QCE Mathematical Methods21 October 2026

QCAA Maths Methods formula sheet: what is and is not on it (QCE)

Quick answer

The QCAA Mathematical Methods formula book that every QCE Maths Methods student is given is three printed pages. It prints mensuration, graph equations, logarithm laws, calculus rules, four trigonometry items and the statistics and probability rules, and it is provided in both external papers (and by your teacher in IA2 and IA3). It does not print the quadratic formula, the index laws, tan, radian or exact-value trigonometry or anything on the normal distribution, so those come from memory, and Paper 1 allows nothing else while Paper 2 adds an approved graphics and/or scientific calculator with no CAS.

The formulas below are reproduced from the June 2026 edition of the book (2025 course), with the meaning of each and a worked example added by AusGrader. Modified from the original: © State of Queensland (QCAA) 2025, licensed under CC BY 4.0, re-typeset here with explanation added. The original is the Mathematical Methods 2025 formula book on the QCAA website, and the copy in your exam is the one that counts. Check it against this page before you rely on a rule.

This guide describes the Mathematical Methods 2025 v1.2 syllabus, which Year 12 students sit under from 2026. The 2019 syllabus called the document it provided the "QCAA formula sheet", so older advice about the sheet describes the superseded course. The QCAA Maths Methods subject page holds the past papers, and the external exam guide covers the format and marking.

Do you get a formula sheet in the Methods exam?

Yes, in four assessments. The syllabus conditions say:

Assessment	Who provides the formula book	Other resources
External, Paper 1	The QCAA	None: no notes, calculators, technology or other resources
External, Paper 2	The QCAA	A handheld QCAA-approved graphics calculator (no CAS functionality) and/or a handheld QCAA-approved scientific calculator. No notes or other resources
IA2 (Unit 3 examination)	Your teacher	Students are required to use technology; no notes
IA3 (Unit 4 examination)	Your teacher	Students are required to use technology; no notes

The conditions we hold for IA1, the problem-solving and modelling task, do not mention the book. The two internal papers are covered in the IA2 and IA3 guide. The book itself says nothing about where it is issued or what calculators are allowed, so those rules come from the syllabus alone.

What is on the QCAA Maths Methods formula sheet?

The book prints formulas and no explanations. It has no key for its symbols: it does not say that $s$ is a slant height, that $A$ in a prism is the base area, or what $z$ , $\hat{p}$ and $n$ stand for in the confidence interval. The "What it does" column below uses the usual meanings, and those words are ours, not QCAA's. The worked examples are also ours.

Mensuration (page 1)

Formula	What it does	Worked example
$C = 2\pi r$	Circumference of a circle	$r = 7$ gives $C = 14\pi$
$A = \pi r^2$	Area of a circle	$r = 3$ gives $A = 9\pi$
$A = bh$	Area of a parallelogram (base times perpendicular height)	$b = 8$ , $h = 5$ gives $A = 40$
$A = \frac{1}{2}(a + b)h$	Area of a trapezium ( $a$ and $b$ are the parallel sides)	$a = 6$ , $b = 10$ , $h = 4$ gives $\frac{1}{2}(16)(4) = 32$
$A = \frac{1}{2}bh$	Area of a triangle	$b = 10$ , $h = 6$ gives $A = 30$
$S = \pi r s + \pi r^2$	Total surface area of a cone ( $s$ is the slant height)	$r = 3$ , $s = 5$ gives $15\pi + 9\pi = 24\pi$
$S = 2\pi r h + 2\pi r^2$	Total surface area of a cylinder	$r = 2$ , $h = 5$ gives $20\pi + 8\pi = 28\pi$
$S = 4\pi r^2$	Surface area of a sphere	$r = 3$ gives $S = 36\pi$
$V = \frac{1}{3}\pi r^2 h$	Volume of a cone	$r = 3$ , $h = 4$ gives $V = 12\pi$ (the same cone has $s = 5$ )
$V = \pi r^2 h$	Volume of a cylinder	$r = 2$ , $h = 5$ gives $V = 20\pi$
$V = Ah$	Volume of a prism ( $A$ is the area of the base)	$A = 12$ , $h = 5$ gives $V = 60$
$V = \frac{1}{3}Ah$	Volume of a pyramid	A 6 by 6 square base ( $A = 36$ ) with $h = 5$ gives $V = 60$
$V = \frac{4}{3}\pi r^3$	Volume of a sphere	$r = 3$ gives $V = 36\pi$

