Curriculum

VCE Maths Methods

11, 12

Community-maintained — may not exactly match your study design

Unit 1 — Functions, graphs, algebra, calculus and probability

Functions and graphs

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Factor Theorem $(x - a) is a factor of P (x) ⟺ P (a) = 0$ Practise
Remainder Theorem $P (x) = Q (x) (x - a) + P (a)$ Practise
Leading Term Determines End Behaviour $P (x) \sim a_{n} x^{n} as x \to \pm \infty$ Practise
Horizontal Translation $y = f (x - h)$ Practise
Vertical Translation $y = f (x) + k$ Practise

Not yet covered

Identifying and sketching polynomial functions up to degree 4 (qualitative, not formula-driven)
Domain and interval notation (no dedicated formula)
Quadratic function turning point via completing the square (covered by vertex form in algebra)

Algebra

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Quadratic Formula $x = \frac{- b \pm b ^{2} - 4 a c}{2 a}$ Practise
Discriminant $Δ = b^{2} - 4 a c$ Practise
Vertex Form $y = a (x - h)^{2} + k$ Practise
Axis of Symmetry $x = - \frac{b}{2 a}$ Practise
Sum of Roots $α + β = - \frac{b}{a}$ Practise
Product of Roots $α β = \frac{c}{a}$ Practise
Product of Powers $a^{m} \cdot a^{n} = a^{m + n}$ Practise
Quotient of Powers $\frac{a ^{m}}{a ^{n}} = a^{m - n}$ Practise
Power of a Power $(a^{m})^{n} = a^{mn}$ Practise
Negative Exponent $a^{- n} = \frac{1}{a ^{n}}$ Practise
Zero Exponent $a^{0} = 1 (a \neq = 0)$ Practise
Change of Base $lo g_{a} b = \frac{l o g _{c} b}{l o g _{c} a}$ Practise
Log Product Rule $lo g_{a} (x y) = lo g_{a} x + lo g_{a} y$ Practise
Log Quotient Rule $lo g_{a} (\frac{x}{y}) = lo g_{a} x - lo g_{a} y$ Practise
Log Power Rule $lo g_{a} (x^{n}) = n \cdot lo g_{a} x$ Practise
Log of Base $lo g_{a} a = 1$ Practise
Log of One $lo g_{a} 1 = 0$ Practise

Not yet covered

Factorisation of cubic and quartic polynomials (no specific formula — covered by factor theorem)

Calculus — introduction

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Power Rule $\frac{d}{d x} (x^{n}) = n x^{n - 1}$ Practise
Constant Multiple Rule $\frac{d}{d x} [c \cdot f (x)] = c \cdot f^{'} (x)$ Practise
Sum/Difference Rule $\frac{d}{d x} [f (x) \pm g (x)] = f^{'} (x) \pm g^{'} (x)$ Practise

Not yet covered

First principles / limit definition of the derivative (conceptual, no formula in corpus)
Rate of change interpretation (qualitative, no specific formula)

Probability and statistics

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Factorial Definition $n! = n \times (n - 1)! (n \geq 1, 0! = 1)$ Practise
Permutation Formula $^{n} P_{r} = \frac{n !}{( n - r )!}$ Practise
Combination Formula $^{n} C_{r} = (r n) = \frac{n !}{r ! ( n - r )!}$ Practise

Not yet covered

Addition and multiplication rules for probability (no dedicated formula)
Representation of sample spaces and Venn/Karnaugh diagrams (no formula in corpus)
Conditional probability definition P(A|B) = P(A n B) / P(B)
Independence condition P(A n B) = P(A)P(B)

Unit 2 — Functions, relations, calculus and probability

Functions and relations

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Unit Circle: sin, cos, tan $P (θ) = (cos θ, sin θ)$ Practise
sin^2 x + cos^2 x = 1 $sin^{2} x + cos^{2} x = 1$ Practise
sin(-x) = -sin(x) $sin (- x) = - sin x$ Practise
cos(-x) = cos(x) $cos (- x) = cos x$ Practise
Natural Exponential $e = lim_{n \to \infty} (1 + \frac{1}{n})^{n}$ Practise
Inverse Relationship $lo g_{a} (a^{x}) = x and a^{l o g_{a} x} = x$ Practise
Exponential Growth/Decay $y = A \cdot b^{t}$ Practise

Not yet covered

Exact values for sine/cosine/tangent at standard angles (covered by unit-circle, but no table in formula form)
Graphs of circular functions — amplitude, period, phase shift (no dedicated formula — covered by transformations)
Composite functions and inverse functions (no specific formula in corpus)
Logarithmic function graphs and properties

