There are in total learning goals. Check the goals you have mastered and click the following button to see your level of mastery.
Congratulation! You have mastered about of learning goals.
Algebra and Geometry of Functions
F1: I can use function notations to describe functions.
F2: I can evaluate and graph functions.
F3: I can find domain, range and intercepts of a function.
F4: I can find the composition of functions and recognize a function as the composition of functions.
F5: I can perform mathematical operations on polynomials and factor polynomials.
F6: I can perform mathematical operations on rational expressions.
F7: I can perform mathematical operations on radical expressions and rationalize denominators or numerators.
F8: I can solve equations and inequalities.
F9: I can evaluate trigonometric functions and determine the measure of the angle from a special trigonometric equation.
F10: I can solve problems on right triangles using trigonometric identities.
Limits
L1: I can explain how the idea of a limit is involved in solving the the tangent problem.
L2: I can explain how the idea of a limit is involved in solving the area problem.
L3: I can explain the definition of the limit of a function using numerical, and graphical methods.
L4: I can provide an example that the numerical method fails.
L5: (CORE) I can find the limit of a function at a point using algebraic methods and limit laws.
L6: (CORE) I can explain the relationship between one-sided and two-sided limits.
L7: (CORE) I can evaluate the limit of a function by using the squeeze theorem.
L8: I can using correct notation, describe an infinite limit.
L9: (CORE) I can find the limit of a function at the infinity using algebraic methods.
Continuity
C1: I can explain the three conditions for continuity at a point.
C2: (CORE) I can describe three kinds of discontinuities and provide examples.
C3: (CORE) I can determine whether and when a function is continuous over a given interval using the definition of continuity.
C4: I can state the theorem for limits of composite functions.
C5: (CORE) I can use the theorem for limits of composite functions evaluate limits.
C6: I can state the intermediate value theorem and provide examples and counterexamples.
C7: (CORE) I can apply the intermediate value theorem to solve problems such as determine whether an equation has a solution over a given interval.
Derivatives
D1: (CORE) I can find the derivative of a function at a point and as a function using the definition.
D2: (CORE) I can state the connection between derivatives and continuity, and provide examples.
D3: I can determine whether or when a function is differentiable over an interval using the definition.
D4: (CORE) I can use derivative notations and calculate higher derivatives.
D5: (CORE) I can find the equation of the tangent line to a function at a point.
D6: I can correctly interpret a rate of change as a derivative in context and find the value.
D7: (CORE) I can find derivatives of power and trigonometric functions, and their linear combinations.
D8: (CORE) I can find derivatives of functions using the product rule and the quotient rule.
D9: (CORE) I can find derivatives of composite functions using the chain rule.
D10: (CORE) I can find derivatives by using multiple rules in combination.
D11: (CORE) I can find the derivative of an implicitly-defined function using implicit differentiation.
D12: I can find the slope of the tangent line to a curve defined by an implicit function.
Applications of Derivatives
A1: I can set up equations for relationships among derivatives in a related rates problems and find the rate of change of one quantity that depends on the rate of change of other quantities.
A2: I can find the linearization of a given function and use it to estimate the value of a function at a given point.
A3: I can use differential approximation to calculate the change in a quantity, the relative error, and percentage error.
A4: (CORE) I can find the critical values of a function.
A5: I can use the Extreme Value Theorem to find the absolute maximum and minimum values of a continuous function over a closed interval.
A6: I can demonstrate understanding of the Mean Value Theorem using examples and counterexamples.
A7: (CORE) I can state three important corollaries of the Mean Value Theorem.
A8: I can explain how the sign of the first derivative affects the shape of the graph of a function.
A9: (CORE) I can find intervals of increasing and decreasing of a function.
A10: (CORE) I can find local extrema of a function using the First and Second Derivative Tests.
A11: I can determine the intervals of concavity of a function and find all of its points of inflection.
A12: I can find horizontal, vertical and oblique (slanted) asymptotes of a function using rules of limits.
A13: I can sketch the graph of a function manually.
A14: (CORE) I can set up and use differential calculus to solve applied optimization problems.
A15: (CORE) I can find the general antiderivative of a given function.
A16: I can use anti-differentiation to solve initial-value problems.
Integrals and Applications
I1: I can use sigma (summation) notation to calculate sums of powers of integers.
I2: (CORE) I can approximate area between curves using Riemann sums, and interpret a definite integral as the limit of Riemann sums.
I3: I can evaluate integrals using geometry and the properties of definite integrals.
I4: I can explain the connection between the Mean Value Theorem and the Fundamental Theorem of Calculus part 1 (\(\frac{\operatorname{d}}{\operatorname{d} x}\int_a^xf(t)\operatorname{d}t=f(x)\)).
I5: (CORE) I can evaluate a definite integral using the Fundamental Theorem of Calculus.
I6: I can explain the relationship between differentiation and integration.
I7: I can describe the meaning of the mean value theorem for integrals.
I8: I can calculate the average value of a function.
I9: (CORE) I can evaluate a definite integral using integration rules.
I10: I can use the net change theorem to solve applied problems.
I11: (CORE) I can use substitution to evaluate indefinite integrals and definite integrals.
I12: (CORE) I can find the area of a region between two curves using definite integrals.