Mathematics

A gentle, CAPS-aligned first tour of Grade 4 mathematics — from place value and the four operations to fractions, tenths, measurement, time, shapes and data. Every idea comes twice, once as clear Theory and once as a Visual picture from everyday South African life, with worked examples and plenty of practice.

A complete, CAPS-aligned Grade 5 maths journey — from big whole numbers, factors and multiples, through fractions and decimals, into measurement, perimeter, shapes, transformations and bar graphs. Every idea comes twice: a precise Theory explanation and an intuition-first Visual picture, with worked examples rooted in everyday South African life and dozens of practice problems that guide with hints and full solutions.

A complete, CAPS-aligned Grade 6 maths journey — from big whole numbers and fractions to percentages, ratio, rate, measurement, patterns and data. Every idea comes twice, as a precise Theory and an intuition-first Visual, with worked examples rooted in everyday South African life and dozens of practice problems that guide with hints and full solutions.

A Grade 7 Mathematics pathway for understanding, practice and exam readiness. Short explanations lead to a concrete model, a worked example, a misconception check and four graduated questions with hints and full reasoning. It follows the CAPS Senior Phase strands while keeping reading load manageable for young learners.

A complete, CAPS-aligned Grade 8 mathematics course — from the laws of exponents through algebra, graphs, geometry, the Theorem of Pythagoras, measurement and probability. Every idea is taught twice: once rigorously as Theory and once through an everyday Visual picture, with worked examples rooted in South African life and practice problems that come with hints and full solutions.

A complete, CAPS-aligned Grade 9 mathematics course that carries every idea in two modes — rigorous Theory and intuition-first Visual. From the laws of exponents and factorisation to straight-line graphs, triangle geometry and tree diagrams, each lesson is grounded in everyday South African life, with worked examples and practice problems that build from confidence to challenge.

A full CAPS-NSC Grade 10 Mathematics course complementing Caelum's equations intensive. Theory and Visual modes cover algebra and exponents, equations, patterns, all four function families, trigonometry, Euclidean and analytical geometry, finance, statistics and Venn-diagram probability, with IEB enrichment and Cambridge IGCSE alignment.

From your first balance-scale equation to the quadratic formula: a complete, CAPS-aligned Grade 10 journey through solving equations. Every concept comes in two modes — rigorous Theory and intuition-first Visual — with worked examples from everyday South African life and over a hundred practice problems with hints and full solutions.

A Grade 11 Mathematics exam-preparation pathway: CAPS core content with IEB-compatible reasoning, proof, graph interpretation and multi-step applications. Each lesson supplies a concise explanation, a visual model, worked reasoning, a misconception check and four graded practice questions with hints and fully explained answers.

A focused Grade 12 course covering arithmetic and geometric series, logarithms and inverse functions, annuities and amortisation, differential calculus, and compound-angle trigonometry. Every example is set in a South African context, from stokvel savings to home loans and Eskom pylons.

A rigorous first course in linear algebra for university study and serious self-directed learners: systems and elimination, vector spaces and linear maps, orthogonality and least squares, determinants, eigenvalues and the singular value decomposition — with computation, geometry and proof given equal weight.

A university first-year foundation in mathematics for South African students: single-variable calculus, linear algebra, discrete mathematics and probability. Every idea arrives in two modes — rigorous Theory and intuition-first Visual — with worked examples grounded in everyday South African life and practice problems that climb from routine to demanding.

The second-year core of a university mathematics degree: calculus stretched into several dimensions, linear algebra deepened into eigenvalues and inner-product spaces, differential equations, and the numerical methods that make it all computable. Every idea arrives twice — once rigorously, once through an everyday picture — with worked examples grounded in South African life and over fifty practice problems with full solutions.

A rigorous third-year pure-mathematics course spanning real analysis, abstract algebra, an introduction to complex analysis, and first steps in partial differential equations. Every idea arrives in two modes — precise Theory and intuition-first Visual — with worked proofs, grounded analogies and plenty of practice.