Algebra — sequences, series, and binomial

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nth term of arithmetic sequence $T_{n} = a + (n - 1) d$ Practise
Sum of arithmetic series $S_{n} = \frac{n}{2} (a + l)$ Practise
nth term of geometric sequence $T_{n} = a \cdot r^{n - 1}$ Practise
Sum of geometric series $S_{n} = a (\frac{1 - r ^{n}}{1 - r}) (r \neq = 1)$ Practise
Sum to infinity $S_{\infty} = \frac{a}{1 - r} (∣ r ∣ < 1)$ Practise
Sigma Notation for Arithmetic Series $\sum_{i = 1}^{n} i = \frac{n ( n + 1 )}{2}$ Practise
Pascal's Rule $(r n + 1) = (r n) + (r - 1 n)$ Practise
Binomial Theorem $(a + b)^{n} = \sum_{r = 0}^{n} (r n) a^{n - r} b^{r}$ Practise
Middle Term of Binomial $T_{\frac{n}{2} + 1} = (n /2 n) a^{n /2} b^{n /2} (n even)$ Practise

Calculus — derivatives and applications

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Power Rule $\frac{d}{d x} (x^{n}) = n x^{n - 1}$ Practise
Constant Multiple Rule $\frac{d}{d x} [c \cdot f (x)] = c \cdot f^{'} (x)$ Practise
Sum/Difference Rule $\frac{d}{d x} [f (x) \pm g (x)] = f^{'} (x) \pm g^{'} (x)$ Practise
Product Rule $\frac{d}{d x} [f (x) g (x)] = f^{'} (x) g (x) + f (x) g^{'} (x)$ Practise
Quotient Rule $\frac{d}{d x} [\frac{f ( x )}{g ( x )}] = \frac{f ^{'} ( x ) g ( x ) - f ( x ) g ^{'} ( x )}{[ g ( x ) ] ^{2}}$ Practise
Chain Rule $\frac{d}{d x} [f (g (x))] = f^{'} (g (x)) \cdot g^{'} (x)$ Practise

Not yet covered

Derivative of exponential function e^x (corpus has e^x derivative only in exponentials-logs, not in differentiation category)
Stationary points — finding and classifying (no specific formula — application of f'(x) = 0)
Tangent and normal line equations at a point (covered by point-gradient form of a line)
Sketching gradient functions (conceptual, no formula)

Probability — discrete random variables

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Expected Value $E (X) = \sum_{x} x \cdot P (X = x)$ Practise
Variance $Var (X) = E (X^{2}) - [E (X)]^{2}$ Practise
Standard Deviation $σ = Var (X)$ Practise
E(aX + b) = a E(X) + b $E (a X + b) = a E (X) + b$ Practise
Var(aX + b) = a^2 Var(X) $Var (a X + b) = a^{2} Var (X)$ Practise

Not yet covered

Conditional probability P(A|B) = P(A n B) / P(B) (repeated from Unit 1 — no formula in corpus)
Discrete probability distribution properties and expected value of a function g(X) (no specific formula in corpus)

Unit 3 — Further functions, calculus and probability

Functions and graphs

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sin(A + B) = sin A cos B + cos A sin B $sin (A + B) = sin A cos B + cos A sin B$ Practise
cos(A + B) = cos A cos B - sin A sin B $cos (A + B) = cos A cos B - sin A sin B$ Practise
tan x = sin x / cos x $tan x = \frac{s i n x}{c o s x}$ Practise
sin(2x) = 2 sin x cos x $sin (2 x) = 2 sin x cos x$ Practise
cos(2x) = cos^2(x) - sin^2(x) $cos (2 x) = cos^{2} x - sin^{2} x$ Practise
1 + tan^2(x) = sec^2(x) $1 + tan^{2} x = sec^{2} x$ Practise
Derivative of e^x $\frac{d}{d x} e^{x} = e^{x}$ Practise
Derivative of ln(x) $\frac{d}{d x} ln x = \frac{1}{x} (x > 0)$ Practise

Not yet covered

Exact values for sine/cosine/tangent at standard angles (no table in formula form)
Reciprocal circular functions sec, cosec, cot (no formulas in corpus)
Inverse circular functions arcsine, arccosine, arctan (no formulas in corpus)