Graph equations (page 1)

These are the standard forms. The syllabus asks you to recognise how the parameters change each graph, so the useful skill is reading features straight off the equation.

Equation	What the parameters do	Worked example
$y = a(x - h)^2 + k$	Quadratic in turning point form: turning point $(h, k)$	$y = 2(x - 3)^2 + 1$ has turning point $(3, 1)$ , opens up, and cuts the $y$ -axis at $2(9) + 1 = 19$
$y = a(x - x_1)(x - x_2)$	Quadratic in factorised form: $x$ -intercepts $x_1$ and $x_2$	$y = 2(x - 1)(x - 5)$ cuts the $x$ -axis at 1 and 5. The turning point is at $x = 3$ , where $y = 2(2)(-2) = -8$
$y = a(x - h)^3 + k$	Cubic with a stationary point of inflection at $(h, k)$	$y = -(x - 2)^3 + 4$ has its point of inflection at $(2, 4)$ and cuts the $y$ -axis at $-(-8) + 4 = 12$
$y = a(x - x_1)(x - x_2)(x - x_3)$	Cubic in factorised form: $x$ -intercepts $x_1$ , $x_2$ , $x_3$	$y = (x + 2)(x - 1)(x - 3)$ cuts the $x$ -axis at $-2$ , 1 and 3, and the $y$ -axis at $(2)(-1)(-3) = 6$
$(x - h)^2 + (y - k)^2 = r^2$	Circle with centre $(h, k)$ and radius $r$	$(x - 1)^2 + (y + 2)^2 = 9$ has centre $(1, -2)$ and radius 3
$y = a\sqrt{x - h} + k$	Square root graph starting at $(h, k)$	$y = 2\sqrt{x - 1} + 3$ starts at $(1, 3)$ , so the domain is $x \ge 1$ . At $x = 5$ , $y = 2(2) + 3 = 7$
$y = \frac{a}{x - h} + k$	Reciprocal graph with vertical asymptote $x = h$ and horizontal asymptote $y = k$	$y = \frac{2}{x - 3} + 1$ has asymptotes $x = 3$ and $y = 1$ . At $x = 4$ , $y = 3$
$y = r^{(x-h)} + k \quad (r > 0)$	Exponential graph with horizontal asymptote $y = k$	$y = 2^{(x-1)} + 3$ has asymptote $y = 3$ and cuts the $y$ -axis at $2^{-1} + 3 = 3.5$
$y = \log_a(x - h) + k \quad (a > 1)$	Logarithmic graph with vertical asymptote $x = h$	$y = \log_2(x - 1) + 3$ has asymptote $x = 1$ . At $x = 3$ , $y = \log_2(2) + 3 = 4$
$y = a\sin\left(b(x - h)\right) + k$	Sine graph: amplitude $\lvert a \rvert$ , horizontal shift $h$ , midline $y = k$	$y = 3\sin\left(2(x - \frac{\pi}{4})\right) + 1$ has amplitude 3, midline $y = 1$ , maximum 4 and minimum $-2$
$y = a\cos\left(b(x - h)\right) + k$	Cosine graph with the same parameters	$y = 5\cos(2x) - 1$ has maximum 4, minimum $-6$ and, because $b = 2$ , a period of $\pi$

The book prints the equations but not the period rule. That the period is $\frac{2\pi}{b}$ (for $b > 0$ ) is something you need to know.

