KMHS Mathematics Department. Algebra 2

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1 KMHS Mathematics Department Algebra 2

2 Chapter 1 Polynomials

3 Section 1 Adding and Subtracting with Polynomials 2

4 Section 2 Multiplying with Polynomials 3

5 Section 3 Simplifying Algebraic Expressions Follow the order of operations to solve: PEMDAS Parenthesis Exponents Multiplying Dividing Addition Subtraction 4

6 Section 4 Dividing with Polynomials 5

7 Chapter 2 Factoring

8 Section 1 Factoring by Greatest Common Factor 7

9 Section 2 Factoring by Difference of Two Perfect Squares 8

10 Section 3 Factoring by Grouping 9

11 Section 4 Factoring Trinomials Factoring Trinomials Example #1: x 2 + 9x + 18 Process: Step #1 Place the square root of 1st term in two different parenthesis: Answer: (x )(x ) Step#2 Put two numbers that multiply to give you the last number and adds up to the middle term. *The rules for positive and negative numbers being added and multiplied apply: Final Answer: (x + 6)(x + 3) Example #2: x 2 11x + 18 Answer: (x - 9)(x 2) Example #3: x 2 7x 18 Answer: (x - 9)(x + 2) Example #4: x 2 + 7x 18 Answer: (x + 9)(x - 2) 10

12 Section 5 Eyeglasses/Decomposition 11

13 Section 6 Factor Completely 12

14 Chapter 3 Rational Expressions

15 Section 1 Rational Expressions 14

16 Section 2 Reducing Rational Expressions 15

17 Section 3 Multiplying and Dividing Rational Expressions 16

18 Section 4 Complex Fractions 17

19 Section 5 Adding or Subtracting Rational Expressions 18

20 Chapter 4 Functions

21 Section 1 Function Notation h (x) = x+1, find: h(4) Step #1 plug the value in the parenthesis in for x in the problem h (4) = 4+1 Step #2 Simplify the problem h (4) = 5 20

22 Section 2 Composition of Functions f (x) = x 6 and g (x) = x + 1 find: f g (4) Step #1 plug the value in the parenthesis in to the functions closest to it g (4) = 4+1 Step #2 Plug the answer from Step #1 into the next function g (4) = 5 f(5)= 5-6 = -1 Step#3 When you are out of functions you are at your final answer f g (4) = -1 21

23 Section 3 Inverse Functions Creating a Inverse Function f (x) = x 6 Step #1 X and f(x) switch places: x = f(x) - 6 Step #2 Solve for f(x): X + 6 = f(x) Step#3 Move the f(x) to the left side of the function and attach a negative 1 onto it in the exponent area: f -1 (x)=x+6 22

24 Section 4 Graph of a Function A graph of a function presents the answers of a function in a graph form Vertical Line Test: if you can draw a vertical line that crosses the graph of a function in more then one place it is not a function 23

25 Chapter 5 Radicals

26 Section 1 Perfect Squares 25

27 Section 2 Simplyfing Radicals 26

28 Section 3 Adding and Subtracting Radicals 27

29 Section 4 Multiplying Radicals 28

30 Section 5 Dividing Radicals 29

31 Section 6 Rationalizing a Denominator 30

32 Section 7 Rationalizing a Binomial Denominator 31

33 Section 8 Radical Equations 32

34 Chapter 6 Imaginary Numbers

35 Section 1 Pure Imaginary 34

36 Section 2 Adding or Subtracting Imaginary Numbers 35

37 Section 3 Complex Number Sheet 36

38 Chapter 7 Quadratics

39 Section 1 Solving Quadratics by Factoring 38

40 Section 2 Solving Quadratics by the Quadratic Formula 39

41 Section 3 Discriminant Solving Quadratics by the Quadratic Formula 40

42 Section 4 Sum of the Roots and Product of the Roots 41

43 Section 5 Writing a Quadratic When the Roots Are Given 42

44 Section 6 Solving 2 Variable Equations with Add/Subtract Method Step #1 Get the same number opposite sign in front of one of your variables. Step#2 Add your 2 equations together: this will cancel out one of our variables. Step #3 Solve for your remaining Variable. Step #4 Plug in your answer from Step#3 into one of the original equations and solve for the other variable Step #5 Check 43

45 Section 7 Solving 2 Variable Equations with Substitution Method Step #1 Get one variable by itself Step#2 Plug on equation into the other equation. Step #3 Solve for your remaining Variable. Step #4 Plug in your answer from Step#3 into one of the original equations and solve for the other variable Step #5 Check 44

46 Section 8 Solving 2 Variable Equations with Add/Subtract Method Step #1 Get one variable by itself Step#2 Plug one equation into the other equation. Step #3 Solve for your remaining Variable through factoring, solving for it, or quadratic formula. Step #4 Plug in your answer from Step#3 into one of the original equations and solve for the other variable you should get two pairs of answers Step #5 Check 45

