Mathematics 100 Final Exam Review Package
                                             UBCEngineering Undergraduate Society
                    Attempt questions to the best of your ability. This review package consists of 24 pages, including 1 cover
                 page and 39 questions. Problems are ranked in difficulty as (∗) for easy, (∗∗) for medium, and (∗ ∗ ∗) for
                 difficult.
                      Solutions posted at: https://ubcengineers.ca/tutoring/
                    If you believe that there is an error in these solutions, or have any questions, comments, or suggestions
                 regarding EUS Tutoring sessions, please e-mail us at: tutoring@ubcengineers.ca. If you are interested in
                 helping with EUS tutoring sessions in the future or other academic events run by the EUS, please e-mail
                 vpacademic@ubcengineers.ca.
                    Some of the problems in this package were not created by the EUS. Those problems originated from one
                 of the following sources:
                    • Schuam’s Outline of Calculus 2 ed; Ayres Jr., Frank
                    • Calculus – Early Transcendentals 7 ed; Stewart, James
                    • Calculus – 3 ed; Spivak, Michael
                    • Calculus Volume 1 2 ed; Apostol, Tom
                 All solutions prepared by the EUS.
                         Want a warm up?                 Short on study time?                Want a challenge?
                   These are the easier problems   These cover most of the material   These are some tougher questions
                            2, 3, 4, 5, 7            12, 14, 17, 19, 22, 25, 37, 38         15, 26, 44, 47, 48, 50
                                               EUS Health and Wellness Study Tips
                    • Eat Healthy—Your body needs fuel to get through all of your long hours studying. You should eat
                      a variety of food (not just a variety of ramen) and get all of your food groups in.
                    • Take Breaks—Your brain needs a chance to rest: take a fifteen minute study break every couple of
                      hours. Staring at the same physics problem until your eyes go numb won’t help you understand the
                      material.
                    • Sleep—We have all been told we need 8 hours of sleep a night, university shouldn’t change this. Get
                      to know how much sleep you need and set up a regular sleep schedule.
                                                               Good Luck!
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               Mathematics 100                    Final Exam Review Package                        Page 2 of 24
           (∗)  1. A nuclear waste pile initially has 1000 kg of waste in it. After 5 days, there is 800 kg of waste left. Also,
                   at the instant after t = 5, more waste, of mass M is then dumped on the pile. After 20 additional days,
                   there is 700 kg of waste in the pile. How much waste M was dumped in the pile?
           (∗)  2. A particle moves along a straight line starting at t = 0 according to the following law:
                   s(t) = 2t3 − 12t2 + 18t − 5. Find:
                    (i) points where it stops
                   (ii) points where it changes direction
                   (iii) the net displacement after 2 seconds
                   (iv) the total distance travelled after 3 seconds
                   (v) the average velocity over the first 3 seconds
                  Mathematics 100                         Final Exam Review Package                                 Page 3 of 24
             (∗)   3. A spherical balloon has radius 10 cm. If it loses a little bit of air, such that its radius decreases by 0.05
                      cm. By approximately how much will the volume decrease?
                                  x+1
             (∗)   4. If f(x) = e      , then find h(x), where h is the inverse function f−1(x) of f.
                                2+ex
             (∗)   5. Determine the value of the limit. lim xsinx
                                                         x→∞ 2
                                                              x +5
                  Mathematics 100                         Final Exam Review Package                                 Page 4 of 24
             (∗)   6. If y′′(x) = 7x + 8, and y(2) = 3, y′(1) = 2, find y(x).
                                                                         1−√1−x2
            (∗∗)   7. Evaluate the limit without L’Hopital’s Rule. lim          2
                                                                     x→0      x
            (∗∗)   8. Evaluate the limit lim x−sinx.
                                         x→0 tanx−x