things you should know for pre-calculus pre-ap pre-calculus mrs. richter 2013 – 2014
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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