WACE Methods, both sections.

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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)

Six topics, two sections

Built for Mathematics Methods ATAR Year 12, Units 3 and 4, on the syllabus effective from 2025: every topic of Unit 3 (further differentiation, integrals, discrete random variables) and Unit 4 (the logarithmic function, continuous random variables and the normal distribution, interval estimates for proportions), with calculator-free and calculator-assumed questions in the style of both sections of the ATAR examination. Not built for Mathematics Applications or Specialist, or for school-based assessment.

Topic 3.1: Further differentiation and applications

Topic 3.2: Integrals

Topic 3.3: Discrete random variables

Topic 4.1: The logarithmic function

Topic 4.2: Continuous random variables and the normal distribution

Topic 4.3: Interval estimates for proportions

Section	Questions	Weight
Section One: Calculator-free	5 to 10 questions on Units 3 and 4, answered without a calculator.	35% of the examination
Section Two: Calculator-assumed	8 to 13 questions on Units 3 and 4, with up to three calculators (CAS assumed), notes on two sheets of A4 and a formula sheet.	65% of the examination

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