- arithmetic, including working with fractions
- ratio, proportion, and percentages
- manipulation of algebraic expressions
- factoring algebraic expressions
- solving linear equations
- solving linear inequalities
- lines and graphs
- simultaneously solving two equations in two unknowns
- working with quadratic equations
- working with higher degree equations
- working with exponents and radicals
- word problems

- working with rational exponents
- understanding the idea of a function
- working with graphs of functions
- working with quadratic functions
- working with exponential functions
- working with logarithmic functions
- understanding how to compose functions
- working with absolute value
- understanding trigonometric values, especially radians
- working with trigonometric identities

- understanding limits
- finding the equation of a tangent to a curve
- differentiating with the chain rule
- doing implicit differentiation
- finding where a function is increasing or decreasing
- finding the maxima and/or minima of polynomials
- finding the maxima and/or minima of other functions
- graphing rational functions
- finding the derivatives of trigonometric functions
- finding the derivatives of exponential functions
- finding the derivatives of logarithmic functions

- finding the derivative of definite integrals
- finding the integrals of derivatives (that is, computing anti-derivatives and using the Fundamental Theorem of Calculus)
- evaluating definite integrals
- evaluating indefinite integrals
- working with integrals as an area under a graph
- finding the area of regions bounded by straight lines
- finding the area of regions bounded by other graphs

- finding the integrals of trigonometric functions
- finding the integrals of exponential and logarithmic functions
- finding volumes by slicing
- understanding rectilinear motion
- understanding work
- being able to integrate by parts
- being able to integrate using substitutions

- computing improper integrals
- using l'Hôpital's rules
- finding the sums of particular power series
- working with Taylor series
- finding the sum of an infinite series
- working with complex numbers
- solving differential equations of the form
*dy*/*dt*=*ky* - solving initial-value problems
- solving separable differential equations