CLEP Calculus study plan

Evaluate limits graphically, numerically, and algebraically, including one-sided limits

Apply limit laws and algebraic manipulation (factoring, rationalizing, common denominators) to resolve indeterminate forms

Distinguish removable, jump, and infinite discontinuities and classify them from a given function

State and apply the formal epsilon-delta definition of a limit at an introductory level

Compute derivatives from the limit definition for polynomial and simple radical functions

Apply power, constant multiple, sum, product, and quotient rules fluently

Differentiate composite functions using the chain rule in nested and multi-layer forms

Differentiate trigonometric, exponential, and logarithmic functions

Perform implicit differentiation and solve for dy/dx

Differentiate inverse trigonometric functions and apply logarithmic differentiation

Solve related-rates problems by setting up and differentiating a geometric relationship

Interpret derivatives as instantaneous rates of change and as slopes of tangent lines

Find critical points and use first and second derivative tests to classify extrema

Determine intervals of increase/decrease and concavity, and locate inflection points

Apply the Mean Value Theorem and Rolle's Theorem to verify conditions and conclusions

Solve applied optimization problems with constrained variables

Sketch accurate curves from derivative sign information

Compute antiderivatives using the power rule and basic trigonometric and exponential forms

Evaluate definite integrals using the Fundamental Theorem of Calculus

Approximate definite integrals with left, right, midpoint, and trapezoidal sums and compare to exact values

Interpret definite integrals as net signed area and as accumulated change

Apply u-substitution to indefinite and definite integrals, changing limits of integration

Use integration by parts and recognize when it is the appropriate technique

Set up and evaluate area between curves and volumes of solids of revolution

Apply the Mean Value Theorem for Integrals

Review limit, derivative, and integral techniques in interleaved practice rather than blocked practice

Diagnose recurring error patterns from prior weeks' logs and correct them

Complete full-length timed practice under exam conditions

Manage pacing to finish all sections within time limits

Re-drill the highest-frequency differential and integral techniques to automaticity

Re-solve every previously missed problem without notes

Verify formula recall for rules, theorems, and standard integrals

Simulate final-day exam pacing and confirm test-day logistics