QCAA Methods Formula Sheet Explained (2025 Formula Book)
The official QCAA Methods formula sheet is called the Mathematical Methods 2025 formula book. Students also call the same supplied document a formula booklet. QCAA supplies it for both external assessment papers, and this independent interactive version explains how to recognise and use its formulas.
Independent study resource: Sylligence is not affiliated with or endorsed by QCAA. Check the official PDF before an assessment because QCAA can update supplied materials.
Open the official Mathematical Methods 2025 formula book.
Mensuration
Circle circumference and area
C = 2πr; A = πr²
The interactive page explains when to use this supplied formula family, its symbols and units, and a common mistake to avoid.
Plane-shape areas
A = bh; A = ½(a+b)h; A = ½bh
The interactive page explains when to use this supplied formula family, its symbols and units, and a common mistake to avoid.
Total surface area
cone: πrs+πr²; cylinder: 2πrh+2πr²; sphere: 4πr²
The interactive page explains when to use this supplied formula family, its symbols and units, and a common mistake to avoid.
Volumes
cone: ⅓πr²h; cylinder: πr²h; prism: Ah; pyramid: ⅓Ah; sphere: ⁴⁄₃πr³
The interactive page explains when to use this supplied formula family, its symbols and units, and a common mistake to avoid.
Equations of graphs
Quadratic functions
y = a(x-h)²+k; y = a(x-x₁)(x-x₂)
The interactive page explains when to use this supplied formula family, its symbols and units, and a common mistake to avoid.
Cubic functions
y = a(x-h)³+k; y = a(x-x₁)(x-x₂)(x-x₃)
The interactive page explains when to use this supplied formula family, its symbols and units, and a common mistake to avoid.
Circle equation
(x-h)²+(y-k)² = r²
The interactive page explains when to use this supplied formula family, its symbols and units, and a common mistake to avoid.
Square-root and reciprocal graphs
y = a√(x-h)+k; y = a/(x-h)+k
The interactive page explains when to use this supplied formula family, its symbols and units, and a common mistake to avoid.
Exponential and logarithmic graphs
y = r^(x-h)+k; y = logₐ(x-h)+k
The interactive page explains when to use this supplied formula family, its symbols and units, and a common mistake to avoid.
Sine and cosine graphs
y = a sin(b(x-h))+k; y = a cos(b(x-h))+k
The interactive page explains when to use this supplied formula family, its symbols and units, and a common mistake to avoid.
Logarithms
Logarithm definition
logₐx = b if and only if aᵇ = x
The interactive page explains when to use this supplied formula family, its symbols and units, and a common mistake to avoid.
Product, quotient and power laws
logₐ(xy)=logₐx+logₐy; logₐ(x/y)=logₐx-logₐy; logₐ(xⁿ)=nlogₐx
The interactive page explains when to use this supplied formula family, its symbols and units, and a common mistake to avoid.
Change of base and values
logₐx = logᵦx/logᵦa; logₐ1=0; logₐa=1
The interactive page explains when to use this supplied formula family, its symbols and units, and a common mistake to avoid.
Calculus
Derivative from first principles
f′(x) = lim h→0 [f(x+h)-f(x)]/h
The interactive page explains when to use this supplied formula family, its symbols and units, and a common mistake to avoid.
Definite integral as a sum
∫ₐᵇf(x)dx ≈ Σf(xᵢ)δx
The interactive page explains when to use this supplied formula family, its symbols and units, and a common mistake to avoid.
Fundamental theorem
∫ₐᵇf(x)dx = F(b)-F(a), where F′=f
The interactive page explains when to use this supplied formula family, its symbols and units, and a common mistake to avoid.
Sum and constant rules
derivatives and integrals distribute over sums; constants factor out
The interactive page explains when to use this supplied formula family, its symbols and units, and a common mistake to avoid.
Power rules
d(xⁿ)/dx = nxⁿ⁻¹; ∫xⁿdx = xⁿ⁺¹/(n+1)+c
The interactive page explains when to use this supplied formula family, its symbols and units, and a common mistake to avoid.
Exponential calculus
d(eˣ)/dx=eˣ; d(eᶠ)/dx=f′eᶠ; corresponding integrals
The interactive page explains when to use this supplied formula family, its symbols and units, and a common mistake to avoid.
