## Cheat Sheet

# 1,001 Pre-Calculus Practice Problems For Dummies

Pre-calculus draws from algebra, geometry, and trigonometry and combines these topics to prepare you for the techniques you need to succeed in calculus. This cheat sheet provides the most frequently used formulas, with brief descriptions of what the letters and symbols represent. Counting techniques are also here, letting you count numbers of events without actually having to list all the ways to do them. Also, you find a step-by-step description of how to *complete the square* — most useful when you’re working with conic sections and other equations with specific formats.

## Frequently Used Pre-Calculus Formulas

*Mathematical formulas* are equations that are always true. You can use them in algebra, geometry, trigonometry, and many other mathematical applications, including pre-calculus. Refer to these formulas when you need a quick reminder of exactly what those equations are and which measures or inputs are needed.

## Counting Techniques for Pre-Calculus

Counting the number of ways to perform a task is fairly simple — until the number of choices gets too large. Here are three counting techniques used in pre-calculus:

**Permutations:**How many ways you can choose*r*things from a total of*n*things when the order of your choices matters**Combinations:**How many ways you can choose*r*things from a total of*n*things when the order of your choices doesn’t matter**Multiplication principle:**How many different possibilities exist if you choose 1 from*a*things, 1 from*b*things, 1 from*c*things, 1 from*d*things, and so on.

Use the following formulas for these counting techniques:

## Completing the Square for Pre-Calculus

Quadratic equations are written in many different formats, depending on what the current application is. Completing the square is helpful when you’re writing conics in their standard form, and you can use this method to solve for the solutions of a quadratic equation. Here’s how to solve for *x* in the quadratic equations *ax*^{2} + *bx *+ *c *= 0 and 2*x*^{2} +7*x *‒ 15 = 0 by completing the square: