VIC · VCAAQ&A
Math MethodsQ&A by dot point
A short Q&A bank for every VIC 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
- Algebraic manipulation of polynomial, exponential and logarithmic expressions, including index laws, logarithm laws, factorisation, and the solution of linear, quadratic, polynomial, exponential and logarithmic equations15Q&A pairs
- Average rates of change between two points, the gradient of a chord, the gradient at a point as a limit, and the derivative of polynomial functions using the power rule8Q&A pairs
- Sketch cubic and quartic polynomials, identifying intercepts, end behaviour, turning points and points of inflection, and using factored form to read roots and multiplicities3Q&A pairs
- Linear, quadratic, cubic and quartic polynomial functions, basic exponential functions , logarithmic functions , and the standard transformations (dilation, reflection, translation)10Q&A pairs
- Define inverse and composite functions, identify when an inverse function exists (one-to-one), find inverse functions algebraically, and graph inverse and composite functions3Q&A pairs
- Sketch and analyse linear functions of the form , including finding gradient, - and -intercepts, equations of parallel and perpendicular lines, and solving linear equations and inequalities4Q&A pairs
- Apply the factor theorem and the remainder theorem to factorise polynomials and to solve polynomial equations5Q&A pairs
- Counting principles (multiplication principle, permutations and combinations), set notation, simple probability, conditional probability and the addition / multiplication rules6Q&A pairs
- Apply the rules of probability (addition, multiplication, conditional), the counting principles (permutations and combinations), and use these to find probabilities in compound experiments10Q&A pairs
- Sketch and analyse quadratic functions in standard, factored and turning-point form, including finding vertex, axis of symmetry, intercepts and using the discriminant to classify roots7Q&A pairs
- Simplify and operate on surd expressions and apply the laws of indices to rational and negative exponents5Q&A pairs
- Apply translations, dilations and reflections to the graph of a function , including the form and the effect of each parameter on the graph5Q&A pairs
Unit 2: Functions, calculus and probability
- Use differentiation to analyse the behaviour of functions, including locating and classifying stationary points, finding tangent and normal equations, and solving optimisation problems4Q&A pairs
- Define and apply the binomial distribution to model the number of successes in independent Bernoulli trials, including computing probabilities, expected value and variance4Q&A pairs
- Antidifferentiation as the reverse of differentiation, the antiderivative of polynomial functions via the power rule, the constant of integration, and the use of an initial condition to determine a specific antiderivative6Q&A pairs
- Sketch and analyse trigonometric functions and , identifying amplitude, period, phase and vertical translation, and solve trig equations over a specified interval4Q&A pairs
- Differentiate exponential (, ) and logarithmic (, ) functions, including composite functions via the chain rule3Q&A pairs
- Differentiate sine, cosine and tangent functions and their compositions via the chain rule5Q&A pairs
- Define a discrete random variable and its probability distribution, and compute expected value (mean) and variance for given distributions3Q&A pairs
- Sketch and analyse exponential functions of the form , identifying key features (intercepts, asymptote, domain, range) and applying transformations4Q&A pairs
- Composite functions and , the existence and form of inverse functions , the relationship between a function and its inverse (reflection in , domain and range swap), and the one-to-one restriction9Q&A pairs
- Define logarithms as the inverse of exponentials, apply the laws of logarithms, sketch logarithmic graphs and solve exponential equations using logs3Q&A pairs
- Bernoulli trials and sequences of Bernoulli trials, sample data analysis (mean, median, mode, range), simulation of random processes, and the relationship between theoretical probability and observed relative frequency12Q&A pairs
- Trigonometric functions , and , the unit circle, exact values at standard angles, transformations of trig graphs, and solving trigonometric equations6Q&A pairs
Unit 3
- Bernoulli trials, the binomial distribution , its probability function , mean , and variance5Q&A pairs
- Graphs of circular functions , and , their key features (period, amplitude, asymptotes), exact values at standard angles, and graphs of the form5Q&A pairs
- Average and instantaneous rates of change, the definition of the derivative as a limit , and the use of this definition to differentiate from first principles4Q&A pairs
- The product, quotient and chain rules of differentiation, and the derivatives of standard functions for , , , , and6Q&A pairs
- Discrete random variables, their probability distributions, the expected value (mean) , the variance and the standard deviation4Q&A pairs
- Graphs of exponential functions (in particular ) and logarithmic functions (in particular ), including their key features and the inverse relationship4Q&A pairs
- The factor theorem and the remainder theorem for polynomial functions, the method of equating coefficients, and the factorisation of cubic and quartic polynomials over the rationals5Q&A pairs
- Applications of differentiation to optimisation problems (maximising or minimising a quantity subject to constraints) and to rates of change in modelled real-world contexts5Q&A pairs
- Graphs of polynomial functions and key features including stationary points and points of inflection, intercepts, asymptotes, end behaviour, and the graphs of power functions for and the modulus function3Q&A pairs
- Random experiments, sample spaces, events and probabilities, including the addition rule, conditional probability , the multiplication rule, and the concept of independence3Q&A pairs
- Solution of polynomial equations of low degree with real coefficients, exponential and logarithmic equations using properties such as , and circular equations using exact unit-circle values10Q&A pairs
- Equations of tangents and normals to graphs of functions, stationary points and points of inflection, use of the first and second derivatives to classify stationary points, and curve sketching10Q&A pairs
- Transformations from to (dilation, reflection, translation), composite functions and the conditions for their existence, and inverse functions with the link to one-to-one functions6Q&A pairs
Unit 4
- Antidifferentiation as the reverse of differentiation, including the antiderivatives of for and , , , and , and the use of the constant of integration4Q&A pairs
- The use of definite integrals to find the area between a curve and the -axis, and the area between two curves on a closed interval, including handling sign changes of the integrand5Q&A pairs
- Applications of integration including the average value of a function on a closed interval, total change from a rate of change function, and kinematics (displacement and distance from velocity)15Q&A pairs
- Approximate confidence intervals for a population proportion based on the sample proportion , including the standard 90, 95 and 99 percent intervals and their interpretation7Q&A pairs
- Continuous random variables, their probability density functions, cumulative distribution functions, expected value (mean), variance and standard deviation, and computation of probabilities as definite integrals5Q&A pairs
- The definite integral, the fundamental theorem of calculus linking definite integration to antidifferentiation, and the properties of the definite integral over intervals5Q&A pairs
- Hybrid (piecewise-defined) functions, their continuity and differentiability conditions, inverse functions where defined, and the reflection of in the line11Q&A pairs
- The use of substitution to evaluate integrals of the form , recognising the reverse of the chain rule8Q&A pairs
- The normal distribution with mean and standard deviation , the standard normal , the use of the empirical 68/95/99.7 rule, and computation of normal probabilities and inverse probabilities using technology or standard tables10Q&A pairs
- The application of differentiation, including the chain rule, to related rates of change problems involving two or more time-dependent quantities7Q&A pairs
- The sample proportion as a random variable, the sampling distribution of for repeated samples of size from a population with true proportion , and the normal approximation for large6Q&A pairs