# Final exam information

From UBCMATH WIKI

## Contents |

### Final exam date and time

The schedule for final exams is usually released in October.

### 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. - 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. - 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

- a number of
**multiple choice questions**, - some
**short answer problems**(show work, enter answer in a box) and - a few
**longer problems**.

#### 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).

- 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.
- A page on the wiki of practice problems.

### 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 **only if they are required for one of the questions on the exam**.

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 | $\pi r s$ | |