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

Mixed Topic Worksheet Grades 8/9: Day 031

Grades 8/9Non-calculator

  1. Question 1. Graph of y = cos x, with cos 40^° = 0.766
    (a) Use it to write down cos 320^° [1]
    (b) Use it to write down cos 140^° [1]

    Show worked answerHide worked answer
    1. (a) B1: 0.766
    2. (b) B1: -0.766
    Answer: (a) 0.766; (b) -0.766
    Calculating Values of Trig Functions Using Graphs
    xy-1-0.50.511803600
    [2 marks]

  2. Question 2. Tom simplifies dfracx²+x-6x²-x-2 and gets dfracx+3x-1.
    Is Tom correct? Show your working.

    Show worked answerHide worked answer
    1. M1: (x+3)(x-2) or (x-2)(x+1)
    2. M1: cancels (x-2)
    3. A1: dfracx+3x+1, so Tom is not correct
    Answer: No, the correct simplified fraction is dfracx+3x+1
    Algebraic Fractions Involving Factorising
    [3 marks]

  3. Question 3. The product of two consecutive positive integers is 462. Use algebra to work out the two integers.

    Show worked answerHide worked answer
    1. M1: n(n + 1) = 462 so n² + n - 462 = 0
    2. M1: (n - 21)(n + 22) = 0
    3. A1: 21 and 22
    Answer: 21 and 22
    Proof with Consecutive Numbers
    [3 marks]

  4. Question 4. For events A and B, n(A)=30, n(B)=24, n(Acap B)=10 and n(A'cap B')=16. An item is chosen at random. Work out P(B'mid A).

    Show worked answerHide worked answer
    1. M1: A only =20
    2. M1: 20/30
    3. A1: 2/3
    Answer: 2/3
    Conditional Probability with Venn Diagrams
    [3 marks]

  5. Question 5. The point P(-6, 8) lies on the circle x² + y² = 100
    Find an equation of the tangent to the circle at P.

    Show worked answerHide worked answer
    1. M1: gradient of OP = -dfrac43, so gradient of tangent = dfrac34
    2. M1: y - 8 = dfrac34(x + 6)
    3. A1: 4y = 3x + 50 (or y = dfrac34x + 12.5)
    Answer: 4y = 3x + 50
    Finding Equations of Tangents to Circles
    [3 marks]
📅 Free lesson: Tue 17th NovSave your place →

Mixed Topic Worksheet Grades 8/9: Day 031

Grades 8/9Non-calculator

  1. Question 1. Graph of y = cos x, with cos 40^° = 0.766
    (a) Use it to write down cos 320^° [1]
    (b) Use it to write down cos 140^° [1]

    [2 marks]
    xy-1-0.50.511803600
    Show worked answerHide worked answer
    1. (a) B1: 0.766
    2. (b) B1: -0.766
    Answer: (a) 0.766; (b) -0.766
    Calculating Values of Trig Functions Using Graphs

  2. Question 2. Tom simplifies dfracx²+x-6x²-x-2 and gets dfracx+3x-1.
    Is Tom correct? Show your working.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: (x+3)(x-2) or (x-2)(x+1)
    2. M1: cancels (x-2)
    3. A1: dfracx+3x+1, so Tom is not correct
    Answer: No, the correct simplified fraction is dfracx+3x+1
    Algebraic Fractions Involving Factorising

  3. Question 3. The product of two consecutive positive integers is 462. Use algebra to work out the two integers.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: n(n + 1) = 462 so n² + n - 462 = 0
    2. M1: (n - 21)(n + 22) = 0
    3. A1: 21 and 22
    Answer: 21 and 22
    Proof with Consecutive Numbers

  4. Question 4. For events A and B, n(A)=30, n(B)=24, n(Acap B)=10 and n(A'cap B')=16. An item is chosen at random. Work out P(B'mid A).

    [3 marks]
    Show worked answerHide worked answer
    1. M1: A only =20
    2. M1: 20/30
    3. A1: 2/3
    Answer: 2/3
    Conditional Probability with Venn Diagrams

  5. Question 5. The point P(-6, 8) lies on the circle x² + y² = 100
    Find an equation of the tangent to the circle at P.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: gradient of OP = -dfrac43, so gradient of tangent = dfrac34
    2. M1: y - 8 = dfrac34(x + 6)
    3. A1: 4y = 3x + 50 (or y = dfrac34x + 12.5)
    Answer: 4y = 3x + 50
    Finding Equations of Tangents to Circles
📅 Free live lesson: Tuesday 17th NovemberSave your free place →

Mixed Topic Worksheet Grades 8/9: Day 031

Grades 8/9Non-calculator

  1. Question 1. Graph of y = cos x, with cos 40^° = 0.766
    (a) Use it to write down cos 320^° [1]
    (b) Use it to write down cos 140^° [1]

    Show worked answerHide worked answer
    1. (a) B1: 0.766
    2. (b) B1: -0.766
    Answer: (a) 0.766; (b) -0.766
    Calculating Values of Trig Functions Using Graphs
    xy-1-0.50.511803600
    [2 marks]

  2. Question 2. Tom simplifies dfracx²+x-6x²-x-2 and gets dfracx+3x-1.
    Is Tom correct? Show your working.

    Show worked answerHide worked answer
    1. M1: (x+3)(x-2) or (x-2)(x+1)
    2. M1: cancels (x-2)
    3. A1: dfracx+3x+1, so Tom is not correct
    Answer: No, the correct simplified fraction is dfracx+3x+1
    Algebraic Fractions Involving Factorising
    [3 marks]

  3. Question 3. The product of two consecutive positive integers is 462. Use algebra to work out the two integers.

    Show worked answerHide worked answer
    1. M1: n(n + 1) = 462 so n² + n - 462 = 0
    2. M1: (n - 21)(n + 22) = 0
    3. A1: 21 and 22
    Answer: 21 and 22
    Proof with Consecutive Numbers
    [3 marks]

  4. Question 4. For events A and B, n(A)=30, n(B)=24, n(Acap B)=10 and n(A'cap B')=16. An item is chosen at random. Work out P(B'mid A).

    Show worked answerHide worked answer
    1. M1: A only =20
    2. M1: 20/30
    3. A1: 2/3
    Answer: 2/3
    Conditional Probability with Venn Diagrams
    [3 marks]

  5. Question 5. The point P(-6, 8) lies on the circle x² + y² = 100
    Find an equation of the tangent to the circle at P.

    Show worked answerHide worked answer
    1. M1: gradient of OP = -dfrac43, so gradient of tangent = dfrac34
    2. M1: y - 8 = dfrac34(x + 6)
    3. A1: 4y = 3x + 50 (or y = dfrac34x + 12.5)
    Answer: 4y = 3x + 50
    Finding Equations of Tangents to Circles
    [3 marks]