THINGS YOU SHOULD KNOW FOR

PRE-CALCULUS

Pre-AP Pre-Calculus

Mrs. Richter

2013 – 2014

Kinds of numbers• Natural (counting) numbers: {1, 2, 3, 4, ….}• Whole numbers: {0, 1, 2, 3, 4, ….}• Integers: {…., -3, -2, -2, 0, 1, 2, 3, …}• Rational number: can be written as a fraction• Terminating number: 7/4 = 1.75• Infinitely repeating: 4/11 = 0.363636…..• Irrational: infinitely nonrepeating

• Example: =1.7320508…. π=3.14159265….

Bounded IntervalsInterval Notation

Interval Type Inequality Notation

Graph

[a, b] Closed a ≤ x ≤ b

(a, b) Open a < x < b

[a, b) Half-open a ≤ x < b

(a, b] Half-open a < x ≤ b

Properties of Exponents

Scientific NotationScientific Notation

Math work Expanded form

mi 93,000,000 mi

g .000053 g

8,600 ft

in

Absolute Value• The absolute value of a real number a is

Examples:

, since -4<0,

, since is negative,

Important formulas

• Distance Formula

• Midpoint formula

• Slope

• Slope-intercept form

Solving Equations• Graphically: use graphing feature on calculator

• Type equation into y=, make sure there is a 0 in the other y=

• Algebraically: without the use of a calculator• Factoring• Completing the square• Quadratic Formula

Factoring

Completing the Square• To solve

Completing the Square Example• Solve

(divide by 4)

(subtract

(now complete the square)

Quadratic Formula• From the form , use the following formula to find the

values of x.

Quadratic Formula example• Solve the equation

• First you must subtract 5 from both sides to get it into the correct format

• (now substitute into the QF)

Practice Problems• Pg. 12-13: 47, 52, 57, 60, 69

• Pg. 20-23: 13, 21, 54, 63

• Pg. 29-30: 15, 19, 65

• Pg. 40: 21, 23, 25

• Pg. 50: (follow directions for each section) 3, 13, 15, 19, 23, 60

• Pg. 64: (solve inequalities by any method) 1, 11, 17, 23