IB Higher Level

Topic 1 – Core: Algebra

Video tutorials for every part of this topic, in course order.

50 tutorials19 sections
Sequences and Series
Working with Sequences and Series
Definition and finding the nth term→Recurrence relationships→Sigma notation→
Arithmetic Progressions
Arithmetic progressions→Sum of the first n terms→Finding a and d given two terms→Working with consecutive terms→
Geometric Series
Geometric series→
Logarithmic and Exponential Functions
Exponential Functions and Logarithms
Simplifying and expanding→
The Exponential Function ex and Natural Log Functions
x”>The exponential function ex→Sketching exponential graphs based on transformations→The natural logarithmic function, ln x→
Permutations and Combinations
Permutations and Combinations
Permutations of n different items→Permutations of r items from n different items→Combinations of n different items→Combining combinations→
Sequences and Series
Binomial Expansion
Binomial expansion→Exam Questions – Binomial expansion, comparing coefficients→Exam Questions – Binomial expansion, estimating a value→Exam Questions – Binomial expansion, other→
Proof by mathematical induction
Sum of Series
Proof of the sum of the series ∑r→Proof of the sum of the series ∑r²→Proof of the sum of the series ∑r³→Proof for other series→Exam Questions – Sum of series→
Various Types of Proofs
Exam Questions – Divisibility and multiple tests→Exam Questions – Recurrence relations→
Complex Numbers
Complex Numbers
Real and imaginary numbers→Addition, subtraction and multiplying complex numbers and simplifying powers of i→Division of a complex number by a complex number→Argand diagrams→Modulus and argument of a complex number→Solving problems with complex numbers→Square roots of a complex number→Solving quadratic equations with complex roots→Solving cubic equations→Solving quartic equations→Exam Questions – Complex numbers→Exam Questions – Finding roots→Modulus-argument form of a complex number→Exponential Form (Euler’s relation)→Multiplication and division rules for mod and argument of two complex numbers→Exam Questions – Further complex numbers→Complex numbers specimen questions (mixed exam boards)→
De Moivre’s Theorem
De Moivre’s theorem→Exam Questions – Expressing sin(nθ) and cos(nθ) in terms of sinθ and cosθ→nθ and cosnθ in terms of sin(kθ) and cos(kθ)”>Expressing sinnθ and cosnθ in terms of sin(kθ) and cos(kθ)→nth roots of a complex number→Exam Questions – nth roots of a complex number→
Systems of Linear Equations
Solutions of systems of linear equations
Solutions of systems of linear equations→

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