Algebra from Class 9 to 12: linear equations and pairs of equations, quadratics, polynomials, exponents, surds and logarithms, complex numbers, arithmetic progressions, permutations and combinations, and probability. Several topics have both a concept page and a solved-examples page.
12 reference pages
What a quadratic equation is, solving by factoring, completing the square and the quadratic formula, solved examples on word problems, and the nature of roots.
Simplifying and rationalizing expressions with square roots, with worked examples including a telescoping sum.
Polynomials in one place: degree, zeroes and coefficients, the division algorithm, the remainder and factor theorems, and factorising with identities, with worked examples.
Arithmetic progressions: spotting one, the nth term, the sum of n terms, finding how many terms give a sum, worked examples, common mistakes and practice questions.
Probability: the basic formula, the addition rule, independent and dependent events, conditional probability and Bayes' theorem, with worked examples and common mistakes.
Logarithms: what they mean, common, natural and binary logs, the rules and change of base, solving a log equation, counting digits with log 2, and common mistakes.
Complex numbers: the imaginary unit, modulus, argument and conjugate, multiplying and dividing, finding the argument in the right quadrant, powers of i, and common mistakes.
Permutations and combinations: the multiplication principle, nPr and nCr, identical items, circular arrangements, choose-then-arrange, worked examples, common mistakes and practice questions.
How to solve a one-variable linear equation step by step, including fractions and the variable on both sides, with a phrase-to-expression table and worked word and age problems.
Pair of linear equations by every method: forming them from a word problem, the ratio test, substitution, elimination, cross-multiplication and reducible equations, with worked examples.
All the laws of exponents in one table, including zero, negative and fractional exponents, with worked examples on simplifying, one-base rewriting and solving for an exponent, and common mistakes.
Five worked Math Olympiad-style problems for grade 7: a Fibonacci-like sequence, an exponent equation, percentages with overlap, consecutive integers, and clock arithmetic.