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Grade 12 Math Courses - PEI Curriculum

Discover PEI's Grade 12 math options, from advanced calculus to workplace mathematics. Choose your path and prepare for post-secondary education or career success with our comprehensive course offerings.

Mathematics 12 (MAT621A)

Pre-Calculus 12 (MAT621B)

Advanced Mathematics and Calculus 12 (MAT611B)

Apprenticeship and Workplace Mathematics 12 (MAT631A)

PEI Grade 12 Math Curriculum - Advanced Courses and Pathways

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CO_ID	Curriculum Outcome	StudyPug Topic
PI.CO.PC12.RF1	Demonstrate understanding of operations on and compositions of functions:	Function notation (advanced) Composite functions Adding functions Subtracting functions Multiplying functions Dividing functions Operations with functions Inequalities of combined functions Difference quotient: applications of functions

PI.CO.PC12.RF2

Demonstrate understanding of horizontal and vertical translations on graphs of functions and related equations:

Transformations of functions: Horizontal translations

Transformations of functions: Vertical translations

PI.CO.PC12.RF3

Demonstrate understanding of horizontal and vertical stretches on graphs of functions and related equations:

Transformations of functions: Horizontal stretches

Transformations of functions: Vertical stretches

PI.CO.PC12.RF4

Apply translations and stretches to graphs and equations of functions:

Combining transformations of functions

PI.CO.PC12.RF5

Demonstrate understanding of reflections on graphs of functions and related equations:

Reflection across the y-axis: y = f(-x)

Reflection across the x-axis: y = -f(x)

Even and odd functions

PI.CO.PC12.RF6

Demonstrate understanding of inverses of relations:

Inverse functions

One to one functions

Finding inverse trigonometric function from its graph

Evaluating inverse trigonometric functions

Finding inverse reciprocal trigonometric function from its graph

Inverse reciprocal trigonometric function: finding the exact value

PI.CO.PC12.RF7

Demonstrate understanding of logarithms:

What is a logarithm?

Converting from logarithmic form to exponential form

Evaluating logarithms without a calculator

Common logarithms

Natural log: ln

Evaluating logarithms using change-of-base formula

Quotient rule of logarithms

Combining product rule and quotient rule in logarithms

Evaluating logarithms using logarithm rules

PI.CO.PC12.RF8

Demonstrate understanding of product quotient and power laws of logarithms:

Solving logarithmic equations

Product rule of logarithms

Graphing logarithmic functions

PI.CO.PC12.RF9

Graph and analyze exponential and logarithmic functions:

Graphing exponential functions

Graphing transformations of exponential functions

Finding an exponential function given its graph

Finding a logarithmic function given its graph

PI.CO.PC12.RF10

Solve problems involving exponential and logarithmic equations:

Solving exponential equations with logarithms

Exponential growth and decay by a factor

Exponential decay: Half-life

Exponential growth and decay by percentage

Solving exponential equations using exponent rules

PI.CO.PC12.RF11

Demonstrate understanding of factoring polynomials of degree greater than 2:

Polynomial long division

Polynomial synthetic division

Rational zero theorem

Factor by taking out the greatest common factor

Factor by grouping

Factoring difference of squares:

x^2 - y^2

Factoring trinomials

Fundamental theorem of algebra

Factoring difference of cubes

Factoring sum of cubes

Descartes' rule of signs

PI.CO.PC12.RF12

Graph and analyze polynomial functions:

Characteristics of polynomial graphs

Determining the equation of a polynomial function

Applications of polynomial functions

Characteristics of quadratic functions

Transformations of quadratic functions

Quadratic function in general form: y = ax^2 + bx + c

Converting from general to vertex form by completing the square

Shortcut: Vertex formula

Graphing quadratic functions: General form VS. Vertex form

Finding the quadratic functions for given parabolas

Multiplicities of polynomials

Imaginary zeros of polynomials

Quadratic function in vertex form: y = a(x-p)^2 + q

Solving polynomial inequalities

PI.CO.PC12.RF13

Graph and analyze radical functions:

Radical functions and transformations

Square root of a function

Solving radical equations

Basic radical functions

PI.CO.PC12.RF14

Graph and analyze rational functions:

What is a rational function?

Point of discontinuity

Slant asymptote

Solving rational equations

Solving rational inequalities

Applications of rational equations

Graphing reciprocals of linear functions

Vertical asymptote

Horizontal asymptote

Graphs of rational functions

Graphing reciprocals of quadratic functions

PI.CO.PC12.PC1

Solve problems involving fundamental counting principle permutations and combinations:

Fundamental counting principle

Factorial notation

Path counting problems

Problems involving both permutations and combinations

Permutation vs. Combination

PI.CO.PC12.PC2

Expand powers of a binomial using binomial theorem:

Pascal's triangle

Binomial theorem

PI.CO.PC12.T1

Demonstrate understanding of angles in standard position expressed in degrees and radians:

Angle in standard position

Coterminal angles

Reference angle

Converting between degrees and radians

PI.CO.PC12.T2

Develop and apply the equation of the unit circle:

PI.CO.PC12.T3

Solve problems using six trigonometric ratios for angles expressed in radians and degrees:

Find the exact value of trigonometric ratios

ASTC rule in trigonometry (All Students Take Calculus)

Trigonometric ratios of angles in radians

Radian measure and arc length

PI.CO.PC12.T4

Graph and analyze trigonometric functions sine cosine and tangent to solve problems:

Sine graph: y = sin x

Cosine graph: y = cos x

Tangent graph: y = tan x

Cotangent graph: y = cot x

Secant graph: y = sec x

Cosecant graph: y = csc x

Graphing transformations of trigonometric functions

Determining trigonometric functions given their graphs

PI.CO.PC12.T5

Solve algebraically and graphically first and second degree trigonometric equations:

Solving first degree trigonometric equations

Solving second degree trigonometric equations

Solving trigonometric equations involving multiple angles

Solving trigonometric equations using pythagorean identities

Solving trigonometric equations using sum and difference identities

Solving trigonometric equations using double-angle identities

PI.CO.PC12.T6

Prove trigonometric identities using reciprocal quotient Pythagorean sum or difference and double-angle identities:

Quotient identities and reciprocal identities

Pythagorean identities

Sum and difference identities

Double-angle identities

Cofunction identities

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