QCE Specialist Mathematics21 October 2026

QCAA Specialist Maths formula sheet: the full book, Paper 1 and Paper 2

Quick answer

In QCAA Specialist Mathematics the QCAA hands you the QCAA Specialist Mathematics formula book in both external papers, and your teacher must supply it in IA2 and IA3. Paper 1 is technology-free and allows nothing else. Paper 2 adds a handheld QCAA-approved graphics calculator (no CAS functionality) and/or a handheld QCAA-approved scientific calculator. The book is eight printed pages of formula tables with no worked examples or symbol legend, and every table is set out below.

The rules here come from the Specialist Mathematics 2025 v1.0 syllabus, which Year 12 students sit from 2026, and the formulas come from the QCAA Specialist Mathematics 2025 formula book (cover dated June 2026, no version number printed). The 2019 syllabus called the document it supplied the "QCAA formula sheet", so older advice describes the superseded course. This is a guide to the QCAA Specialist Maths external exam every QCE Specialist Maths student sits; the subject page holds the past papers.

Do you get a formula sheet in the Specialist Maths 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 book itself says nothing about assessment, so these rules come from the syllabus. The two internal papers are covered in the IA2 and IA3 guide.

What is the difference between Paper 1 and Paper 2?

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

Paper 1 is technology-free: no calculator of any kind.
Paper 2 is technology-active, with the calculator rules in the table above.

One calculator rule changed. The 2019 syllabus required a QCAA-approved graphics calculator (no CAS) in Paper 2 and allowed a scientific calculator as well. The 2025 syllabus says you may use a graphics calculator and/or a scientific calculator.

Check your model against QCAA's approved lists before the day. QCAA's 2026 memo (044/26) says the lists were updated. The lists are on the QCAA website, so read the current copy rather than a screenshot from a friend.

What is in the Specialist Maths formula book?

Eight printed pages, numbered "1 of 8" to "8 of 8", in this order:

Printed page	Tables
1	Mensuration; Graph equations; Logarithms
2	Calculus; Trigonometry
3	Statistics
4	Additional Calculus for Specialist Mathematics
5	Additional Trigonometry for Specialist Mathematics; Graph equations for Specialist Mathematics
6	Additional Statistics for Specialist Mathematics; Real and complex numbers
7	Matrices
8	Vectors; Physical constant

Modified from the QCAA Specialist Mathematics 2025 formula book, © State of Queensland (QCAA), CC BY 4.0. The formulas are as printed. The row labels are the book's where it prints one, and ours where it leaves a row unnamed (for example the derivative and integral rows, and the "turning point form" and "factored form" labels on the quadratic and cubic). The book does not define any symbols, so none are defined here either.

What does the Specialist Maths formula sheet say?

Printed page 1: mensuration, graph equations and logarithms

Mensuration:

Name	Formula
Circumference of a circle	$C = 2\pi r$
Area of a circle	$A = \pi r^{2}$
Area of a parallelogram	$A = bh$
Area of a trapezium	$A = \frac{1}{2}(a + b)h$
Area of a triangle	$A = \frac{1}{2}bh$
Total surface area of a cone	$S = \pi r s + \pi r^{2}$
Total surface area of a cylinder	$S = 2\pi r h + 2\pi r^{2}$
Surface area of a sphere	$S = 4\pi r^{2}$
Volume of a cone	$V = \frac{1}{3}\pi r^{2} h$
Volume of a cylinder	$V = \pi r^{2} h$
Volume of a prism	$V = Ah$
Volume of a pyramid	$V = \frac{1}{3}Ah$
Volume of a sphere	$V = \frac{4}{3}\pi r^{3}$

Graph equations:

