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

Mixed Topic Worksheet Grades 8/9: Day 030

Grades 8/9Calculator

  1. Question 1. a = 48, correct to the nearest integer.
    b = 6.2, correct to 1 decimal place.
    Work out the lower bound of a ÷ b

    Show worked answerHide worked answer
    1. M1: lower bound of a is 47.5 and upper bound of b is 6.25
    2. M1: 47.5 ÷ 6.25
    3. A1: 7.6
    Answer: 7.6
    Combining Upper & Lower Bounds
    [3 marks]

  2. Question 2. Solve tan x = 0.8 for 0^° ≤ x ≤ 360^°. Give your answers correct to 1 decimal place

    Show worked answerHide worked answer
    1. M1: x = tan⁻¹0.8
    2. M1: add 180^° (graph repeats every 180^°)
    3. A1: 38.7^° and 218.7^°
    Answer: x = 38.7^° and x = 218.7^°
    Solving Trigonometric Equations Using a Graph
    [3 marks]

  3. Question 3. By completing the square, solve x² - 6x + 2 = 0. Give your answers correct to 2 decimal places.

    Show worked answerHide worked answer
    1. M1: (x - 3)² - 7 = 0
    2. M1 A1: x = 3 ± √7 = 5.65 or 0.35
    Answer: x = 5.65 or x = 0.35
    Solving Quadratics by Completing the Square (a = 1)
    [3 marks]

  4. Question 4. The graph of y = x² is translated by the vector beginpmatrix 3 -5 endpmatrix
    Find the equation of the translated graph in the form y = x² + bx + c

    Show worked answerHide worked answer
    1. M1: replace x with x - 3: (x - 3)²
    2. M1: subtract 5: y = (x - 3)² - 5
    3. M1: x² - 6x + 9 - 5
    4. A1: y = x² - 6x + 4
    Answer: y = x² - 6x + 4
    Translations Along the x- & y-Axes
    [4 marks]

  5. Question 5. ABC is a straight line with AB:BC=2:3. overrightarrowOA=mathbfa+2mathbfb and overrightarrowAB=4mathbfa-2mathbfb. Find overrightarrowOC in terms of mathbfa and mathbfb.

    Show worked answerHide worked answer
    1. M1: overrightarrowAC=5/2overrightarrowAB=10mathbfa-5mathbfb
    2. M1: overrightarrowOC=mathbfa+2mathbfb+10mathbfa-5mathbfb
    3. A1: 11mathbfa-3mathbfb
    Answer: overrightarrowOC=11mathbfa-3mathbfb
    Vectors Along a Straight Line
    [3 marks]
📅 Free lesson: Tue 17th NovSave your place →

Mixed Topic Worksheet Grades 8/9: Day 030

Grades 8/9Calculator

  1. Question 1. a = 48, correct to the nearest integer.
    b = 6.2, correct to 1 decimal place.
    Work out the lower bound of a ÷ b

    [3 marks]
    Show worked answerHide worked answer
    1. M1: lower bound of a is 47.5 and upper bound of b is 6.25
    2. M1: 47.5 ÷ 6.25
    3. A1: 7.6
    Answer: 7.6
    Combining Upper & Lower Bounds

  2. Question 2. Solve tan x = 0.8 for 0^° ≤ x ≤ 360^°. Give your answers correct to 1 decimal place

    [3 marks]
    Show worked answerHide worked answer
    1. M1: x = tan⁻¹0.8
    2. M1: add 180^° (graph repeats every 180^°)
    3. A1: 38.7^° and 218.7^°
    Answer: x = 38.7^° and x = 218.7^°
    Solving Trigonometric Equations Using a Graph

  3. Question 3. By completing the square, solve x² - 6x + 2 = 0. Give your answers correct to 2 decimal places.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: (x - 3)² - 7 = 0
    2. M1 A1: x = 3 ± √7 = 5.65 or 0.35
    Answer: x = 5.65 or x = 0.35
    Solving Quadratics by Completing the Square (a = 1)

