## Day 1

- Simplifying radicals without a calculator
- Using completing the square to solve quadratics without a calculator

## Day 2

- Algebraic manipulation involving radicals
- General quadratic equation practice

## Day 3

- Using exponents to describe repeated operations
- Exponent rules

## Day 4

- Quiz on various methods involving quadratics, simplifying radicals

A major theme of this course has been the idea that it is often useful to say the same thing in different ways -- as one way can make aspects of the truth more apparent than another. For example, the factored form of a quadratic equation makes the roots more apparent, while the vertex form makes the vertex more apparent. Your choice of which way to express something should be guided by the context of what you are trying to achieve.

Another major theme of algebra is the idea that there are some operations on objects that work, no matter what the objects are. For example:

the concept of "2 *things* plus 5 *things* gives you 7 *things*" holds, no matter what the things are (as long as they are the *same things*). So even though the "thing" \(\sqrt{3}\) *looks* more complicated than *x*, you can still do the same stuff with it.

Is something unclear? Leave a comment below: