Foundations for College Mathematics, Grade 11 (College)

Unit 1: Mathematical Models

Graphing and solving quadratic relations from real-world data; exploring negative and zero exponents; and graphing, comparing, and solving problems with exponential relations.

• Building tables of values and graphing quadratic relations
• Interpreting meaningful values from a quadratic graph
• What a, h, and k do to a parabola's graph
• Sketching quadratic graphs from vertex form
• Expanding and simplifying quadratic expressions
• Converting vertex form to standard form
• Factoring trinomials
• Connecting factors to the graph's x-intercepts
• Solving real-world quadratic problems by factoring or graphing

• What negative exponents and zero as an exponent mean
• Evaluating expressions with integer exponents and rational bases
• Exponent rules for multiplying, dividing, and powers of powers
• Graphing simple exponential relations by hand
• Connecting numeric, graphical, and algebraic exponential representations
• Telling exponential relations apart from linear and quadratic ones

• Collecting and graphing data that fits an exponential model
• Describing characteristics of real-world exponential relations
• Posing and solving problems using exponential graphs
• Solving problems using exponential equations

Unit 2: Personal Finance

Compound interest and its link to exponential growth; comparing financial services and credit costs; and the costs of owning and operating a vehicle.

• Compound interest as repeated simple interest
• The link between compound interest and exponential growth
• Using the compound interest formula to find amount or principal
• Calculating total interest earned or paid
• Using the TVM Solver to find interest rate or number of periods
• How changing time, rate, or period affects an investment or loan

• Comparing savings alternatives and their costs
• Comparing investment alternatives by risk and return
• Comparing costs and incentives of credit and debit cards
• Credit card interest rates and the effect of delayed payments
• Applying the compound interest formula to purchases on credit

• Comparing vehicle insurance costs
• Comparing the costs of buying versus leasing a vehicle
• Solving problems with fixed and variable vehicle costs

Unit 3: Geometry and Trigonometry

Representing real-world 2D shapes and 3D objects, solving design problems, and using the primary trig ratios and the sine and cosine laws in acute triangles.

• Recognizing real-world applications of geometric shapes
• Representing 3D objects with drawing tools and software
• Creating nets, plans, and patterns from physical models
• Solving design problems with given constraints

• Solving right-triangle problems with primary trig ratios
• Verifying the sine law and the cosine law
• Choosing between the sine law and the cosine law
• Solving real-world triangle problems with metric and imperial measurements

Unit 4: Data Management

Designing, collecting, and organizing one-variable data; measures of central tendency and spread; and probability, including theoretical and experimental probability.

• Designing questionnaires and experiments for one-variable data
• Collecting one-variable data from secondary sources
• Population versus sample and why sampling is necessary
• Sampling techniques and collecting primary data
• Types of one-variable data and graphical forms
• Properties of common data distributions

• Calculating measures of central tendency and spread
• Choosing the appropriate measure of central tendency or spread
• Comparing two or more data sets using central tendency and spread
• Solving problems by interpreting and analysing secondary-source data

• Identifying probability in the media and its representations
• Determining theoretical probability
• Determining experimental probability
• Comparing theoretical and experimental probability
• How experimental probability approaches theoretical probability with more trials
• Connecting probability and statistics in the media