Foundations for College Mathematics, Grade 12 (College)

Exponent laws for multiplying, dividing, and powers of powers

I can find the exponent laws for multiplying, dividing, and raising a power to a power.

Simplifying expressions with integer exponents

I can simplify algebraic expressions with integer exponents.

Investigating the value of a power with a rational exponent

I can investigate what a power with a rational exponent means.

Evaluating numerical expressions with rational exponents and bases

I can evaluate numerical expressions with rational exponents and rational bases.

Solving simple exponential equations numerically and graphically

I can solve simple exponential equations numerically and graphically.

Solving real-world exponential problems with a graph or table of values

I can solve real-world exponential problems using a graph or table of values.

Solving exponential equations using a common base

I can solve exponential equations by finding a common base.

Interpreting graphs to describe a relationship

I can interpret a graph to describe the relationship it shows.

Describing trends from graphs to make predictions

I can describe a trend from a graph and use it to make a prediction.

Identifying the units of a rate of change from a graph or table

I can identify the units of a rate of change from a graph or table.

Identifying and comparing rate of change: zero, constant, or changing

I can identify whether a rate of change is zero, constant, or changing, and compare two graphs.

Comparing linear, quadratic, and exponential graphs by initial conditions and rate of change

I can compare linear, quadratic, and exponential graphs by their initial conditions and rate of change.

Selecting a linear, quadratic, or exponential model for data

I can select and use a linear, quadratic, or exponential model to represent real data.

Solving equations of the form xⁿ = a using rational exponents

I can solve equations of the form xⁿ = a using rational exponents.

Determining a variable's value from a real-world formula

I can find the value of a variable in a real-world formula.

Connecting formulas to linear, quadratic, and exponential functions

I can connect formulas to linear, quadratic, and exponential functions.

Solving multi-step real-world problems using formulas

I can solve multi-step real-world problems using formulas.

Gathering information about mathematical modelling in occupations and college programs

I can find and describe how occupations and college programs use mathematical modelling.

Key features and real-world applications of annuities

I can describe the key features and real-world uses of annuities.

Investigating the effects of changing annuity conditions

I can investigate how changing an annuity's conditions affects its outcome.

Solving for the amount, present value, and regular payment of an annuity

I can solve for the amount, present value, and regular payment of an annuity.

The advantages of starting annuity deposits earlier

I can show the advantages of starting annuity deposits earlier.

Mortgage features and comparing mortgage types

I can describe mortgage features and compare different types of mortgages.

Reading and interpreting an amortization table

I can read and interpret a mortgage amortization table.

Generating an amortization table and calculating total mortgage interest

I can generate an amortization table and calculate total mortgage interest.

Investigating the effects of varying payment periods, payments, and rates on a mortgage

I can investigate how payment periods, payments, and rates affect a mortgage's cost and length.

Gathering information about the costs of owning and renting

I can gather information about the costs of owning and renting accommodation.

Comparing the advantages and disadvantages of renting versus owning

I can compare the advantages and disadvantages of renting versus owning.

Solving problems with fixed and variable costs of accommodation

I can solve problems with the fixed and variable costs of owning or renting.

Estimating the living costs of different households

I can estimate living costs for different kinds of households.

Designing and presenting a savings plan for a long-term goal

I can design and present a savings plan for a long-term goal.

Designing, explaining, and justifying a monthly budget from a case study

I can design, explain, and justify a monthly budget from a case study.

Identifying factors in the affordability of accommodation

I can identify the factors that affect whether accommodation is affordable.

Adjusting a budget for changed circumstances

I can adjust a budget when circumstances change.

Gathering information about personal finance applications in occupations

I can find and describe how occupations and college programs use personal finance math.

Converting between the imperial and metric systems

I can convert between the imperial and metric systems as needed.

Solving real-world problems with areas of rectangles, triangles, circles, and composite shapes

I can solve real-world problems with the areas of rectangles, triangles, circles, and composite shapes.

Solving real-world problems with volumes and surface areas of prisms, cylinders, and composite figures

I can solve 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

I can recognize and explain why optimal dimensions matter in real applications.

Determining the optimal dimensions of a 2D shape for a given constraint

I can find the optimal dimensions of a 2D shape for a given constraint.

Determining the optimal dimensions of a prism or cylinder for a given constraint

I can find the optimal dimensions of a 3D prism or cylinder for a given constraint.

Solving real-world 2D problems with right and acute triangles

I can solve real-world 2D problems using right and acute triangles.

Connecting trigonometric ratios of obtuse angles to acute angles

I can connect trig ratios of obtuse angles to those of acute angles.

Determining the sine, cosine, and tangent of obtuse angles

I can determine the sine, cosine, and tangent of obtuse angles.

Solving real-world problems with oblique triangles using the sine and cosine laws

I can solve real-world oblique triangle problems using the sine law and cosine law.

Gathering information about trigonometry applications in occupations

I can find and describe how occupations and college programs use trigonometry.

Distinguishing situations needing one-variable versus two-variable analysis

I can tell when a situation needs one-variable or two-variable data analysis.

Designing questionnaires and experiments for two-variable data

I can design a fair questionnaire or experiment to gather two-variable data.

Collecting and organizing two-variable data from primary and secondary sources

I can collect and organize two-variable data from primary and secondary sources.

Creating a scatter plot for two-variable data

I can create a scatter plot to summarize two-variable data.

Determining the equation of a line of best fit

I can determine the equation of a line of best fit.

Interpreting a line of best fit and reasons for misinterpretation

I can interpret a line of best fit and recognize reasons for misinterpretation.

Assessing whether a linear model is appropriate by examining correlation

I can assess whether a linear model fits two-variable data by checking correlation.

Drawing and judging conclusions from two-variable data analysis

I can draw and judge conclusions from two-variable data analysis.

Recognizing and interpreting common statistical terms used in the media

I can recognize and interpret common statistical terms used in the media.

Describing and solving problems using media indices

I can describe media indices and solve problems using them.

Interpreting media statistics and explaining how statistics are used and misused

I can interpret media statistics and explain how they can be used or misused.

Assessing the validity of conclusions presented in the media

I can assess the validity of conclusions presented in the media.

Gathering information about data management applications in occupations

I can find and describe how occupations and college programs use data management.