47 Section 9 Solving 2 Var Quad System of Equations with Add/Subtract Step #1 Get the same number opposite sign in front of one of your variables. Step#2 Add your 2 equations together: this will cancel out one of our variables. Step #3 Solve for your remaining Variable you will get two answers. Step #4 Plug in your answer from Step#3 into one of the original equations and solve for the other variable you will get two more answers. Step #5 Check 46

48 Section 10 Solving a 3 by 3 System of Equation Step #1 Label your 3 equations A, B, and C Step#2 Pick 2 equations and cancel out one of the variables and Label the new equation D Step #3 Pick 2 different original equations and cancel out the same variable is in step #2 and Label the new equation E Step #4 Use either addition & subtraction method or substitution method to solve for the remaining 2 variables in D, E Step#5 Plug in the two answers you found in Step #4 into one of the original equations (A, B, or C) and solve for the 3rd and final variable Step #6 Check 47

49 Chapter 8 Absolute Value and Rational Expression

50 Section 1 Absolute Value Equations 49

51 Section 2 Absolute Value Inequalities 50

52 Section 3 Solving Rational Equations 51

53 Section 4 Solving Rational Inequalities 52

54 Chapter 9 Exponents

55 Section 1 Laws of Exponents 54

56 Section 2 Zero and Negative Exponents 55

57 Section 3 Fractional Exponents 56

58 Section 4 Solving Equations with Fractional Exponents 57

59 Section 5 Solving Exponential Equations 58

60 Chapter 10 Statistics

61 Section 1 Measure of Central Tendency 60

62 Section 2 Measure of Central Tendency Frequency Chart xi = represents the data fi = represents the frequency or number of times each piece of data appears 61

63 Section 3 Variance and Standard Deviation x = represents the data x with the line over it= mean n = number of data Σ = sum of the data SD = Standard Deviation 62

64 Section 4 Percentile B) change this to a decimal 0.67 xi ' fi ' 16 ' 6 ' 17 ' 4 ' C) Move the decimal point 2 places to the right the final answer is 19 is in the 67th percentile 19 ' 8 ' 22 ' 3 ' What Percentile is 19 in? Step#1 A) Add up the total frequency column: = 21(This is the Denominator) B) Add up the Frequency of the #s that 19 is larger then and half of the frequency of 19(This total becomes our Numerator): /2 = 14 Step# 2 A) Make a fraction out of the two #s in step #1 14/21 63

65 Chapter 11 Probability

66 Section 1 Counting Principal Choosing a lunch of sandwich, drink, and dessert from 5 sandwiches, 6 drinks, and 3 desserts? In the Counting Principal Multiply all your options together to get your total number of choices: 5 x 6 x 3 = 90 Possible options 65

67 Section 2 Combination & Permutation 66

68 Section 3 Probability Probability of an Event Number of Outcomes P(E) = Event/Total *or Event: What is the Probability that you pick a Queen or a King out of a deck of cards? P(Queen or King) = 4/52 + 4/52 = 8/52 = 2/13 *and Event: What is the Probability that you pick a Queen replace it then a King out of a deck of cards? P(Queen and King ) = 4/52 * 4/52 = 1/169 67

69 Section 4 Probability with Two Outcomes 68

70 Section 5 Probability with Two Outcomes: At Least/At Most 69

71 Section 6 Binomial Expansion 70

72 Section 7 Finding a Single Term 71

73 Chapter 12 Sequences

74 Section 1 Sequences 2, 4, 6, 8, 10, 12, 14.. Arithmetic Sequence has a common difference(same # being added over and over). Common Difference d = 2 2, 4, 8, 16, 32, 64, Geometric Sequence has a common multiple(same # being multiplied over and over). Common Multiple r = 2 73

75 Section 2 Arithmetic Sequences 74

76 Section 3 Geometric Sequences 75

77 Section 4 Sigma Notation 76

78 Section 5 Arithmetic Series Sheet 77

79 Section 6 Geometric Series Sheet 78

80 Section 7 Recursive Sequences 79

81 Chapter 13 Remaining Topics

82 Section 1 Worksheets Trigonometry of the Right Triangle Angles and Quadrants Quadrant Angles Radian Measure Unit Circle Special Angles Calculator for Trig Functions Reducing Trig Functions Law of Cosines Law of Sines Law of Sines and Cosines Word Problems Basic Identities Proving Trig Identities Trig IDs Graphing Sine Curves Graphing Cosine Curves Finding Remaining Trig Functions Inverse Trig Functions Formula Sheet Using Sum Difference Double and Half Angle Formulas Solving Trig Equations Solving Trig Equations by Factoring Solving Trig Equations by the Quadratic Formula 81

Topic Outline for Integrated Algebra 2 and Trigonometry-R One Year Program with Regents in June

Topic Outline for Integrated Algebra 2 and Trigonometry-R One Year Program with Regents in June Integrated Algebra 2 & Trigonometry - R Semester 1 1. Rational Expressions 7 Days A. Factoring A2.A.7 Factor