A cuboid measures 12 cm by 4 cm by 3 cm.
    Work out the length of a diagonal of the cuboid that joins two opposite corners.

    Show worked answerHide worked answer
    1. M1: 12² + 4² = 160 (the diagonal of the base)
    2. M1: 160 + 3² = 169
    3. A1: √169 = 13 cm
    Answer: 13 cm
    3D Pythagoras
    [3 marks]

  2. Question 2. The histogram shows information about the times, t minutes, that some people waited at a clinic.
    Work out the frequency for the class 10 < t ≤ 20.

    Show worked answerHide worked answer
    1. M1: 2.5 × (20 - 10)
    2. A1: 25
    Answer: 25
    Interpreting Histograms
    Time, t (minutes)Frequency density0123401020304050
    [2 marks]

  3. Question 3. AB is a diameter of a circle and C is on the circle. Angle ABC=3x^° and angle BAC=(2x+10)^°. Work out x.

    Show worked answerHide worked answer
    1. M2: angle ACB=90^° (semicircle), so 3x+2x+10+90=180
    2. A1: x=16
    Answer: x=16
    Combining Circle Theorems
    [3 marks]

  4. Question 4. Solve y = x² - 2x and y = 3 - x Give each answer correct to 2 decimal places

    Show worked answerHide worked answer
    1. M1: x² - 2x = 3 - x so x² - x - 3 = 0
    2. M1: x = dfrac1 ± √132
    3. A2: x = 2.30, y = 0.70 and x = -1.30, y = 4.30
    Answer: x = 2.30, y = 0.70 or x = -1.30, y = 4.30
    Solving Quadratic Simultaneous Equations
    [4 marks]

  5. Question 5. overrightarrowWX = (k + 2)mathbfa + 9mathbfb overrightarrowYZ = 8mathbfa + 6mathbfb
    WX is parallel to YZ.
    Work out the value of k.

    Show worked answerHide worked answer
    1. M1: (k + 2) = 8 × dfrac96
    2. M1: k + 2 = 12
    3. A1: 10
    Answer: 10
    Vectors Along a Straight Line
    [3 marks]