WA · SCSAQ&A
Math MethodsQ&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 events0Q&A pairs
- Sketch curves using intercepts, stationary points, their nature, points of inflection, asymptotes and end behaviour0Q&A pairs
- Establish and use the derivative of the exponential function, including the chain rule for e raised to a function of x0Q&A pairs
- Establish and use the derivative of the natural logarithm function, including the chain rule for the logarithm of a function of x0Q&A pairs
- Establish and use the derivatives of sine, cosine and tangent functions, including the chain rule for trigonometric functions of a function of x0Q&A pairs
- Define discrete random variables and construct and verify discrete probability distributions, including finding unknown probabilities0Q&A pairs
- Construct discrete probability distributions, calculate expected value and variance, and apply the binomial distribution to repeated independent trials0Q&A pairs
- Calculate and interpret the expected value (mean) of a discrete random variable and apply it to decision contexts such as fair games0Q&A pairs
- Differentiate and integrate exponential and natural logarithm functions and apply them to growth, decay and other modelling contexts0Q&A pairs
- Apply the product, quotient and chain rules to differentiate functions, and use the derivative in optimisation, rates of change and curve sketching4Q&A pairs
- 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 shape0Q&A pairs
- Solve optimisation problems by modelling a quantity as a function of one variable and using the derivative to find and justify extreme values0Q&A pairs
- Interpret the derivative as an instantaneous rate of change and use the chain rule to relate the rates of change of connected quantities0Q&A pairs
- Use the Bernoulli distribution to model a single two-outcome trial and find its mean and variance0Q&A pairs
- Establish and apply the product rule and the quotient rule to differentiate products and quotients of functions2Q&A pairs
- Find and interpret the second derivative, determine concavity and points of inflection, and apply the second derivative test0Q&A pairs
- Calculate and interpret the variance and standard deviation of a discrete random variable, including the effect of a linear transformation0Q&A pairs
Unit 4
- Find antiderivatives of standard functions, include the constant of integration, and determine a particular antiderivative from an initial condition0Q&A pairs
- Calculate the area enclosed between two curves by integrating the difference of the upper and lower functions over the correct interval1Q&A pairs
- Use the distribution of the sample proportion to construct and interpret approximate confidence intervals for a population proportion0Q&A pairs
- Use probability density functions to find probabilities, mean and variance for continuous random variables, and apply the normal distribution with standardisation1Q&A pairs
- Find antiderivatives, evaluate definite integrals using the Fundamental Theorem of Calculus, and apply integration to areas, total change and kinematics0Q&A pairs
- Apply integration to straight-line motion, recovering velocity from acceleration and displacement from velocity, and distinguishing displacement from distance travelled1Q&A pairs
- Relate the margin of error to confidence level and sample size, and determine the sample size needed for a required margin of error0Q&A pairs
- Use probability density functions to find probabilities as areas, determine an unknown constant, and compute the mean and variance by integration0Q&A pairs
- Standardise a normal variable to a z-score and calculate normal probabilities, including finding a value from a given probability2Q&A pairs
- Interpret the definite integral as a limit of Riemann sums and as the signed area between a curve and the x-axis0Q&A pairs
- State and apply the Fundamental Theorem of Calculus to evaluate definite integrals and to differentiate integral functions1Q&A pairs
- Describe the normal distribution, its symmetry and parameters, and apply the empirical 68-95-99.7 rule0Q&A pairs
- Describe the sampling distribution of the sample proportion, including its mean, standard error and approximate normality for large samples0Q&A pairs
- Use the definite integral of a rate of change to find the total or net change in a quantity over an interval0Q&A pairs