Name	Formula
Quadratic (turning point form)	$y = a(x - h)^{2} + k$
Quadratic (factored form)	$y = a(x - x_{1})(x - x_{2})$
Cubic	$y = a(x - h)^{3} + k$
Cubic (factored form)	$y = a(x - x_{1})(x - x_{2})(x - x_{3})$
Circle	$(x - h)^{2} + (y - k)^{2} = r^{2}$
Square root	$y = a\sqrt{x - h} + k$
Reciprocal	$y = \frac{a}{(x - h)} + k$
Exponential	$y = r^{(x - h)} + k \quad (\text{where } r \gt 0)$
Logarithmic	$y = \log_{a}(x - h) + k \quad (\text{where } a \gt 1)$
Trigonometric (sine)	$y = a\sin\big(b(x - h)\big) + k$
Trigonometric (cosine)	$y = a\cos\big(b(x - h)\big) + k$

Logarithms:

Name	Formula
Exponents and logarithms	$a^{x} = b \Leftrightarrow x = \log_{a}(b)$
Logarithmic laws and definitions	$\log_{a}(x) + \log_{a}(y) = \log_{a}(xy)$
	$\log_{a}(x^{n}) = n\log_{a}(x)$
	$\log_{a}(x) - \log_{a}(y) = \log_{a}\left(\frac{x}{y}\right)$
	$\log_{a}(x) = \frac{\log_{b}(x)}{\log_{b}(a)}$
	$\log_{a}(1) = 0$
	$\log_{a}(a) = 1$

Printed page 2: calculus and trigonometry

Calculus:

Name	Formula
Derivative from first principles	$f'(x) = \lim_{h \to 0} \frac{f(x + h) - f(x)}{h}$
Definite integral as limit of sums	$\int_{a}^{b} f(x)\,dx \approx \text{limit of sums } \sum_{i} f(x_{i})\,\delta x_{i}$
Fundamental theorem	$\int_{a}^{b} f(x)\,dx = F(b) - F(a)$
Derivative of a sum	$\frac{d}{dx}\big(f(x) + g(x)\big) = \frac{d}{dx}f(x) + \frac{d}{dx}g(x)$
Integral of a sum	$\int \big(f(x) + g(x)\big)\,dx = \int f(x)\,dx + \int g(x)\,dx$
Constant multiple	$\int k\,f(x)\,dx = k\int f(x)\,dx$
Power rule (derivative)	$\frac{d}{dx}x^{n} = nx^{n-1}$
Power rule (integral)	$\int x^{n}\,dx = \frac{x^{n+1}}{n+1} + c \quad \text{for } n \neq -1$
Exponential (derivative)	$\frac{d}{dx}e^{x} = e^{x}$
Exponential, composite	$\frac{d}{dx}e^{f(x)} = f'(x)\,e^{f(x)}$
Exponential (integral)	$\int e^{x}\,dx = e^{x} + c$
Natural log (derivative)	$\frac{d}{dx}\ln(x) = \frac{1}{x}$
Natural log, composite	$\frac{d}{dx}\ln\big(f(x)\big) = \frac{f'(x)}{f(x)}$
1/x (integral)	$\int \frac{1}{x}\,dx = \ln(x) + c \quad \text{for } x \gt 0$
Sine (derivative)	$\frac{d}{dx}\sin(x) = \cos(x)$
Sine, composite	$\frac{d}{dx}\sin\big(f(x)\big) = f'(x)\cos\big(f(x)\big)$
Sine (integral)	$\int \sin(x)\,dx = -\cos(x) + c$
Cosine (derivative)	$\frac{d}{dx}\cos(x) = -\sin(x)$
Cosine, composite	$\frac{d}{dx}\cos\big(f(x)\big) = -f'(x)\sin\big(f(x)\big)$
Cosine (integral)	$\int \cos(x)\,dx = \sin(x) + c$
Chain rule	$\text{If } y = f(u) \text{ and } u = g(x) \text{ then } \frac{dy}{dx} = \frac{dy}{du} \times \frac{du}{dx}$
Product rule	$\frac{d}{dx}(uv) = u\frac{dv}{dx} + v\frac{du}{dx}$
Quotient rule	$\frac{d}{dx}\left(\frac{u}{v}\right) = \dfrac{v\frac{du}{dx} - u\frac{dv}{dx}}{v^{2}}$
Trapezoidal rule	$\int_{a}^{b} f(x)\,dx \approx \frac{w}{2}\Big[f(x_{0}) + 2\big(f(x_{1}) + f(x_{2}) + f(x_{3}) + \dots + f(x_{n-1})\big) + f(x_{n})\Big], \quad \text{where } w = \frac{b-a}{n}$

