HSC Mathematics Practical Solutions

Study mathematical logic, propositions, truth tables, and logical equivalences.

Learn about matrix operations, determinants, inverse of matrices, and applications.

Master trigonometric ratios, identities, and equations. Foundation for advanced mathematics.

Advanced concepts including inverse trigonometric functions, their properties, and graphs.

Understand the combined equation of two lines, angles, and general second-degree equations.

Explore vector algebra, 3D coordinate systems, and their geometrical applications.

Study equations of lines and planes in space, angles, and shortest distance calculations.

Learn optimization techniques using linear programming problems (LPPs) and graphical methods.

Apply derivatives to find tangents, normals, approximations, and rate of change.

Advanced applications including increasing/decreasing functions, maxima and minima.

Understand the fundamental theorem of calculus and the basic properties of definite integrals.

Learn advanced evaluation techniques and properties for definite integration.

Use definite integrals to find the area under simple curves and the area between two curves.

Learn to form and solve differential equations, including variable separable and linear methods.

Study random variables, probability mass function (p.m.f.), and cumulative distribution function (c.d.f.).

Understand Bernoulli trials and the binomial distribution, including its mean and variance.