Logarithms (page 1)

Formula	What it does	Worked example
$a^x = b \Leftrightarrow x = \log_a(b)$	Converts between index and logarithm form	$5^3 = 125$ means $\log_5(125) = 3$
$\log_a(x) + \log_a(y) = \log_a(xy)$	Product law	$\log_2(4) + \log_2(8) = \log_2(32) = 5$
$\log_a(x) - \log_a(y) = \log_a\left(\frac{x}{y}\right)$	Quotient law	$\log_5(50) - \log_5(2) = \log_5(25) = 2$
$\log_a(x^n) = n\log_a(x)$	Power law	$\log_2(8^2) = 2\log_2(8) = 6$
$\log_a(x) = \frac{\log_b(x)}{\log_b(a)}$	Change of base	$\log_4(8) = \frac{\log_2(8)}{\log_2(4)} = \frac{3}{2}$
$\log_a(1) = 0$	Log of 1 is 0	$\log_7(1) = 0$
$\log_a(a) = 1$	Log of the base is 1	$\log_7(7) = 1$

Put together, the laws solve equations by hand. To solve $\log_2(x) + \log_2(x - 2) = 3$ , combine the left side into $\log_2\left(x(x - 2)\right) = 3$ , so $x^2 - 2x = 8$ and $(x - 4)(x + 2) = 0$ . Reject $x = -2$ because $\log_2(-2)$ is undefined, which leaves $x = 4$ .

Calculus (page 2)

Formula	What it does	Worked example
$f'(x) = \lim_{h \to 0} \frac{f(x + h) - f(x)}{h}$	Derivative from first principles	$f(x) = x^2$ : $\frac{(x+h)^2 - x^2}{h} = \frac{2xh + h^2}{h} = 2x + h$ , which tends to $2x$
$\int_a^b f(x)\,dx \approx \text{limit of sums } \sum_i f(x_i)\,\delta x_i$	The definite integral as a limit of sums of strip areas	Four right-endpoint strips of width 0.5 under $y = x^2$ from 0 to 2: $0.5(0.25 + 1 + 2.25 + 4) = 3.75$ . More strips would close in on the exact area
$\int_a^b f(x)\,dx = F(b) - F(a)$	Fundamental theorem of calculus, where $F$ is an antiderivative of $f$	$\int_1^3 2x\,dx = \left[x^2\right]_1^3 = 9 - 1 = 8$
$\frac{d}{dx}\left(f(x) + g(x)\right) = \frac{d}{dx}f(x) + \frac{d}{dx}g(x)$	Differentiate a sum term by term	$\frac{d}{dx}(x^3 + \sin(x)) = 3x^2 + \cos(x)$
$\int \left(f(x) + g(x)\right) dx = \int f(x)\,dx + \int g(x)\,dx$	Integrate a sum term by term	$\int (x^2 + e^x)\,dx = \frac{x^3}{3} + e^x + c$
$\int k\,f(x)\,dx = k\int f(x)\,dx$	A constant factor comes outside the integral	$\int 6x^2\,dx = 6 \cdot \frac{x^3}{3} = 2x^3 + c$
$\frac{d}{dx}x^n = nx^{n-1}$	Power rule for derivatives	$\frac{d}{dx}x^{-2} = -2x^{-3}$
$\int x^n\,dx = \frac{x^{n+1}}{n + 1} + c \quad (n \neq -1)$	Power rule for integrals	$\int x^3\,dx = \frac{x^4}{4} + c$
$\frac{d}{dx}e^x = e^x$ and $\frac{d}{dx}e^{f(x)} = f'(x)\,e^{f(x)}$	Derivative of an exponential	$\frac{d}{dx}e^{3x^2} = 6x\,e^{3x^2}$
$\int e^x\,dx = e^x + c$	Integral of $e^x$	$\int_0^1 e^x\,dx = e - 1$
$\frac{d}{dx}\ln(x) = \frac{1}{x}$ and $\frac{d}{dx}\ln\left(f(x)\right) = \frac{f'(x)}{f(x)}$	Derivative of a natural logarithm	$\frac{d}{dx}\ln(x^2 + 1) = \frac{2x}{x^2 + 1}$
$\int \frac{1}{x}\,dx = \ln(x) + c \quad (x > 0)$	Integral of $\frac{1}{x}$	$\int_1^e \frac{1}{x}\,dx = \ln(e) - \ln(1) = 1$
$\frac{d}{dx}\sin(x) = \cos(x)$ and $\frac{d}{dx}\sin\left(f(x)\right) = f'(x)\cos\left(f(x)\right)$	Derivative of sine	$\frac{d}{dx}\sin(x^2) = 2x\cos(x^2)$
$\int \sin(x)\,dx = -\cos(x) + c$	Integral of sine	$\int_0^{\pi} \sin(x)\,dx = \left[-\cos(x)\right]_0^{\pi} = 1 - (-1) = 2$
$\frac{d}{dx}\cos(x) = -\sin(x)$ and $\frac{d}{dx}\cos\left(f(x)\right) = -f'(x)\sin\left(f(x)\right)$	Derivative of cosine	$\frac{d}{dx}\cos(3x) = -3\sin(3x)$
$\int \cos(x)\,dx = \sin(x) + c$	Integral of cosine	$\int_0^{\pi/2} \cos(x)\,dx = \sin\left(\frac{\pi}{2}\right) - \sin(0) = 1$
If $y = f(u)$ and $u = g(x)$ then $\frac{dy}{dx} = \frac{dy}{du} \times \frac{du}{dx}$	Chain rule	$y = (3x + 1)^4$ : with $u = 3x + 1$ , $\frac{dy}{dx} = 4u^3 \times 3 = 12(3x + 1)^3$
$\frac{d}{dx}(uv) = u\frac{dv}{dx} + v\frac{du}{dx}$	Product rule	$u = x^2$ , $v = e^x$ : $x^2e^x + 2x\,e^x = x\,e^x(x + 2)$
$\frac{d}{dx}\left(\frac{u}{v}\right) = \frac{v\frac{du}{dx} - u\frac{dv}{dx}}{v^2}$	Quotient rule	$u = \sin(x)$ , $v = x$ : $\frac{x\cos(x) - \sin(x)}{x^2}$

