Basic Algebra and Functions
Logic, the real numbers, and the algebra everything after this depends on.
01Reasoning and LogicPropositions and connectives, building truth tables, the conditional and its converse, inverse and contrapositive, logical equivalence and De Morgan's laws, and the standard methods of proof.100 questions02The Real Number SystemThe sets of numbers and how they nest, the field axioms and what each one licenses, closure, the difference between rational and irrational numbers, and how to prove that a number is irrational.100 questions03Algebraic OperationsDivide one polynomial by another, use the remainder and factor theorems to avoid most of that division, factorise a cubic completely, and find unknown constants by equating coefficients.100 questions04Exponential and Logarithmic FunctionsThe laws of indices and logarithms, the exponential function and its inverse, change of base, solving exponential and logarithmic equations, and reducing a relationship to linear form.100 questions05FunctionsDomain and range, injective and surjective mappings, composite functions and the order that matters, inverse functions and when they exist, and why restricting a domain is often the price of an inverse.100 questions06The Modulus FunctionThe definition of |x| and its V-shaped graph, sketching y = |f(x)|, solving modulus equations by splitting into cases or squaring, handling modulus inequalities in both directions, and the triangle inequality.100 questions07Cubic Functions and EquationsThe shape of a cubic, the relationships between the roots and the coefficients, symmetric functions of the roots, forming a new equation whose roots are related to the old ones, and what a cubic's roots must look like.100 questions