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Grade 12 Math Courses - New Brunswick Curriculum

Discover New Brunswick's Grade 12 Pre-Calculus B 120 course. Advance your mathematical skills with quadratic functions, sequences, and an introduction to calculus, preparing you for post-secondary success.

Financial and Workplace Mathematics 120

Foundations 120

Pre-Calculus A 120

Pre-Calculus B 120

Calculus 120

NBCC Skilled Trades and Work-Ready Math 120

New Brunswick Grade 12 Math Curriculum - Pre-Calculus B 120

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SCO_ID	Curriculum Outcome - Elaborations	StudyPug Topic
NB.SCO.PCB120.RF1	Demonstrate an understanding of the characteristics of quadratic functions: Analyze characteristics of quadratic functions including domain, range, vertex, axis of symmetry, and intercepts	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 Quadratic function in vertex form: y = a(x-p)^2 + q

NB.SCO.PCB120.RF2

Solve problems that involve quadratic equations: Apply factoring, graphing, and quadratic formula methods to solve quadratic equations

Solving quadratic equations by factoring

Solving quadratic equations by completing the square

Using quadratic formula to solve quadratic equations

Nature of roots of quadratic equations: The discriminant

Applications of quadratic equations

Solving quadratic inequalities

Arithmetic mean vs. Geometric mean

NB.SCO.PCB120.RF3

Analyze arithmetic and geometric sequences and series to solve problems: Determine terms, sums, and applications of arithmetic and geometric sequences and series

Polynomial long division

Polynomial synthetic division

Polynomial functions

Remainder theorem

Arithmetic sequences

Arithmetic series

Geometric sequences

Geometric series

Infinite geometric series

Fundamental theorem of algebra

Descartes' rule of signs

NB.SCO.PCB120.RF4

Demonstrate an understanding of reciprocal functions: Graph and analyze reciprocal functions including domain, range, and asymptotes

Characteristics of polynomial graphs

Determining the equation of a polynomial function

Applications of polynomial functions

Graphing reciprocals of linear functions

Multiplicities of polynomials

Imaginary zeros of polynomials

Solving polynomial inequalities

Graphing reciprocals of quadratic functions

NB.SCO.PCB120.RF5

Demonstrate an understanding of rational expressions and equations: Simplify rational expressions and solve rational equations

Solving rational equations

Simplifying rational expressions and restrictions

Adding and subtracting rational expressions

Multiplying rational expressions

Dividing rational expressions

Applications of rational equations

Simplifying complex fractions

Partial fraction decomposition

NB.SCO.PCB120.RF6

Demonstrate an understanding of absolute value functions: Graph and solve absolute value functions and equations

What is a rational function?

Point of discontinuity

Slant asymptote

Solving rational inequalities

Absolute value functions

Solving absolute value equations

Solving absolute value inequalities

Vertical asymptote

Horizontal asymptote

Graphs of rational functions

NB.SCO.PCB120.RF7

Analyze quadratic inequalities in one variable: Solve and graph quadratic inequalities in one variable

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

NB.SCO.PCB120.RF8

Solve systems of linear-quadratic and quadratic-quadratic equations graphically and algebraically: Apply graphing and algebraic methods to solve systems of equations

System of linear equations

System of linear-quadratic equations

System of quadratic-quadratic equations

NB.SCO.PCB120.PCB1

Apply the fundamental counting principle to solve problems: Use the fundamental counting principle in various problem-solving contexts

Fundamental counting principle

NB.SCO.PCB120.PCB2

Determine the number of permutations of n elements taken r at a time: Calculate and apply permutations in problem-solving situations

Factorial notation

Path counting problems

Permutation vs. Combination

NB.SCO.PCB120.PCB3

Determine the number of combinations of n elements taken r at a time: Calculate and apply combinations in problem-solving situations

Problems involving both permutations and combinations

NB.SCO.PCB120.PCB4

Expand powers of a binomial using the binomial theorem: Apply the binomial theorem to expand and find specific terms in binomial expressions

Pascal's triangle

Binomial theorem

NB.SCO.PCB120.L1

Demonstrate an understanding of limits and limit notation: Evaluate limits using graphs, tables, and algebraic methods

Finding limits from graphs

Introduction to Calculus - Limits

NB.SCO.PCB120.L2

Evaluate limits of functions and recognize continuity: Determine limits at a point, one-sided limits, and limits at infinity

Intermediate value theorem

Finding limits algebraically - direct substitution

Finding limits algebraically - when direct substitution is not possible

NB.SCO.PCB120.L3

Determine limits of trigonometric functions: Evaluate limits involving trigonometric functions and identities

Squeeze theorem

l'Hospital's rule

NB.SCO.PCB120.L4

Apply limits to define and understand derivatives: Use limit definition to find derivatives of functions

Infinite limits - vertical asymptotes

Limits at infinity - horizontal asymptotes

Definition of derivative

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