QLD · QCAASyllabus
Math Methods syllabus, dot point by dot point
Every dot point in the QLD Math Methods syllabus, with a focused answer for each one. Click any dot point for a worked explainer, past exam questions, and links to related dot points. Generated by Claude Opus and reviewed by Better Tuition Academy tutors.
Unit 1: Algebra, statistics and functions
Module overview →- How are arithmetic and geometric sequences analysed?Define arithmetic and geometric sequences, find the $n$th term and the sum of the first $n$ terms, and apply to real-world contexts5 min answer →
- What counting and probability principles does QCE Math Methods Unit 1 introduce?Counting techniques (multiplication principle, permutations and combinations), simple probability, conditional probability and the addition and multiplication rules8 min answer →
- How are financial calculations done?Apply simple interest, compound interest and depreciation models to financial calculations, including future value, present value and effective annual rate5 min answer →
- What functions and graphs does QCE Math Methods Unit 1 introduce, and how are they analysed?Functions and graphs introduced in Year 11, including linear, quadratic, cubic, polynomial, exponential and logarithmic functions; their key features, intercepts and transformations8 min answer →
- How are linear and quadratic functions analysed?Sketch and analyse linear and quadratic functions, finding gradient, intercepts, vertex and discriminant, and solving linear and quadratic equations and inequalities5 min answer →
- What additional algebraic skills does QCE Math Methods Unit 1 introduce?Index and logarithm laws, factorisation techniques, solving polynomial equations, and the relationship between exponential and logarithmic functions8 min answer →
- How are polynomial functions analysed?Sketch and analyse polynomial functions of degree 3 and 4, using factored form to read roots and multiplicities, and applying the factor and remainder theorems5 min answer →
- How are probability and counting applied?Apply the rules of probability (addition, multiplication, conditional), permutations and combinations to calculate probabilities of compound events5 min answer →
- How are arithmetic and geometric sequences and series defined and computed in QCE Math Methods Unit 1?Arithmetic and geometric sequences and series, including the general term formulas, sum formulas, and applications to growth and decay problems8 min answer →
- How are simultaneous equations solved?Solve systems of simultaneous linear equations in two and three variables, including by substitution, elimination, and matrix methods, and interpret the results graphically4 min answer →
- How are surds and exponents simplified?Simplify expressions involving surds and apply the laws of indices to rational and negative exponents4 min answer →
- How are transformations applied to function graphs?Apply translations, dilations and reflections to the graph of a function, including the form $y = a f(b(x - h)) + k$ and the effect of each parameter4 min answer →
Unit 2: Calculus
Module overview →- Topic 3: Introduction to differential calculusDefine the derivative of a function as a limit and use first principles to find the derivative of a polynomial function5 min answer →
- How are exponential, logarithmic and trigonometric functions extended in QCE Math Methods Unit 2?Exponential, logarithmic and trigonometric functions (including their graphs and transformations), and applications to growth and decay and periodic phenomena8 min answer →
- Topic 1: Exponential functionsGraph and analyse exponential functions of the form $y = a \cdot b^x + c$, identifying key features (intercepts, asymptote, domain, range) and applying transformations5 min answer →
- Topic 1: Exponential functionsModel exponential growth and decay using $y = A \cdot r^t$ or $y = A e^{kt}$, including problems involving population growth, radioactive decay, depreciation and continuous compound interest6 min answer →
- Topic 1: Exponential functionsRecall and apply the laws of indices to simplify expressions and solve equations involving rational and negative exponents5 min answer →
- How is differential calculus introduced in QCE Math Methods Unit 2?Introduction to differential calculus, including the gradient at a point, the derivative as a function, and the power rule for derivatives of polynomial functions8 min answer →
- Topic 1: Exponential functionsDefine logarithms as the inverse of exponentials, apply the laws of logarithms, and solve exponential equations using logarithms6 min answer →
- Topic 3: Introduction to differential calculusApply the power rule, the sum rule, and the constant-multiple rule to differentiate polynomial functions, and use the derivative to find tangent and normal line equations5 min answer →
- What discrete probability distributions does QCE Math Methods Unit 2 introduce?Discrete probability distributions, including the uniform discrete distribution and an introduction to the Bernoulli distribution, with calculations of expected value and variance8 min answer →
