WACE Methods practice questions

Original questions for all six topics: four-option practice, and short response questions in the style of both sections with every answer checked and justifications read by Mia.

Section One	Calculator-free, 35%, 50 minutes working
Section Two	Calculator-assumed, 65%, 100 minutes working
Questions	5 to 10 in Section One, 8 to 13 in Section Two
Section Two allows	Up to three calculators (CAS assumed), two A4 sheets of notes, a formula sheet

Try 4 questions

Question 1Practice

Table of values. When x = 1: f(x) = 3, f'(x) = −1, g(x) = 2, g'(x) = 6. When x = 2: f(x) = 1, f'(x) = 4, g(x) = 3, g'(x) = −2. When x = 3: f(x) = 5, f'(x) = 5, g(x) = 1, g'(x) = 2.
$x$	$f(x)$	$f'(x)$	$g(x)$	$g'(x)$
1	3	−1	2	6
2	1	4	3	−2
3	5	5	1	2

The table gives values of the functions

f

and

g

and their derivatives: at

x

= 1

f

= 3

f'

= -1

g

= 2

g'

= 6

; at

x

= 2

f

= 1

f'

= 4

g

= 3

g'

= -2

; at

x

= 3

f

= 5

f'

= 5

g

= 1

g'

= 2

. Given

h(x)

= x\,f(g(x))

, what is

h'(2)

Question 2Practice

A Bernoulli random variable

X

has parameter

p

= 0.3

. What is

\text{Var}(X)

Question 3Practice

The diagram shows the curve

y

= \frac{4}{x}

and the line

y

= 5 - x

. What is the exact area of the shaded region enclosed between them?

Question 4Practice

A class simulated 599 random samples of size 96 from a population with

p

= 0.4

and recorded each sample proportion

\hat{p}

. The histogram shows the results (frequencies: 0.25 to 0.30, 10; 0.30 to 0.35, 81; 0.35 to 0.40, 215; 0.40 to 0.45, 207; 0.45 to 0.50, 69; 0.50 to 0.55, 17). Which statement best describes this distribution?

Next step

Take the free test Take the course tour

Questions people ask

Are these past examination questions?

No. Every question is original, written for the syllabus effective from 2025.