What is in SACE Mathematical Methods Stage 2

Six topics: further differentiation and applications, discrete random variables, integral calculus, logarithmic functions, continuous random variables and the normal distribution, and sampling and confidence intervals. Three are calculus and three are statistics.

Weeks before your first paper

Hours a week for General Maths

Topic 1: Further differentiation and applications

Topic 2: Discrete random variables

Topic 3: Integral calculus

Topic 4: Logarithmic functions

Topic 5: Continuous random variables and the normal distribution

Topic 6: Sampling and confidence intervals

26 weeks, 104 hours in all

Start with Topic 1

Further differentiation and applications: 16 of your hours. It is 3 of the 30 questions on each timed check, 17%.

Hours per topic
Topic	Your hours	Share of the checks
Topic 1: Further differentiation and applications	16	17%
Topic 2: Discrete random variables	16	17%
Topic 3: Integral calculus	16	17%
Topic 4: Logarithmic functions	16	17%
Topic 5: Continuous random variables and the normal distribution	16	17%
Topic 6: Sampling and confidence intervals	16	17%

Week by week

Week 1Topic 1: Further differentiation and applications
Week 2Topic 1: Further differentiation and applications
Week 3Topic 1: Further differentiation and applications
Week 4Topic 1: Further differentiation and applications
Week 5Topic 2: Discrete random variables
Week 6Topic 2: Discrete random variables
Week 7Topic 2: Discrete random variables
Week 8Topic 2: Discrete random variables
Week 9Topic 3: Integral calculus
Week 10Topic 3: Integral calculus
Week 11Topic 3: Integral calculus
Week 12Topic 3: Integral calculus
Week 13Topic 4: Logarithmic functions
Week 14Topic 4: Logarithmic functions
Week 15Topic 4: Logarithmic functions
Week 16Topic 4: Logarithmic functions
Week 17Topic 5: Continuous random variables and the normal distribution
Week 18Topic 5: Continuous random variables and the normal distribution
Week 19Topic 5: Continuous random variables and the normal distribution
Week 20Topic 5: Continuous random variables and the normal distribution
Week 21Topic 6: Sampling and confidence intervals
Week 22Topic 6: Sampling and confidence intervals
Week 23Topic 6: Sampling and confidence intervals
Week 24Topic 6: Sampling and confidence intervals
Week 25A timed check and two short response questions, then review every lost mark
Week 26A timed check and two short response questions, then review every lost mark

Check your topics with the free test

The examination	130 minutes, 100 marks, 30% of the subject
Booklets	Two question booklets of 50 marks, about 65 minutes each
Allowed	A graphics calculator throughout, two A4 sheets of handwritten notes, a formula sheet
Answers	Working shown; three significant figures unless a question says otherwise

Calculus: topics 1, 3 and 4

Further differentiation: rates of change, the chain, product and quotient rules, exponential and trigonometric functions, the second derivative, points of inflection, curve sketching and optimisation.
Integral calculus: anti-derivatives and initial conditions, areas from rectangle sums to the fundamental theorem, areas between curves, and total change, displacement and distance.
Logarithmic functions: natural logarithms and their laws, solving exponential equations in models, the graph of ln x and its transformations, and the derivatives and integrals that involve ln.

Statistics: topics 2, 5 and 6

Discrete random variables: probability distributions, expected value and standard deviation, and the Bernoulli and binomial distributions.
Continuous random variables and the normal distribution: density functions, normal probabilities and quantiles, and the sum and mean of a sample with the central limit theorem.
Sampling and confidence intervals: intervals for a population mean and for a population proportion, and the margin of error.

Try 2 questions

Question 1Practice

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

The table gives values of the functions

f

and

g

and their derivatives. At

x

= 1

f

= 2

f'

= 5

g

= 3

g'

= -2

. At

x

= 3

f

= 4

f'

= -1

g

= 1

g'

= 6

. Let

h(x)

= x\,f(g(x))

. What is

h'(1)

Question 2Practice

X

has a binomial distribution with

n

= 4

and

p

= \frac{1}{3}

. What is

P(X

= 2)

Next step

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Questions people ask

Which syllabus does the course follow?

The SACE Board's Stage 2 Mathematical Methods subject outline, as reissued for 2025, with all six topics.

How is the subject assessed?

School assessment is 70%: skills and applications tasks (50%) and a mathematical investigation (20%). The external examination is the other 30%.

Is Stage 1 content examined?

The examination is on the six Stage 2 topics, and Stage 1 Mathematics is assumed, so functions, first derivatives and probability rules appear inside its questions.