The trapezoidal rule, with $n$ strips of equal width $w$ , is too long for the table:

\int_a^b f(x)\,dx \approx \frac{w}{2}\left[f(x_0) + 2\left(f(x_1) + f(x_2) + f(x_3) + \ldots + f(x_{n-1})\right) + f(x_n)\right], \quad \text{where } w = \frac{b - a}{n}

Worked example: for $\int_0^2 x^2\,dx$ with $n = 4$ , $w = 0.5$ and the values are $0, 0.25, 1, 2.25, 4$ . So $\frac{0.5}{2}\left[0 + 2(3.5) + 4\right] = 2.75$ (the exact value is $\frac{8}{3}$ ).

The book prints the derivative of a function inside an exponential, a natural logarithm, a sine and a cosine, but only the basic integrals of $e^x$ , $\frac{1}{x}$ , $\sin(x)$ and $\cos(x)$ . The trapezoidal rule in the book has no plus sign before the dots in the middle bracket; the version above adds it.

Trigonometry (page 2)

Only four items.

Formula	What it does	Worked example
$c^2 = a^2 + b^2 - 2ab\cos(C)$	Cosine rule: find a side from two sides and the included angle, or an angle from three sides	$a = 5$ , $b = 8$ , $C = 60^\circ$ : $c^2 = 25 + 64 - 80\cos(60^\circ) = 49$ , so $c = 7$
$\frac{a}{\sin(A)} = \frac{b}{\sin(B)} = \frac{c}{\sin(C)}$	Sine rule: sides over the sines of their opposite angles. The syllabus requires the ambiguous case	$A = 30^\circ$ , $a = 4$ , $B = 45^\circ$ : $b = \frac{4\sin(45^\circ)}{\sin(30^\circ)} = 4\sqrt{2}$
$\text{area} = \frac{1}{2}bc\sin(A)$	Area of a triangle from two sides and the included angle	$b = 6$ , $c = 8$ , $A = 30^\circ$ : $\frac{1}{2}(6)(8)\left(\frac{1}{2}\right) = 12$
$\sin^2(A) + \cos^2(A) = 1$	Pythagorean identity	If $\sin(A) = \frac{3}{5}$ with $A$ acute, $\cos^2(A) = 1 - \frac{9}{25} = \frac{16}{25}$ , so $\cos(A) = \frac{4}{5}$

Statistics and probability (page 3)

Formula	What it does	Worked example
$(x + y)^n = x^n + \binom{n}{1}x^{n-1}y + \ldots + \binom{n}{r}x^{n-r}y^r + \ldots + y^n$	Binomial theorem	$(2x - 1)^3$ : the coefficients are 1, 3, 3, 1, so $8x^3 - 12x^2 + 6x - 1$
$P(X = r) = \binom{n}{r}p^r(1 - p)^{n-r}$	Binomial probability of $r$ successes in $n$ trials	$n = 4$ , $p = \frac{1}{2}$ , $r = 2$ : $6 \times \frac{1}{16} = \frac{3}{8}$
