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# VCE Maths Methods External Assessment Practice Questions

Looking for some more practice questions for the VCE Maths Methods External Assessment?

You’ve come to the right place. Whether you’re just beginning to study or looking to complete some last minute revision, these questions will help refresh and lock in the knowledge you’ve already built, as well as offering some helpful tips on how to answer the questions.

So, let’s dive in!

## VCE Maths Methods External Assessment Practice Questions

### Question 1

Differentiate 3ex2 with regards to x. (1 mark)

### Question 2

Evaluate f'(-1) where f(x) = \frac{e^x}{2+x} (2 marks)

### Question 3

Assume that f'(x)=x^2 + 2x.

Given that f(0) = 1, determine f(x). (2 marks)

## Question 4

The following information applies to questions 4–6.

Let h:RR, h(x) = \frac{1}{2}Cos(3x)+1

State the range of h. (1 mark)

## Question 5

What is the period of h? (1 mark)

## Question 6

Solve h(x) = 1 for x ∈ R. (2 marks)

## Question 7

The following information applies to questions 7 and 8.

Consider the function: f:R\{-1} → R, f(x)= \frac{3}{1+x} -1.

Identify the asymptotes of f. (1 mark)

## Question 8

For what values of x is f(x) < -2. (2 marks)

## Question 9

The following information applies to questions 9 and 10.

A web service company runs a number of servers. Each year, it is known that the probability a hard drive fails is \frac{9}{16}, the probability that the water cooling system fails is \frac{3}{16} and the probability that both fail is \frac{1}{16}.

What is the probability that a server suffers from only hard drive failure? (1 mark)

## Question 10

If four servers are selected at random, what is the probability that exactly three servers suffer hard drive failure, given that at least one of these four servers have undergone hard drive failure? Leave all numbers in exponent form (i.e. do not calculate 93). (2 marks)

## Question 11

Let f:[0,∞ ) → R, where f(x)=2 e^{-3x}+1. Determine the domain and rule of f^{-1}, the inverse function of f. (2 marks)

## Question 12

For the function g[0,∞ ) → R, g(x) = \frac{1}{2}x^{2}, find the area enclosed between g and the line y=x. (2 marks)

## Question 13

Now consider the functions g(x) = \frac{1}{2}x^{2} and f(x) = αx, where (0,1).

What value of ensures that the area enclosed between g and f is equal to \frac{1}{2}? (4 marks)

## Question 14

The following information concerns questions 14–18:

Define p(x) = ln(\frac{1}{x})+ln(1 - x)

State the maximal domain and range of p. (2 marks)

## Question 15

Find the gradient to p at the point x=a. (1 mark)

## Question 16

Find the equation of the tangent to p at x=\frac{1}{2}. (1 mark)

## Question 17

Find the equation of the line perpendicular to p at the point (1/2, p(1/2)). (1 mark)

## Question 18

Why is p a one-to-one function? (1 mark)

## Question 19

Consider a line y=b-x  which intersects the function f:[0,∞ ) → R, f(x)=x^{3}-2x. At which x values (correct to two decimal places) is the acute angle between this line and the tangent to f 50o? (3 marks)

## Question 20

Consider the transformation defined by the following sequence of steps: a reflection about the y axis, a dilation by 2 in the y direction, a translation of +3 in the x direction, a translation by +1 in the y direction.

What is the image of the function y=x^{2}-x under this transformation? (3 marks)

## Question 21

Does the function above intersect the image you determined in question 20? If so, what are the intersections? (2 marks)

## Question 22

The following information applies to questions 22–25.

A Zoologist is investigating the lifespan of Tigers in captivity. She has discovered that, on average, Tigers live for 15 years in captivity, and that only 10% of tigers live for more than 20 years.

Assuming that the lifespan of Tigers is normally distributed, what is the standard deviation of this distribution (to 2 decimal places)? (2 marks)

## Question 23

What is the probability, to two decimal places, that a tiger survives for at least 18 years, given that it has survived for 16 years? (2 marks)

## Question 24

Given a zoo population with 5 tigers that are older than 16 years, what is the probability that fewer than 3 of these tigers survive to reach their 18th birthday? (2 marks)

## Question 25

Assume there are n tigers (of any age) in a zoo.

Find the probability that at least one of these tigers survives to the age of 17, and hence determine the number of tigers the zoo must acquire to ensure that there is at least a 95% chance that at least one survives to the age of 21. (2 marks)

## Answers for VCE Maths Methods Questions

Studying the night before your VCE Maths Methods exam? Check out our 7-step night routine to acing your exam here!

## And, you’ve finished all the questions!

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Also studying for other VCE external assessments? Check out our practice questions!

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Scott McColl is a content writer with Art of Smart and a Civil Engineering student at Monash University. In between working and studying, Scott enjoys playing music and working on programming projects.

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