SACE Math Methods exam 2026Exam: Mon 2 Nov · SACE Board timetable

Your SACE Math Methods exam: Monday 2 November 2026

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When and how long

Mathematical MethodsMonday 2 November 20269.00 am start2 h 10 min

SACE Board: morning exams start at 9 am and afternoon exams at 1.30 pm, South Australian time (8 am and 12.30 pm in the Northern Territory). Some subjects have additional time for reading only; schools get day-by-day instructions at the start of Term 4. Language exams run earlier in October.

Source: SACE examinations timetable 2026 (SACE Board), checked Wednesday 23 September 2026. Where a start time, reading time or duration isn't shown, the timetable doesn't publish it: check your personal timetable and the front of your paper.

What the exam covers

We don't have past-paper frequency data for this exam, so here is the course, module by module. Make sure every module is covered.

Night-before and exam-morning checklists

The night before

Morning exams start at 9 am and afternoon exams at 1.30 pm, South Australian time.^[1]
Some subjects have extra time for reading only: check the day-by-day instructions your school gets at the start of Term 4.^[1]
Some exams are electronic: check with your school how yours runs.^[1]
Pack your equipment the night before, set two alarms and sleep.^[2]

Exam morning

Eat a real breakfast and arrive early.^[2]
Leave your phone and other electronic devices outside the exam room.^[2]

Exam-week survival kit: The last 7 days · The night before and exam morning · What to bring, and what's banned · How to use reading time · If you're sick or something goes wrong · Handling exam-week stress.

Last-week revision

SACE Math Methods cram sheet

Key formulas, definitions and facts copied from our Math Methods syllabus pages. One page when printed.

Topic 1: Further Differentiation and Applications

Increasing and decreasing

A function is increasing where $f'(x)>0$ and decreasing where $f'(x)<0$ . Marking the sign of $f'$ on a number line is the fastest way to see the overall shape.

From: Curve sketching with derivatives

Second-derivative test

At a stationary point where $f'(a)=0$ :

f''(a)<0 \Rightarrow \text{local maximum}, \qquad f''(a)>0 \Rightarrow \text{local minimum}.

From: Optimisation problems

Product rule

\frac{d}{dx}\big[u\,v\big]=u'v+uv'

From: The product and quotient rules

Concavity

A curve is concave up on an interval if $f''(x)>0$ throughout (it curves like a cup, gradient increasing) and concave down if $f''(x)<0$ (it curves like a cap, gradient decreasing).

From: The second derivative and concavity

Topic 2: Discrete Random Variables

Conditions for a valid distribution

0\le P(X=x)\le 1 \quad\text{for every } x, \qquad \sum_{\text{all }x} P(X=x)=1.

From: Discrete random variables and distributions

Expected value (mean)

E(X)=\mu=\sum_{\text{all }x} x\,P(X=x).

From: Expected value and variance

Binomial probability

P(X=x)=\binom{n}{x}p^x(1-p)^{n-x}, \qquad x=0,1,2,\dots,n,

where

\binom{n}{x}=\dfrac{n!}{x!\,(n-x)!}

counts the arrangements of

x

successes among

n

trials.

From: The Bernoulli and binomial distributions

Topic 3: Integral Calculus

Core antidifferentiation rules

\int x^n\,dx=\frac{x^{n+1}}{n+1}+C\ (n\ne -1), \qquad \int \frac{1}{x}\,dx=\ln|x|+C,

\int e^{x}\,dx=e^{x}+C, \qquad \int e^{kx}\,dx=\frac{1}{k}e^{kx}+C.

From: Antidifferentiation

Area above the x-axis

A=\int_a^b f(x)\,dx \qquad (f(x)\ge 0 \text{ on } [a,b]).

From: Area under a curve

Area between two curves

A=\int_a^b \big(f_{\text{top}}(x)-f_{\text{bottom}}(x)\big)\,dx,

where

a

and

b

are the x-coordinates of the intersection points and

f_{\text{top}}\ge f_{\text{bottom}}

[a,b]

From: Areas between curves

Fundamental Theorem of Calculus

\int_a^b f(x)\,dx=\Big[F(x)\Big]_a^b=F(b)-F(a), \qquad \text{where } F'(x)=f(x).

From: The definite integral and Fundamental Theorem

Topic 4: Logarithmic Functions

The strategy

Isolate the exponential term on one side.
Take logs of both sides ( $\ln$ for base $e$ , otherwise any base + change of base).
Use the power law $\log(a^x)=x\log a$ to bring the exponent down.
Solve the resulting linear equation for $x$ .

From: Solving exponential equations

Domain: $x>0$ (you cannot take the log of zero or a negative number).

From: Graphs of logarithmic functions

Laws of logarithms

\log_a(xy)=\log_a x+\log_a y \qquad\text{(product law)}

\log_a\!\left(\frac{x}{y}\right)=\log_a x-\log_a y \qquad\text{(quotient law)}

\log_a(x^n)=n\log_a x \qquad\text{(power law)}

From: The laws of logarithms

Derivatives of e^x and ln x

\frac{d}{dx}e^x=e^x, \qquad \frac{d}{dx}\ln x=\frac{1}{x}\ (x>0).

From: Derivatives of exponential and log functions

Topic 5: Continuous Random Variables and the Normal Distribution

Mean and variance of a continuous variable

\mu=E(X)=\int_{-\infty}^{\infty} x\,f(x)\,dx, \qquad \operatorname{Var}(X)=\int_{-\infty}^{\infty} x^2 f(x)\,dx-\mu^2.

From: Continuous random variables and PDFs

The 68-95-99.7 rule

P(\mu-\sigma\le X\le \mu+\sigma)\approx 0.68

P(\mu-2\sigma\le X\le \mu+2\sigma)\approx 0.95

P(\mu-3\sigma\le X\le \mu+3\sigma)\approx 0.997

From: The normal distribution

Standardising a value

z=\frac{x-\mu}{\sigma}.

The z-score is the number of standard deviations

x

lies above (

z>0

) or below (

z<0

) the mean.

From: Z-scores and normal probabilities

Topic 6: Sampling and Confidence Intervals

Confidence interval for a mean

\bar{x}\pm z^*\frac{\sigma}{\sqrt{n}},

where

\bar{x}

is the sample mean,

\sigma

the population standard deviation,

n

the sample size, and

z^*

the critical z-value for the chosen confidence level.

From: Confidence intervals for a mean

Margin of error

E=z^*\frac{\sigma}{\sqrt{n}}.

From: Margin of error and sample size

Mean and standard error of the sample mean

\mu_{\bar X}=\mu, \qquad \sigma_{\bar X}=\frac{\sigma}{\sqrt{n}}.

The quantity

\dfrac{\sigma}{\sqrt{n}}

is called the standard error of the mean.

From: Sample means and sampling distributions