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

Mixed Topic Worksheet Grades 8/9: Day 073

Grades 8/9Non-calculator

  1. Question 1. The graph of y = sin x is shown for 0^° ≤ x ≤ 360^°. sin 30^° = 0.5. sin x = k has solutions x = 210 and x = 330 in this range. Work out the value of k.

    Show worked answerHide worked answer
    1. M1: sin 210^° = -sin 30^° (graph below the x axis)
    2. A1: k = -0.5
    Answer: k = -0.5
    Solving Trigonometric Equations Using a Graph
    xy-1-0.50.511803600
    [2 marks]

  2. Question 2. On a histogram, the bar for the class 10 < x ≤ 30 is 6 cm high.
    The frequency of this class is 60.
    The frequency of the class 30 < x ≤ 40 is 35.
    Work out the height, in cm, of the bar for the class 30 < x ≤ 40.

    Show worked answerHide worked answer
    1. M1: 60 ÷ (30 - 10) and 35 ÷ (40 - 30)
    2. M1: 6 ÷ 3 or 3.5 × 2
    3. A1: 7
    Answer: 7
    Sketching Histograms
    [3 marks]

  3. Question 3. Simplify fully dfracx²-x-12x²-16

    Show worked answerHide worked answer
    1. M1: (x-4)(x+3)
    2. M1: (x-4)(x+4)
    3. A1: dfracx+3x+4
    Answer: dfracx+3x+4
    Algebraic Fractions Involving Factorising
    [3 marks]

  4. Question 4. y is directly proportional to the square root of x.
    y = 12 when x = 9.
    Find the value of y when x = 25.

    Show worked answerHide worked answer
    1. M1: y = k√x
    2. M1: 12 = k × 3, so k = 4
    3. A1: y = 4 × 5 = 20
    Answer: 20
    Direct & Inverse Proportion with Functions
    [3 marks]

  5. Question 5. The circle C, centre O, has equation x² + y² = 34
    P is the point (5, -3) on C.
    Find an equation of the tangent to C at P.

    Show worked answerHide worked answer
    1. M1: Gradient of OP = -dfrac35
    2. M1: Tangent gradient dfrac53, so y + 3 = dfrac53(x - 5)
    3. A1: 5x - 3y = 34 or an equivalent form
    Answer: 5x - 3y = 34
    Finding Equations of Tangents to Circles
    [3 marks]
📅 Free lesson: Tue 17th NovSave your place →

Mixed Topic Worksheet Grades 8/9: Day 073

Grades 8/9Non-calculator

  1. Question 1. The graph of y = sin x is shown for 0^° ≤ x ≤ 360^°. sin 30^° = 0.5. sin x = k has solutions x = 210 and x = 330 in this range. Work out the value of k.

    [2 marks]
    xy-1-0.50.511803600
    Show worked answerHide worked answer
    1. M1: sin 210^° = -sin 30^° (graph below the x axis)
    2. A1: k = -0.5
    Answer: k = -0.5
    Solving Trigonometric Equations Using a Graph

  2. Question 2. On a histogram, the bar for the class 10 < x ≤ 30 is 6 cm high.
    The frequency of this class is 60.
    The frequency of the class 30 < x ≤ 40 is 35.
    Work out the height, in cm, of the bar for the class 30 < x ≤ 40.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: 60 ÷ (30 - 10) and 35 ÷ (40 - 30)
    2. M1: 6 ÷ 3 or 3.5 × 2
    3. A1: 7
    Answer: 7
    Sketching Histograms

  3. Question 3. Simplify fully dfracx²-x-12x²-16

    [3 marks]
    Show worked answerHide worked answer
    1. M1: (x-4)(x+3)
    2. M1: (x-4)(x+4)
    3. A1: dfracx+3x+4
    Answer: dfracx+3x+4
    Algebraic Fractions Involving Factorising

  4. Question 4. y is directly proportional to the square root of x.
    y = 12 when x = 9.
    Find the value of y when x = 25.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: y = k√x
    2. M1: 12 = k × 3, so k = 4
    3. A1: y = 4 × 5 = 20
    Answer: 20
    Direct & Inverse Proportion with Functions

  5. Question 5. The circle C, centre O, has equation x² + y² = 34
    P is the point (5, -3) on C.
    Find an equation of the tangent to C at P.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: Gradient of OP = -dfrac35
    2. M1: Tangent gradient dfrac53, so y + 3 = dfrac53(x - 5)
    3. A1: 5x - 3y = 34 or an equivalent form
    Answer: 5x - 3y = 34
    Finding Equations of Tangents to Circles
📅 Free live lesson: Tuesday 17th NovemberSave your free place →

Mixed Topic Worksheet Grades 8/9: Day 073

Grades 8/9Non-calculator

  1. Question 1. The graph of y = sin x is shown for 0^° ≤ x ≤ 360^°. sin 30^° = 0.5. sin x = k has solutions x = 210 and x = 330 in this range. Work out the value of k.

    Show worked answerHide worked answer
    1. M1: sin 210^° = -sin 30^° (graph below the x axis)
    2. A1: k = -0.5
    Answer: k = -0.5
    Solving Trigonometric Equations Using a Graph
    xy-1-0.50.511803600
    [2 marks]

  2. Question 2. On a histogram, the bar for the class 10 < x ≤ 30 is 6 cm high.
    The frequency of this class is 60.
    The frequency of the class 30 < x ≤ 40 is 35.
    Work out the height, in cm, of the bar for the class 30 < x ≤ 40.

    Show worked answerHide worked answer
    1. M1: 60 ÷ (30 - 10) and 35 ÷ (40 - 30)
    2. M1: 6 ÷ 3 or 3.5 × 2
    3. A1: 7
    Answer: 7
    Sketching Histograms
    [3 marks]

  3. Question 3. Simplify fully dfracx²-x-12x²-16

    Show worked answerHide worked answer
    1. M1: (x-4)(x+3)
    2. M1: (x-4)(x+4)
    3. A1: dfracx+3x+4
    Answer: dfracx+3x+4
    Algebraic Fractions Involving Factorising
    [3 marks]

  4. Question 4. y is directly proportional to the square root of x.
    y = 12 when x = 9.
    Find the value of y when x = 25.

    Show worked answerHide worked answer
    1. M1: y = k√x
    2. M1: 12 = k × 3, so k = 4
    3. A1: y = 4 × 5 = 20
    Answer: 20
    Direct & Inverse Proportion with Functions
    [3 marks]

  5. Question 5. The circle C, centre O, has equation x² + y² = 34
    P is the point (5, -3) on C.
    Find an equation of the tangent to C at P.

    Show worked answerHide worked answer
    1. M1: Gradient of OP = -dfrac35
    2. M1: Tangent gradient dfrac53, so y + 3 = dfrac53(x - 5)
    3. A1: 5x - 3y = 34 or an equivalent form
    Answer: 5x - 3y = 34
    Finding Equations of Tangents to Circles
    [3 marks]