Trigonometry:

Name	Formula
Cosine rule	$c^{2} = a^{2} + b^{2} - 2ab\cos(C)$
Sine rule	$\frac{a}{\sin(A)} = \frac{b}{\sin(B)} = \frac{c}{\sin(C)}$
Area of a triangle	$\text{area} = \frac{1}{2}bc\sin(A)$
Pythagorean identity	$\sin^{2}(A) + \cos^{2}(A) = 1$

Printed page 3: statistics

Name	Formula
Binomial theorem	$(x + y)^{n} = x^{n} + \binom{n}{1}x^{n-1}y + \dots + \binom{n}{r}x^{n-r}y^{r} + \dots + y^{n}$
Binomial probability	$P(X = r) = \binom{n}{r}p^{r}(1 - p)^{n-r}$
Discrete random variable X, mean	$E(X) = \mu = \sum p_{i}x_{i}$
Discrete random variable X, variance	$\mathrm{Var}(X) = \sum p_{i}(x_{i} - \mu)^{2}$
Discrete random variable X, standard deviation	$\sqrt{\mathrm{Var}(X)}$
Continuous random variable X, mean	$E(X) = \mu = \int_{-\infty}^{\infty} x\,p(x)\,dx$
Continuous random variable X, variance	$\mathrm{Var}(X) = \sigma^{2} = \int_{-\infty}^{\infty} (x - \mu)^{2}\,p(x)\,dx$
Bernoulli distribution, mean	$p$
Bernoulli distribution, variance	$p(1 - p)$
Binomial distribution, mean	$np$
Binomial distribution, variance	$np(1 - p)$
Sample proportion, mean	$p$
Sample proportion, standard deviation	$\sqrt{\dfrac{p(1 - p)}{n}}$
Approximate confidence interval for p	$\left(\hat{p} - z\sqrt{\dfrac{\hat{p}(1 - \hat{p})}{n}},\ \hat{p} + z\sqrt{\dfrac{\hat{p}(1 - \hat{p})}{n}}\right)$
Approximate margin of error	$z\sqrt{\dfrac{\hat{p}(1 - \hat{p})}{n}}$
Complementary probability	$P(\overline{A}) = 1 - P(A)$
General addition rule for probability	$P(A \cup B) = P(A) + P(B) - P(A \cap B)$
Probability of independent events	$P(A \cap B) = P(A)P(B)$
Conditional probability	$P(A \cap B) = P(A \mid B)\,P(B)$

