§-Math Methods syllabus
TAS · TASC← Math Methods
Math Methods syllabus, dot point by dot point
Every dot point in the TAS Math Methods syllabus, with a focused answer for each. Click any dot point for a worked explainer, past exam questions and links to related points.
Unit 3
Module overview →How do we differentiate sine, cosine and tangent, and combine them with the chain, product and quotient rules?
Establish and use the derivatives of sin x, cos x and tan x, including with the chain, product and quotient rules.
How do we describe a discrete random variable and when does the binomial distribution apply?
Construct probability distributions for discrete random variables, find their mean and variance, and apply the binomial distribution.
How do exponential and logarithmic functions behave, and how do we differentiate and apply them?
Exponential and logarithmic functions: graphs, laws, the number e, derivatives and growth and decay models
How do we differentiate products, quotients and composites, and use the result to optimise and sketch?
Further differentiation and applications: product, quotient and chain rules, curve sketching, optimisation and rates of change
How do calculus operations connect position, velocity and acceleration in straight-line motion?
Relate position, velocity and acceleration through differentiation and integration for rectilinear motion.
What does the second derivative tell us about the shape of a graph?
Use the second derivative to determine concavity, locate points of inflection, and apply the second derivative test.
Unit 4
Module overview →How do we reverse the derivatives of exponential and trigonometric functions to find their antiderivatives?
Find antiderivatives of exponential and trigonometric functions and apply them in definite integrals.
How do we find the area enclosed between two curves rather than under a single curve?
Calculate the area enclosed between two curves using definite integration.
How do we describe continuous random variables and work with the normal distribution?
Use probability density functions and the normal distribution, including standardisation to z-scores, to find probabilities.
What is integration, how is it the reverse of differentiation, and how do we find areas?
Find antiderivatives and definite integrals and use them to calculate areas and solve rate problems.
How do we estimate a population proportion from a sample and express the uncertainty?
Use the distribution of sample proportions to construct and interpret confidence intervals for a population proportion.
How does a sample proportion vary from sample to sample, and what distribution does it follow?
Understand random sampling and describe the distribution of the sample proportion, including its mean and standard deviation.
How do we estimate a definite integral when we cannot find an antiderivative?
Use the trapezoidal rule to approximate definite integrals and areas under curves.