- Topic 2: Trigonometric functionsDefine radian measure of angle and relate to arc length; evaluate exact values of sine, cosine and tangent of common angles using the unit circle5 min answer →
- Topic 3: Introduction to differential calculusUse the derivative to find stationary points of a polynomial function and classify them, and apply differentiation to simple optimisation problems6 min answer →
- Topic 2: Trigonometric functionsSketch and analyse graphs of $y = a \sin(b(x - h)) + k$ and $y = a \cos(b(x - h)) + k$, identifying amplitude, period, phase shift and vertical translation5 min answer →
- Topic 2: Trigonometric functionsState and apply the Pythagorean identity $\sin^2 \theta + \cos^2 \theta = 1$, and use it together with related identities to simplify expressions and solve equations5 min answer →
Unit 3: Further calculus and statistics
Module overview →- Topic 2: IntegralsFind antiderivatives of standard functions including polynomial, exponential and trigonometric forms, evaluate definite integrals using the Fundamental Theorem of Calculus, and recognise the definite integral as the limit of a Riemann sum9 min answer →
- Topic 2: IntegralsApply the definite integral to find the area under a curve, the area between two curves, the average value of a function, and to solve kinematics problems involving displacement, velocity and acceleration9 min answer →
- Topic 1: Further differentiation and applicationsDifferentiate exponential and logarithmic functions, including compositions of the form $e^{f(x)}$ and $\ln(f(x))$, and apply the derivatives to model and analyse rates of change8 min answer →
- Topic 1: Further differentiation and applicationsDifferentiate trigonometric functions, including compositions of the form $\sin(f(x))$, $\cos(f(x))$ and $\tan(f(x))$, working in radians7 min answer →
- Topic 3: Discrete random variablesDefine a discrete random variable and its probability distribution, calculate the expected value $E(X)$ and the variance $\mathrm{Var}(X)$ and standard deviation, and recognise the Bernoulli distribution as the single-trial case8 min answer →
- Topic 1: Further differentiation and applicationsUse the first and second derivative to analyse the behaviour of a function (intervals of increase and decrease, stationary points and their nature, concavity and inflection), and apply the derivative to solve optimisation and rates of change problems in context9 min answer →
- Topic 1: Further differentiation and applicationsApply the product, quotient and chain rules, including in combination, to differentiate functions built from polynomial, exponential, logarithmic and trigonometric components8 min answer →
- Topic 3: Discrete random variablesRecognise the binomial distribution $X \sim \mathrm{Bin}(n, p)$ as the count of successes in $n$ independent Bernoulli trials, apply the binomial probability formula and use CAS, and use the formulas $E(X) = np$ and $\mathrm{Var}(X) = np(1 - p)$9 min answer →
Unit 4: Further calculus and statistical inference
Module overview →- Topic 2: Trigonometric functions and integration applicationsApply the definite integral to compute the area between curves (including curves that change relative order), the average value of a function, and kinematics quantities (displacement, distance, position) from velocity and acceleration9 min answer →
- Topic 3: Continuous random variables, the normal distribution, and statistical inferenceDefine a continuous random variable, its probability density function (pdf), cumulative distribution function (cdf), and compute probabilities, expected value (mean), variance and standard deviation as definite integrals9 min answer →
- Topic 1: Further differentiation and applicationsApply the product, quotient and chain rules to differentiate composite functions involving exponential, logarithmic, polynomial and trigonometric pieces, including logarithmic differentiation and the differentiation of inverse functions9 min answer →
- Topic 1: Further differentiation and applicationsApply implicit differentiation to find $\frac{dy}{dx}$ from equations relating $x$ and $y$ that cannot be expressed in the form $y = f(x)$, and apply differentiation to related rates problems9 min answer →
- Topic 2: Trigonometric functions and integration applicationsIntegrate trigonometric functions including $\sin(kx)$, $\cos(kx)$ and $\sec^2(kx)$, and apply the linear reverse-chain rule for integrals of the form $f(ax+b)$8 min answer →
- Topic 3: Continuous random variables, the normal distribution, and statistical inferenceApply the normal distribution $N(\mu, \sigma^2)$ and the standardisation $Z = (X - \mu)/\sigma$ to compute normal probabilities and inverse probabilities, including the empirical 68-95-99.7 rule9 min answer →
- Topic 3: Continuous random variables, the normal distribution, and statistical inferenceApply the sampling distribution of the sample proportion $\hat{p}$ (mean $p$, standard deviation $\sqrt{p(1-p)/n}$) and construct approximate confidence intervals $\hat{p} \pm z^* \sqrt{\hat{p}(1-\hat{p})/n}$ for a population proportion9 min answer →