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

Exponent and Logarithms

  • SL 1.2: Exponents and Logarithms 
    • Properties of logarithms
    • Solving exponential equations, including using a logarithm
    • Numerical evaluation of logarithms using technology
    • Exponential Equations

Proofs

  • 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