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Grade 12 Math Courses - Manitoba Curriculum

Discover Manitoba's Grade 12 Pre-Calculus Mathematics (40S) course. Prepare for advanced math studies with a comprehensive curriculum aligned to provincial standards and university prerequisites.

Grade 12 Applied Mathematics (40S)

Grade 12 Essential Mathematics (40S) - Half Course 5

Grade 12 Essential Mathematics (40S) - Half Course 6

Grade 12 Pre-Calculus Mathematics (40S)

Manitoba Grade 12 Math Curriculum - Pre-Calculus 40S

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GO_ID	Outcome	StudyPug Topic
MB.GO.12P.T.1	Demonstrate an understanding of angles in standard position, expressed in degrees and radians:	Angle in standard position Coterminal angles Reference angle Converting between degrees and radians Trigonometric ratios of angles in radians

MB.GO.12P.T.2

Develop and apply the equation of the unit circle:

MB.GO.12P.T.3

Solve problems using the 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)

Radian measure and arc length

MB.GO.12P.T.4

Graph and analyze the 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

MB.GO.12P.T.5

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

Determining non-permissible values for trig expressions

Solving trigonometric equations using pythagorean identities

Solving trigonometric equations using sum and difference identities

Solving trigonometric equations using double-angle identities

MB.GO.12P.T.6

Prove trigonometric identities using various identities:

Quotient identities and reciprocal identities

Pythagorean identities

Sum and difference identities

Double-angle identities

Cofunction identities

MB.GO.12P.P.1

Apply the fundamental counting principle to solve problems:

Fundamental counting principle

Path counting problems

MB.GO.12P.P.2

Determine the number of permutations of n elements taken r at a time to solve problems:

Factorial notation

MB.GO.12P.P.3

Determine the number of combinations of n different elements taken r at a time to solve problems:

Problems involving both permutations and combinations

Permutation vs. Combination

MB.GO.12P.P.4

Expand powers of a binomial using the binomial theorem:

Pascal's triangle

Binomial theorem

MB.GO.12P.R.1

Demonstrate an 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

MB.GO.12P.R.2

Demonstrate an understanding of horizontal and vertical translations on function graphs and equations:

Transformations of functions: Horizontal translations

Transformations of functions: Vertical translations

MB.GO.12P.R.3

Demonstrate an understanding of horizontal and vertical compressions and stretches on function graphs:

Transformations of functions: Horizontal stretches

Transformations of functions: Vertical stretches

MB.GO.12P.R.4

Apply translations, compressions and stretches to the graphs and equations of functions:

Combining transformations of functions

Even and odd functions

MB.GO.12P.R.5

Demonstrate an understanding of reflections on function graphs and equations:

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

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

MB.GO.12P.R.6

Demonstrate an 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

MB.GO.12P.R.7

Demonstrate an 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

MB.GO.12P.R.8

Demonstrate an understanding of the product, quotient and power laws of logarithms:

Product rule of logarithms

Quotient rule of logarithms

Combining product rule and quotient rule in logarithms

Evaluating logarithms using logarithm rules

MB.GO.12P.R.9

Graph and analyze exponential and logarithmic functions:

Graphing exponential functions

Graphing transformations of exponential functions

Finding an exponential function given its graph

Graphing logarithmic functions

Finding a logarithmic function given its graph

MB.GO.12P.R.10

Solve problems that involve exponential and logarithmic equations:

Solving logarithmic equations

Converting from exponential form to logarithmic form

Solving exponential equations with logarithms

Solving exponential equations using exponent rules

MB.GO.12P.R.11

Demonstrate an understanding of factoring polynomials of degree greater than 2:

Polynomial long division

Polynomial synthetic division

Remainder theorem

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

MB.GO.12P.R.12

Graph and analyze polynomial functions:

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

Graphing quadratic functions: General form VS. Vertex form

Finding the quadratic functions for given parabolas

Multiplicities of polynomials

Imaginary zeros of polynomials

Solving polynomial inequalities

MB.GO.12P.R.13

Graph and analyze radical functions:

Radical functions and transformations

Square root of a function

Solving radical equations

Operations with radicals

Basic radical functions

MB.GO.12P.R.14

Graph and analyze rational functions:

What is a rational function?

Point of discontinuity

Slant asymptote

Solving rational equations

Solving rational inequalities

Graphing reciprocals of linear functions

Vertical asymptote

Horizontal asymptote

Graphs of rational functions

Graphing reciprocals of quadratic functions

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