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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

Develop and apply the equation of the unit circle

Unit circle

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

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

Transformations of functions: Horizontal translations

Transformations of functions: Vertical translations

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

Transformations of functions: Horizontal stretches

Transformations of functions: Vertical stretches

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

Combining transformations of functions

Even and odd functions

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)

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

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

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

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

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

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

Demonstrate an understanding of factoring polynomials of degree greater than 2

Polynomial long division

Polynomial synthetic division

Remainder theorem

Factor 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&apos; rule of signs

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

Graph and analyze radical functions

Radical functions and transformations

Square root of a function

Solving radical equations

Operations with radicals

Basic radical functions

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

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

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

Prove trigonometric identities using various identities

Quotient identities and reciprocal identities

Pythagorean identities

Sum and difference identities

Double-angle identities

Cofunction identities

Apply the fundamental counting principle to solve problems

Fundamental counting principle

Path counting problems

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

Factorial notation

Permutations

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

Combinations

Problems involving both permutations and combinations

Permutation vs. Combination

Expand powers of a binomial using the binomial theorem

Pascal's triangle

Binomial theorem

We’ve got answers to some popular questions.

Manitoba Grade 12 Math FAQ

Explore Manitoba's Grade 12 Pre-Calculus Mathematics (40S) curriculum. Align with provincial standards and prepare for advanced math studies.