$E(X) = \mu = \sum p_i x_i$	Mean of a discrete random variable	$x = 1, 2, 3$ with $p = 0.2, 0.5, 0.3$ : $0.2 + 1.0 + 0.9 = 2.1$
$\mathrm{Var}(X) = \sum p_i (x_i - \mu)^2$	Variance of a discrete random variable	Same table: $0.2(1.1)^2 + 0.5(0.1)^2 + 0.3(0.9)^2 = 0.242 + 0.005 + 0.243 = 0.49$
$\sqrt{\mathrm{Var}(X)}$	Standard deviation	$\sqrt{0.49} = 0.7$
$E(X) = \mu = \int_{-\infty}^{\infty} x\,p(x)\,dx$	Mean of a continuous random variable, with $p(x)$ its probability density function	$p(x) = 2x$ on $0 \le x \le 1$ and 0 elsewhere: $\int_0^1 2x^2\,dx = \frac{2}{3}$
$\mathrm{Var}(X) = \sigma^2 = \int_{-\infty}^{\infty} (x - \mu)^2\,p(x)\,dx$	Variance of a continuous random variable	Same $p(x)$ : $\int_0^1 \left(x - \frac{2}{3}\right)^2 2x\,dx = \frac{1}{2} - \frac{8}{9} + \frac{4}{9} = \frac{1}{18}$
Bernoulli: mean $p$ , variance $p(1 - p)$	A single trial with probability of success $p$	$p = 0.3$ : mean 0.3, variance $0.3 \times 0.7 = 0.21$
Binomial: mean $np$ , variance $np(1 - p)$	Number of successes in $n$ independent trials	$n = 50$ , $p = 0.2$ : mean 10, variance $50 \times 0.2 \times 0.8 = 8$
Sample proportion: mean $p$ , standard deviation $\sqrt{\dfrac{p(1 - p)}{n}}$	Centre and spread of the sample proportion $\hat{p}$	$p = 0.5$ , $n = 100$ : $\sqrt{\dfrac{0.25}{100}} = 0.05$
$\left(\hat{p} - z\sqrt{\dfrac{\hat{p}(1 - \hat{p})}{n}},\ \hat{p} + z\sqrt{\dfrac{\hat{p}(1 - \hat{p})}{n}}\right)$	Approximate confidence interval for the population proportion $p$	$\hat{p} = 0.5$ , $n = 100$ , $z = 1.96$ : the margin is $1.96 \times 0.05 = 0.098$ , so the interval is $(0.402, 0.598)$
$z\sqrt{\dfrac{\hat{p}(1 - \hat{p})}{n}}$	Approximate margin of error	Same values: $0.098$ . Quadrupling $n$ halves it, because $n$ sits under the square root
$P(\overline{A}) = 1 - P(A)$	Complement	$P(A) = 0.35$ gives $P(\overline{A}) = 0.65$
$P(A \cup B) = P(A) + P(B) - P(A \cap B)$	General addition rule	$0.5 + 0.4 - 0.2 = 0.7$
$P(A \cap B) = P(A)P(B)$	Independent events	$P(A) = 0.3$ , $P(B) = 0.5$ , independent: $0.15$
$P(A \cap B) = P(A \mid B)P(B)$	Conditional probability, multiplication form	$P(B) = 0.5$ , $P(A \mid B) = 0.6$ : $P(A \cap B) = 0.3$

