Core Mathematics

Universal sets, subsets, complements, De Morgan’s laws, and solving real-world word problems using three-set Venn diagrams.

Rational vs irrational numbers, simplifying surds, rationalizing binomial surds, and scientific notation calculations.

Laws of indices, fractional and negative exponents, exponential equations, and fundamental properties of logarithms.

Expanding binomials and trinomials, factorization by grouping, difference of two squares, and quadratic trinomial factorization.

Simplifying algebraic fractions, condition for undefined fractions, and operations (+, -, ×, ÷) on rational expressions.

Techniques for solving multi-step linear equations, clearing algebraic fractions using LCM, and solving word problems.

Solving linear inequalities, the sign reversal rule, combined inequalities, and graphing solution sets on the real number line.

Elimination method, substitution method, graphical intersection method, and practical commercial word problems.

Sharing in ratios, direct and inverse proportion, rates of work (man-hours, water pipes), profit/loss, and discount.

Transforming algebraic formulas, dealing with brackets, roots, powers, and variables appearing in multiple terms.

Types of relations, domain, codomain, range, function notation f(x), composite functions, and drawing linear graphs from tables.

Constant of proportionality, modeling direct, inverse, joint, and partial variation, and solving real-world word problems.

Types of angles, complementary and supplementary angles, vertically opposite angles, and angles on parallel lines (alternate, corresponding, interior).

Properties of convex polygons, sum of interior angles (2n - 4) × 90°, sum of exterior angles = 360°, regular polygons, and angle calculations.

Length of line segment (distance formula), midpoint of two points, gradient (slope) of a straight line, and equation of a straight line (y = mx + c).

Perimeter and area of triangles, parallelograms, trapeziums, circles, sectors, segments, and composite plane figures.

Discrete and continuous data, tally charts, frequency distribution tables, bar charts, pie charts, and mean, median, mode of ungrouped data.