Calculus — differentiation rules and applications

Community-maintained — may not exactly match your study design

Chain Rule $\frac{d}{d x} [f (g (x))] = f^{'} (g (x)) \cdot g^{'} (x)$ Practise
Product Rule $\frac{d}{d x} [f (x) g (x)] = f^{'} (x) g (x) + f (x) g^{'} (x)$ Practise
Quotient Rule $\frac{d}{d x} [\frac{f ( x )}{g ( x )}] = \frac{f ^{'} ( x ) g ( x ) - f ( x ) g ^{'} ( x )}{[ g ( x ) ] ^{2}}$ Practise
d/dx(sin x) = cos x $\frac{d}{d x} (sin x) = cos x$ Practise
d/dx(cos x) = -sin x $\frac{d}{d x} (cos x) = - sin x$ Practise
d/dx(tan x) = sec^2(x) $\frac{d}{d x} (tan x) = sec^{2} x$ Practise
d/dx(e^x) = e^x $\frac{d}{d x} (e^{x}) = e^{x}$ Practise

Not yet covered

Differentiation of logarithmic functions (corpus has log-derivative in exponentials-logs, not in differentiation formulas)
Rates of change and applications (no specific formulas — conceptual)
Concavity and points of inflection (no specific formula)

Probability — binomial distribution

Community-maintained — may not exactly match your study design

Binomial Probability Mass Function $P (X = k) = (k n) p^{k} (1 - p)^{n - k}$ Practise
Binomial Mean $E (X) = n p$ Practise
Binomial Variance $Var (X) = n p (1 - p)$ Practise
Z-Score $z = \frac{x - μ}{σ}$ Practise

Not yet covered

Binomial coefficient nCr notation for binomial probability (covered by combination formula in Unit 1)

Unit 4 — Calculus, probability and statistical inference

Calculus — integration and applications

Community-maintained — may not exactly match your study design

Power Rule for Integration $\int x^{n} d x = \frac{x ^{n + 1}}{n + 1} + C (n \neq = - 1)$ Practise
Constant Multiple Rule for Integration $\int k f (x) d x = k \int f (x) d x$ Practise
Sum Rule for Integration $\int [f (x) + g (x)] d x = \int f (x) d x + \int g (x) d x$ Practise
Integral of e^x $\int e^{x} d x = e^{x} + C$ Practise
Integral of sin x $\int sin x d x = - cos x + C$ Practise
Integral of cos x $\int cos x d x = sin x + C$ Practise
Integral of 1/x $\int \frac{1}{x} d x = ln ∣ x ∣ + C (x \neq = 0)$ Practise
Integral of sec^2 x $\int sec^{2} x d x = tan x + C$ Practise
Integration by Substitution $\int_{a}^{b} f (g (x)) g^{'} (x) d x = \int_{g (a)}^{g (b)} f (u) d u$ Practise
Definite Integral Linear Property $\int_{a}^{b} [f (x) + g (x)] d x = \int_{a}^{b} f (x) d x + \int_{a}^{b} g (x) d x$ Practise
General Solution of dy/dx = f(x) $y = \int f (x) d x + C$ Practise
Proportional Rate of Change $\frac{d N}{d t} = k N$ Practise
Exponential Growth and Decay $y = A e^{k x}$ Practise

Not yet covered

Area between curves (no specific formula — application of definite integral linearity)
Integration by parts (not a separate formula in corpus — deferred)
Volume of revolution around x-axis (V = pi int [f(x)]^2 dx — no formula in corpus)

Probability — normal distribution

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Normal Distribution PDF $f (x) = \frac{1}{σ 2 π} e^{- \frac{( x - μ ) ^{2}}{2 σ ^{2}}}$ Practise
Z-Score $z = \frac{x - μ}{σ}$ Practise
Expected Value $E (X) = \sum_{x} x \cdot P (X = x)$ Practise
Variance $Var (X) = E (X^{2}) - [E (X)]^{2}$ Practise
Standard Deviation $σ = Var (X)$ Practise

Not yet covered

Normal distribution probability table lookup (no formula — reference table)
Central Limit Theorem statement (conceptual, not formula-driven)
Normal approximation to the binomial distribution (no specific formula in corpus)

Statistical inference — confidence intervals

Community-maintained — may not exactly match your study design

Margin of Error $ME = z^{*} \frac{σ}{n}$ Practise
CI for Proportion $\overset{p}{^} \pm z^{*} \frac{p ^ ( 1 - p ^ )}{n}$ Practise
Sample Size Formula $n = (\frac{z ^{*} σ}{ME})^{2}$ Practise
CI for Mean (Known sigma) $\overset{x}{ˉ} \pm z^{*} \frac{σ}{n}$ Practise

Not yet covered

t-distribution confidence interval for unknown sigma (corpus has mean-unknown-sigma but Methods uses known-sigma at this level)
Interpretation of confidence intervals (qualitative, not formula-driven)