Printed page 4: additional calculus

Name	Formula
Natural log (derivative)	$\frac{d}{dx}\ln(x) = \frac{1}{x}$
1/x (integral)	$\int \frac{1}{x}\,dx = \ln\lvert x\rvert + c \quad \text{for } x \neq 0$
Natural log, composite	$\frac{d}{dx}\ln\big(f(x)\big) = \frac{f'(x)}{f(x)}$
f'/f (integral)	$\int \frac{f'(x)}{f(x)}\,dx = \ln\lvert f(x)\rvert + c \quad \text{for } f(x) \neq 0$
Tangent (derivative)	$\frac{d}{dx}\tan(x) = \sec^{2}(x)$
sec squared (integral)	$\int \sec^{2}(x)\,dx = \tan(x) + c$
Inverse sine (derivative)	$\frac{d}{dx}\sin^{-1}\left(\frac{x}{a}\right) = \frac{1}{\sqrt{a^{2} - x^{2}}}$
Inverse sine (integral)	$\int \frac{1}{\sqrt{a^{2} - x^{2}}}\,dx = \sin^{-1}\left(\frac{x}{a}\right) + c$
Inverse cosine (derivative)	$\frac{d}{dx}\cos^{-1}\left(\frac{x}{a}\right) = \frac{-1}{\sqrt{a^{2} - x^{2}}}$
Inverse cosine (integral)	$\int \frac{-1}{\sqrt{a^{2} - x^{2}}}\,dx = \cos^{-1}\left(\frac{x}{a}\right) + c$
Inverse tangent (derivative)	$\frac{d}{dx}\tan^{-1}\left(\frac{x}{a}\right) = \frac{a}{a^{2} + x^{2}}$
Inverse tangent (integral)	$\int \frac{a}{a^{2} + x^{2}}\,dx = \tan^{-1}\left(\frac{x}{a}\right) + c$
Integration by parts	$\int u\frac{dv}{dx}\,dx = uv - \int v\frac{du}{dx}\,dx$
Volume of a solid of revolution, about the x-axis	$V = \pi\int_{a}^{b}\big[f(x)\big]^{2}\,dx$
Volume of a solid of revolution, about the y-axis	$V = \pi\int_{a}^{b}\big[f(y)\big]^{2}\,dy$
Simpson's rule	$\int_{a}^{b} f(x)\,dx \approx \frac{w}{3}\Big[f(x_{0}) + 4\big[f(x_{1}) + f(x_{3}) + \dots\big] + 2\big[f(x_{2}) + f(x_{4}) + \dots\big] + f(x_{n})\Big], \quad \text{where } w = \frac{b-a}{n}$
Simple harmonic motion	$\text{If } \frac{d^{2}x}{dt^{2}} = -\omega^{2}x \text{ then } x = A\sin(\omega t + \alpha) \text{ or } x = A\cos(\omega t + \beta)$
	$v^{2} = \omega^{2}\left(A^{2} - x^{2}\right)$
	$T = \frac{2\pi}{\omega}$
	$f = \frac{1}{T}$
Acceleration	$a = \frac{dv}{dt} = \frac{d^{2}x}{dt^{2}} = v\frac{dv}{dx} = \frac{d}{dx}\left(\frac{1}{2}v^{2}\right)$

Printed page 5: additional trigonometry and graph equations

Additional trigonometry:

Name	Formula
Pythagorean identities	$\sin^{2}(A) + \cos^{2}(A) = 1$
	$\tan^{2}(A) + 1 = \sec^{2}(A)$
	$\cot^{2}(A) + 1 = \operatorname{cosec}^{2}(A)$
Angle sum and difference identities	$\sin(A + B) = \sin(A)\cos(B) + \cos(A)\sin(B)$
	$\sin(A - B) = \sin(A)\cos(B) - \cos(A)\sin(B)$
	$\cos(A + B) = \cos(A)\cos(B) - \sin(A)\sin(B)$
	$\cos(A - B) = \cos(A)\cos(B) + \sin(A)\sin(B)$
Double-angle identities	$\sin(2A) = 2\sin(A)\cos(A)$
	$\cos(2A) = \cos^{2}(A) - \sin^{2}(A)$
	$\cos(2A) = 1 - 2\sin^{2}(A)$
	$\cos(2A) = 2\cos^{2}(A) - 1$
Product identities	$\sin(A)\sin(B) = \frac{1}{2}\big(\cos(A - B) - \cos(A + B)\big)$
	$\cos(A)\cos(B) = \frac{1}{2}\big(\cos(A - B) + \cos(A + B)\big)$
	$\sin(A)\cos(B) = \frac{1}{2}\big(\sin(A + B) + \sin(A - B)\big)$
	$\cos(A)\sin(B) = \frac{1}{2}\big(\sin(A + B) - \sin(A - B)\big)$

The book prints the three forms of the cosine double-angle identity as one chained equation. They are separated here so each fits a row.

Graph equations for Specialist Mathematics:

Name	Formula
Sphere	$(x - h)^{2} + (y - k)^{2} + (z - l)^{2} = r^{2}$
Circle	$(x - h)^{2} + (y - k)^{2} = r^{2}$
Ellipse	$\frac{(x - h)^{2}}{a^{2}} + \frac{(y - k)^{2}}{b^{2}} = 1$
Hyperbola (x-direction)	$\frac{(x - h)^{2}}{a^{2}} - \frac{(y - k)^{2}}{b^{2}} = 1$
Hyperbola (y-direction)	$\frac{(y - k)^{2}}{a^{2}} - \frac{(x - h)^{2}}{b^{2}} = 1$

The book prints the two hyperbola equations side by side under one name, with a squared under the y term in the second. The direction labels are ours.

