# Final exam information

## Contents

### Final exam date and time

Dec 15, 3:30pm. Check your SSC for your room assignment, which varies by section.

### Review sessions

Faculty will be available for review sessions at the following places and times:

Day Time Room Instructor
Tues, Dec 12 10am-12pm MATX 1100 Keshet
1pm-2pm
3pm-5pm Yeager
Wed, Dec 13 12pm-2pm WOOD 1 Cytrynbaum
3pm-5pm GEOG 200 Sankar
Thu, Dec 14 10am-12pm GEOG 200 (Enrolment Room Bookings changed it from HENN 202) Stephan

Unless otherwise noted, bring problems to work on. Instructors will circulate to address questions while you work alone or with your pals. Instructors will expect to encounter problems from old exams, quizzes from all sections and the 2016 quiz document online, webwork, OSH, and the textbook.

### What will the exam look like?

#### Content

• The material covered by the final exam includes material from Chapters 1-15 of the course notes. See the Course calendar for detailed readings. You will not be asked to calculate phase shifts in periodic functions.
• The best way to study is to do lots of problems. Questions similar to both the WeBWorK assignments and the OSH will appear on the final exam. For additional problems, look at the back of each chapter of course notes and the review problems in Chapter 16, as well as course notes from the various sections.
• The difficulty of the exam will be similar to that of the midterms although you will probably find that you are not as pressed for time.
• There will be a slight emphasis on the material covered since the Midterm but the exam will definitely be cumulative.

#### Format

The final exam will consist of

• some multiple choice questions and
• some written answer problems where you will be expected to show your work and justify your conclusions

#### Practice for the final exam

• Exams from previous years are available on the Math Department website. Keep in mind that the material varies from year to year so some problems appearing on old exams might not be relevant this year. Similarly, some topics covered this year might not appear on any of the old exams.
• The 2015 exam (not yet posted on the site above).
• Problems from past exams are now posted on the new MATH102/Question Challenge wiki . This site is a place to work on the solutions and to post hints and comments for your classmates and you.
• Hints and solutions to many of these old exams are available on the Math Exam Resources page.
• Problems at the back of each chapter of the course notes (see menu for link) have answers at the end of the course notes in the appendices.
• Most sections post their quizzes and lecture notes (containing problems worked on in class)
• Re-do your old webwork and OSH assignments, peeking at the solutions as little as possible. Ditto the two versions of the midterm.
• A page on the wiki of practice problems.

While you're studying, think about ways to verify your work 'without access to a solutions key. This is a handy skill to have on an exam, but it also helps you solidify your conceptual understanding of the topics.

### Final exam room assignments

Follow the official UBC exam schedule.

### Exam formulae list

The following tables contain formulae that will be provided on the final exam if they are required for one of the questions on the exam. Since a formula only appears on the actual exam if needed, the content of the formula list is a bit of a hint ;)

Linear regression
Without intercept $y=ax$ with $a=\frac{\sum_{i=0}^nx_iy_i}{\sum_{i=0}^nx_i^2}$
With intercept $y=ax+b$ with
$b=\bar{y}-a\bar{x}$ and $a=\frac{P_{avg}-\bar{x}\bar{y}}{x_{avg}^2-\bar{x}^2}$,
where $\bar{x}=\frac{1}{n}\sum_{i=0}^n x_i$, $\bar{y}=\frac{1}{n}\sum_{i=0}^n y_i$,
$P_{avg}=\frac{1}{n}\sum_{i=0}^n x_iy_i$, $x_{avg}^2=\frac{1}{n}\sum_{i=0}^n x_i^2$.
Trig identities
$a^2=b^2+c^2-2bc\cos(\theta)$
$\displaystyle \frac{a}{\sin(A)}=\frac{b}{\sin(B)}$
$\sin(A+B) = \sin(A)\cos(B) + \cos(A)\sin(B)$
$\cos(A+B) = \cos(A)\cos(B) - \sin(A)\sin(B)$
Special triangles trig values
$\theta$ $\sin(\theta)$ $\cos(\theta)$
$\dfrac{\pi}{6}$ $\dfrac{1}{2}$ $\dfrac{\sqrt{3}}{2}$
$\dfrac{\pi}{4}$ $\dfrac{\sqrt{2}}{2}$ $\dfrac{\sqrt{2}}{2}$
$\dfrac{\pi}{3}$ $\dfrac{\sqrt{3}}{2}$ $\dfrac{1}{2}$
Geometric formulae (volume, area)
Quantity Formula
Volume of sphere $\dfrac{4}{3} \pi r^3$
Surface area of sphere $4\pi r^2$
Volume of cone $\dfrac{1}{3} \pi r^2h$
Surface area of cone $\pi r s$