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

Mixed Topic Worksheet Grades 8/9: Day 055

Grades 8/9Non-calculator

  1. Question 1. The graph of y = 3cos x - 2 is drawn for 0^° ≤ x ≤ 360^°. Write down the coordinates of the minimum point.

    Show worked answerHide worked answer
    1. M1: minimum of cos x is -1 at x = 180^°
    2. A1: y = 3(-1) - 2 = -5
    Answer: (180^°, -5)
    Transforming Trigonometric Graphs
    [2 marks]

  2. Question 2. The table shows information about the ages, a years, of 86 members of a gym.
    Work out the frequency density for the class 20 < a ≤ 40.

    Show worked answerHide worked answer
    1. M1: 86 - (12 + 28 + 16)
    2. M1: 30 ÷ (40 - 20)
    3. A1: 1.5
    Answer: 1.5
    Sketching Histograms
    Age, a (years)Frequency0 < a ≤ 101210 < a ≤ 202820 < a ≤ 4040 < a ≤ 6016
    [3 marks]

  3. Question 3. The area of a circle is 50π cm².
    Work out the diameter of the circle.
    Give 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: r² = 50
    2. M1: r = √50 = 5√2
    3. A1: 10√2
    Answer: 10√2 cm
    Simplifying Surds
    [3 marks]

  4. Question 4. Solve
    y = dfrac12x
    y = x + 1

    Show worked answerHide worked answer
    1. M1: dfrac12x = x + 1 so x² + x - 12 = 0
    2. M1: (x + 4)(x - 3) = 0
    3. A2: x = 3, y = 4 and x = -4, y = -3
    Answer: x = 3, y = 4 or x = -4, y = -3
    Solving Quadratic Simultaneous Equations
    [4 marks]

  5. Question 5. Circle C: x² + y² = 18
    Line L: y = x + 7
    Sam says L is a tangent to C. Is Sam correct?
    You must show your working.

    Show worked answerHide worked answer
    1. M1: x² + (x + 7)² = 18
    2. M1: 2x² + 14x + 31 = 0
    3. A1: 14² - 4 × 2 × 31 = -52 < 0, so L does not meet C: Sam is not correct
    Answer: No: L does not meet C
    Finding Equations of Tangents to Circles
    [3 marks]
📅 Free lesson: Tue 17th NovSave your place →

Mixed Topic Worksheet Grades 8/9: Day 055

Grades 8/9Non-calculator

  1. Question 1. The graph of y = 3cos x - 2 is drawn for 0^° ≤ x ≤ 360^°. Write down the coordinates of the minimum point.

    [2 marks]
    Show worked answerHide worked answer
    1. M1: minimum of cos x is -1 at x = 180^°
    2. A1: y = 3(-1) - 2 = -5
    Answer: (180^°, -5)
    Transforming Trigonometric Graphs

  2. Question 2. The table shows information about the ages, a years, of 86 members of a gym.
    Work out the frequency density for the class 20 < a ≤ 40.

    [3 marks]
    Age, a (years)Frequency0 < a ≤ 101210 < a ≤ 202820 < a ≤ 4040 < a ≤ 6016
    Show worked answerHide worked answer
    1. M1: 86 - (12 + 28 + 16)
    2. M1: 30 ÷ (40 - 20)
    3. A1: 1.5
    Answer: 1.5
    Sketching Histograms

  3. Question 3. The area of a circle is 50π cm².
    Work out the diameter of the circle.
    Give 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: r² = 50
    2. M1: r = √50 = 5√2
    3. A1: 10√2
    Answer: 10√2 cm
    Simplifying Surds

  4. Question 4. Solve
    y = dfrac12x
    y = x + 1

    [4 marks]
    Show worked answerHide worked answer
    1. M1: dfrac12x = x + 1 so x² + x - 12 = 0
    2. M1: (x + 4)(x - 3) = 0
    3. A2: x = 3, y = 4 and x = -4, y = -3
    Answer: x = 3, y = 4 or x = -4, y = -3
    Solving Quadratic Simultaneous Equations

  5. Question 5. Circle C: x² + y² = 18
    Line L: y = x + 7
    Sam says L is a tangent to C. Is Sam correct?
    You must show your working.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: x² + (x + 7)² = 18
    2. M1: 2x² + 14x + 31 = 0
    3. A1: 14² - 4 × 2 × 31 = -52 < 0, so L does not meet C: Sam is not correct
    Answer: No: L does not meet C
    Finding Equations of Tangents to Circles
📅 Free live lesson: Tuesday 17th NovemberSave your free place →

Mixed Topic Worksheet Grades 8/9: Day 055

Grades 8/9Non-calculator

  1. Question 1. The graph of y = 3cos x - 2 is drawn for 0^° ≤ x ≤ 360^°. Write down the coordinates of the minimum point.

    Show worked answerHide worked answer
    1. M1: minimum of cos x is -1 at x = 180^°
    2. A1: y = 3(-1) - 2 = -5
    Answer: (180^°, -5)
    Transforming Trigonometric Graphs
    [2 marks]

  2. Question 2. The table shows information about the ages, a years, of 86 members of a gym.
    Work out the frequency density for the class 20 < a ≤ 40.

    Show worked answerHide worked answer
    1. M1: 86 - (12 + 28 + 16)
    2. M1: 30 ÷ (40 - 20)
    3. A1: 1.5
    Answer: 1.5
    Sketching Histograms
    Age, a (years)Frequency0 < a ≤ 101210 < a ≤ 202820 < a ≤ 4040 < a ≤ 6016
    [3 marks]

  3. Question 3. The area of a circle is 50π cm².
    Work out the diameter of the circle.
    Give 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: r² = 50
    2. M1: r = √50 = 5√2
    3. A1: 10√2
    Answer: 10√2 cm
    Simplifying Surds
    [3 marks]

  4. Question 4. Solve
    y = dfrac12x
    y = x + 1

    Show worked answerHide worked answer
    1. M1: dfrac12x = x + 1 so x² + x - 12 = 0
    2. M1: (x + 4)(x - 3) = 0
    3. A2: x = 3, y = 4 and x = -4, y = -3
    Answer: x = 3, y = 4 or x = -4, y = -3
    Solving Quadratic Simultaneous Equations
    [4 marks]

  5. Question 5. Circle C: x² + y² = 18
    Line L: y = x + 7
    Sam says L is a tangent to C. Is Sam correct?
    You must show your working.

    Show worked answerHide worked answer
    1. M1: x² + (x + 7)² = 18
    2. M1: 2x² + 14x + 31 = 0
    3. A1: 14² - 4 × 2 × 31 = -52 < 0, so L does not meet C: Sam is not correct
    Answer: No: L does not meet C
    Finding Equations of Tangents to Circles
    [3 marks]