Mathematics 3201 (Academic)

Unit 1: Logarithms and Financial Mathematics

Logarithms as inverse exponents and the laws of logarithms, plus compound interest, loans, credit, and cost-and-benefit decisions such as renting, leasing, and buying.

• Logarithmic and exponential form
• The laws of logarithms
• Evaluating logarithms

• Compound interest
• Simple versus compound interest
• Loans and credit options
• Buying, leasing and renting decisions

Unit 2: Set Theory

Sets, subsets, and universal sets, Venn diagrams and set notation, and solving problems with unions, intersections, and complements.

• Sets, subsets and Venn regions
• Solving problems with set operations
• Applications of set theory

Unit 3: Rational Expressions and Polynomial Functions

Rational expressions and equations (non-permissible values, simplifying, operations, and solving) and polynomial functions of degree up to three (characteristics, graphs, and modelling).

• Non-permissible values and simplifying
• Adding and subtracting rational expressions
• Multiplying and dividing rational expressions
• Solving rational equations

• Characteristics of polynomial functions
• Modelling data with polynomial functions

Unit 4: Exponential and Logarithmic Functions

Exponential and logarithmic functions as models, solving exponential equations, logarithmic scales, and the characteristics of these functions from graphs and equations.

• Fitting exponential and logarithmic models
• Solving exponential equations and scales

• Describing and matching exp/log functions

Unit 5: Sinusoidal Functions

Angles in degrees and radians and the characteristics, graphs, and modelling of sinusoidal (sine-based) functions.

• Degrees, radians and sinusoidal graphs
• Equations and models of sinusoidal functions

Unit 6: Probability, Permutations and Combinations

Odds and probability, mutually-exclusive and non-mutually-exclusive events, dependent and independent events, and counting with the Fundamental Counting Principle, permutations, and combinations.

• Odds and probability
• Solving and deciding with probability

• Mutually-exclusive and non-mutually-exclusive events
• Dependent and independent events

• The Fundamental Counting Principle
• Factorials and factorial notation
• Solving equations with factorials

• Permutations
• Permutations with repeated elements
• Combinations
• Probability with combinations