Printed page 6: additional statistics, real and complex numbers

Additional statistics:

Name	Formula
Inclusion-exclusion principle	$\lvert A \cup B\rvert = \lvert A\rvert + \lvert B\rvert - \lvert A \cap B\rvert$
	$\lvert A \cup B \cup C\rvert = \lvert A\rvert + \lvert B\rvert + \lvert C\rvert - \lvert A \cap B\rvert - \lvert A \cap C\rvert - \lvert B \cap C\rvert + \lvert A \cap B \cap C\rvert$
Permutation	${}^{n}P_{r} = \frac{n!}{(n - r)!} = n \times (n - 1) \times (n - 2) \times \dots \times (n - r + 1)$
Combination	${}^{n}C_{r} = \binom{n}{r} = \frac{n!}{r!\,(n - r)!}$
Probability density function of the exponential distribution	$f(t) = \lambda e^{-\lambda t} \quad \text{for } t \geq 0,\ \lambda \gt 0$
Exponential random variable, mean	$\frac{1}{\lambda}$
Exponential random variable, standard deviation	$\frac{1}{\lambda}$
Sample means, mean	$\mu$
Sample means, standard deviation	$\frac{\sigma}{\sqrt{n}}$
Approximate margin of error	$E = z\,\dfrac{s}{\sqrt{n}}$
Approximate confidence interval for the mean	$\left(\bar{x} - z\dfrac{s}{\sqrt{n}},\ \bar{x} + z\dfrac{s}{\sqrt{n}}\right)$

Real and complex numbers:

Name	Formula
Complex number forms	$z = a + bi = r\big(\cos(\theta) + i\sin(\theta)\big) = r\,\mathrm{cis}(\theta)$
Modulus	$\lvert z\rvert = r = \sqrt{a^{2} + b^{2}}$
Argument	$\mathrm{Arg}(z) = \theta,\quad \tan(\theta) = \frac{b}{a},\quad -\pi \lt \theta \leq \pi,\ a \neq 0$
	$\arg(z) = \mathrm{Arg}(z) + 2\pi n,\quad n \in \mathbb{Z}$
Product	$z_{1}z_{2} = r_{1}r_{2}\,\mathrm{cis}(\theta_{1} + \theta_{2})$
Quotient	$\frac{z_{1}}{z_{2}} = \frac{r_{1}}{r_{2}}\,\mathrm{cis}(\theta_{1} - \theta_{2})$
De Moivre's theorem	$z^{n} = r^{n}\,\mathrm{cis}(n\theta)$

Printed page 7: matrices

The book prints matrix symbols in bold italic.

Name	Formula
Commutative law for addition	$\boldsymbol{A} + \boldsymbol{B} = \boldsymbol{B} + \boldsymbol{A}$
Additive identity	$\boldsymbol{A} + \boldsymbol{0} = \boldsymbol{A}$
Additive inverse	$\boldsymbol{A} + (-\boldsymbol{A}) = \boldsymbol{0}$
Multiplicative identity	$\boldsymbol{A}\boldsymbol{I} = \boldsymbol{A} = \boldsymbol{I}\boldsymbol{A}$
Multiplicative inverse	$\boldsymbol{A}\boldsymbol{A}^{-1} = \boldsymbol{I} = \boldsymbol{A}^{-1}\boldsymbol{A}$
Left distributive law	$\boldsymbol{A}(\boldsymbol{B} + \boldsymbol{C}) = \boldsymbol{A}\boldsymbol{B} + \boldsymbol{A}\boldsymbol{C}$
Right distributive law	$(\boldsymbol{B} + \boldsymbol{C})\boldsymbol{A} = \boldsymbol{B}\boldsymbol{A} + \boldsymbol{C}\boldsymbol{A}$
Determinant	$\text{If } \boldsymbol{A} = \begin{bmatrix} a & b \\ c & d \end{bmatrix} \text{ then } \det(\boldsymbol{A}) = ad - bc$
Multiplicative inverse matrix	$\boldsymbol{A}^{-1} = \begin{bmatrix} a & b \\ c & d \end{bmatrix}^{-1} = \frac{1}{\det(\boldsymbol{A})}\begin{bmatrix} d & -b \\ -c & a \end{bmatrix},\quad \det(\boldsymbol{A}) \neq 0$
Linear transformation: dilation of factor a parallel to the x-axis and factor b parallel to the y-axis	$\begin{bmatrix} a & 0 \\ 0 & b \end{bmatrix}$
Linear transformation: rotation of angle $\theta$ anticlockwise about the origin	$\begin{bmatrix} \cos(\theta) & -\sin(\theta) \\ \sin(\theta) & \cos(\theta) \end{bmatrix}$
Linear transformation: reflection in the line $y = x\tan(\theta)$	$\begin{bmatrix} \cos(2\theta) & \sin(2\theta) \\ \sin(2\theta) & -\cos(2\theta) \end{bmatrix}$

