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

Mixed Topic Worksheet Grades 8/9: Day 061

Grades 8/9Non-calculator

  1. Question 1. Solve cos(x + 20^°) = 0.5 for 0^° ≤ x ≤ 360^°.

    Show worked answerHide worked answer
    1. M1: x + 20 = 60 or 300
    2. A1: x = 40^° and x = 280^°
    Answer: x = 40^° and x = 280^°
    Solving Trigonometric Equations Using a Graph
    [2 marks]

  2. Question 2. P(A mid B) = 0.5 and P(B) = 0.36. Work out P(A cap B).

    Show worked answerHide worked answer
    1. M1: 0.5 × 0.36
    2. A1: 0.18
    Answer: 0.18
    Conditional Probability with Venn Diagrams
    [2 marks]

  3. Question 3. Simplify fully √243 - √48
    Give your answer in the form a√3, where a is an integer.

    Show worked answerHide worked answer
    1. M1: √243 = √81 × 3 = 9√3
    2. M1: √48 = √16 × 3 = 4√3
    3. A1: 5√3
    Answer: 5√3
    Simplifying Surds
    [3 marks]

  4. Question 4. Prove algebraically that the sum of the squares of two consecutive integers is equal to 1 more than twice the product of the two integers.

    Show worked answerHide worked answer
    1. M1: n² + (n + 1)² = n² + n² + 2n + 1
    2. A1: 2n² + 2n + 1
    3. C1: 2n(n + 1) + 1 = 2n² + 2n + 1, which is the same
    Answer: 2n(n + 1) + 1
    Proof with Consecutive Numbers
    [3 marks]

  5. Question 5. The circle C, centre O, has equation x² + y² = 45
    P is the point (6, 3) on C.
    The tangent to C at P meets the x-axis at A and the y-axis at B.
    Work out the area of triangle OAB.

    Show worked answerHide worked answer
    1. M1: Gradient of OP = dfrac36 = dfrac12
    2. M1: Tangent gradient -2, so y - 3 = -2(x - 6)
    3. A1: y = -2x + 15
    4. M1: A(7.5, 0) and B(0, 15)
    5. A1: Area = dfrac12 × 7.5 × 15 = 56.25
    Answer: 56.25
    Finding Equations of Tangents to Circles
    [5 marks]
📅 Free lesson: Tue 17th NovSave your place →

Mixed Topic Worksheet Grades 8/9: Day 061

Grades 8/9Non-calculator

  1. Question 1. Solve cos(x + 20^°) = 0.5 for 0^° ≤ x ≤ 360^°.

    [2 marks]
    Show worked answerHide worked answer
    1. M1: x + 20 = 60 or 300
    2. A1: x = 40^° and x = 280^°
    Answer: x = 40^° and x = 280^°
    Solving Trigonometric Equations Using a Graph

  2. Question 2. P(A mid B) = 0.5 and P(B) = 0.36. Work out P(A cap B).

    [2 marks]
    Show worked answerHide worked answer
    1. M1: 0.5 × 0.36
    2. A1: 0.18
    Answer: 0.18
    Conditional Probability with Venn Diagrams

  3. Question 3. Simplify fully √243 - √48
    Give your answer in the form a√3, where a is an integer.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: √243 = √81 × 3 = 9√3
    2. M1: √48 = √16 × 3 = 4√3
    3. A1: 5√3
    Answer: 5√3
    Simplifying Surds

  4. Question 4. Prove algebraically that the sum of the squares of two consecutive integers is equal to 1 more than twice the product of the two integers.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: n² + (n + 1)² = n² + n² + 2n + 1
    2. A1: 2n² + 2n + 1
    3. C1: 2n(n + 1) + 1 = 2n² + 2n + 1, which is the same
    Answer: 2n(n + 1) + 1
    Proof with Consecutive Numbers

  5. Question 5. The circle C, centre O, has equation x² + y² = 45
    P is the point (6, 3) on C.
    The tangent to C at P meets the x-axis at A and the y-axis at B.
    Work out the area of triangle OAB.

    [5 marks]
    Show worked answerHide worked answer
    1. M1: Gradient of OP = dfrac36 = dfrac12
    2. M1: Tangent gradient -2, so y - 3 = -2(x - 6)
    3. A1: y = -2x + 15
    4. M1: A(7.5, 0) and B(0, 15)
    5. A1: Area = dfrac12 × 7.5 × 15 = 56.25
    Answer: 56.25
    Finding Equations of Tangents to Circles
📅 Free live lesson: Tuesday 17th NovemberSave your free place →

Mixed Topic Worksheet Grades 8/9: Day 061

Grades 8/9Non-calculator

  1. Question 1. Solve cos(x + 20^°) = 0.5 for 0^° ≤ x ≤ 360^°.

    Show worked answerHide worked answer
    1. M1: x + 20 = 60 or 300
    2. A1: x = 40^° and x = 280^°
    Answer: x = 40^° and x = 280^°
    Solving Trigonometric Equations Using a Graph
    [2 marks]

  2. Question 2. P(A mid B) = 0.5 and P(B) = 0.36. Work out P(A cap B).

    Show worked answerHide worked answer
    1. M1: 0.5 × 0.36
    2. A1: 0.18
    Answer: 0.18
    Conditional Probability with Venn Diagrams
    [2 marks]

  3. Question 3. Simplify fully √243 - √48
    Give your answer in the form a√3, where a is an integer.

    Show worked answerHide worked answer
    1. M1: √243 = √81 × 3 = 9√3
    2. M1: √48 = √16 × 3 = 4√3
    3. A1: 5√3
    Answer: 5√3
    Simplifying Surds
    [3 marks]

  4. Question 4. Prove algebraically that the sum of the squares of two consecutive integers is equal to 1 more than twice the product of the two integers.

    Show worked answerHide worked answer
    1. M1: n² + (n + 1)² = n² + n² + 2n + 1
    2. A1: 2n² + 2n + 1
    3. C1: 2n(n + 1) + 1 = 2n² + 2n + 1, which is the same
    Answer: 2n(n + 1) + 1
    Proof with Consecutive Numbers
    [3 marks]

  5. Question 5. The circle C, centre O, has equation x² + y² = 45
    P is the point (6, 3) on C.
    The tangent to C at P meets the x-axis at A and the y-axis at B.
    Work out the area of triangle OAB.

    Show worked answerHide worked answer
    1. M1: Gradient of OP = dfrac36 = dfrac12
    2. M1: Tangent gradient -2, so y - 3 = -2(x - 6)
    3. A1: y = -2x + 15
    4. M1: A(7.5, 0) and B(0, 15)
    5. A1: Area = dfrac12 × 7.5 × 15 = 56.25
    Answer: 56.25
    Finding Equations of Tangents to Circles
    [5 marks]