# H611 Placement Exam Study Guide

<span style="color:darkred">The placement exam for H611 will be held in class during the first class meeting.</span> Students who pass the placement exam will be exempt from taking H611, and students who do not pass the placement exam will be required to take H611.

There are three sections to the placement exam:

1. Mathematical Operations
2. Calculus and Limits
3. Linear Algebra

**To pass this exam, you must score at least 70% total, and at least 60% of each section.**

The exam is broken into three sections, each containing concepts *very similar* to the following:

## Mathematical Operations

| Subject | Example |
| -------------- | ------------------------------------------------------------ |
| Log Rules | Calculate $\log_2(8)$. How might we simplify $\ln(1) - \ln(e)$ |
| Polynomials | What are the zeros for a polynomial? What is a "function"? |
| Inverses | What is the inverse of a function like $1/x$? |
| Function Shape | What does the function $\cos(x)$ look like? What about $x^3$? |

## Calculus and Limits

| Subject | Example |
| --------------------- | ------------------------------------------------------------ |
| Infinite Integrals | How can you find the area $\int_0^\infty f(x)\,dx$ using limits? |
| Curve Behavior | *"Where is the [...]?"* (inflection point, saddle point, etc.) |
| Basic Derivatives | *No need to memorize basic derivatives. You'll be given them :)* |
| Finding Maxima/Minima | How to use differentiation and algebra to find maxima/minima |
| Undefined Limits | What are examples of non-differentiable points on a curve? |
| Integration | Find $\int x^2\,dx$. What does it all mean? |
| Chain Rule | How does the chain rule work? |

## Linear Algebra

| Subject | Example |
| ---------------------------- | ------------------------------------------------------------ |
| Matrix Multiplication | Given $3\times 3$ matrices $A$ and $B$, calculate the matrix $AB$ |
| Singular Value Decomposition | Interpret $U$, $\Sigma$, and $V$. |
| Systems of Equations | Given a set of equations, how do we determine consistency? |
| Eigenspace | Define eigenvalues and eigenvectors for a 2-by-2 matrix. |
| Row Operations | How do these work? |
| Reduced Row Echelon Form | What information can we gather from a matrix's RREF? |
| Linear Independence | How can we determine if vectors are linearly independent? |