Printed page 8: vectors and the physical constant

The book prints vector symbols in bold italic and unit vectors with a hat.

Name	Formula
Magnitude (2D)	$\lvert\boldsymbol{a}\rvert = \left\lvert\begin{pmatrix} a_{1} \\ a_{2} \end{pmatrix}\right\rvert = \sqrt{a_{1}^{2} + a_{2}^{2}}$
Magnitude (3D)	$\lvert\boldsymbol{a}\rvert = \left\lvert\begin{pmatrix} a_{1} \\ a_{2} \\ a_{3} \end{pmatrix}\right\rvert = \sqrt{a_{1}^{2} + a_{2}^{2} + a_{3}^{2}}$
Direction	$\tan(\theta) = \frac{y}{x},\quad x \neq 0$
Unit vector	$\hat{\boldsymbol{n}} = \frac{\boldsymbol{n}}{\lvert\boldsymbol{n}\rvert}$
Scalar (dot) product	$\boldsymbol{a}\cdot\boldsymbol{b} = \lvert\boldsymbol{a}\rvert\lvert\boldsymbol{b}\rvert\cos(\theta)$
Scalar (dot) product, 2D	$\boldsymbol{a}\cdot\boldsymbol{b} = \begin{pmatrix} a_{1} \\ a_{2} \end{pmatrix}\cdot\begin{pmatrix} b_{1} \\ b_{2} \end{pmatrix} = a_{1}b_{1} + a_{2}b_{2}$
Scalar (dot) product, 3D	$\boldsymbol{a}\cdot\boldsymbol{b} = \begin{pmatrix} a_{1} \\ a_{2} \\ a_{3} \end{pmatrix}\cdot\begin{pmatrix} b_{1} \\ b_{2} \\ b_{3} \end{pmatrix} = a_{1}b_{1} + a_{2}b_{2} + a_{3}b_{3}$
Vector equation of a line	$\boldsymbol{r} = \boldsymbol{a} + t\boldsymbol{d}$
Parametric equations of a line	$x = a_{1} + t d_{1},\quad y = a_{2} + t d_{2},\quad z = a_{3} + t d_{3}$
Cartesian equation of a line	$\frac{x - a_{1}}{d_{1}} = \frac{y - a_{2}}{d_{2}} = \frac{z - a_{3}}{d_{3}}$
Vector (cross) product	$\boldsymbol{a}\times\boldsymbol{b} = \lvert\boldsymbol{a}\rvert\lvert\boldsymbol{b}\rvert\sin(\theta)\,\hat{\boldsymbol{n}}$
Vector (cross) product, components	$\boldsymbol{a}\times\boldsymbol{b} = \begin{pmatrix} a_{1} \\ a_{2} \\ a_{3} \end{pmatrix}\times\begin{pmatrix} b_{1} \\ b_{2} \\ b_{3} \end{pmatrix} = \begin{pmatrix} a_{2}b_{3} - a_{3}b_{2} \\ a_{3}b_{1} - a_{1}b_{3} \\ a_{1}b_{2} - a_{2}b_{1} \end{pmatrix}$
Scalar projection	$\boldsymbol{a}\text{ on }\boldsymbol{b} = \lvert\boldsymbol{a}\rvert\cos(\theta) = \boldsymbol{a}\cdot\hat{\boldsymbol{b}}$
Vector projection	$\boldsymbol{a}\text{ on }\boldsymbol{b} = \lvert\boldsymbol{a}\rvert\cos(\theta)\,\hat{\boldsymbol{b}} = (\boldsymbol{a}\cdot\hat{\boldsymbol{b}})\,\hat{\boldsymbol{b}} = \left(\frac{\boldsymbol{a}\cdot\boldsymbol{b}}{\boldsymbol{b}\cdot\boldsymbol{b}}\right)\boldsymbol{b}$
Vector equation of a plane	$\boldsymbol{r}\cdot\boldsymbol{n} = \boldsymbol{a}\cdot\boldsymbol{n}$
Cartesian equation of a plane	$ax + by + cz + d = 0$

