Exam Likelihood Breakdown
Skills organized by how likely they are to appear as standalone exam questions in MATH 139.
Important Disclaimer
These likelihood ratings are not official and are not endorsed by your university or professors. We have no contact with course instructors and no insider information about exam content. These ratings are based solely on our team's experience analyzing past exams, taking similar courses, and understanding typical curriculum patterns. Take this as a rough guide only — your actual exam may differ significantly. Always consult your course syllabus, professor's guidance, and official study materials as your primary resources.
How to Read This Guide
Don't skip "Essential" or "Low" skills! They're foundational — you need them to solve higher-likelihood problems.
Frequently tested. Know how to find tangent line equations using point-slope form.
Common on exams for piecewise functions and continuity questions. Check both left and right limits.
Foundation for computing limits. Know sum, product, quotient, and composition rules.
Know how to identify vertical asymptotes and determine if limit approaches positive or negative infinity.
Common for finding horizontal asymptotes. Compare degrees of numerator and denominator.
Tested via piecewise functions where you must find values that make f continuous.
Know derivatives of arcsin, arctan, and arcsec at minimum. Often appears in implicit differentiation.
Synthesizes many skills: intercepts, asymptotes, intervals of increase/decrease, concavity, inflection points.
Classic word problems. Set up constraint and objective function, substitute, differentiate, find critical points.
Know basic antiderivatives and plus C. Reverse the derivative rules. Often the last topic before final.
Differentiate both sides with respect to x, use chain rule on y terms, then solve for dy/dx.
Classic word problems: ladders, cones, shadows. Draw diagram, write equation, differentiate with respect to t.
Often tested as part of function analysis. Know domain restrictions from denominators, square roots, and logarithms.
Foundation for many calculus problems. Know behavior, roots, and end behavior for curve sketching.
Important for limit problems involving asymptotes. Know how to identify vertical and horizontal asymptotes.
Appears in derivative and growth/decay problems. Know properties of e^x and general exponential rules.
Essential for logarithmic differentiation and solving equations. Know log rules and ln properties.
Useful for products/quotients with many terms or variable exponents like x^x. Take ln of both sides.
Use L(x) = f(a) + f prime a times (x-a) to approximate function values near x=a. Tangent line approximation.
Tested on every exam. Master factoring, conjugates, and algebraic manipulation for indeterminate forms.
Expect at least one limit definition problem. Know both forms. Show all steps.
Used constantly. Memorize both rules and practice combining with chain rule. Common source of errors.
Memorize all six trig derivatives. Frequently combined with chain rule and product/quotient rules.
Know d/dx of e^x equals e^x and d/dx of ln x equals 1/x. Chain rule applications are very common.
Used in nearly every derivative problem. Practice nested functions and combining with other rules.
Foundation for optimization. Find where f prime equals 0 or undefined. Check endpoints on closed intervals.
Use first or second derivative test. Know difference between local and absolute extrema.
On closed intervals: evaluate f at critical points AND endpoints. Compare all values for absolute max/min.
Occasionally needed for limit problems or partial fractions. Usually a tool rather than tested directly.
Rarely tested directly but understanding shifts and stretches helps with curve sketching.
May appear in word problems involving exponential models. Know the standard forms for growth and decay.
Coverage varies by instructor. If covered, know sinh and cosh derivatives and their similarity to trig.
Coverage varies. If tested, know the statement and how to find c where f prime c equals average rate of change.
Coverage varies by instructor. If covered, use for 0/0 or infinity/infinity forms only.
Business calculus topic not typically covered in MATH 139.