eBook
HL 1.2 - Function basics
SL 2.2: Concept of a function and its domain, range & graph; function notationSL 2.3: Graphs of functionsSL 2.5: Composite functions; finding the domain of a composite function You studied linear equations...
eBook
HL 1.1 - Linear equations
PLT: Solving systems of linear equations in two variables (two unknowns)SL 2.1: Different forms of the equation of a straight line; gradient; intercepts; parallel & perpendicular linesSL 2.4: Finding...
eBook
HL 5.3 - Mathematical induction
HL 1.15: Proof by mathematical induction The basic deductive proof methods covered in Sections 5.1 (deductive proof) and 5.2 (proof by contradiction) can be awkward or ineffective for attempting to prove...
eBook
HL 5.2 - Proof by contradiction
HL 1.15: Proof by contradiction If we have tried unsuccessfully to perform a deductive proof of a statement - and cannot find a counterexample - we might next try to give a proof by contradiction (sometimes...
eBook
HL 5.1 - Deductive proof and counterexamples
SL 1.6: Simple deductive proof, numerical and algebraic; how to lay out a left-hand side (LHS) to right-hand side (RHS) proof; the symbols and notation for equality and identityHL 1.15: Use of a counterexample...
Teaching resources & guidance
Transformations of graphs
Preliminary Questions 𝅛 Teaching Notes 𝅛 Teaching Materials 𝅛 Focused Assessments 𝅛 Quizzes & Tests ⭕ Learning Objectives SL and HL students: HL students only: • describing horizontal and vertical...
External assessment
Review Tests
Worked solutions are available for each of the ten review tests on the Review Tests worked solutions page. All of the questions on these review tests have been composed to be similar to IB exam questions....
External assessment
Review Tests worked solutions
go to worked solutions ↴ This page contains fully worked solutions for all of the 9 Review Tests. The number of marks have been indicated for each question (and each separate part of each question) on...
External assessment
Paper 1 exam (SL & HL)
Paper 1 is the non-calculator examination for Mathematics: Analysis and Approaches. It assesses whether students can recognise mathematical structure, select an appropriate analytical method, carry it...
DP essentials
Extended essay 2027
A Brief Teacher’s Guide to the 2027 IBDP Extended Essay Supervising a student on their Extended Essay (EE) can be a rewarding part of teaching in the International Baccalaureate Diploma Programme (IBDP)....