Mathematics for College Technology, Grade 12 (College)
Ontario · Grade 12 · Mathematics — the complete curriculum-aligned outline, taught skill by skill by MapleMind's AI tutor.
4Units
12Lessons
57Skills
Unit 1: Exponential Functions
Graphing and solving exponential equations, and connecting exponential equations to logarithms — algebraically and with technology.
Graphing and Comparing Exponential Functions
- How changing the base or the sign of the exponent affects an exponential graph
Solving Exponential Equations Graphically
- Solving simple exponential equations numerically and graphically
- Solving exponential equations by the intersection of two exponential graphs
- Posing and solving real-world exponential problems with a graph
Solving Exponential Equations Algebraically
- Simplifying expressions with integer and rational exponents
- Solving exponential equations using a common base
- The logarithm as the inverse of exponentiation
- Approximating the logarithm of a number to any base with technology
- Connecting logarithmic and exponential equations
- Posing and solving real-world exponential problems by rewriting in logarithmic form
Unit 2: Polynomial Functions
Investigating, graphing, and factoring polynomial functions; solving polynomial equations; and connecting formulas to real-world variables and applications.
Investigating Graphs of Polynomial Functions
- Recognizing polynomial expressions and functions
- Comparing graphical and algebraic representations of polynomial functions
- Describing key features of polynomial function graphs
- Distinguishing polynomial functions from sinusoidal and exponential functions
Connecting Graphs and Equations of Polynomial Functions
- Evaluating polynomial functions in function notation
- Posing and solving real-world problems using polynomial function graphs
- Recognizing the limitations and domain/range restrictions of polynomial models
- Factoring polynomial expressions up to degree four
- Connecting a polynomial function's factored form to its x-intercepts and sketching its graph
- Connecting the real roots of a polynomial equation to its graph's x-intercepts
Solving Problems Involving Polynomial Equations
- Solving polynomial equations up to degree four
- Solving real-world problems involving polynomial functions and equations
- Identifying and explaining the roles of constants and variables in a formula
- Expanding and simplifying polynomial expressions with more than one variable
- 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 3: Trigonometric Functions
Trig ratios for angles up to 360 degrees; the sine law, cosine law, and multi-step triangle problems; and sinusoidal functions modelling periodic real-world phenomena.
Applying Trigonometric Ratios
- Exact sine, cosine, and tangent values of special angles
- Determining sine, cosine, and tangent for angles from 0° to 360°
- Finding two angles from 0° to 360° with the same trig ratio value
- Solving multi-step 2D and 3D right-triangle problems
- Solving oblique triangle problems including the ambiguous case
Connecting Graphs and Equations of Sinusoidal Functions
- Connecting the sine and cosine ratios to the sine and cosine functions
- Representing a sinusoidal function with an equation given its graph or properties
- Collecting and graphing data that fits a sinusoidal model
- Identifying periodic and sinusoidal functions and their domain/range restrictions
- Posing and solving real-world sinusoidal function problems
Solving Problems Involving Sinusoidal Functions
- Sketching sine and cosine graphs and describing their key properties
- Investigating the roles of d and c in vertical and horizontal sinusoidal translations
- Investigating the roles of a and k in reflections and stretches of sinusoidal graphs
- Determining amplitude, period, and phase shift, and sketching transformed sinusoidal graphs
Unit 4: Applications of Geometry
Representing, adding, and subtracting vectors; solving real-world 2D and 3D geometry problems; and determining circle properties, arcs, and sectors.
Modelling With Vectors
- Recognizing vectors and their real-world applications
- Representing a vector as a directed line segment
- Resolving a vector into vertical and horizontal components
- Representing a vector as a directed line segment given its components
- Determining the sum or difference of two vectors
- Solving real-world problems with vector addition and subtraction
Solving Problems Involving Geometry
- Gathering information about real-world geometric shapes in technology-related fields
- Converting between the imperial and metric systems
- Solving real-world problems with areas of rectangles, parallelograms, trapezoids, triangles, circles, and composite shapes
- Solving real-world problems with volumes and surface areas of spheres, prisms, and cylinders
Solving Problems Involving Circle Properties
- Recognizing and describing arcs, tangents, secants, chords, and angles of circles
- Determining arc length and the area of a sector or segment
- Investigating circle properties involving chords, central and inscribed angles, and tangents
- Solving real-world problems involving circle properties
Every skill above, taught one-on-one — free to try, no credit card.
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