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

Mixed Topic Worksheet Grades 8/9: Day 024

Grades 8/9Calculator

  1. Question 1. Matthew says that 3√20 is greater than 2√45. Is Matthew correct? Show your working.

    Show worked answerHide worked answer
    1. M1: 3√20 = 3√4 × 5 = 6√5
    2. M1: 2√45 = 2√9 × 5 = 6√5
    3. A1: Not correct, they are equal
    Answer: No. Both are equal to 6√5
    Simplifying Surds
    [3 marks]

  2. Question 2. Solve 3cos x + 2 = 0 for 0^° ≤ x ≤ 360^°. Give your answers correct to 1 decimal place

    Show worked answerHide worked answer
    1. M1: cos x = -dfrac23, so x = cos⁻¹≤ft(-dfrac23)
    2. M1: 360^° - 131.8^°
    3. A1: 131.8^° and 228.2^°
    Answer: x = 131.8^° and x = 228.2^°
    Solving Trigonometric Equations Using a Graph
    [3 marks]

  3. Question 3. Solve x² - 5x - 1 = 0 by completing the square. Give your solutions to 2 decimal places.

    Show worked answerHide worked answer
    1. M1: ≤ft(x - frac52)² = 1 + 25/4
    2. M1: x = frac52 ± frac√292
    3. A1: x = 5.19 or x = -0.19
    Answer: x = 5.19 or x = -0.19
    Solving Quadratics by Completing the Square (a = 1)
    [3 marks]

  4. Question 4. The curve y = x² - 5 meets the line y = 4x at two points
    Work out the coordinates of both points

    Show worked answerHide worked answer
    1. M1: x² - 5 = 4x so x² - 4x - 5 = 0
    2. M1: (x - 5)(x + 1) = 0
    3. A2: (5, 20) and (-1, -4)
    Answer: (5, 20) and (-1, -4)
    Solving Quadratic Simultaneous Equations
    [4 marks]

  5. Question 5. The inequality x² - 4x + k > 0 is true for every value of x
    Find the possible values of k

    Show worked answerHide worked answer
    1. M1: completes the square, x² - 4x + k = (x - 2)² + k - 4
    2. M1: the smallest value of the expression is k - 4, which must be greater than 0
    3. A1: k > 4
    Answer: k > 4
    Sketching Quadratic Inequalities
    [3 marks]
📅 Free lesson: Tue 17th NovSave your place →

Mixed Topic Worksheet Grades 8/9: Day 024

Grades 8/9Calculator

  1. Question 1. Matthew says that 3√20 is greater than 2√45. Is Matthew correct? Show your working.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: 3√20 = 3√4 × 5 = 6√5
    2. M1: 2√45 = 2√9 × 5 = 6√5
    3. A1: Not correct, they are equal
    Answer: No. Both are equal to 6√5
    Simplifying Surds

  2. Question 2. Solve 3cos x + 2 = 0 for 0^° ≤ x ≤ 360^°. Give your answers correct to 1 decimal place

    [3 marks]
    Show worked answerHide worked answer
    1. M1: cos x = -dfrac23, so x = cos⁻¹≤ft(-dfrac23)
    2. M1: 360^° - 131.8^°
    3. A1: 131.8^° and 228.2^°
    Answer: x = 131.8^° and x = 228.2^°
    Solving Trigonometric Equations Using a Graph

  3. Question 3. Solve x² - 5x - 1 = 0 by completing the square. Give your solutions to 2 decimal places.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: ≤ft(x - frac52)² = 1 + 25/4
    2. M1: x = frac52 ± frac√292
    3. A1: x = 5.19 or x = -0.19
    Answer: x = 5.19 or x = -0.19
    Solving Quadratics by Completing the Square (a = 1)

  4. Question 4. The curve y = x² - 5 meets the line y = 4x at two points
    Work out the coordinates of both points

    [4 marks]
    Show worked answerHide worked answer
    1. M1: x² - 5 = 4x so x² - 4x - 5 = 0
    2. M1: (x - 5)(x + 1) = 0
    3. A2: (5, 20) and (-1, -4)
    Answer: (5, 20) and (-1, -4)
    Solving Quadratic Simultaneous Equations

  5. Question 5. The inequality x² - 4x + k > 0 is true for every value of x
    Find the possible values of k

    [3 marks]
    Show worked answerHide worked answer
    1. M1: completes the square, x² - 4x + k = (x - 2)² + k - 4
    2. M1: the smallest value of the expression is k - 4, which must be greater than 0
    3. A1: k > 4
    Answer: k > 4
    Sketching Quadratic Inequalities
📅 Free live lesson: Tuesday 17th NovemberSave your free place →

Mixed Topic Worksheet Grades 8/9: Day 024

Grades 8/9Calculator

  1. Question 1. Matthew says that 3√20 is greater than 2√45. Is Matthew correct? Show your working.

    Show worked answerHide worked answer
    1. M1: 3√20 = 3√4 × 5 = 6√5
    2. M1: 2√45 = 2√9 × 5 = 6√5
    3. A1: Not correct, they are equal
    Answer: No. Both are equal to 6√5
    Simplifying Surds
    [3 marks]

  2. Question 2. Solve 3cos x + 2 = 0 for 0^° ≤ x ≤ 360^°. Give your answers correct to 1 decimal place

    Show worked answerHide worked answer
    1. M1: cos x = -dfrac23, so x = cos⁻¹≤ft(-dfrac23)
    2. M1: 360^° - 131.8^°
    3. A1: 131.8^° and 228.2^°
    Answer: x = 131.8^° and x = 228.2^°
    Solving Trigonometric Equations Using a Graph
    [3 marks]

  3. Question 3. Solve x² - 5x - 1 = 0 by completing the square. Give your solutions to 2 decimal places.

    Show worked answerHide worked answer
    1. M1: ≤ft(x - frac52)² = 1 + 25/4
    2. M1: x = frac52 ± frac√292
    3. A1: x = 5.19 or x = -0.19
    Answer: x = 5.19 or x = -0.19
    Solving Quadratics by Completing the Square (a = 1)
    [3 marks]

  4. Question 4. The curve y = x² - 5 meets the line y = 4x at two points
    Work out the coordinates of both points

    Show worked answerHide worked answer
    1. M1: x² - 5 = 4x so x² - 4x - 5 = 0
    2. M1: (x - 5)(x + 1) = 0
    3. A2: (5, 20) and (-1, -4)
    Answer: (5, 20) and (-1, -4)
    Solving Quadratic Simultaneous Equations
    [4 marks]

  5. Question 5. The inequality x² - 4x + k > 0 is true for every value of x
    Find the possible values of k

    Show worked answerHide worked answer
    1. M1: completes the square, x² - 4x + k = (x - 2)² + k - 4
    2. M1: the smallest value of the expression is k - 4, which must be greater than 0
    3. A1: k > 4
    Answer: k > 4
    Sketching Quadratic Inequalities
    [3 marks]