MATH 1220 is the second half of Kwantlen's calculus sequence, and it is a different kind of difficulty from the first. Differentiation is an algorithm: there is always a rule that applies. Integration is a search — you look at an integral and decide which of six or seven techniques might work, and sometimes the answer is that none of them do. Students who were comfortable in MATH 1120 are often surprised by how much judgement MATH 1220 asks for, and that surprise is the normal starting point, not a warning sign.
What is covered in KPU MATH 1220?
KPU's calendar description covers a lot of ground in one sentence: you learn to integrate algebraic and elementary transcendental functions and apply those skills to appropriate problems, and you study the fundamental theorem of calculus, the integral calculus of parametric curves, Taylor polynomials, sequences and series, and simple differential equations. Unpacked, that is:
- Antiderivatives and the indefinite integral: reversing differentiation, and why the constant matters
- Riemann sums and the definite integral: area as a limit of sums, before any shortcut appears
- The Fundamental Theorem of Calculus: both directions — differentiating an integral, and evaluating one
- Techniques of integration: substitution, integration by parts, trigonometric integrals and substitution, and partial fractions
- Applications: areas between curves, volumes of revolution, arc length, average value and work
- Improper integrals: infinite limits, infinite discontinuities, and deciding whether a value exists at all
- Parametric curves: arc length and area for curves given parametrically, picking up where MATH 1120 left them
- Sequences and series: convergence tests, power series, and radius of convergence
- Taylor polynomials: approximating a function near a point, and bounding the error
- Simple differential equations: separable equations and the initial-value problems that go with them
Three credits, with the ASTR and QUAN attributes.
Who MATH 1220 is for, and what you need to get in
The prerequisite is one of MATH 1120, MATH 1130 with a C+, or MATH 1140 with a B−.
Those grade requirements are not decoration. A student who passes MATH 1140 with a C+ has completed a first calculus course and still cannot enter MATH 1220 — the required grade is B−. If MATH 1220 is on your program map, the grade you need in your first calculus course is a planning decision you have to make at the start of that course, not at the end.
MATH 1220 then opens most of the second-year sequence: MATH 2321 Multivariate Calculus needs it with a C, MATH 2721 Complex Numbers and Linear Algebra needs it, MATH 2821 Multivariate and Vector Calculus needs it alongside MATH 2721 or MATH 1152, and MATH 2232 Linear Algebra accepts it with a C. If you are heading toward mathematics, physics or an engineering pathway, this course is the hinge the rest of the degree turns on.
Common challenges students face in MATH 1220
There is no algorithm for choosing a technique
This is the central difficulty of the course, and it is genuinely new. In MATH 1120, seeing a product tells you to use the product rule. In MATH 1220, seeing a product might mean parts, might mean substitution, might mean a trigonometric identity first. Recognition is a skill built by volume and reflection, not by reading worked examples.
Integration by parts gets applied blindly
Choosing u and dv badly turns one hard integral into a harder one. Students often push through the resulting mess rather than backing up and choosing differently, and lose ten minutes on an exam that has none to spare.
Series convergence becomes a memory game
There are eight or nine tests, each with conditions, and students memorise the list without learning which shapes of series suggest which test. Then the exam gives a series that fits three tests and rewards the one that finishes in two lines.
Taylor polynomials feel unmotivated
Writing a Taylor polynomial is mechanical once you have the derivatives. Understanding what it is for — that you are trading an intractable function for a polynomial you can actually compute, within a controllable error — is what makes the error bound worth caring about.
The differentiation from last term has decayed
MATH 1220 uses MATH 1120's derivatives constantly, and a summer or a semester in between is enough for them to go rusty. Time lost re-deriving a trigonometric derivative is time not spent on the integral itself.
How Learn4Less helps you succeed in MATH 1220
We build a decision procedure for integrals
Rather than drilling each technique separately, we work on the first fifteen seconds: what to look at in an integrand, what each feature suggests, and how to tell quickly that a chosen route is not working. That is the skill the exam tests.
We work from your section's material
KPU sections differ in pace and in how much weight goes on series versus applications. We work from your assignments, your WeBWorK sets and your instructor's notes rather than a generic outline.
We repair the differential calculus in place
If the sticking point is really a derivative you have forgotten, we fix it inside the integration problem instead of sending you back a term. You keep moving on the current material.
We make series tests into a map, not a list
Each test gets tied to the shape of series it is good at. A factorial suggests one thing, an alternating sign another, a rational function a third. Recognition replaces recall.
MATH 1220 exam and midterm preparation
Unseen integrals, timed
Assessment structure varies by section, so your course outline is the authority on weighting. What is constant is that you will meet integrals you have not seen. We practise exactly that: unfamiliar problems, on the clock, with the technique choice left to you.
KPU's sample finals
The KPU library keeps sample finals on course reserve, searchable by instructor. KPU cautions that the real exam may differ markedly, and that is fair — but the style, the length and the balance of topics are informative, and they cost nothing. We work through them and look for the pattern in what you miss.
Checking your own work
Between sessions, our free integral calculator works definite and indefinite integrals step by step, including improper integrals and divergence, so you can find where a long computation went wrong rather than only learning that it did.
Writing for partial credit
Integration answers are long, and a marker who cannot follow your substitution cannot award most of the marks for it. We work on stating the substitution, changing the limits, and keeping the write-up readable under time pressure.
Why choose Learn4Less for MATH 1220 tutoring?
Integral calculus is a core subject for us
We tutor the integral calculus course at UBC, SFU and KPU, which means we see where the same technique goes wrong across three different curricula and know which explanations actually land.
Sessions built around your own problems
Bring the assignment that is due, the WeBWorK question that keeps being marked wrong, or the midterm you want to understand rather than file away.
Online anywhere, in person in Vancouver
Most sessions run online, across Canada and the United States, with screen sharing and live work on the same page. In-person sessions are available in the Vancouver area subject to tutor availability; we do not currently run sessions on KPU's campuses.
Free tools, no session required
The integral calculator, the derivative calculator and our concept reviews are open to anyone.
Frequently Asked Questions
What grade do I need in my first calculus course to take MATH 1220?
A pass in MATH 1120, a C+ in MATH 1130, or a B− in MATH 1140. The requirement is different for each because the three courses cover different amounts of the groundwork MATH 1220 assumes.
Is MATH 1220 harder than MATH 1120?
Different, and harder in a specific way. The individual computations are longer, and there is no rule that tells you what to do first. Students who coped with MATH 1120 by pattern matching usually find MATH 1220 harder; students who understood why the rules worked usually find it manageable.
Which courses need MATH 1220?
MATH 2321 Multivariate Calculus, MATH 2721 Complex Numbers and Linear Algebra, and MATH 2821 Multivariate and Vector Calculus all require it, and MATH 2232 Linear Algebra accepts it. It is the standard prerequisite for the second year of a mathematics, physics or engineering pathway at KPU.
I took MATH 1130 instead of MATH 1120. Am I behind?
Not behind, but you will want to check two things. MATH 1220 needs a C+ in MATH 1130 rather than a bare pass, and MATH 1130 does not cover parametric curves, which MATH 1220 returns to. That gap is small and worth closing early rather than in week ten.
When should I get a tutor for MATH 1220?
The techniques stack, so the useful moment is early — around integration by parts, which is where most students first notice that the method is no longer obvious. Waiting until series usually means two problems at once.
