§-Math Methods Q&A
WA · SCSA← Math Methods
Math Methods Q&A by dot point
A short Q&A bank for every WA 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 3
Recognise binomial conditions and calculate exact and cumulative binomial probabilities, using complements for at-least and at-most events
Sketch curves using intercepts, stationary points, their nature, points of inflection, asymptotes and end behaviour
Establish and use the derivative of the exponential function, including the chain rule for e raised to a function of x
Establish and use the derivative of the natural logarithm function, including the chain rule for the logarithm of a function of x
Establish and use the derivatives of sine, cosine and tangent functions, including the chain rule for trigonometric functions of a function of x
Define discrete random variables and construct and verify discrete probability distributions, including finding unknown probabilities
Construct discrete probability distributions, calculate expected value and variance, and apply the binomial distribution to repeated independent trials
Calculate and interpret the expected value (mean) of a discrete random variable and apply it to decision contexts such as fair games
Differentiate and integrate exponential and natural logarithm functions and apply them to growth, decay and other modelling contexts
Apply the product, quotient and chain rules to differentiate functions, and use the derivative in optimisation, rates of change and curve sketching
Find and apply the mean np and variance np(1-p) of a binomial distribution and describe the effect of n and p on its shape
Solve optimisation problems by modelling a quantity as a function of one variable and using the derivative to find and justify extreme values
Interpret the derivative as an instantaneous rate of change and use the chain rule to relate the rates of change of connected quantities
Use the Bernoulli distribution to model a single two-outcome trial and find its mean and variance
Establish and apply the product rule and the quotient rule to differentiate products and quotients of functions
Find and interpret the second derivative, determine concavity and points of inflection, and apply the second derivative test
Calculate and interpret the variance and standard deviation of a discrete random variable, including the effect of a linear transformation
Unit 4
Find antiderivatives of standard functions, include the constant of integration, and determine a particular antiderivative from an initial condition
Calculate the area enclosed between two curves by integrating the difference of the upper and lower functions over the correct interval
Use the distribution of the sample proportion to construct and interpret approximate confidence intervals for a population proportion
Use probability density functions to find probabilities, mean and variance for continuous random variables, and apply the normal distribution with standardisation
Find antiderivatives, evaluate definite integrals using the Fundamental Theorem of Calculus, and apply integration to areas, total change and kinematics
Apply integration to straight-line motion, recovering velocity from acceleration and displacement from velocity, and distinguishing displacement from distance travelled
Relate the margin of error to confidence level and sample size, and determine the sample size needed for a required margin of error
Use probability density functions to find probabilities as areas, determine an unknown constant, and compute the mean and variance by integration
Standardise a normal variable to a z-score and calculate normal probabilities, including finding a value from a given probability
Interpret the definite integral as a limit of Riemann sums and as the signed area between a curve and the x-axis
State and apply the Fundamental Theorem of Calculus to evaluate definite integrals and to differentiate integral functions
Describe the normal distribution, its symmetry and parameters, and apply the empirical 68-95-99.7 rule
Describe the sampling distribution of the sample proportion, including its mean, standard error and approximate normality for large samples
Use the definite integral of a rate of change to find the total or net change in a quantity over an interval