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

Mixed Topic Worksheet Grades 8/9: Day 010

Grades 8/9Calculator

  1. Question 1. The graph of y = 2sin(x + 30^°) + 1 is drawn. Work out the value of y when x = 100^°. Give your answer correct to 3 significant figures.

    Show worked answerHide worked answer
    1. M1: y = 2sin 130^° + 1
    2. A1: 2.53
    Answer: 2.53
    Transforming Trigonometric Graphs
    [2 marks]

  2. Question 2. A rectangle has an area of 18 cm² and a length of √12 cm. Work out the width of the rectangle, giving your answer in the form a√b where a and b are integers and b is as small as possible.

    Show worked answerHide worked answer
    1. M1: dfrac18√12 = dfrac182√3 = dfrac9√3
    2. M1: dfrac9√33
    3. A1: 3√3 cm
    Answer: 3√3 cm
    Rationalising Denominators of the Form √a
    [3 marks]

  3. Question 3. Solve x² - 10x + 5 = 0 by completing the square
    Give the solutions in the form a ± b√c where a, b and c are integers.

    Show worked answerHide worked answer
    1. M1: (x - 5)² - 25 + 5 = 0
    2. M1: (x - 5)² = 20
    3. M1: x - 5 = ±√20 and √20 = 2√5
    4. A1: x = 5 ± 2√5
    Answer: x = 5 ± 2√5
    Solving Quadratics by Completing the Square (a = 1)
    [4 marks]

  4. Question 4. The graph of y = x² - 3x is translated by the vector beginpmatrix -1 4 endpmatrix
    Find the equation of the translated graph.
    Give your answer in the form y = x² + bx + c

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

  5. Question 5. The point P(6, -3) lies on the circle x² + y² = 45
    Find an equation of the tangent to the circle at P.

    Show worked answerHide worked answer
    1. M1: gradient of OP = -dfrac36 = -dfrac12
    2. M1: tangent gradient 2 and y + 3 = 2(x - 6)
    3. A1: y = 2x - 15
    Answer: y = 2x - 15
    Finding Equations of Tangents to Circles
    [3 marks]
📅 Free lesson: Tue 17th NovSave your place →

Mixed Topic Worksheet Grades 8/9: Day 010

Grades 8/9Calculator

  1. Question 1. The graph of y = 2sin(x + 30^°) + 1 is drawn. Work out the value of y when x = 100^°. Give your answer correct to 3 significant figures.

    [2 marks]
    Show worked answerHide worked answer
    1. M1: y = 2sin 130^° + 1
    2. A1: 2.53
    Answer: 2.53
    Transforming Trigonometric Graphs

  2. Question 2. A rectangle has an area of 18 cm² and a length of √12 cm. Work out the width of the rectangle, giving your answer in the form a√b where a and b are integers and b is as small as possible.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: dfrac18√12 = dfrac182√3 = dfrac9√3
    2. M1: dfrac9√33
    3. A1: 3√3 cm
    Answer: 3√3 cm
    Rationalising Denominators of the Form √a

  3. Question 3. Solve x² - 10x + 5 = 0 by completing the square
    Give the solutions in the form a ± b√c where a, b and c are integers.

    [4 marks]
    Show worked answerHide worked answer
    1. M1: (x - 5)² - 25 + 5 = 0
    2. M1: (x - 5)² = 20
    3. M1: x - 5 = ±√20 and √20 = 2√5
    4. A1: x = 5 ± 2√5
    Answer: x = 5 ± 2√5
    Solving Quadratics by Completing the Square (a = 1)

  4. Question 4. The graph of y = x² - 3x is translated by the vector beginpmatrix -1 4 endpmatrix
    Find the equation of the translated graph.
    Give your answer in the form y = x² + bx + c

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

  5. Question 5. The point P(6, -3) lies on the circle x² + y² = 45
    Find an equation of the tangent to the circle at P.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: gradient of OP = -dfrac36 = -dfrac12
    2. M1: tangent gradient 2 and y + 3 = 2(x - 6)
    3. A1: y = 2x - 15
    Answer: y = 2x - 15
    Finding Equations of Tangents to Circles
📅 Free live lesson: Tuesday 17th NovemberSave your free place →

Mixed Topic Worksheet Grades 8/9: Day 010

Grades 8/9Calculator

  1. Question 1. The graph of y = 2sin(x + 30^°) + 1 is drawn. Work out the value of y when x = 100^°. Give your answer correct to 3 significant figures.

    Show worked answerHide worked answer
    1. M1: y = 2sin 130^° + 1
    2. A1: 2.53
    Answer: 2.53
    Transforming Trigonometric Graphs
    [2 marks]

  2. Question 2. A rectangle has an area of 18 cm² and a length of √12 cm. Work out the width of the rectangle, giving your answer in the form a√b where a and b are integers and b is as small as possible.

    Show worked answerHide worked answer
    1. M1: dfrac18√12 = dfrac182√3 = dfrac9√3
    2. M1: dfrac9√33
    3. A1: 3√3 cm
    Answer: 3√3 cm
    Rationalising Denominators of the Form √a
    [3 marks]

  3. Question 3. Solve x² - 10x + 5 = 0 by completing the square
    Give the solutions in the form a ± b√c where a, b and c are integers.

    Show worked answerHide worked answer
    1. M1: (x - 5)² - 25 + 5 = 0
    2. M1: (x - 5)² = 20
    3. M1: x - 5 = ±√20 and √20 = 2√5
    4. A1: x = 5 ± 2√5
    Answer: x = 5 ± 2√5
    Solving Quadratics by Completing the Square (a = 1)
    [4 marks]

  4. Question 4. The graph of y = x² - 3x is translated by the vector beginpmatrix -1 4 endpmatrix
    Find the equation of the translated graph.
    Give your answer in the form y = x² + bx + c

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

  5. Question 5. The point P(6, -3) lies on the circle x² + y² = 45
    Find an equation of the tangent to the circle at P.

    Show worked answerHide worked answer
    1. M1: gradient of OP = -dfrac36 = -dfrac12
    2. M1: tangent gradient 2 and y + 3 = 2(x - 6)
    3. A1: y = 2x - 15
    Answer: y = 2x - 15
    Finding Equations of Tangents to Circles
    [3 marks]