Which series tests should go on a Calculus II final formula sheet?

The divergence test, geometric and p-series, comparison and limit comparison, the integral test, the alternating series test, and the ratio and root tests, each with its conditions and when to reach for it. Add the standard Maclaurin series with their intervals and Taylor's inequality.

Is an aid sheet allowed on a Calculus II final?

It depends on the course. Some allow one handwritten page, some supply a formula sheet without series results, and many allow nothing. The syllabus or exam instructions decide; if they are silent, ask the instructor before the exam.

How much of the Calculus II final is series?

Often the largest single part, frequently a third or more of the points, because it is the newest material. Integration methods and applications make up most of the rest.

Do I have to memorize the Maclaurin series?

Usually yes for e to the x, sine, cosine, 1 over 1 minus x, and ln(1+x), and often arctangent. Most other series on the exam are built from these by substitution, multiplication, differentiation, or integration.

How is this different from the Calculus II midterm page?

The midterm page covers integration techniques only. This page covers the cumulative final, where series, power series, and Taylor series carry the most weight.

Calculus IIFinal exam8 topics

Calculus II final exam study sheet

The Calculus II final is cumulative, and the series unit from the end of the term is usually its largest block: convergence tests, interval of convergence, and Taylor series. Integration methods return both as their own questions and inside volume and arc length setups. Parametric and polar curves appear on finals in courses that reached them, often as one or two shorter problems.

Call it a formula sheet, an exam aid sheet, a crib sheet or revision notes; for Calculus II it is mostly a decision table for series and a method menu for integrals.

Make this from your notes Unlock this sheet

Preview of the one-page Calculus II Final exam study sheet — the final exam sheet, free preview

The scope

What this exam usually covers

These are the problem types a cumulative Calculus II final usually grades. Series questions tend to carry the most points.

Choosing an integration method A batch of integrals with no hint about the technique: substitution, parts, trig powers, trig substitution, or partial fractions. Picking the wrong method early costs the whole problem.
Volumes and other applications Disk, washer, or shell set up about an axis other than x or y, plus arc length, surface area, or a work problem. Radii measured to the wrong axis is the common lost point.
Improper integrals Written as limits, with a convergence decision, either by evaluating or by comparing to a p-integral. Discontinuities inside the interval get missed.
Series convergence tests A set of series where you name the test, check its conditions, and conclude. Points go for stating the conditions (positive, decreasing, limit equals zero), not just the verdict.
Absolute versus conditional convergence Alternating series where you must test both the series and its absolute values, then classify. The alternating series error bound is a frequent short follow-up.
Power series and interval of convergence Ratio test for the radius, then a separate test at each endpoint. Leaving the endpoints untested is the most common partial-credit loss on the final.
Taylor and Maclaurin series Build a series from a known one by substitution, differentiation, or integration; find a Taylor polynomial; bound the error with Taylor's inequality or the alternating bound.
Parametric and polar Slope of a parametric curve, polar to Cartesian conversion, and area inside a polar curve. Included only in courses that covered this unit.

Usually later

Differential equations (separable equations, slope fields, logistic growth) and conic sections appear in some Calculus II syllabi and not others. Hydrostatic force, center of mass, and probability applications are also course-dependent. If the review sheet does not list them, give their space to series and Taylor polynomials.

The rules

What a note sheet is usually allowed to include

Calculus II finals often run stricter than the midterms on notes, because a list of series tests and Maclaurin expansions answers a large share of the exam. Common versions are no notes at all, a department formula sheet with trig identities but no series, or one handwritten page you prepare yourself. Canadian courses that permit an exam aid sheet usually fix its size and say whether both sides count; UK and Australian modules that allow a crib sheet say so in the exam rubric. Follow the written rule for your section. Either way, this page works as a study sheet: writing the decision table out is how most students learn it.

The sheet

The matching library sheet

A one-page reference for the whole topic, fact-checked, with the first part free to read. This exam page does not repeat it. Use it to see the material, then make a shorter study sheet from the notes your section actually used.

Calculus II: Sequences & Series reference sheet — the free part in text.
Unlock the full reference sheet to edit, print or save it as a PDF.
Unlock the full Final exam sheet, written for this exam's scope. The free part is in the preview above.

Make your own for this exam

Upload the series lectures and the integration problem sets together, and say in the focus step what the review session stressed, such as endpoints or the error bound. Pick one page, or front and back if the final allows it.

Make this from your notes

FAQ

Questions

Which series tests should go on a Calculus II final formula sheet?: The divergence test, geometric and p-series, comparison and limit comparison, the integral test, the alternating series test, and the ratio and root tests, each with its conditions and when to reach for it. Add the standard Maclaurin series with their intervals and Taylor's inequality.
Is an aid sheet allowed on a Calculus II final?: It depends on the course. Some allow one handwritten page, some supply a formula sheet without series results, and many allow nothing. The syllabus or exam instructions decide; if they are silent, ask the instructor before the exam.
How much of the Calculus II final is series?: Often the largest single part, frequently a third or more of the points, because it is the newest material. Integration methods and applications make up most of the rest.
Do I have to memorize the Maclaurin series?: Usually yes for e to the x, sine, cosine, 1 over 1 minus x, and ln(1+x), and often arctangent. Most other series on the exam are built from these by substitution, multiplication, differentiation, or integration.
How is this different from the Calculus II midterm page?: The midterm page covers integration techniques only. This page covers the cumulative final, where series, power series, and Taylor series carry the most weight.