In the confidence interval, $z$ is the quantile of the standard normal distribution that matches the confidence level. The book does not say so. The value 1.96 for 95% confidence is standard, and the syllabus says quantiles are found with technology, so a technology-free paper gives you no way to find $z$ yourself.

What is not on the formula sheet?

We compared the book line by line with the Units 1 to 4 subject matter in the 2025 syllabus. The syllabus asks for each of these, and the book does not print it.

Not printed	What the syllabus asks for	Unit
The quadratic formula and the discriminant	Solve quadratics with the quadratic formula (exact and approximate answers) and use the discriminant to count solutions	1
Surd rules	Simplify square roots with perfect square factors, rationalise denominators and use the four operations on surds	1
Index laws	Negative and fractional indices, radicals as fractional indices, scientific notation	2
The meaning of $\binom{n}{r}$	The book uses the symbol in two formulas and prints no factorial or combination definition	1, 3
Radian measure and exact values	Radians and degrees, arc lengths and sector areas, exact values of $\cos$ , $\sin$ and $\tan$ at multiples of $\frac{\pi}{6}$ and $\frac{\pi}{4}$	1
$\tan$	The unit circle definition of $\tan(\theta)$ and the graph of $y = \tan(x)$	1
Period of a sine or cosine graph	The effect of $a$ , $b$ , $h$ and $k$ on $y = a\sin\left(b(x - h)\right) + k$	1
Straight line formulas	The syllabus calls a link to linear functions assumed knowledge for tangents and normals	2
The definition of independence	Independence of $A$ from $B$ , defined as $P(A \mid B) = P(A)$ . The book prints only $P(A \cap B) = P(A \mid B)P(B)$ and $P(A \cap B) = P(A)P(B)$ , so to find $P(A \mid B)$ you divide the first by $P(B)$ yourself	1
Integrals of the form $\int f(ax + b)\,dx$	Determine indefinite integrals of this form. The book has only the basic integrals of $e^x$ , $\frac{1}{x}$ , $\sin(x)$ and $\cos(x)$	3
Area between two curves	Calculate the area between curves. The book has the fundamental theorem for one function	4
Motion relationships	Displacement from velocity or acceleration with initial values, and velocity as the rate of change of displacement	2, 3, 4
Probability density function properties	Probabilities of a continuous random variable as integrals, and the cumulative distribution function. The book uses $p(x)$ without defining it	4
The normal distribution	The notation $X \sim N(\mu, \sigma^2)$ , standardised $z$ -scores, probabilities and quantiles. The book has no density, no standardisation formula and no table, and the syllabus says tables are not required	4
The standardised sample proportion	$\dfrac{\hat{p} - p}{\sqrt{\hat{p}(1 - \hat{p})/n}}$ being approximately standard normal for large samples	4
Definitions of $z$ , $\hat{p}$ and $n$	The book uses them in the interval and margin of error without a key	4

Three kinds of item sit in that list. Some are formulas you must memorise (quadratic formula, exact values, index laws, surd rules). Some are methods, not formulas (area between curves, motion problems, the second derivative test), so nothing on any sheet could replace them. And some are done with technology in Paper 2 (normal probabilities and quantiles).