Physical constant:

Name	Value
Magnitude of mean acceleration due to gravity on Earth	$g = 9.8\ \mathrm{m\,s^{-2}}$

What is not in the Specialist Maths formula book?

We checked all eight printed pages. These are not printed, which is a statement about the book and not about the exam:

No normal distribution formula and no standard normal table. The letter $z$ appears in the confidence interval and margin of error rows and is never defined.
No derivative of sec, cosec or cot, and no integral of tan. No partial fractions or substitution rule.
No sum-to-product, half-angle or $\tan(A \pm B)$ identities.
No Euler's formula, complex conjugate or roots formula.
No differential equation methods and no arc length formula.
No symbol legend and no instructions for using the book.

The syllabus tells you what you must be able to do, and the book does not say it is complete. Anything on this list that you rely on is a formula to learn.

Where does the formula book catch students out?

A few things in the book are easy to misread.

Conditional probability is printed in product form. The book gives $P(A \cap B) = P(A \mid B)\,P(B)$ , not $P(A \mid B) = \frac{P(A \cap B)}{P(B)}$ . You rearrange it.
The natural log integral appears twice with different conditions. Page 2 prints $\int \frac{1}{x}\,dx = \ln(x) + c$ for $x \gt 0$ , with no absolute value. Page 4 prints $\ln\lvert x\rvert + c$ for $x \neq 0$ . The page 4 form is the more general one.
Symbols are undefined. The cone surface area uses $s$ and the book never says what it is.
The projection rows share a label. Scalar projection and vector projection are both printed as " $\boldsymbol{a}$ on $\boldsymbol{b}$ ".
The book says cosec, not csc. It uses the cosec spelling in the Pythagorean identity.
The inverse trigonometric rows use $\frac{x}{a}$ . The derivative and integral rows are printed in the general $a$ form, not just in $x$ .

What changed for formulas in the 2025 course?

Three changes in the Unit 3 and 4 subject matter touch formulas. They come from the 2025 syllabus and our comparison with the 2019 one, and the current book prints each of them.

The exponential distribution gained a mean and a standard deviation. The 2019 syllabus named the probability density function only. The 2025 syllabus prints $f(t)=\lambda e^{-\lambda t}$ for $t\ge 0$ and states that the mean and the standard deviation are both $\frac{1}{\lambda}$ . The book prints the density and both values on page 6, and no cumulative distribution function.
Simpson's rule became examinable without technology. The 2019 wording was "using technology". The 2025 wording is "with and without technology", and the syllabus prints the formula, so it can now be examined by hand in Paper 1. The book prints it on page 4, with the trapezoidal rule on page 2.
Margin of error is named. The syllabus prints $E=z\frac{s}{\sqrt{n}}$ and asks you to use the relationship between margin of error, level of confidence and sample size. The book prints that formula on page 6.

Where do you practise using it?

