← IB Class AA
Number and Algebra
Chapter Overview
Number and algebra covers arithmetic and geometric sequences/series, binomial expansion for both positive integer and general exponents, laws of logarithms and exponential functions. Complex numbers in Cartesian and polar form (HL), De Moivres theorem. Proof by induction, contradiction, and counterexample (HL). Counting principles including permutations and combinations.
Topics Covered
- Arithmetic Sequences and Series
- Geometric Sequences and Series
- Binomial Theorem
- Logarithms and Exponentials
- Complex Numbers (HL)
- De Moivres Theorem (HL)
- Mathematical Induction (HL)
- Counting Principles
- Proof Methods
Key Formulas
un = a + (n-1)d
Sn = n/2(2a + (n-1)d)
un = arn-1
(a+b)n = sum C(n,k) an-k bk
loga(xy) = loga(x) + loga(y)
z = r(cos A + i sin A) (HL)
Real-World Applications
Applications: Compound interest, population growth, music theory, cryptography.
Study Tips
Tip: Practice proofs regularly
Tip: Master the difference between SL and HL content
Tip: Use IB formula booklet references