Topics

• Work with integers, rationals, powers, roots, and scientific notation.
• Apply advanced BODMAS, large-number arithmetic, and factorization.
• Operate with fractions/decimals, recurring decimals, and percentages.
• Use Pythagoras; find surface area and volume of solids.
• Handle advanced unit conversions and speed–distance–time.
• Manipulate expressions, equations, inequalities, and basic factorization.
• Interpret graphs; analyze data, variance, and SD (intro).
• Solve ratio/proportion, profit–loss, and simple interest.
• Attempt Olympiad-style problems and outline simple proofs.

Detailed Syllabus

Number system: integer/rational operations; laws of exponents; square/cube roots; write and compute in scientific notation.

Order & arithmetic: mixed operations with brackets and indices; estimate and compute with large numbers; HCF/LCM; prime factorization.

Fractions/decimals/percent: all four operations; convert recurring decimals to fractions; percentage change and reverse percentage.

Geometry: Pythagoras’ theorem in right triangles; nets and formulae for surface area/volume (prisms, cylinders, cones, spheres).

Measurement & kinematics: multi-step metric conversions; compound speed–distance–time problems with average speed.

Algebra: expand/simplify; solve linear equations/inequalities; factor simple quadratics; translate words to algebra.

Data & statistics: read and create graphs; summarize data; variance and standard deviation (concept and basic computation).

Ratio & proportion: direct proportion problems; profit, loss, discount; simple interest with 𝐼= 𝑃𝑟𝑡 I = Prt.

Problem solving: non-routine/Olympiad-style tasks requiring reasoning, pattern finding, and clear written justification.