  4. Question 4. The graph of y = x² is translated by the vector beginpmatrix 3 -5 endpmatrix
    Find the equation of the translated graph in the form y = x² + bx + c

    [4 marks]
    Show worked answerHide worked answer
    1. M1: replace x with x - 3: (x - 3)²
    2. M1: subtract 5: y = (x - 3)² - 5
    3. M1: x² - 6x + 9 - 5
    4. A1: y = x² - 6x + 4
    Answer: y = x² - 6x + 4
    Translations Along the x- & y-Axes

  5. Question 5. ABC is a straight line with AB:BC=2:3. overrightarrowOA=mathbfa+2mathbfb and overrightarrowAB=4mathbfa-2mathbfb. Find overrightarrowOC in terms of mathbfa and mathbfb.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: overrightarrowAC=5/2overrightarrowAB=10mathbfa-5mathbfb
    2. M1: overrightarrowOC=mathbfa+2mathbfb+10mathbfa-5mathbfb
    3. A1: 11mathbfa-3mathbfb
    Answer: overrightarrowOC=11mathbfa-3mathbfb
    Vectors Along a Straight Line
📅 Free live lesson: Tuesday 17th NovemberSave your free place →

Mixed Topic Worksheet Grades 8/9: Day 030

Grades 8/9Calculator

  1. Question 1. a = 48, correct to the nearest integer.
    b = 6.2, correct to 1 decimal place.
    Work out the lower bound of a ÷ b

    Show worked answerHide worked answer
    1. M1: lower bound of a is 47.5 and upper bound of b is 6.25
    2. M1: 47.5 ÷ 6.25
    3. A1: 7.6
    Answer: 7.6
    Combining Upper & Lower Bounds
    [3 marks]

  2. Question 2. Solve tan x = 0.8 for 0^° ≤ x ≤ 360^°. Give your answers correct to 1 decimal place

    Show worked answerHide worked answer
    1. M1: x = tan⁻¹0.8
    2. M1: add 180^° (graph repeats every 180^°)
    3. A1: 38.7^° and 218.7^°
    Answer: x = 38.7^° and x = 218.7^°
    Solving Trigonometric Equations Using a Graph
    [3 marks]

  3. Question 3. By completing the square, solve x² - 6x + 2 = 0. Give your answers correct to 2 decimal places.

    Show worked answerHide worked answer
    1. M1: (x - 3)² - 7 = 0
    2. M1 A1: x = 3 ± √7 = 5.65 or 0.35
    Answer: x = 5.65 or x = 0.35
    Solving Quadratics by Completing the Square (a = 1)
    [3 marks]

  4. Question 4. The graph of y = x² is translated by the vector beginpmatrix 3 -5 endpmatrix
    Find the equation of the translated graph in the form y = x² + bx + c

    Show worked answerHide worked answer
    1. M1: replace x with x - 3: (x - 3)²
    2. M1: subtract 5: y = (x - 3)² - 5
    3. M1: x² - 6x + 9 - 5
    4. A1: y = x² - 6x + 4
    Answer: y = x² - 6x + 4
    Translations Along the x- & y-Axes
    [4 marks]

  5. Question 5. ABC is a straight line with AB:BC=2:3. overrightarrowOA=mathbfa+2mathbfb and overrightarrowAB=4mathbfa-2mathbfb. Find overrightarrowOC in terms of mathbfa and mathbfb.

    Show worked answerHide worked answer
    1. M1: overrightarrowAC=5/2overrightarrowAB=10mathbfa-5mathbfb
    2. M1: overrightarrowOC=mathbfa+2mathbfb+10mathbfa-5mathbfb
    3. A1: 11mathbfa-3mathbfb
    Answer: overrightarrowOC=11mathbfa-3mathbfb
    Vectors Along a Straight Line
    [3 marks]