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

Mixed Topic Worksheet Grades 8/9: Day 025

Grades 8/9Non-calculator

  1. Question 1. Here is the graph of y = sin x for 0^° ≤ x ≤ 360^°. The straight line y = k meets the graph at exactly one point. Write down the two possible values of k.

    Show worked answerHide worked answer
    1. M1: reads the greatest and least values of y on the graph, at the turning points where x = 90 and x = 270
    2. A1: k = 1 and k = -1
    Answer: k = 1 or k = -1
    Sketching sin, cos & tan
    xy-1-0.50.511803600
    [2 marks]

  2. Question 2. A pyramid has a rectangular base 16 cm by 12 cm. Its apex is 24 cm vertically above the centre of the base. Work out the length of a sloping edge.

    Show worked answerHide worked answer
    1. M1: half the base diagonal = 1/2√16² + 12² = 10
    2. M1: √10² + 24²
    3. A1: 26 cm
    Answer: 26 cm
    3D Pythagoras
    [3 marks]

  3. Question 3. P(B)=0.4, P(Acap B)=0.3 and P(Acup B)=0.7. Work out P(A'mid B').

    Show worked answerHide worked answer
    1. M1: P(A)=0.7+0.3-0.4=0.6
    2. M1: P(A'cap B')=1-0.7=0.3 and P(B')=0.6
    3. A1: 0.5
    Answer: 0.5
    Conditional Probability with Venn Diagrams
    [3 marks]

  4. Question 4. A, B and D are on a circle, centre O, with D on the minor arc AB.
    Angle OAB = 24^°
    Work out angle ADB.
    Give reasons for each stage.

    Show worked answerHide worked answer
    1. M1: angle AOB = 180 - 2 × 24
    2. M1: (360 - 132) ÷ 2
    3. A1: angle ADB = 114^°
    4. C1: OAB is isosceles (radii); angles around a point add to 360^°; angle at the circumference is half that at the centre
    Answer: 114^°
    Combining Circle Theorems
    24°OABDNot drawn accurately
    [4 marks]

  5. Question 5. Solve 12 + x - x² > 0

    Show worked answerHide worked answer
    1. M1: x²-x-12 < 0
    2. M1: (x - 4)(x + 3) < 0
    3. A1: -3 < x < 4
    Answer: -3 < x < 4
    Solving Quadratic Inequalities
    [3 marks]
📅 Free lesson: Tue 17th NovSave your place →

Mixed Topic Worksheet Grades 8/9: Day 025

Grades 8/9Non-calculator

  1. Question 1. Here is the graph of y = sin x for 0^° ≤ x ≤ 360^°. The straight line y = k meets the graph at exactly one point. Write down the two possible values of k.

    [2 marks]
    xy-1-0.50.511803600
    Show worked answerHide worked answer
    1. M1: reads the greatest and least values of y on the graph, at the turning points where x = 90 and x = 270
    2. A1: k = 1 and k = -1
    Answer: k = 1 or k = -1
    Sketching sin, cos & tan

  2. Question 2. A pyramid has a rectangular base 16 cm by 12 cm. Its apex is 24 cm vertically above the centre of the base. Work out the length of a sloping edge.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: half the base diagonal = 1/2√16² + 12² = 10
    2. M1: √10² + 24²
    3. A1: 26 cm
    Answer: 26 cm
    3D Pythagoras

  3. Question 3. P(B)=0.4, P(Acap B)=0.3 and P(Acup B)=0.7. Work out P(A'mid B').

    [3 marks]
    Show worked answerHide worked answer
    1. M1: P(A)=0.7+0.3-0.4=0.6
    2. M1: P(A'cap B')=1-0.7=0.3 and P(B')=0.6
    3. A1: 0.5
    Answer: 0.5
    Conditional Probability with Venn Diagrams

  4. Question 4. A, B and D are on a circle, centre O, with D on the minor arc AB.
    Angle OAB = 24^°
    Work out angle ADB.
    Give reasons for each stage.

    [4 marks]
    24°OABDNot drawn accurately
    Show worked answerHide worked answer
    1. M1: angle AOB = 180 - 2 × 24
    2. M1: (360 - 132) ÷ 2
    3. A1: angle ADB = 114^°
    4. C1: OAB is isosceles (radii); angles around a point add to 360^°; angle at the circumference is half that at the centre
    Answer: 114^°
    Combining Circle Theorems

  5. Question 5. Solve 12 + x - x² > 0

    [3 marks]
    Show worked answerHide worked answer
    1. M1: x²-x-12 < 0
    2. M1: (x - 4)(x + 3) < 0
    3. A1: -3 < x < 4
    Answer: -3 < x < 4
    Solving Quadratic Inequalities
📅 Free live lesson: Tuesday 17th NovemberSave your free place →

Mixed Topic Worksheet Grades 8/9: Day 025

Grades 8/9Non-calculator

  1. Question 1. Here is the graph of y = sin x for 0^° ≤ x ≤ 360^°. The straight line y = k meets the graph at exactly one point. Write down the two possible values of k.

    Show worked answerHide worked answer
    1. M1: reads the greatest and least values of y on the graph, at the turning points where x = 90 and x = 270
    2. A1: k = 1 and k = -1
    Answer: k = 1 or k = -1
    Sketching sin, cos & tan
    xy-1-0.50.511803600
    [2 marks]

  2. Question 2. A pyramid has a rectangular base 16 cm by 12 cm. Its apex is 24 cm vertically above the centre of the base. Work out the length of a sloping edge.

    Show worked answerHide worked answer
    1. M1: half the base diagonal = 1/2√16² + 12² = 10
    2. M1: √10² + 24²
    3. A1: 26 cm
    Answer: 26 cm
    3D Pythagoras
    [3 marks]

  3. Question 3. P(B)=0.4, P(Acap B)=0.3 and P(Acup B)=0.7. Work out P(A'mid B').

    Show worked answerHide worked answer
    1. M1: P(A)=0.7+0.3-0.4=0.6
    2. M1: P(A'cap B')=1-0.7=0.3 and P(B')=0.6
    3. A1: 0.5
    Answer: 0.5
    Conditional Probability with Venn Diagrams
    [3 marks]

  4. Question 4. A, B and D are on a circle, centre O, with D on the minor arc AB.
    Angle OAB = 24^°
    Work out angle ADB.
    Give reasons for each stage.

    Show worked answerHide worked answer
    1. M1: angle AOB = 180 - 2 × 24
    2. M1: (360 - 132) ÷ 2
    3. A1: angle ADB = 114^°
    4. C1: OAB is isosceles (radii); angles around a point add to 360^°; angle at the circumference is half that at the centre
    Answer: 114^°
    Combining Circle Theorems
    24°OABDNot drawn accurately
    [4 marks]

  5. Question 5. Solve 12 + x - x² > 0

    Show worked answerHide worked answer
    1. M1: x²-x-12 < 0
    2. M1: (x - 4)(x + 3) < 0
    3. A1: -3 < x < 4
    Answer: -3 < x < 4
    Solving Quadratic Inequalities
    [3 marks]