The question bank holds the QCAA external examination Paper 1 and Paper 2 for 2020 to 2025 with their marking guides. Treat a Paper 1 set as a rehearsal: formula book open, no calculator, and a note of every formula you reached for that was not printed. Then repeat it with Paper 2 and a calculator you are allowed to use. The most tested topics and hardest topics guides show where the marks are, and the wider picture sits in the Specialist Mathematics study guide.

The 2025 subject report describes a cohort that sat the 2019 course. It prints no formula book of its own, so it says nothing about what the current book contains. The 2025 syllabus names Mathematical Methods Units 1 to 4 as assumed knowledge, so check the Methods formula sheet for anything you lean on from that course.

Frequently asked questions

Do you get a formula sheet in QCAA Specialist Mathematics Paper 1?

Yes. The 2025 syllabus says the QCAA provides the QCAA Specialist Mathematics formula book in both external papers. Paper 1 is technology-free: no notes, calculators, technology or other resources. In IA2 and IA3 the teacher must provide the same formula book.

Is it called a formula sheet or a formula book?

The 2025 syllabus and the cover both say formula book. The 2019 syllabus said formula sheet. Students still search for the formula sheet, and both names point at the QCAA document supplied in the exam.

Can I use a CAS calculator in Specialist Mathematics Paper 2?

No. The syllabus allows a handheld QCAA-approved graphics calculator with no CAS functionality, and/or a handheld QCAA-approved scientific calculator. Under the 2019 syllabus a graphics calculator was required in Paper 2. Under the 2025 syllabus you may use one.

What is not printed in the Specialist Mathematics formula book?

No normal distribution formula or z table (z appears in the confidence interval rows but is never defined), no derivatives of sec, cosec or cot, no integral of tan, no sum-to-product, half-angle or tan(A plus or minus B) identities, no Euler's formula, complex conjugate or roots formula, no differential equation methods and no arc length formula. Not printed does not mean not examinable, so check the syllabus for what you must be able to do.

Does the formula book give conditional probability as P(A|B) = P(A and B) / P(B)?

No. The book prints the product form, P(A and B) = P(A|B)P(B). If you want the division form, you rearrange it yourself.

Does the formula book define its symbols?

No. The eight pages are formula tables only, with no symbol legend, worked examples or instructions. For example, the cone surface area uses s without saying what it is, and the confidence interval rows use z without saying how to find it.

What changed in Specialist Mathematics Units 3 and 4 for 2025 that affects formulas?

The 2025 syllabus prints the mean and standard deviation of the exponential distribution (both 1/lambda), which the 2019 syllabus did not. It also changes Simpson's rule from technology-only to with and without technology, and prints the Simpson's rule formula. The current formula book prints both.

Is the Mathematical Methods formula book part of Specialist Mathematics?

The 2025 syllabus names Mathematical Methods Units 1 to 4 as assumed knowledge for the external papers, and IA2 and IA3 may assume Methods content. The Specialist book is its own document, so check anything you lean on from Methods against the Methods book.

Sources

Specialist Mathematics 2025 formula book, QCAA, June 2026, pp. 1-8. The formula tables reproduced on this page, with the page numbers as printed. The cover is dated June 2026 and prints no version number.
Specialist Mathematics 2025 v1.0 General senior syllabus, QCAA, January 2024, pp. 25-34, 37-46. Unit 3 and 4 subject matter with printed formulas, and the IA2, IA3 and external assessment conditions on who provides the formula book and what technology is allowed.
Specialist Mathematics 2019 v1.2 General Senior Syllabus, QCAA, August 2018, pp. 37, 41, 50. Superseded version, cited for the earlier name (QCAA formula sheet), the Paper 2 graphics calculator requirement and the Simpson's rule technology wording.
Specialist Mathematics subject report, 2025 cohort, QCAA, January 2026. Transition-period report: the cohort sat the 2019 course, and the report prints no formula book of its own.
Memo 044/26: Scientific and graphics calculator lists (updated 2026) now available, QCAA, August 2026, p. 1. Existence of the approved scientific and graphics calculator lists for external assessment.
AusGrader question bank, QCE Specialist Mathematics, AusGrader. QCAA external examination Paper 1 and Paper 2 for 2020 to 2025, with marking guides.

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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