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VCE Mathematical Methods/Exam One Practice One

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Instructions

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Reading Time: 15 minutes
Writing Time: 60 minutes

  • Students are permitted to use: pencils, pens, highlighters, erasers, sharpeners, rulers, protractors, set-squares, aids for curve sketching
  • Students are NOT permitted to use: blank sheets of paper, white-out, any type of technology
  • Any diagrams used are NOT drawn to scale unless otherwise indicated
  • Students must answer all the questions in the space provided
  • In questions where more than one mark is available, appropriate working MUST be shown
  • When instructed to use calculus, an appropriate derivative or anti-derivative MUST be shown

Questions

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Question 1

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(a) Given , solve for x.


(b) If and state the transformations required to change g into f





[1 + 2 = 3 marks]

Question 2

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Let and .

(a) Evaluate









(b) Hence factorise P(x) given that .









(c) Hence sketch the graph of P








[2+2+2 = 6 marks]

Question 3

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Let . Use calculus to find the co-ordinates of the stationary point.








[3 marks]

Question 4

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A garden path can be modelled with the equation where .

(a)Sketch the garden path over the domain specified.









(b) If the x-axis represents a fence, use calculus to determine the area between the path and the fence.








[2+2 = 4 marks]

Question 5

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State the equations of the tangent and the normal of the function when












[2 marks]


Question 6

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Shirley either eats lamingtons or a muesli bar for morning tea. If Shirley eats lamingtons one day, then the probability she will eat lamingtons the next day is 0.5. If Shirley eats a muesli bar one day, the probability that she will eat a muesli bar the next day is 0.3. If Shirley eats a muesli bar on Tuesday, what is the probability she will eat lamingtons on Thursday?









[2 marks]

Question 7

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