Algebra review and mathematical induction
Algebra for IB Analysis and Approaches HL: powers, polynomials, quadratic equations, inequalities, induction and the binomial theorem, with IB questions.
This topic reviews the algebra used throughout the whole Analysis and Approaches HL course and adds two tools specific to HL: proof by mathematical induction and the binomial theorem. Both appear almost every year in Paper 1.
Suggested order
Sections 1 to 4 are a review: if you already have them under control, go straight to induction and the binomial theorem. At the end of the topic you will find IB exam questions grouped by type, so that you can practise each technique separately.
Operations with fractions, powers and first- and second-degree equations from ESO.
Sections in this topic
Real numbers, powers and radicals
Number sets, recurring decimals, laws of powers and radicals, rationalising, rounding, significant figures and scientific notation in IB AA HL.
3 worked examples Section 2Polynomials: remainder and factor theorems
Divide polynomials, apply the remainder and factor theorems, find parameters and factorise, with 3 worked examples for IB Analysis and Approaches HL.
3 worked examples Section 3Quadratic equations and the discriminant
Solve quadratic equations, use the discriminant, sum and product of roots, and equations with a parameter. IB Analysis and Approaches HL.
3 worked examples Section 4Inequalities and absolute value
Inequality rules, sign tables for inequalities and absolute value: equations, inequalities and the triangle inequality, for IB Analysis and Approaches HL.
3 worked examples Section 5Proof and mathematical induction
Direct proof, counterexample, contradiction and step-by-step induction, with sums, divisibility and inequalities. IB Analysis and Approaches HL.
3 worked examples Section 6Binomial theorem
Factorials, binomial coefficients, Pascal's triangle and the binomial theorem: general term, term in x^k and negative or fractional exponents (HL).
3 worked examples End of topicIB exam questions: topic 1
IB exam questions on algebra, induction and the binomial theorem (Analysis and Approaches HL), grouped by type and level, with worked solutions.
108 exercises · 16 ★★★ levelStuck on this topic?
Tell us where you get lost and we will tell you how to tackle it. Álvaro replies on WhatsApp.
Message us on WhatsApp