Unit 4

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

How do we solve equations that relate a function to its own rate of change?

Solve separable and linear first order differential equations and apply them to models.

Solving separable and first order linear differential equations using the integrating factor, with applications to growth and mixing, worked examples and pitfalls, for TCE Mathematics Specialised.

9 min read →

How can we draw reliable conclusions about a population from a single sample?

Use the distribution of the sample mean and the central limit theorem to construct confidence intervals.

Sampling distribution of the mean, the central limit theorem and confidence intervals for a population mean, with worked examples and pitfalls for TCE Mathematics Specialised.

9 min read →

Which techniques let us integrate functions that the basic rules cannot handle?

Integrate using substitution, integration by parts and partial fractions, and find volumes of revolution.

Integration by substitution, by parts and by partial fractions, plus volumes of revolution, with fully worked examples and pitfalls for TCE Mathematics Specialised.

9 min read →