The book also has nothing on sequences and series, finance, matrices, vectors, complex numbers, integration by substitution or by parts, or hypothesis testing. None of those appear in the Methods Units 1 to 4 subject matter either, so their absence is not a gap. They belong to other subjects.

What is the difference between Paper 1 and Paper 2?

Same formula book, same 90 minutes working time and 5 minutes perusal, 25% each. Technology is the only variable the syllabus changes.

Paper 1 is technology-free. Anything that needs a decimal has to be left exact or estimated by hand. That makes these rows the ones to practise by hand: the log laws, the power, chain, product and quotient rules, the trapezoidal rule with a few strips, the cosine rule with an angle that has an exact cosine, binomial coefficients, and the confidence interval with friendly numbers.
Paper 2 is technology-active, with the calculator rules in the table above. The syllabus says normal probabilities and quantiles are found using technology, and binomial means and variances are calculated using technology and algebraic methods.

Check your calculator model against QCAA's approved lists before the day. QCAA's 2026 memo (044/26) says the lists were updated, and that the instructions for resetting or clearing approved graphics calculators before and after the external exam changed. Teachers are asked to review those instructions for the models their students use. The lists themselves are on the QCAA website, so read the current copy, not a screenshot from a friend.

What do technology-free questions ask you to do by hand?

The formula book does not do the technology-free work for you. QCAA's 2023 to 2025 reports (those cohorts sat the 2019 course, with its own formula sheet) describe Paper 1 questions that were won or lost on a skill, not a lookup:

Exact answers (2023, Paper 1, Question 19). The effective response simplified $\frac{10}{\ln 2}\ln(2x) - \frac{10}{\ln 2}\ln(x/16)$ with log laws to $\frac{10}{\ln 2}\ln(32) = 50$ exactly, with no calculator.
Estimation (2024, Paper 1, Question 18). The question needed the cosine rule to connect the sides to one given angle. The report says many students could progress part of the way but could not convert the progressing calculation to a reasonable approximation. The effective excerpt reached $h = \sqrt{624/25} \approx 5$ and compared it with the 4 m requirement.
Algebra before calculus (2024, Paper 1, Question 13b). Many students could not integrate correctly because they made errors expanding a squared bracket and simplifying.
Confidence intervals (2025, Paper 1, Question 12). The report says many students struggle to determine confidence intervals in technology-free situations.
Logarithmic equations (2025, Paper 1, Question 15). The effective response applied the power law $\log_b(a^n) = n\log_b(a)$ , recognised the quadratic $a^2 = 2a + 8$ with $a = \log_2(x)$ , solved for both roots and checked one by substitution.

Where do you practise using it?

The question bank holds marked past-paper questions from Paper 1 and Paper 2 for 2020 to 2025, 116 questions on each paper across the six years. Do a Paper 1 set with only the book open and no calculator, the way QCAA sets the conditions, and note every time you reach for a rule that is not printed. That list is your memory work, and the table above is where to start it.

To see which topics the papers test most and where students lose marks, read the most tested topics and hardest topics guides. Everything else about the subject sits on the Mathematical Methods study guide, and other subjects are on the QCE hub.

Frequently asked questions

Do you get a formula sheet in QCAA Mathematical Methods Paper 1?

Yes. The syllabus says the QCAA provides the QCAA Mathematical Methods formula book for both external papers. Paper 1 is technology-free and allows nothing else: no notes, calculators, technology or other resources. In IA2 and IA3 the teacher must provide the same formula book.

Is the formula sheet the same in Paper 1 and Paper 2?

The syllabus names one document, the QCAA Mathematical Methods formula book, as provided for both papers. What differs between the papers is the technology: none in Paper 1, and in Paper 2 a handheld QCAA-approved graphics calculator (no CAS functionality) and/or a handheld QCAA-approved scientific calculator.

What is on the QCAA Maths Methods formula book?

