MATH 141 Exam Topics & Study Guide
Skills organized by how likely they are to appear as standalone exam questions in MATH 141.
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.
Definite integrals appear on every MATH 141 exam at McGill. Expect 3-5 questions from basic FTC to area/volume applications.
FTC is tested heavily in MATH 141. Part 1 (d/dx of integrals) and Part 2 (evaluation) both appear on midterm and final.
U-substitution is the most common MATH 141 technique. Appears on every exam, often combined with other methods.
IBP appears on every MATH 141 exam. Expect 1-2 standalone problems plus use within other techniques.
Trig sub is heavily tested in MATH 141. Know which substitution for each radical form—this appears on every exam.
Partial fractions are a MATH 141 staple. Expect rational functions with linear and quadratic factors on both midterm and final.
Improper integrals appear on both MATH 141 midterm and final. Expect convergence/divergence and evaluation with limits.
Area between curves is classic MATH 141. Expect 1-2 questions requiring intersection points and correct integral setup.
Disk/washer problems appear on every MATH 141 exam. Visualizing the solid and choosing inner/outer radii is key.
Shell method is tested frequently in MATH 141, often alongside washers. Know when shells give an easier setup.
Geometric series are foundational for MATH 141 series work. Know the sum formula and recognize disguised geometric series.
The ratio test dominates MATH 141 series problems. Expect 2-3 convergence questions using this test on the final.
Power series convergence is a major MATH 141 final topic. Finding radius/interval and testing endpoints appears every year.
Taylor series are heavily weighted on the MATH 141 final. This late-course topic gets significant exam coverage. Know e^x, sin x, cos x, ln(1+x) by heart.
Error bounds are a key MATH 141 final topic. Lagrange remainder problems appear regularly—later material is weighted more.
Binomial series appear on MATH 141 finals as a Taylor series application. This late-course topic is weighted heavily.
Indefinite integrals in MATH 141 are usually part of technique problems rather than standalone questions.
Trig integrals (sin^m cos^n) appear on MATH 141 exams. Know strategies for odd/even powers.
Comparison for improper integrals shows up 1-2 times per MATH 141 exam. Know comparisons with 1/x^p.
Average value is a quick MATH 141 topic. The formula is simple—these are often free points on exams.
Arc length appears occasionally in MATH 141. Setup is straightforward but computation can be tedious.
Surface area of revolution appears occasionally in MATH 141. Similar setup to arc length.
Center of mass problems appear on some MATH 141 exams. Know the integral formulas for 1D and 2D.
PDF problems appear occasionally in MATH 141. Basic setup: area under curve = 1, integrate for P(a<=X<=b).
General series strategy is tested throughout MATH 141's series unit. Know which test to try first.
Integral test appears in MATH 141 for p-series type problems. Remember the three conditions to verify.
Comparison tests for series appear regularly in MATH 141. Useful when ratio/root tests are inconclusive.
AST appears on MATH 141 finals. Also know the error bound: |error| <= first omitted term.
Absolute vs conditional convergence is tested on MATH 141 finals. Late-course topic with good exam weight.
Basic antiderivatives are assumed knowledge in MATH 141. Not tested alone but needed everywhere.
Long division is a tool for MATH 141 partial fractions. Not tested standalone.
Conceptual background for MATH 141. Not directly tested but underlies many problems.
Riemann sum concepts in MATH 141 are setup for integrals. Rarely tested standalone.
Computing integrals via Riemann sums is conceptual in MATH 141. May appear as one midterm question.
Series notation in MATH 141 is setup for convergence tests. Rarely standalone questions.
The harmonic series is a MATH 141 reference point for comparisons. Know it diverges.
Telescoping series appear occasionally in MATH 141. Recognize partial fractions that cancel.
Parametric tangents may appear briefly in MATH 141. More emphasis in MATH 222.
Polar area appears occasionally on MATH 141 finals. Know A = (1/2) integral r^2 d-theta and how to find limits.