OntarioON Grade 12 Foundations for College Math (MAP4C)
Video lessons and practice for every MAP4C topic. Aligned to what Ontario schools teach in Grade 12 Foundations for College Mathematics, College Preparation.
ON Grade 12 Foundations for College Math | StudyPugHelp
OE_ID | Expectations | StudyPug Topic |
|---|---|---|
ON.OE.12FC.A1.1 | 12FC.A1.1: Determine, through investigation, the exponent laws for multiplying and dividing algebraic expressions involving exponents and the exponent law for simplifying algebraic expressions involving a power of a power |
ON.OE.12FC.A1.2 | 12FC.A1.2: Simplify algebraic expressions containing integer exponents using the laws of exponents |
ON.OE.12FC.A1.3 | 12FC.A1.3: Determine, through investigation using a variety of tools and strategies, the value of a power with a rational exponent |
ON.OE.12FC.A1.4 | 12FC.A1.4: Evaluate, with or without technology, numerical expressions involving rational exponents and rational bases |
ON.OE.12FC.A1.5 | 12FC.A1.5: Solve simple exponential equations numerically and graphically, with technology |
ON.OE.12FC.A1.6 | 12FC.A1.6: Solve problems involving exponential equations arising from real-world applications by using a graph or table of values generated with technology from a given equation |
ON.OE.12FC.A1.7 | 12FC.A1.7: Solve exponential equations in one variable by determining a common base |
ON.OE.12FC.A2.1 | 12FC.A2.1: Interpret graphs to describe a relationship, using language and units appropriate to the context |
ON.OE.12FC.A2.2 | 12FC.A2.2: Describe trends based on given graphs, and use the trends to make predictions or justify decisions |
ON.OE.12FC.A2.3 | 12FC.A2.3: Recognize that graphs and tables of values communicate information about rate of change, and use a given graph or table of values for a relation to identify the units used to measure rate of change |
ON.OE.12FC.A2.4 | 12FC.A2.4: Identify when the rate of change is zero, constant, or changing, given a table of values or a graph of a relation, and compare two graphs by describing rate of change |
ON.OE.12FC.A2.5 | 12FC.A2.5: Compare, through investigation with technology, the graphs of pairs of relations by describing the initial conditions and the behaviour of the rates of change |
ON.OE.12FC.A2.6 | 12FC.A2.6: Recognize that a linear model corresponds to a constant increase or decrease over equal intervals and that an exponential model corresponds to a constant percentage increase or decrease over equal intervals, select a model to represent the relationship between numerical data graphically and algebraically, using a variety of tools and strategies, and solve related problems |
ON.OE.12FC.A3.1 | 12FC.A3.1: Solve equations of the form x^n = a using rational exponents |
ON.OE.12FC.A3.2 | 12FC.A3.2: Determine the value of a variable of degree no higher than three, using a formula drawn from an application, by first substituting known values and then solving for the variable, and by first isolating the variable and then substituting known values |
ON.OE.12FC.A3.3 | 12FC.A3.3: Make connections between formulas and linear, quadratic, and exponential functions, using a variety of tools and strategies |
ON.OE.12FC.A3.4 | 12FC.A3.4: Solve multi-step problems requiring formulas arising from real-world applications |
ON.OE.12FC.C1.1 | 12FC.C1.1: Perform required conversions between the imperial system and the metric system using a variety of tools, as necessary within applications |
ON.OE.12FC.C1.2 | 12FC.C1.2: Solve problems involving the areas of rectangles, triangles, and circles, and of related composite shapes, in situations arising from real-world applications |
ON.OE.12FC.C1.3 | 12FC.C1.3: Solve problems involving the volumes and surface areas of rectangular prisms, triangular prisms, and cylinders, and of related composite figures, in situations arising from real-world applications |
ON.OE.12FC.C2.1 | 12FC.C2.1: Recognize, through investigation using a variety of tools and strategies, and explain the significance of optimal perimeter, area, surface area, and volume in various applications |
ON.OE.12FC.C2.2 | 12FC.C2.2: Determine, through investigation using a variety of tools and strategies, the optimal dimensions of a two-dimensional shape in metric or imperial units for a given constraint |
ON.OE.12FC.C2.3 | 12FC.C2.3: Determine, through investigation using a variety of tools and strategies, the optimal dimensions of a right rectangular prism, a right triangular prism, and a right cylinder in metric or imperial units for a given constraint |