Logarithmic calculus
d(ln x)/dx=1/x; d(ln f)/dx=f′/f; corresponding integrals
The interactive page explains when to use this supplied formula family, its symbols and units, and a common mistake to avoid.
Trigonometric calculus
derivatives and integrals of sin, cos and composite angles
The interactive page explains when to use this supplied formula family, its symbols and units, and a common mistake to avoid.
Chain, product and quotient rules
standard composite, product and quotient derivative rules
The interactive page explains when to use this supplied formula family, its symbols and units, and a common mistake to avoid.
Trapezoidal rule
∫ₐᵇf(x)dx ≈ w/2[y₀+2(y₁+…+yₙ₋₁)+yₙ], w=(b-a)/n
The interactive page explains when to use this supplied formula family, its symbols and units, and a common mistake to avoid.
Trigonometry
Cosine rule
c² = a²+b²-2ab cos C
The interactive page explains when to use this supplied formula family, its symbols and units, and a common mistake to avoid.
Sine rule
a/sin A = b/sin B = c/sin C
The interactive page explains when to use this supplied formula family, its symbols and units, and a common mistake to avoid.
Triangle area
A = ½bc sin A
The interactive page explains when to use this supplied formula family, its symbols and units, and a common mistake to avoid.
Pythagorean identity
sin²A+cos²A=1
The interactive page explains when to use this supplied formula family, its symbols and units, and a common mistake to avoid.
Probability and statistics
Binomial theorem
(x+y)ⁿ = Σ nCr xⁿ⁻ʳyʳ
The interactive page explains when to use this supplied formula family, its symbols and units, and a common mistake to avoid.
Binomial probability
P(X=x) = nCx pˣ(1-p)ⁿ⁻ˣ
The interactive page explains when to use this supplied formula family, its symbols and units, and a common mistake to avoid.
Discrete mean and spread
E(X)=Σxᵢpᵢ; Var(X)=Σpᵢ(xᵢ-μ)²; σ=√Var(X)
The interactive page explains when to use this supplied formula family, its symbols and units, and a common mistake to avoid.
Continuous mean and variance
E(X)=∫xf(x)dx; Var(X)=∫(x-μ)²f(x)dx
The interactive page explains when to use this supplied formula family, its symbols and units, and a common mistake to avoid.
Bernoulli and binomial moments
Bernoulli: p, p(1-p); binomial: np, np(1-p)
The interactive page explains when to use this supplied formula family, its symbols and units, and a common mistake to avoid.
Sample proportion
E(p̂)=p; σp̂=√[p(1-p)/n]
The interactive page explains when to use this supplied formula family, its symbols and units, and a common mistake to avoid.
Confidence interval and margin of error
p̂ ± z√[p̂(1-p̂)/n]; E=z√[p̂(1-p̂)/n]
The interactive page explains when to use this supplied formula family, its symbols and units, and a common mistake to avoid.
Probability laws
complement, addition, independent intersection and conditional probability laws
The interactive page explains when to use this supplied formula family, its symbols and units, and a common mistake to avoid.
How to use this Mathematical Methods formula reference
- Search by topic, formula name, symbol or use case.
- Expand the equation and check every symbol and unit.
- Attempt a question without the explanation open.
- Use the common-mistake prompt to check your working.
Read free Mathematical Methods notes and start practising free.
Questions about the Mathematical Methods formula book or booklet
Is the QCAA Methods formula book supplied in the external exam?
Yes. Under the current Mathematical Methods assessment conditions, the QCAA formula book is supplied for both Paper 1 and Paper 2. Confirm conditions for your cohort in current official documents.
Are the QCAA Methods formula book, formula sheet and formula booklet the same thing?
Students use all three names for the supplied document. QCAA's official title is the Mathematical Methods 2025 formula book; this Sylligence page is an independent explanation of it.
Do I only need to learn the formulas in the book?
No. Questions still test recognition, rearrangement, exact working, assumptions, interpretation and mathematical reasoning.
Source and attribution
Modified from Mathematical Methods 2025 formula book, © State of Queensland (QCAA) 2025, licensed under CC BY 4.0. See the QCAA copyright notice. Sylligence added the search, grouping, explanations, symbol definitions and mistake checks.