Foundations for College Mathematics, Grade 12 (College)

Unit 1: Mathematical Models

Powers with rational exponents and exponential equations; reading trends from graphs and comparing rates of change; and connecting formulas to linear, quadratic, and exponential relations in real-world problems.

• Exponent laws for multiplying, dividing, and powers of powers
• Simplifying expressions with integer exponents
• Investigating the value of a power with a rational exponent
• Evaluating numerical expressions with rational exponents and bases

• Solving simple exponential equations numerically and graphically
• Solving real-world exponential problems with a graph or table of values
• Solving exponential equations using a common base

• Interpreting graphs to describe a relationship
• Describing trends from graphs to make predictions
• Identifying the units of a rate of change from a graph or table
• Identifying and comparing rate of change: zero, constant, or changing

• Comparing linear, quadratic, and exponential graphs by initial conditions and rate of change
• Selecting a linear, quadratic, or exponential model for data

• Solving equations of the form xⁿ = a using rational exponents
• Determining a variable's value from a real-world formula
• Connecting formulas to linear, quadratic, and exponential functions
• Solving multi-step real-world problems using formulas
• Gathering information about mathematical modelling in occupations and college programs

Unit 2: Personal Finance

Understanding annuities and mortgages; comparing owning and renting accommodation; and designing, justifying, and adjusting budgets for real-life situations.

• Key features and real-world applications of annuities
• Investigating the effects of changing annuity conditions
• Solving for the amount, present value, and regular payment of an annuity
• The advantages of starting annuity deposits earlier

• Mortgage features and comparing mortgage types
• Reading and interpreting an amortization table
• Generating an amortization table and calculating total mortgage interest
• Investigating the effects of varying payment periods, payments, and rates on a mortgage

• Gathering information about the costs of owning and renting
• Comparing the advantages and disadvantages of renting versus owning
• Solving problems with fixed and variable costs of accommodation
• Estimating the living costs of different households

• Designing and presenting a savings plan for a long-term goal
• Designing, explaining, and justifying a monthly budget from a case study
• Identifying factors in the affordability of accommodation
• Adjusting a budget for changed circumstances
• Gathering information about personal finance applications in occupations

Unit 3: Geometry and Trigonometry

Solving real-world area, volume, and surface area problems; investigating optimal dimensions; and using trigonometric ratios, the sine law, and the cosine law for acute and obtuse triangles.

• Converting between the imperial and metric systems
• Solving real-world problems with areas of rectangles, triangles, circles, and composite shapes
• Solving real-world problems with volumes and surface areas of prisms, cylinders, and composite figures

• Recognizing and explaining the significance of optimal perimeter, area, surface area, and volume
• Determining the optimal dimensions of a 2D shape for a given constraint
• Determining the optimal dimensions of a prism or cylinder for a given constraint

• Solving real-world 2D problems with right and acute triangles
• Connecting trigonometric ratios of obtuse angles to acute angles
• Determining the sine, cosine, and tangent of obtuse angles
• Solving real-world problems with oblique triangles using the sine and cosine laws
• Gathering information about trigonometry applications in occupations

Unit 4: Data Management

Collecting, graphing, and analysing two-variable data with lines of best fit; and understanding how the media, advertising, and occupations use and misuse statistics.

• Distinguishing situations needing one-variable versus two-variable analysis
• Designing questionnaires and experiments for two-variable data
• Collecting and organizing two-variable data from primary and secondary sources
• Creating a scatter plot for two-variable data
• Determining the equation of a line of best fit

• Interpreting a line of best fit and reasons for misinterpretation
• Assessing whether a linear model is appropriate by examining correlation
• Drawing and judging conclusions from two-variable data analysis

• Recognizing and interpreting common statistical terms used in the media
• Describing and solving problems using media indices
• Interpreting media statistics and explaining how statistics are used and misused
• Assessing the validity of conclusions presented in the media
• Gathering information about data management applications in occupations