§-Section

Unit 3

6 dot points, in syllabus order. Each dot point has a focused answer, with exam-style questions and worked answers where available.

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.

How to move between position, velocity and acceleration using differentiation and integration, with sign and direction interpretation for straight-line motion in TCE Mathematics Methods.

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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.

A discrete random variable has a probability distribution from which you compute expected value and variance; the binomial distribution models the count of successes in a fixed number of independent trials.

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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

Index and log laws, the natural base e, derivatives of e^x and ln x, and exponential growth and decay modelling for TCE Mathematics Methods Unit 3.

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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

Product, quotient and chain rules, second-derivative curve sketching, optimisation and rates of change for TCE Mathematics Methods Unit 3, with worked TASC-style examples.

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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.

How the sign of the second derivative gives concavity, how to find and confirm points of inflection, and how the second derivative test classifies stationary points for TCE Mathematics Methods Unit 3.

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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.

Derivatives of sin x, cos x and tan x, why radians are required, and how to combine them with the chain, product and quotient rules for TCE Mathematics Methods Unit 3.

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