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

Mixed Topic Worksheet Grades 8/9: Day 086

Grades 8/9Calculator

  1. Question 1. The graph of y = 2x is translated by the vector beginpmatrix 0 3 endpmatrix
    Work out the coordinates of the point where the translated graph crosses the y-axis.

    Show worked answerHide worked answer
    1. M1: the translated graph is y = 2x + 3
    2. A1: 2⁰ + 3 = 4, so (0, 4)
    Answer: (0, 4)
    Translations Along the x- & y-Axes
    [2 marks]

  2. Question 2. A pyramid has a square base of side 6 cm. Its apex is 4 cm above the centre. Work out a sloping edge to 1 decimal place.

    Show worked answerHide worked answer
    1. M1: half diagonal √18, edge √18 + 4²
    2. A1: 5.8 cm
    Answer: 5.8 cm
    3D Pythagoras
    [2 marks]

  3. Question 3. A circle has circumference 40 cm, to the nearest cm. Work out the lower bound of its radius. Give your answer to 3 significant figures.

    Show worked answerHide worked answer
    1. M1: use the lower bound of the circumference
    2. M1: 39.5 ÷ (2π)
    3. A1: 6.29 cm
    Answer: 6.29 cm
    Combining Upper & Lower Bounds
    [3 marks]

  4. Question 4. y is directly proportional to √x
    y = 12 when x = 16
    Work out the value of y when x = 49

    Show worked answerHide worked answer
    1. M1: y = k√x and 12 = k × 4
    2. A1: k = 3
    3. A1: y = 3 × 7 = 21
    Answer: y = 21
    Direct & Inverse Proportion with Functions
    [3 marks]

  5. Question 5. The height, h metres, of a ball t seconds after it is thrown is h = 20t-5t² for 0 ≤ t ≤ 4. Work out for how many seconds the ball is more than 15 m above the ground.

    Show worked answerHide worked answer
    1. M1: 20t-5t² > 15
    2. M1: t²-4t+3 < 0
    3. M1: (t-1)(t-3) < 0, so 1 < t < 3
    4. A1: 2 seconds
    Answer: 2
    Solving Quadratic Inequalities
    [4 marks]
📅 Free lesson: Tue 17th NovSave your place →

Mixed Topic Worksheet Grades 8/9: Day 086

Grades 8/9Calculator

  1. Question 1. The graph of y = 2x is translated by the vector beginpmatrix 0 3 endpmatrix
    Work out the coordinates of the point where the translated graph crosses the y-axis.

    [2 marks]
    Show worked answerHide worked answer
    1. M1: the translated graph is y = 2x + 3
    2. A1: 2⁰ + 3 = 4, so (0, 4)
    Answer: (0, 4)
    Translations Along the x- & y-Axes

  2. Question 2. A pyramid has a square base of side 6 cm. Its apex is 4 cm above the centre. Work out a sloping edge to 1 decimal place.

    [2 marks]
    Show worked answerHide worked answer
    1. M1: half diagonal √18, edge √18 + 4²
    2. A1: 5.8 cm
    Answer: 5.8 cm
    3D Pythagoras

  3. Question 3. A circle has circumference 40 cm, to the nearest cm. Work out the lower bound of its radius. Give your answer to 3 significant figures.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: use the lower bound of the circumference
    2. M1: 39.5 ÷ (2π)
    3. A1: 6.29 cm
    Answer: 6.29 cm
    Combining Upper & Lower Bounds

  4. Question 4. y is directly proportional to √x
    y = 12 when x = 16
    Work out the value of y when x = 49

    [3 marks]
    Show worked answerHide worked answer
    1. M1: y = k√x and 12 = k × 4
    2. A1: k = 3
    3. A1: y = 3 × 7 = 21
    Answer: y = 21
    Direct & Inverse Proportion with Functions

  5. Question 5. The height, h metres, of a ball t seconds after it is thrown is h = 20t-5t² for 0 ≤ t ≤ 4. Work out for how many seconds the ball is more than 15 m above the ground.

    [4 marks]
    Show worked answerHide worked answer
    1. M1: 20t-5t² > 15
    2. M1: t²-4t+3 < 0
    3. M1: (t-1)(t-3) < 0, so 1 < t < 3
    4. A1: 2 seconds
    Answer: 2
    Solving Quadratic Inequalities
📅 Free live lesson: Tuesday 17th NovemberSave your free place →

Mixed Topic Worksheet Grades 8/9: Day 086

Grades 8/9Calculator

  1. Question 1. The graph of y = 2x is translated by the vector beginpmatrix 0 3 endpmatrix
    Work out the coordinates of the point where the translated graph crosses the y-axis.

    Show worked answerHide worked answer
    1. M1: the translated graph is y = 2x + 3
    2. A1: 2⁰ + 3 = 4, so (0, 4)
    Answer: (0, 4)
    Translations Along the x- & y-Axes
    [2 marks]

  2. Question 2. A pyramid has a square base of side 6 cm. Its apex is 4 cm above the centre. Work out a sloping edge to 1 decimal place.

    Show worked answerHide worked answer
    1. M1: half diagonal √18, edge √18 + 4²
    2. A1: 5.8 cm
    Answer: 5.8 cm
    3D Pythagoras
    [2 marks]

  3. Question 3. A circle has circumference 40 cm, to the nearest cm. Work out the lower bound of its radius. Give your answer to 3 significant figures.

    Show worked answerHide worked answer
    1. M1: use the lower bound of the circumference
    2. M1: 39.5 ÷ (2π)
    3. A1: 6.29 cm
    Answer: 6.29 cm
    Combining Upper & Lower Bounds
    [3 marks]

  4. Question 4. y is directly proportional to √x
    y = 12 when x = 16
    Work out the value of y when x = 49

    Show worked answerHide worked answer
    1. M1: y = k√x and 12 = k × 4
    2. A1: k = 3
    3. A1: y = 3 × 7 = 21
    Answer: y = 21
    Direct & Inverse Proportion with Functions
    [3 marks]

  5. Question 5. The height, h metres, of a ball t seconds after it is thrown is h = 20t-5t² for 0 ≤ t ≤ 4. Work out for how many seconds the ball is more than 15 m above the ground.

    Show worked answerHide worked answer
    1. M1: 20t-5t² > 15
    2. M1: t²-4t+3 < 0
    3. M1: (t-1)(t-3) < 0, so 1 < t < 3
    4. A1: 2 seconds
    Answer: 2
    Solving Quadratic Inequalities
    [4 marks]