ON.OE.12FC.C3.1 | 12FC.C3.1: Solve problems in two dimensions using metric or imperial measurements, including problems that arise from real-world applications, by determining the measures of the sides and angles of right triangles using the primary trigonometric ratios, and of acute triangles using the sine law and the cosine law |
ON.OE.12FC.C3.2 | 12FC.C3.2: Make connections between primary trigonometric ratios of obtuse angles and of acute angles, through investigation using a variety of tools and strategies |
ON.OE.12FC.C3.3 | 12FC.C3.3: Determine the values of the sine, cosine, and tangent of obtuse angles |
ON.OE.12FC.C3.4 | 12FC.C3.4: Solve problems involving oblique triangles, including those that arise from real-world applications, using the sine law and the cosine law, and using metric or imperial units |
ON.OE.12FC.D1.1 | 12FC.D1.1: Distinguish situations requiring one-variable and two-variable data analysis, describe the associated numerical summaries and graphical summaries, and recognize questions that each type of analysis addresses |
ON.OE.12FC.D1.2 | 12FC.D1.2: Describe characteristics of an effective survey, and design questionnaires or experiments for gathering two-variable data |
ON.OE.12FC.D1.3 | 12FC.D1.3: Collect two-variable data from primary sources, through experimentation involving observation or measurement, or from secondary sources, and organize and store the data using a variety of tools |
ON.OE.12FC.D1.4 | 12FC.D1.4: Create a graphical summary of two-variable data using a scatter plot, with and without technology |
ON.OE.12FC.D1.5 | 12FC.D1.5: Determine an algebraic summary of the relationship between two variables that appear to be linearly related, using a variety of tools and strategies, and solve related problems |
ON.OE.12FC.D2.1 | 12FC.D2.1: Recognize and interpret common statistical terms and expressions used in the media |
ON.OE.12FC.D2.2 | 12FC.D2.2: Describe examples of indices used by the media and solve problems by interpreting and using indices |
ON.OE.12FC.D2.3 | 12FC.D2.3: Interpret statistics presented in the media, and explain how the media, the advertising industry, and others use and misuse statistics to promote a certain point of view |
Grade 12 Foundations for College Mathematics (MAP4C) in Ontario
Ontario's MAP4C course prepares students for college programs by building practical math skills across five main areas: exponential functions, modelling, personal finance, measurement and geometry, and data management. StudyPug covers every unit with clear video lessons and targeted practice problems.
Exponential Functions and Modelling
Students in MAP4C learn the laws of exponents, simplify algebraic expressions, and work with rational exponents. They solve exponential equations numerically, graphically, and by finding a common base. Students also learn to interpret graphs, identify rates of change, and choose between linear and exponential models to represent real-world data.
Personal Finance
This unit covers annuities, mortgages, and personal budgeting — practical skills students will use throughout their lives. Topics include calculating the amount and present value of an ordinary simple annuity, reading amortization tables, comparing renting versus owning accommodation, and designing monthly budgets for realistic case studies.
Measurement and Geometry
MAP4C measurement topics include converting between imperial and metric units, calculating areas and volumes of common shapes and composite figures, and finding optimal dimensions for two-dimensional and three-dimensional shapes. Students apply these skills to real-world problems in trades, construction, and design.
Trigonometry
Students extend their trigonometry knowledge to include obtuse angles and oblique triangles. They use the sine law and the cosine law to solve problems involving triangles in real-world contexts, using both metric and imperial measurements.
Data Management
The data management unit focuses on two-variable data analysis. Students design surveys, collect data, create scatter plots, find lines of best fit, and assess correlation. They also learn to critically evaluate statistics in the media, recognize bias, and interpret common indices used in everyday life.
- Exponential laws and rational exponents
- Solving exponential equations
- Interpreting graphs and rates of change
- Annuities and mortgage calculations
- Personal budgeting and living costs
- Measurement, area, volume, and optimal dimensions
- Trigonometry with oblique triangles using the sine and cosine law
- Two-variable data analysis and scatter plots
- Interpreting and critiquing statistics in the media
StudyPug's MAP4C content is built specifically for Ontario Grade 12 students. Whether you need help with a single topic or want to review an entire unit before a test, you can find exactly what you need in the topic table above.