Mathematics 30-2

Unit 1: Logical Reasoning

General outcome: develop logical reasoning. Numerical and logical reasoning through puzzles and games, and the application of set theory — sets, subsets, unions, intersections and Venn diagrams — as a tool for organizing and counting.

• Problem-solving strategies for puzzles
• Determining winning strategies

• Sets, subsets and Venn diagrams
• Unions, intersections and complements
• Solving problems with set theory

Unit 2: Probability

General outcome: develop critical thinking skills related to uncertainty. Odds versus probability, mutually exclusive and non–mutually exclusive events, the probability of two events (independent, dependent, conditional), the fundamental counting principle, permutations and combinations.

• Odds versus probability
• Assessing validity of statements

• Mutually exclusive events
• Non–mutually exclusive events

• Independent events
• Dependent and conditional events

• Counting arrangements by multiplication
• Counting with restrictions

• Permutations of distinct objects
• Permutations with repetitions and restrictions

• Combinations of distinct objects
• Combinations in counting and probability

Unit 3: Relations and Functions

General outcome: develop algebraic and graphical reasoning through the study of relations. Rational expressions and equations, logarithms and the laws of logarithms, exponential equations, and modelling real data with exponential, logarithmic, polynomial (degree ≤ 3) and sinusoidal functions.

• Equivalent forms and restrictions
• Non-permissible values

• Multiplying and dividing
• Adding and subtracting

• Solving rational equations
• Problems with rational equations

• Logarithms as inverse exponents
• The laws of logarithms

• Solving with a common base
• Solving with logarithms

• Exponential models
• Logarithmic models

• Polynomial functions of degree ≤ 3
• Fitting polynomial models to data

• Amplitude, period, phase and midline
• Fitting sinusoidal models to data

Unit 4: Mathematics Research Project

General outcome: develop an appreciation of the role of mathematics in society. Plan, conduct and present a research investigation on a current event or an area of interest that involves mathematics.

• Planning the investigation
• Conducting the research
• Presenting the findings