Complete Calculus 12 curriculum with video lessons, practice problems, step-by-step solutions, and progress tracking for every topic including limits, derivatives, and integrals.

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Curriculum Outcome

StudyPug Topic

NS.CO.C12.B1

Calculate and interpret average and instantaneous rate of change:

NS.CO.C12.B2

Calculate limits for function values and apply limit properties with and without technology:

NS.CO.C12.B3

Remove removable discontinuities by extending or modifying a function:

NS.CO.C12.B4

Apply the properties of algebraic combinations and composites of continuous functions:

NS.CO.C12.A1

Apply average and instantaneous rates of change to secant line and tangent line slopes:

NS.CO.C12.A2

Demonstrate an understanding of the definition of the derivative:

NS.CO.C12.A3

Demonstrate understanding of implicit differentiation and identify situations that require it:

NS.CO.C12.B5

Find where a function is not differentiable and distinguish between corners cusps discontinuities and vertical tangents:

NS.CO.C12.B6

Derive apply and explain power sum difference product and quotient rules:

NS.CO.C12.B7

Apply the chain rule to composite functions:

NS.CO.C12.B9

Apply the rules for differentiating the six trigonometric functions:

NS.CO.C12.B10

Apply the rules for differentiating the six inverse trigonometric functions:

NS.CO.C12.B11

Calculate and apply derivatives of exponential and logarithmic functions:

NS.CO.C12.B12

Apply Newton's method to approximate zeros of a function:

NS.CO.C12.B13

Estimate the change in a function using differentials and apply them to real world situations:

NS.CO.C12.C2

Understand the development of the slope of a tangent line from the slope of a secant line:

NS.CO.C12.C4

Demonstrate an understanding of the connection between the graphs of f and f:

NS.CO.C12.B14

Solve and interpret related rate problems:

NS.CO.C12.B15

Demonstrate an understanding of critical points and absolute extreme values of a function:

NS.CO.C12.B16

Find the intervals on which a function is increasing or decreasing:

NS.CO.C12.B17

Solve application problems involving maximum or minimum values of a function:

NS.CO.C12.B18

Apply rules for definite integrals:

NS.CO.C12.B19

Apply the Fundamental Theorem of Calculus:

NS.CO.C12.B20

Compute indefinite and definite integrals by the method of substitution:

NS.CO.C12.B21

Apply integration by parts to evaluate indefinite and definite integrals:

NS.CO.C12.B22

Solve problems in which a rate is integrated to find the net change over time:

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:

NS.CO.C12.C9

Construct antiderivatives using the Fundamental Theorem of Calculus:

NS.CO.C12.C10

Find antiderivatives of polynomials e^kx and selected trigonometric functions of kx:

NS.CO.C12.C11

Construct slope fields using technology and interpret them as visualizations of differential equations: