# VCE Mathematical Methods/Exam One Practice One

## Contents

## Instructions[edit]

**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[edit]

### Question 1[edit]

**(a)** Given , solve for *x*.

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

[1 + 2 = 3 marks]

### Question 2[edit]

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[edit]

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

[3 marks]

### Question 4[edit]

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[edit]

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

[2 marks]

### Question 6[edit]

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]