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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.C12.B1
Calculate and interpret average and instantaneous rate of change:
Difference quotient: applications of functions
NS.CO.C12.B2
Calculate limits for function values and apply limit properties with and without technology:
Finding limits from graphs
Finding limits algebraically - direct substitution
Finding limits algebraically - when direct substitution is not possible
Limit laws
NS.CO.C12.B3
Remove removable discontinuities by extending or modifying a function:
Continuity
NS.CO.C12.B4
Apply the properties of algebraic combinations and composites of continuous functions:
Intermediate value theorem
NS.CO.C12.A1
Apply average and instantaneous rates of change to secant line and tangent line slopes:
Limits at infinity - horizontal asymptotes
NS.CO.C12.A2
Demonstrate an understanding of the definition of the derivative:
Definition of derivative
NS.CO.C12.A3
Demonstrate understanding of implicit differentiation and identify situations that require it:
Implicit differentiation
NS.CO.C12.B5
Find where a function is not differentiable and distinguish between corners cusps discontinuities and vertical tangents:
Infinite limits - vertical asymptotes
NS.CO.C12.B6
Derive apply and explain power sum difference product and quotient rules:
Product rule
Quotient rule
Power rule
NS.CO.C12.B7
Apply the chain rule to composite functions:
Chain rule
NS.CO.C12.B9
Apply the rules for differentiating the six trigonometric functions:
Derivative of trigonometric functions
NS.CO.C12.B10
Apply the rules for differentiating the six inverse trigonometric functions:
Derivative of inverse trigonometric functions
NS.CO.C12.B11
Calculate and apply derivatives of exponential and logarithmic functions:
Derivative of exponential functions
Derivative of logarithmic functions
NS.CO.C12.B12
Apply Newton's method to approximate zeros of a function:
l'Hospital's rule
NS.CO.C12.B13
Estimate the change in a function using differentials and apply them to real world situations:
Linear approximation
Estimating Derivatives from a table
NS.CO.C12.C2
Understand the development of the slope of a tangent line from the slope of a secant line:
Slope and equation of tangent line
NS.CO.C12.C4
Demonstrate an understanding of the connection between the graphs of f and f:
Higher order derivatives
NS.CO.C12.B14
Solve and interpret related rate problems:
Related rates
NS.CO.C12.B15
Demonstrate an understanding of critical points and absolute extreme values of a function:
Critical number & maximum and minimum values
NS.CO.C12.B16
Find the intervals on which a function is increasing or decreasing:
Curve sketching
NS.CO.C12.B17
Solve application problems involving maximum or minimum values of a function:
Optimization
NS.CO.C12.B18
Apply rules for definite integrals:
Definite integral
NS.CO.C12.B19
Apply the Fundamental Theorem of Calculus:
Fundamental theorem of calculus
NS.CO.C12.B20
Compute indefinite and definite integrals by the method of substitution:
U-Substitution
NS.CO.C12.B21
Apply integration by parts to evaluate indefinite and definite integrals:
Integration by parts
NS.CO.C12.B22
Solve problems in which a rate is integrated to find the net change over time:
Position velocity acceleration
Volumes of solid with known cross-sections
Arc length
NS.CO.C12.C7
Solve initial value problems of the form dy/dx = f(x) y0 = f(x0) where f(x) is a recognizable derivative:
Order and solutions to differential equations
NS.CO.C12.C9
Construct antiderivatives using the Fundamental Theorem of Calculus:
Antiderivatives
NS.CO.C12.C10
Find antiderivatives of polynomials e^kx and selected trigonometric functions of kx:
Integration using trigonometric identities
NS.CO.C12.C11
Construct slope fields using technology and interpret them as visualizations of differential equations:
Slope fields
NS.CO.C12.D1
Apply and understand how Riemann sums can be used to determine the area under a polynomial curve:
Riemann sum
NS.CO.C12.D4
Compute the area under a curve using numerical integration procedures:
Numerical integration
NS.CO.C12.D5
Apply integration to calculate areas of regions in a plane:
Areas between curves
NS.CO.C12.D6
Apply integration by slices or shells to calculate volumes of solids:
Volumes of solids of revolution - Disc method
Volumes of solid of revolution - Shell method
NS.CO.C12.B23
Solve a differential equation of the form dy/dx = g(x)h(y) in which the variables are separable:
Separable equations
NS.CO.C12.B24
Solve problems involving exponential growth and decay:
Modeling with differential equations
NS.CO.C12.B25
Apply Euler's method to find approximate solutions to differential equations with initial values:
Euler's method

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