Number and Algebra
Learning Objectives
Series, Sequence, and Sigma Notation
- SL 1.0: Scientific Notation
- Number operations in the form a × 10^k where 1 ≤ a < 10 and k is an integer.
- SL 1.1: Sequences and Series
- Find term and sum of an arithmetic sequence
- Find term and sum of an finite geometric sequence
- Find term and sum of an infinite geometric sequence
- SL 1.2: Exponents and Logarithms
- Properties of logarithms
- Solving exponential equations, including using a logarithm
- Numerical evaluation of logarithms using technology
- Exponential Equations
- SL 1.3: Proofs
- Proof by mathematical induction
- Proof by contradiction
- Use of a counterexample to show that a statement is not always true
Counting Principle and Binomial Theorem
- SL 1.4: Binomial Theorem
- The binomial theorem
- Use of Pascal’s triangle
- AHL 1.5: Counting Principles
- Counting principles, including permutations and combinations
- Extension of the binomial theorem to fractional and negative indices