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

Mixed Topic Worksheet Grades 8/9: Day 004

Grades 8/9Calculator

  1. Question 1. y = x² - 4x + 1 is reflected in the y-axis, then translated 3 units right to give y = f(x).
    Work out f(x) in the form y = x² + ax + b where a and b are integers.

    Show worked answerHide worked answer
    1. M1: reflection gives y = x² + 4x + 1
    2. M1: y = (x - 3)² + 4(x - 3) + 1
    3. A1: y = x² - 2x - 2
    Answer: f(x) = x² - 2x - 2
    Reflections in the x- & y-Axes
    [3 marks]

  2. Question 2. The curve y = x² - 14x + 60 has a turning point. Find the coordinates of the turning point.

    Show worked answerHide worked answer
    1. M1: (x - 7)² - 49 + 60
    2. A1: (x - 7)² + 11
    3. A1: (7, 11)
    Answer: (7, 11)
    Solving Quadratics by Completing the Square (a = 1)
    [3 marks]

  3. Question 3. 150 pupils: 84 play football, 62 play rugby and 17 play neither. A pupil who plays football is chosen at random. Work out the probability that this pupil also plays rugby. Give your answer correct to 3 significant figures.

    Show worked answerHide worked answer
    1. M1: at least one =133, so both =84+62-133=13
    2. M1: 13/84
    3. A1: 0.155
    Answer: 0.155
    Conditional Probability with Venn Diagrams
    [3 marks]

  4. Question 4. A, B, C lie on a circle, centre O, radius 7.5 cm. Angle ACB = 38^°
    Work out AB. Give your answer to 3 significant figures.

    Show worked answerHide worked answer
    1. M1: angle AOB = 2 × 38
    2. M1: AB² = 7.5² + 7.5² - 2 × 7.5 × 7.5 × cos 76^°
    3. M1: AB = √85.28...
    4. A1: 9.23
    Answer: 9.23 cm
    Circle Theorems
    38°OABCNot drawn accurately
    [4 marks]

  5. Question 5. Solve (2x - 1)(x + 4) < 0

    Show worked answerHide worked answer
    1. M1: critical values x = dfrac12 and x = -4
    2. M1: test x = 0: (-1)(4) = -4, which is negative, so the region between the roots
    3. A1: -4 < x < dfrac12
    Answer: -4 < x < dfrac12
    Solving Quadratic Inequalities
    [3 marks]
📅 Free lesson: Tue 17th NovSave your place →

Mixed Topic Worksheet Grades 8/9: Day 004

Grades 8/9Calculator

  1. Question 1. y = x² - 4x + 1 is reflected in the y-axis, then translated 3 units right to give y = f(x).
    Work out f(x) in the form y = x² + ax + b where a and b are integers.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: reflection gives y = x² + 4x + 1
    2. M1: y = (x - 3)² + 4(x - 3) + 1
    3. A1: y = x² - 2x - 2
    Answer: f(x) = x² - 2x - 2
    Reflections in the x- & y-Axes

  2. Question 2. The curve y = x² - 14x + 60 has a turning point. Find the coordinates of the turning point.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: (x - 7)² - 49 + 60
    2. A1: (x - 7)² + 11
    3. A1: (7, 11)
    Answer: (7, 11)
    Solving Quadratics by Completing the Square (a = 1)

  3. Question 3. 150 pupils: 84 play football, 62 play rugby and 17 play neither. A pupil who plays football is chosen at random. Work out the probability that this pupil also plays rugby. Give your answer correct to 3 significant figures.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: at least one =133, so both =84+62-133=13
    2. M1: 13/84
    3. A1: 0.155
    Answer: 0.155
    Conditional Probability with Venn Diagrams

  4. Question 4. A, B, C lie on a circle, centre O, radius 7.5 cm. Angle ACB = 38^°
    Work out AB. Give your answer to 3 significant figures.

    [4 marks]
    38°OABCNot drawn accurately
    Show worked answerHide worked answer
    1. M1: angle AOB = 2 × 38
    2. M1: AB² = 7.5² + 7.5² - 2 × 7.5 × 7.5 × cos 76^°
    3. M1: AB = √85.28...
    4. A1: 9.23
    Answer: 9.23 cm
    Circle Theorems

  5. Question 5. Solve (2x - 1)(x + 4) < 0

    [3 marks]
    Show worked answerHide worked answer
    1. M1: critical values x = dfrac12 and x = -4
    2. M1: test x = 0: (-1)(4) = -4, which is negative, so the region between the roots
    3. A1: -4 < x < dfrac12
    Answer: -4 < x < dfrac12
    Solving Quadratic Inequalities
📅 Free live lesson: Tuesday 17th NovemberSave your free place →

Mixed Topic Worksheet Grades 8/9: Day 004

Grades 8/9Calculator

  1. Question 1. y = x² - 4x + 1 is reflected in the y-axis, then translated 3 units right to give y = f(x).
    Work out f(x) in the form y = x² + ax + b where a and b are integers.

    Show worked answerHide worked answer
    1. M1: reflection gives y = x² + 4x + 1
    2. M1: y = (x - 3)² + 4(x - 3) + 1
    3. A1: y = x² - 2x - 2
    Answer: f(x) = x² - 2x - 2
    Reflections in the x- & y-Axes
    [3 marks]

  2. Question 2. The curve y = x² - 14x + 60 has a turning point. Find the coordinates of the turning point.

    Show worked answerHide worked answer
    1. M1: (x - 7)² - 49 + 60
    2. A1: (x - 7)² + 11
    3. A1: (7, 11)
    Answer: (7, 11)
    Solving Quadratics by Completing the Square (a = 1)
    [3 marks]

  3. Question 3. 150 pupils: 84 play football, 62 play rugby and 17 play neither. A pupil who plays football is chosen at random. Work out the probability that this pupil also plays rugby. Give your answer correct to 3 significant figures.

    Show worked answerHide worked answer
    1. M1: at least one =133, so both =84+62-133=13
    2. M1: 13/84
    3. A1: 0.155
    Answer: 0.155
    Conditional Probability with Venn Diagrams
    [3 marks]

  4. Question 4. A, B, C lie on a circle, centre O, radius 7.5 cm. Angle ACB = 38^°
    Work out AB. Give your answer to 3 significant figures.

    Show worked answerHide worked answer
    1. M1: angle AOB = 2 × 38
    2. M1: AB² = 7.5² + 7.5² - 2 × 7.5 × 7.5 × cos 76^°
    3. M1: AB = √85.28...
    4. A1: 9.23
    Answer: 9.23 cm
    Circle Theorems
    38°OABCNot drawn accurately
    [4 marks]

  5. Question 5. Solve (2x - 1)(x + 4) < 0

    Show worked answerHide worked answer
    1. M1: critical values x = dfrac12 and x = -4
    2. M1: test x = 0: (-1)(4) = -4, which is negative, so the region between the roots
    3. A1: -4 < x < dfrac12
    Answer: -4 < x < dfrac12
    Solving Quadratic Inequalities
    [3 marks]