Three printed pages. Page 1 has mensuration, graph equations and logarithm laws. Page 2 has calculus (first principles, the fundamental theorem, derivative and integral rules, the chain, product and quotient rules and the trapezoidal rule) and four trigonometry items. Page 3 has the binomial theorem and binomial probability, random-variable means and variances, sample proportions, the confidence interval and margin of error, and the basic probability rules.

Is the quadratic formula on the Maths Methods formula sheet?

No. The 2025 syllabus asks you to solve quadratics with the quadratic formula and to use the discriminant, and the book prints neither. It also leaves out the index laws, surd rules, radian and exact-value trigonometry, tan, integrals of the f(ax + b) type and anything on the normal distribution, so these come from memory.

Is the normal distribution on the Maths Methods formula sheet?

No. The book has no normal density, no table and no standardisation formula, and it does not define z. The syllabus says normal probabilities and quantiles are calculated with technology and that distribution tables are not required.

Is it called a formula sheet or a formula book?

The 2025 syllabus says formula book. The 2019 syllabus said formula sheet. Students and search engines still use formula sheet, so both names point at the same QCAA document for the current course.

Can I use a CAS calculator in Mathematical Methods Paper 2?

No. The syllabus allows a handheld QCAA-approved graphics calculator with no CAS functionality, and/or a handheld QCAA-approved scientific calculator. QCAA publishes an approved list for each type, and its 2026 memo (044/26) says the instructions for resetting or clearing approved graphics calculators before and after the external exam were updated.

Which Paper 1 skills did QCAA's subject reports flag?

Both cohorts sat the 2019 course. In the 2024 report: algebraic and arithmetic fluency (expanding brackets, simplifying, working with fractions and decimals) and estimating a calculated value in a technology-free two- or three-dimensional problem. In the 2025 report: determining confidence intervals in a technology-free question (Paper 1, Question 12) and solving logarithmic equations that need several logarithmic rules before a quadratic.

Sources

Mathematical Methods 2025 formula book, QCAA, June 2026, pp. 1-3. Every formula reproduced on this page, and the list of what the book does not print. The cover is dated June 2026 and the licence line reads © State of Queensland (QCAA) 2025.
Mathematical Methods 2025 v1.2 General senior syllabus, QCAA, October 2024, pp. 15-30, 35-45. Units 1 to 4 subject matter compared with the book to find what is not printed, and the IA2, IA3 and external assessment conditions: who provides the formula book, what technology Paper 1 and Paper 2 allow.
Mathematical Methods 2019 v1.2 General Senior Syllabus, QCAA, July 2018. Superseded version, cited only for the earlier name of the document, the QCAA formula sheet.
Mathematical Methods subject report, 2025 cohort, QCAA, January 2026, pp. 28-39. Technology-free confidence-interval and logarithmic-equation findings, and the effective-response excerpts.
Mathematical Methods subject report, 2024 cohort, QCAA, January 2025, pp. 25-30. Technology-free algebra and estimation findings (Paper 1, Questions 13b and 18), and the cosine rule question excerpt (Paper 1, Question 18).
Mathematical Methods subject report, 2023 cohort, QCAA, January 2024, pp. 37-38. The technology-free logarithm excerpt (Paper 1, Question 19).
Memo 044/26: Scientific and graphics calculator lists (updated 2026) now available, QCAA, August 2026, pp. 1-2. Existence of the approved scientific and graphics lists for external assessment, and the updated reset or clear instructions for graphics calculators.
AusGrader question bank, QCE Mathematical Methods, AusGrader. Paper 1 and Paper 2 for 2020 to 2025 are held, 116 questions on each paper across the six years (examPapers coverage).

Syllabus and assessment material referenced in this guide is © State of Queensland (Queensland Curriculum and Assessment Authority), licensed under CC BY 4.0. See our QCAA licensing notice. AusGrader is an independent study tool and is not affiliated with, endorsed by, or operated by the QCAA.

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