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Grade 12 Math Courses - Nova Scotia Curriculum

Discover Nova Scotia's Grade 12 math options, from Pre-Calculus to Mathematics Essentials. Choose the right path to meet your academic goals and prepare for post-secondary success.

Grade 12

Pre-Calculus 12

Mathematics at Work 12

Mathematics Essentials 12

Calculus 12

Nova Scotia Grade 12 Math Curriculum - StudyPug

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CO_ID	Curriculum Outcome	StudyPug Topic
NS.CO.PC12.T01	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 Trigonometric ratios of angles in radians

NS.CO.PC12.T02

Develop and apply the equation of the unit circle:

NS.CO.PC12.T03

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)

Radian measure and arc length

NS.CO.PC12.T04

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

Graphing transformations of trigonometric functions

Determining trigonometric functions given their graphs

NS.CO.PC12.T05

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

NS.CO.PC12.T06

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

Quotient identities and reciprocal identities

Pythagorean identities

Sum and difference identities

Double-angle identities

Cofunction identities

NS.CO.PC12.RF01

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

NS.CO.PC12.RF02

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

Transformations of functions: Horizontal translations

Transformations of functions: Vertical translations

NS.CO.PC12.RF03

Demonstrate understanding of effects of horizontal and vertical stretches on function graphs and equations:

Transformations of functions: Horizontal stretches

Transformations of functions: Vertical stretches

NS.CO.PC12.RF04

Apply translations and stretches to graphs and equations of functions:

Combining transformations of functions

NS.CO.PC12.RF05

Demonstrate understanding of effects of reflections on function graphs and equations:

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

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

Even and odd functions

NS.CO.PC12.RF06

Demonstrate understanding of inverses of relations:

Inverse functions

One to one functions

NS.CO.PC12.RF07

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

Converting from exponential form to logarithmic form

NS.CO.PC12.RF08

Demonstrate understanding of 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

NS.CO.PC12.RF09

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

NS.CO.PC12.RF10

Solve problems involving exponential and logarithmic equations:

Solving logarithmic equations

Solving exponential equations with logarithms

Solving exponential equations using exponent rules

NS.CO.PC12.RF11

Demonstrate understanding of factoring polynomials of degree greater than 2:

Polynomial long division

Polynomial synthetic division

Polynomial functions

Remainder theorem

Rational zero theorem

Characteristics of polynomial graphs

Factor by taking out the greatest common factor

Factor by grouping

Factoring difference of squares:

x^2 - y^2

Factoring trinomials

Multiplicities of polynomials

Imaginary zeros of polynomials

Factoring difference of cubes

Factoring sum of cubes

NS.CO.PC12.RF12

Graph and analyze 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

Applications of quadratic functions

NS.CO.PC12.RF13

Graph and analyze radical functions:

Radical functions and transformations

Square root of a function

Solving radical equations

Basic radical functions

NS.CO.PC12.RF14

Graph and analyze rational functions:

Slant asymptote

Graphing reciprocals of linear functions

Vertical asymptote

Horizontal asymptote

Graphs of rational functions

Graphing reciprocals of quadratic functions

NS.CO.PC12.PCB01

Apply fundamental counting principle to solve problems:

Fundamental counting principle

NS.CO.PC12.PCB02

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

Factorial notation

Path counting problems

NS.CO.PC12.PCB03

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

Problems involving both permutations and combinations

NS.CO.PC12.PCB04

Expand powers of a binomial using binomial theorem:

Pascal's triangle

Binomial theorem

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