MATH 140
MATH 140 Exam Topics & Study Guide
Skills organized by how likely they are to appear as standalone exam questions in MATH 140.
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.
Tangent lines appear on every MATH 140 exam. Find slope using derivative, use point-slope form for the equation.
One-sided limits appear on every MATH 140 exam at McGill. Often combined with piecewise functions to test continuity.
Limit properties are foundational in MATH 140. Expect direct application problems on midterm and final.
Computing limits is core MATH 140 material. Expect 3-5 limit problems per exam using factoring, conjugates, and algebraic manipulation.
Infinite limits (vertical asymptotes) appear on every MATH 140 exam. Know how to determine sign from left/right.
Limits at infinity (horizontal asymptotes) are tested heavily in MATH 140. Compare growth rates of polynomials, exponentials, logs.
Continuity questions appear on every MATH 140 exam. Know the three conditions and how to find values that make functions continuous.
The limit definition of derivative appears on MATH 140 midterms. Expect at least one problem using the limit definition directly.
Product and quotient rules are used constantly in MATH 140. Expect multiple problems requiring these rules on every exam.
Trig derivatives are essential in MATH 140. Know all six trig derivatives cold—they appear in almost every derivative problem.
Exponential and log derivatives appear on every MATH 140 exam. Know d/dx[e^x] = e^x and d/dx[ln x] = 1/x and their chain rule forms.
The chain rule is the most important MATH 140 technique. Appears in nearly every derivative problem—master it completely.
Finding critical points is fundamental in MATH 140. Set f'(x) = 0 and find where f'(x) DNE—this appears on every exam.
Min/max problems are core MATH 140. Know first and second derivative tests—expect 2-3 questions per exam.
Finding absolute extrema on closed intervals is tested on every MATH 140 exam. Check critical points AND endpoints.
Curve sketching is a major MATH 140 final topic. Combine all skills: domain, asymptotes, critical points, inflection points, concavity.
Optimization word problems appear on every MATH 140 final. Setting up the function to optimize is the key challenge.
Implicit differentiation appears on every MATH 140 exam. Expect 1-2 problems finding dy/dx from equations like x^2 + y^2 = 1.
Related rates are a MATH 140 classic. Expect word problems with ladders, cones, shadows. Draw diagram, write equation, differentiate with respect to t.
L'Hopital's Rule is heavily tested on MATH 140 finals. Know all indeterminate forms: 0/0, infinity/infinity, and how to convert others.
IVT appears occasionally in MATH 140. Used to prove existence of roots—know the hypotheses (continuous on [a,b]).
Differentiability questions appear in MATH 140 for piecewise functions. Check if limit of derivative exists from both sides.
Inverse trig derivatives appear regularly in MATH 140. Know d/dx[arcsin x], d/dx[arctan x] especially.
Hyperbolic function derivatives may appear on MATH 140 finals. Know sinh, cosh, tanh and their derivatives.
Logarithmic differentiation appears in MATH 140 for products/quotients with many factors or variable exponents like x^x.
The Mean Value Theorem appears on MATH 140 exams as conceptual questions. Know the statement and geometric interpretation.
Rational functions appear throughout MATH 140 for limits, derivatives, and curve sketching.
Exponential functions are foundational in MATH 140. Properties and graphs should be second nature.
Logarithmic functions are used throughout MATH 140. Know log properties for simplification before differentiating.
Growth and decay problems appear in MATH 140 applications. Set up and solve y' = ky type differential equations.
The definition of e is conceptual background in MATH 140. Underlies exponential derivative formulas.
Domain and range are assumed knowledge in MATH 140. Not tested standalone but needed for all function analysis.
Polynomial long division is a tool in MATH 140 for simplifying rational functions. Not tested alone.
Function transformations are prerequisite knowledge for MATH 140. Used in curve sketching but not tested alone.
Polynomial functions are foundational in MATH 140. Properties should be known from precalculus.
Newton's Method appears occasionally on MATH 140 finals. Know the iteration formula x_{n+1} = x_n - f(x_n)/f'(x_n).
Antiderivative introduction is brief in MATH 140—covered mainly in MATH 141. May appear as one question on the final.
Interest and present value problems are application topics in MATH 140. May appear as word problems on finals.