practice problems

MATH 141 – Crash Course

Panicked about cal 2? Haven’t really started to review yet? No worries – we’ve got you covered :D. We’ll be running a crash-course for MATH 141 starting next Wednesday, April 9th, 2014. The aim of the crash will be to teach you the basics of everything you need to succeed and help you focus your studying most efficiently. The schedule:

  • Wednesday April 9th, 7:30-10:30pm – Methods of Integration: learn to integrate any expression. This session includes >100 examples from past exams as well as a complete summary and accessible explanation of each method of integration.
  • Thursday April 10th, 7:30-10:30pm – Applications of Integration: areas, volumes, arc-lengths, surface areas, FTC I&II, MVT. Learn to relate all these subjects to each other and reduce the load on your memory – includes simple explanations that will make the material intuitive and accessible.
  • Friday April 11th, 7:30-10:30pm – Polar & Parametric Everything: this session will cover everything from basic derivatives and tangent lines to curve-sketching, areas, lengths, surface area & more. We’ll look at tons of questions from past exams and consider strategies for dealing with these questions.
  • Saturday April 12th, 3:30-6:30pm – Sequences and Series: discover the easy way to understand sequences and series. We’ll review the tests for convergence and divergence and explain the logic behind them so that you can develop strong intuition about the behaviour of series. You’ll learn to assess the convergence /divergence of most exam-level series at a glance, as well as how to structure a formal solution.

This a small group crash course, which guarantees optimal interaction with the teacher. Sessions are $80/each or all 4 for $210, including detailed notes and tons of practice problems. For more information or to register, contact us at mcgill.calc.help -at- gmail.com.

MATH 141 – Mastery Sessions

The second MATH 141 Mastery Session in preparation for the final exam will be tomorrow, Saturday March 29th from 12:30pm-3:30pm. Mastery 2 – Pre-session Worksheet Be sure to work through the questions and do a quick review of these topics so that you’re familiar with their basic application. As usual, the focus of the session will not be on understanding the ideas at an introductory level; rather, we’ll spend most of our time solving advanced exam-level questions and developing strategies for doing so. See you there!

MATH 141 – Integration Session

No theory. No algebra. No baby questions. As a follow-up to the first Mastery Session for MATH 141 this past Saturday, we’ll be running a session on exam-level integrals this coming Thursday from 6-8pm. Students will be given 30-60s to identify the correct method and setup the integral in an effort to help them develop this most important skill for Hundemer’s exam. We’ll be providing a list of ~30 classic integrals that you should definitely know, as well as an additional ~80 questions taken directly from the past 15 years of MATH 141 exams. The cost will be $5-10/h for students attending the mastery sessions; $15/h for non-mastery students (who can save $5 for every friend they bring); $40 at the door. RSVP by contacting Adaam at McGill.Calc.Help@gmail.com.

Quiz 3 Practice Problems

Word has it that many of you 141 students are overwhelmed and overworked this week. In hopes of reducing your stress a bit, here are the warm-up questions from the quiz 3 prep session, with answers. If you need additional help, just ask. Good luck with midterms!!

MATH 141 – Quiz 1 – More Sample Questions

Here’s a second set of sample questions from the first of this year’s 141 quizzes. As expected, the general structure appears consistent, but the relative level of difficulty is a bit higher here. For example, the Riemann Sum question doesn’t have lower limit a = 0 which means you really have to have a solid understanding of how to work backwards to identify the function. Thanks to Marco for sharing!

1. Evaluate \displaystyle \lim_{n\rightarrow \infty} \sum_{i = 1}^{n}\sin\left(\frac{\pi}{2} + \frac{\pi i}{2n} \right)\cdot \frac{\pi}{2n}

2. \displaystyle \frac{\text{d}}{\text{d}x} \int_{\sqrt{x}}^4 e^{t^2}\text{d}t =

3. Evaluate the following integrals:

    • \displaystyle \int \frac{\pi}{6+x^2} \text{d}x
    • \displaystyle \int \frac{x+5}{x^2 + 10x - 7}\text{d}x
    • \displaystyle \int_a^{b} \frac{1}{x(1+\ln^2 x)}\text{d}x