MATH 139 Exam Topics & Study Guide
Skills organized by how likely they are to appear as standalone exam questions in MATH 139.
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Don't skip "Essential" or "Low" skills! They're foundational — you need them to solve higher-likelihood problems.
Growth and decay problems are emphasized in MATH 139 due to life sciences focus. Expect population growth, radioactive decay, and drug concentration problems.
Computing limits is core MATH 139 material. Expect 3-4 limit problems per exam using factoring, conjugates, and algebraic tricks.
Infinite limits (vertical asymptotes) appear on every MATH 139 exam. Determine the sign by testing from left and right.
Limits at infinity are tested heavily in MATH 139. Know how to find horizontal asymptotes for rational and exponential functions.
Continuity problems appear on every MATH 139 exam. Know the three conditions and how to find values making piecewise functions continuous.
Product and quotient rules are used constantly in MATH 139. Multiple problems on every exam require these rules.
Trig derivatives appear on every MATH 139 exam. Know all six derivatives—they combine with chain rule frequently.
Exponential and log derivatives are essential in MATH 139. Heavy emphasis due to life sciences applications.
The chain rule is the most important MATH 139 derivative technique. Used in nearly every problem—master it completely.
Finding critical points is fundamental in MATH 139. Set f'(x) = 0 and find where f'(x) DNE—appears on every exam.
Min/max problems are core MATH 139 material. Know first and second derivative tests for local extrema.
Absolute extrema on closed intervals are tested on every MATH 139 exam. Check critical points AND endpoints.
Optimization is a major MATH 139 topic with real-world applications. Expect cost, profit, or resource allocation problems on every final.
L'Hopital's Rule is heavily tested on MATH 139 finals. Know 0/0 and infinity/infinity forms and how to convert others.
Implicit differentiation appears on every MATH 139 exam. Expect 1-2 problems finding dy/dx from implicit equations.
Related rates are classic MATH 139 word problems. Expect ladders, cones, shadows, and population growth scenarios.
Rational functions appear in MATH 139 for limits, derivatives, and curve sketching.
Exponential functions are foundational in MATH 139 applications. Properties should be well understood.
Log functions appear throughout MATH 139. Know properties for simplification before differentiating.
Financial math problems appear in MATH 139 applications. Compound interest and present value calculations.
Tangent line problems appear on MATH 139 midterms. Find slope via derivative, write equation using point-slope form.
One-sided limits appear in MATH 139 with piecewise functions. Often used to test continuity conditions.
Limit properties are foundational in MATH 139. Used throughout but rarely tested as standalone questions.
The limit definition may appear on MATH 139 midterms. Less emphasis than MATH 140 but know the concept.
Inverse trig derivatives appear occasionally in MATH 139. Know arcsin and arctan derivatives especially.
Log differentiation appears in MATH 139 for products with many factors or expressions like x^x.
Curve sketching appears on MATH 139 finals. Combine domain, asymptotes, critical points, and concavity.
MVT appears occasionally in MATH 139. Know the statement and basic applications.
Linear approximations appear in MATH 139 as practical applications. Use tangent line to estimate function values.
Domain and range are assumed knowledge in MATH 139. Not tested alone but needed everywhere.
Long division is a tool for MATH 139 rational functions. Not tested standalone.
Transformations are prerequisite knowledge for MATH 139. Used but not directly tested.
Polynomial properties should be known from precalculus. Foundation for MATH 139 work.
Hyperbolic functions are less emphasized in MATH 139 than MATH 140. May appear briefly if covered.
Antiderivatives are briefly introduced in MATH 139. Main coverage is in MATH 141.