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

Mixed Topic Worksheet Grades 8/9: Day 043

Grades 8/9Non-calculator

  1. Question 1. The graph of y = tan x is drawn for 0° ≤ x ≤ 360°. Write down the equations of the vertical asymptotes.

    Show worked answerHide worked answer
    1. B1: x = 90°
    2. B1: x = 270°
    Answer: x = 90° and x = 270°
    Sketching sin, cos & tan
    [2 marks]

  2. Question 2. Mia reflects the graph of y = x² - 6x in the x-axis and writes the new equation as y = -x² - 6x Explain her mistake and write down the correct equation

    Show worked answerHide worked answer
    1. B1: every term must change sign, so -6x becomes +6x
    2. B1: y = -x² + 6x
    Answer: y = -x² + 6x
    Reflections in the x- & y-Axes
    [2 marks]

  3. Question 3. The sum of two numbers is 9
    The sum of their squares is 45
    Work out the two numbers

    Show worked answerHide worked answer
    1. M1: x² + (9 - x)² = 45 so x² - 9x + 18 = 0
    2. M1: (x - 3)(x - 6) = 0
    3. A1: 3 and 6
    Answer: 3 and 6
    Solving Quadratic Simultaneous Equations
    [3 marks]

  4. Question 4. Of 80 pupils, 30 play football, 25 play rugby and 15 play both. A pupil who plays at least one of the sports is chosen. Find the probability that they play both.

    Show worked answerHide worked answer
    1. M1: at least one = 30 + 25 - 15 = 40
    2. M1: dfrac1540
    3. A1: dfrac38
    Answer: dfrac38
    Conditional Probability with Venn Diagrams
    [3 marks]

  5. Question 5. Rationalise the denominator of dfrac14 - √5
    Give your answer in its simplest form.

    Show worked answerHide worked answer
    1. M1: multiply the numerator and the denominator by 4 + √5
    2. M1: denominator 16 - 5 = 11
    3. A1: dfrac4 + √511
    Answer: dfrac4 + √511
    Rationalising Denominators of the Form a ± √b
    [3 marks]
📅 Free lesson: Tue 17th NovSave your place →

Mixed Topic Worksheet Grades 8/9: Day 043

Grades 8/9Non-calculator

  1. Question 1. The graph of y = tan x is drawn for 0° ≤ x ≤ 360°. Write down the equations of the vertical asymptotes.

    [2 marks]
    Show worked answerHide worked answer
    1. B1: x = 90°
    2. B1: x = 270°
    Answer: x = 90° and x = 270°
    Sketching sin, cos & tan

  2. Question 2. Mia reflects the graph of y = x² - 6x in the x-axis and writes the new equation as y = -x² - 6x Explain her mistake and write down the correct equation

    [2 marks]
    Show worked answerHide worked answer
    1. B1: every term must change sign, so -6x becomes +6x
    2. B1: y = -x² + 6x
    Answer: y = -x² + 6x
    Reflections in the x- & y-Axes

  3. Question 3. The sum of two numbers is 9
    The sum of their squares is 45
    Work out the two numbers

    [3 marks]
    Show worked answerHide worked answer
    1. M1: x² + (9 - x)² = 45 so x² - 9x + 18 = 0
    2. M1: (x - 3)(x - 6) = 0
    3. A1: 3 and 6
    Answer: 3 and 6
    Solving Quadratic Simultaneous Equations

  4. Question 4. Of 80 pupils, 30 play football, 25 play rugby and 15 play both. A pupil who plays at least one of the sports is chosen. Find the probability that they play both.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: at least one = 30 + 25 - 15 = 40
    2. M1: dfrac1540
    3. A1: dfrac38
    Answer: dfrac38
    Conditional Probability with Venn Diagrams

  5. Question 5. Rationalise the denominator of dfrac14 - √5
    Give your answer in its simplest form.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: multiply the numerator and the denominator by 4 + √5
    2. M1: denominator 16 - 5 = 11
    3. A1: dfrac4 + √511
    Answer: dfrac4 + √511
    Rationalising Denominators of the Form a ± √b
📅 Free live lesson: Tuesday 17th NovemberSave your free place →

Mixed Topic Worksheet Grades 8/9: Day 043

Grades 8/9Non-calculator

  1. Question 1. The graph of y = tan x is drawn for 0° ≤ x ≤ 360°. Write down the equations of the vertical asymptotes.

    Show worked answerHide worked answer
    1. B1: x = 90°
    2. B1: x = 270°
    Answer: x = 90° and x = 270°
    Sketching sin, cos & tan
    [2 marks]

  2. Question 2. Mia reflects the graph of y = x² - 6x in the x-axis and writes the new equation as y = -x² - 6x Explain her mistake and write down the correct equation

    Show worked answerHide worked answer
    1. B1: every term must change sign, so -6x becomes +6x
    2. B1: y = -x² + 6x
    Answer: y = -x² + 6x
    Reflections in the x- & y-Axes
    [2 marks]

  3. Question 3. The sum of two numbers is 9
    The sum of their squares is 45
    Work out the two numbers

    Show worked answerHide worked answer
    1. M1: x² + (9 - x)² = 45 so x² - 9x + 18 = 0
    2. M1: (x - 3)(x - 6) = 0
    3. A1: 3 and 6
    Answer: 3 and 6
    Solving Quadratic Simultaneous Equations
    [3 marks]

  4. Question 4. Of 80 pupils, 30 play football, 25 play rugby and 15 play both. A pupil who plays at least one of the sports is chosen. Find the probability that they play both.

    Show worked answerHide worked answer
    1. M1: at least one = 30 + 25 - 15 = 40
    2. M1: dfrac1540
    3. A1: dfrac38
    Answer: dfrac38
    Conditional Probability with Venn Diagrams
    [3 marks]

  5. Question 5. Rationalise the denominator of dfrac14 - √5
    Give your answer in its simplest form.

    Show worked answerHide worked answer
    1. M1: multiply the numerator and the denominator by 4 + √5
    2. M1: denominator 16 - 5 = 11
    3. A1: dfrac4 + √511
    Answer: dfrac4 + √511
    Rationalising Denominators of the Form a ± √b
    [3 marks]