QLD · QCAAQ&A
Math MethodsQ&A by dot point
A short Q&A bank for every QLD Math Methods syllabus dot point. Each question and answer is drawn directly from our worked dot-point page, so you can scan key concepts before opening the long-form answer.
Unit 1: Algebra, statistics and functions
- Define arithmetic and geometric sequences, find the th term and the sum of the first terms, and apply to real-world contexts1Q&A pairs
- Counting techniques (multiplication principle, permutations and combinations), simple probability, conditional probability and the addition and multiplication rules0Q&A pairs
- Apply simple interest, compound interest and depreciation models to financial calculations, including future value, present value and effective annual rate0Q&A pairs
- Functions and graphs introduced in Year 11, including linear, quadratic, cubic, polynomial, exponential and logarithmic functions; their key features, intercepts and transformations6Q&A pairs
- Sketch and analyse linear and quadratic functions, finding gradient, intercepts, vertex and discriminant, and solving linear and quadratic equations and inequalities11Q&A pairs
- Index and logarithm laws, factorisation techniques, solving polynomial equations, and the relationship between exponential and logarithmic functions11Q&A pairs
- Sketch and analyse polynomial functions of degree 3 and 4, using factored form to read roots and multiplicities, and applying the factor and remainder theorems0Q&A pairs
- Apply the rules of probability (addition, multiplication, conditional), permutations and combinations to calculate probabilities of compound events6Q&A pairs
- Arithmetic and geometric sequences and series, including the general term formulas, sum formulas, and applications to growth and decay problems5Q&A pairs
- Solve systems of simultaneous linear equations in two and three variables, including by substitution, elimination, and matrix methods, and interpret the results graphically0Q&A pairs
- Simplify expressions involving surds and apply the laws of indices to rational and negative exponents1Q&A pairs
- Apply translations, dilations and reflections to the graph of a function, including the form and the effect of each parameter3Q&A pairs
Unit 2: Calculus
- Define the derivative of a function as a limit and use first principles to find the derivative of a polynomial function0Q&A pairs
- Exponential, logarithmic and trigonometric functions (including their graphs and transformations), and applications to growth and decay and periodic phenomena4Q&A pairs
- Graph and analyse exponential functions of the form , identifying key features (intercepts, asymptote, domain, range) and applying transformations3Q&A pairs
- Model exponential growth and decay using or , including problems involving population growth, radioactive decay, depreciation and continuous compound interest2Q&A pairs
- Recall and apply the laws of indices to simplify expressions and solve equations involving rational and negative exponents6Q&A pairs
- Introduction to differential calculus, including the gradient at a point, the derivative as a function, and the power rule for derivatives of polynomial functions1Q&A pairs
- Define logarithms as the inverse of exponentials, apply the laws of logarithms, and solve exponential equations using logarithms0Q&A pairs
- Apply 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 equations8Q&A pairs
- Discrete probability distributions, including the uniform discrete distribution and an introduction to the Bernoulli distribution, with calculations of expected value and variance0Q&A pairs
- Define radian measure of angle and relate to arc length; evaluate exact values of sine, cosine and tangent of common angles using the unit circle0Q&A pairs
- Use the derivative to find stationary points of a polynomial function and classify them, and apply differentiation to simple optimisation problems0Q&A pairs
- Sketch and analyse graphs of and , identifying amplitude, period, phase shift and vertical translation0Q&A pairs
- State and apply the Pythagorean identity , and use it together with related identities to simplify expressions and solve equations3Q&A pairs
Unit 3: Further calculus and statistics
- Find 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 sum5Q&A pairs
- Apply 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 acceleration3Q&A pairs
- Differentiate exponential and logarithmic functions, including compositions of the form and , and apply the derivatives to model and analyse rates of change4Q&A pairs
- Differentiate trigonometric functions, including compositions of the form , and , working in radians0Q&A pairs
- Define a discrete random variable and its probability distribution, calculate the expected value and the variance and standard deviation, and recognise the Bernoulli distribution as the single-trial case3Q&A pairs
- Use 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 context4Q&A pairs
- Apply the product, quotient and chain rules, including in combination, to differentiate functions built from polynomial, exponential, logarithmic and trigonometric components3Q&A pairs
- Recognise the binomial distribution as the count of successes in independent Bernoulli trials, apply the binomial probability formula and use CAS, and use the formulas and2Q&A pairs
Unit 4: Further calculus and statistical inference
- Apply 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 acceleration4Q&A pairs
- Define 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 integrals2Q&A pairs
- Apply 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 functions4Q&A pairs
- Apply implicit differentiation to find from equations relating and that cannot be expressed in the form , and apply differentiation to related rates problems9Q&A pairs
- Integrate trigonometric functions including , and , and apply the linear reverse-chain rule for integrals of the form2Q&A pairs
- Apply the normal distribution and the standardisation to compute normal probabilities and inverse probabilities, including the empirical 68-95-99.7 rule7Q&A pairs
- Apply the sampling distribution of the sample proportion (mean , standard deviation ) and construct approximate confidence intervals for a population proportion5Q&A pairs