CCSS_MATHAPhigh school
AP Calculus AB
Limits, derivatives, integrals, and the Fundamental Theorem of Calculus - aligned to the College Board AP Calculus AB curriculum. Eight units match the official CED with exam-weight-based assessment allocation. Practice targets the procedural fluency and conceptual understanding tested on the AP exam.
8units
22topics
268questions
~7hours
Course Units
Learning objectives
- Evaluate limits graphically, numerically, and algebraically
- Apply the squeeze theorem and limit properties
- Determine continuity of a function at a point and on an interval
- Evaluate limits involving infinity and identify asymptotic behavior
- Apply the Intermediate Value Theorem to continuous functions
Learning objectives
- Define the derivative as a limit of the difference quotient
- Apply power, constant, sum, and constant multiple rules
- Differentiate trigonometric functions (sin, cos, tan, csc, sec, cot)
- Differentiate exponential and logarithmic functions
- Use the product and quotient rules
Learning objectives
- Apply the chain rule to differentiate composite functions
- Use implicit differentiation on equations not solved for y
- Compute derivatives of inverse functions using the inverse function theorem
- Differentiate inverse trigonometric functions
- Calculate and interpret higher-order derivatives
Topics in this unit
Learning objectives
- Interpret the derivative as a rate of change in applied contexts
- Solve related rates problems using implicit differentiation
- Use linearization and differentials to approximate function values
- Apply L'Hopital's rule to evaluate indeterminate forms
- Analyze straight-line motion using position, velocity, and acceleration
Topics in this unit
Learning objectives
- Apply the Mean Value Theorem and its consequences
- Use the first derivative test to find relative extrema
- Use the second derivative test to determine concavity and classify extrema
- Identify inflection points and intervals of concavity
- Solve optimization problems using calculus techniques
- Sketch curves using first and second derivative analysis
Topics in this unit
Learning objectives
- Approximate area under a curve using Riemann sums and trapezoidal rule
- Apply the Fundamental Theorem of Calculus (both parts)
- Evaluate definite and indefinite integrals using basic rules
- Evaluate integrals using u-substitution
- Interpret the definite integral as net accumulation of change
- Evaluate integrals of common functions (polynomial, trig, exponential, 1/x)
Learning objectives
- Model real-world situations with differential equations
- Sketch and interpret slope fields
- Use Euler's method to approximate solutions
- Solve separable differential equations analytically
- Apply differential equations to exponential growth and decay models
Topics in this unit
Learning objectives
- Find the average value of a function on an interval
- Calculate area between curves using definite integrals
- Compute volumes of solids of revolution using disc and washer methods
- Compute volumes of solids with known cross sections
Topics in this unit