Expressions and Formulas 1.1 Order of Operations (PEMDAS) 1. Parenthesis 2. Exponents 3. Multiply or Divide from left to right 4. Add of Subtract from left to right Please Excuse My Dear Aunt Sally Example 1 Example 2 2 [9 (4-7)] - 8 32-24 (10-6) + 2 Example 3 Example 4 23 + [5(12-8) + 4] 6 Evaluate if a = 2 and b = 3. 2 2 a [ b ( a + a )] Example 5 Evaluate if a = 3, b = 2, and x = 4 x 2 2 a - b Pg 10, 18-48
Real Numbers numbers used in everyday life Properties of Real Numbers 1.2 Rational a number that can be written as a fraction. 2 ex. 9,, 8.26262626, 3, 2.4 3 Irrational a number that can not be written as a fraction. ex. 2,, 3.8152463215684 Natural Numbers counting numbers ex. {1, 2, 3, } Whole Numbers natural numbers plus 0 ex. {0, 1, 2, 3, } Integers whole numbers plus their opposites. ex. {..-2, -1, 0, 1, 2,..} 1-C Real Number Venn Diagram Copyright 2005 Pearson Education, Inc. Slide 1-21
Find each value and then name the set(s) to which it belongs. Real - R, Rational Q, Irrational I, Integer Z, Whole W, and Natural N. Example 1 Example 2 Example 3 18 2 6 24-6 Properties Commutative (order) a + b = b + a or ab = ba Associative (group) (a + b) + c = a + (b + c) or (ab)c = a(bc) Identity (same) a + 0 = a = 0 + a or a 1 = a= 1 a Inverse (opposite) a + (-a) = 0 = (-a) + a or Distributive a(b + c) = ab + ac or (b + c)a = ab + ac Name the property of each. Example 1 Example 2 (3 + 5) + 8 = 3 + (5 + 8) (2 5)7 = 7(5 2) a 1 1 = 1 = a a a Name the additive inverse and multiplicative inverse for each. Example 6 Example 7 2 3 1.3 Example 8 Simplify 2(2x 3y) 8(x + 4y) Pg 17, 20-48
Graphs and Measures of Central Tendencies 1.3 Stem-and-leaf plot displaying data into 2 parts. The stem consist of digits in the greatest common place value and the leaves contain the other value. Example 1 Make a stem-and-leaf plot of the following data: Test Scores 91 73 96 88 79 77 68 84 78 64 83 88 76 84 60 85 83 81 92 97 Measures of Central Tendency 1. Mean average 2. Median middle number 3. Mode the number that happens most often. Example 2 Use the following information to find the mean, median, and mode. Quiz Scores 35 31 32 47 27 42 20 43 45 28 24 30 18 17 40 24 28 50 Pg 23,9-20
1.3 Measures of Central Tendency Algebra 2 Goal: Goal: Measures of Central Tendency: Mean: Median: Mode: Example 1: Look at page. 20 example 2: Use the right side of the stem-and-leaf plot to calculate the median, mode, and mean using paper and pencil methods.
Example 2: Use the same data to calculate the median, mode, and mean using your graphing calculator. Perform the following steps in order to calculate the measures of central tendency with your graphing calculator. 1. Hit STAT 2. Select 1 EDIT by hitting ENTER or the number 1. 3. Enter the numbers you are given into the L1. 4. Hit STAT 5. Move one menu to the right to the CALC menu. 6. Select 1 1 Var Stats by hitting ENTER or the number 1. 7. Hit ENTER again A. What symbol represents the MEAN? B. What symbol represents the MEDIAN? C. What symbol represents the MODE? D. What symbol represents the SUM of the data? E. What symbol represents the Number of data entries? F. What is the minimum value? G. What is the maximum value? H. Are there any extreme value? I. Which piece of data represents the data the best and why? Example 3: Use the data on page 21, example 3 to calculate the median, mode, and mean. Determine which measure of central tendency best fits the data set.
Variable a letter used to represent a number. Solving Equations 1.4 Write an algebraic expression for each. Example 1 three times a number decreased by 2. Example 2 two times the sum of 5 and four times a number. Properties: Reflexive a = a Symmetric if a = b then b = a Transitive if a = b and b = c, then a = c. Substitution if a = b, a may be replaced by b. ***Addition, Subtraction, Multiplication, and Division also exist*** Name the property for each. Example 3 Example 4 x = 5 x + (5 + 7) = 27 x + 4 = 5 + 4 x + 12 = 27 Solve. Example 5 Example 6 Example 7 3y 25 = 13.4 9y + 17 = 80 5 y - 2 = 2 y + 4 6
Solve each for the given variable. Example 8 T = l q ; for l Example 9 P = 2l + 2w; for l Example 10 t 1 = xyz 4 ; for y Pg 31, 6-17, 19-40, 49, 50
Absolute Value the distance a number is from 0. Example 1 Example 2 7-3 Solving Absolute Value Equations 1.5 Example 3 Evaluate -8a 3 if a = -2 Fill in the value of x. x = 5 Example 4 Example 5 k + 9 = 12 2 y + 5 = 8 Example 6 Example 7 3x + 7 + 8 = 5 x + 6 = 2x + 9 Pg 41, 16-40
Solving Inequalities 1.6 Trichotomy Property for any real number a and b: a > b a = b a < b, <, > Solve and Graph. Example 1 Example 2 y + 6 > 3 2 x - 5 7 Is 4 < 7? ***Rule: When multiplying or dividing by (-), SWITCH SIGN*** Example 3 Example 4 24 3a > 42 3 6-3 4 y Example 5 2a 4 a + 8 3 3 Pg 47, 14-40
Compound Inequalities 1.7, - and (intersection ), part in common, - or (union, ), combine. Example 1 a 4 > 2 and a - 3 6 Example 2 7 2 y - 11 or 18 > 4y - 10 Example 3 8 m + 6 14
Example 4 8 x 24 Example 5 x + 2 > 5 Pg 52, 6-42 even