LEARN · EXPLAIN · REVISE
Selective compulsory volume 2
Read the idea, work independently, then explain what changed.
Each section contains concept explanations, three worked examples, ten graded exercises and teacher preparation.
4.1
Concept of a sequence
Connect general terms, recurrence relations and partial sums.
4.2Arithmetic sequences
Derive terms and sums and solve indexed arithmetic models.
4.3Geometric sequences
Connect ratios, indexed powers and finite geometric sums.
4.4Mathematical induction
Build proofs with a verified base, an explicit induction hypothesis and a valid step.
5.1Derivative: concept and meaning
Distinguish average and instantaneous rates and derive tangents from a limit.
5.2Derivative operations
Apply power, product, quotient and chain rules with elementary derivatives.
5.3Applications of derivatives
Use derivative signs, boundary values and models to justify extrema and optimization.