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KMHS Mathematics Department Algebra 2 · Step #3 Solve for your remaining Variable through...
Transcript of KMHS Mathematics Department Algebra 2 · Step #3 Solve for your remaining Variable through...
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KMHS Mathematics Department
Algebra 2
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Chapter 1
Polynomials
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Section 1
Adding and Subtracting with Polynomials
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Section 2
Multiplying with Polynomials
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Follow the order of operations to solve:
PEMDAS
Parenthesis
Exponents
Multiplying Dividing
Addition Subtraction
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Section 3
Simplifying Algebraic Expressions
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Section 4
Dividing with Polynomials
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Chapter 2
Factoring
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Section 1
Factoring by Greatest Common Factor
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Section 2
Factoring by Difference of Two Perfect Squares
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Section 3
Factoring by Grouping
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Factoring Trinomials
Example #1: x2 + 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: x2 − 11x + 18
Answer: (x - 9)(x – 2)
Example #3: x2 − 7x − 18
Answer: (x - 9)(x + 2)
Example #4: x2 + 7x − 18
Answer: (x + 9)(x - 2)
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Section 4
Factoring Trinomials
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Section 5
Eyeglasses/Decomposition
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Section 6
Factor Completely
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Chapter 3
Rational Expressions
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Section 1
Rational Expressions
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Section 2
Reducing Rational Expressions
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Section 3
Multiplying and Dividing Rational Expressions
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Section 4
Complex Fractions
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Section 5
Adding or Subtracting Rational Expressions
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Chapter 4
Functions
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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
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Section 1
Function Notation
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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
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Section 2
Composition of Functions
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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
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Section 3
Inverse Functions
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A graph of a function presents the answers of a function in a graph form
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Section 4
Graph of a Function
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
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Chapter 5
Radicals
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Section 1
Perfect Squares
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Section 2
Simplyfing Radicals
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Section 3
Adding and Subtracting Radicals
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Section 4
Multiplying Radicals
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Section 5
Dividing Radicals
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Section 6
Rationalizing a Denominator
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Section 7
Rationalizing a Binomial Denominator
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Section 8
Radical Equations
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Chapter 6
Imaginary Numbers
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Section 1
Pure Imaginary
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Section 2
Adding or Subtracting Imaginary Numbers
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Section 3
Complex Number Sheet
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Chapter 7
Quadratics
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Section 1
Solving Quadratics by Factoring
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Section 2
Solving Quadratics by the Quadratic Formula
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Section 3
Discriminant Solving Quadratics by the Quadratic Formula
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Section 4
Sum of the Roots and Product of the Roots
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Section 5
Writing a Quadratic When the Roots Are Given
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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
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Section 6
Solving 2 Variable Equations with Add/Subtract Method
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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
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Section 7
Solving 2 Variable Equations with Substitution Method
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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
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Section 8
Solving 2 Variable Equations with Add/Subtract Method
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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
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Section 9
Solving 2 Var Quad System of Equations with Add/Subtract
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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
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Section 10
Solving a 3 by 3 System of Equation
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Chapter 8
Absolute Value and Rational Expression
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Section 1
Absolute Value Equations
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Section 2
Absolute Value Inequalities
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Section 3
Solving Rational Equations
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Section 4
Solving Rational Inequalities
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Chapter 9
Exponents
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Section 1
Laws of Exponents
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Section 2
Zero and Negative Exponents
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Section 3
Fractional Exponents
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Section 4
Solving Equations with Fractional Exponents
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Section 5
Solving Exponential Equations
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Chapter 10
Statistics
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Section 1
Measure of Central Tendency
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xi = represents the data
fi = represents the frequency or number of times each piece of data appears
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Section 2
Measure of Central Tendency Frequency Chart
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x = represents the data
x with the line over it= mean
n = number of data
Σ = sum of the data
SD = Standard Deviation
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Section 3
Variance and Standard Deviation
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xi ' fi '
16 ' 6 '
17 ' 4 '
19 ' 8 '
22 ' 3 '
What Percentile is 19 in?
Step#1 A) Add up the total frequency column: 6 + 4 +8 + 3 = 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): 6 + 4 +8/2 = 14
Step# 2 A) Make a fraction out of the two #s in step #1 14/21
B) change this to a decimal 0.67
C) Move the decimal point 2 places to the right the final answer is 19 is in the 67th percentile
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Section 4
Percentile
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Chapter 11
Probability
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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
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Section 1
Counting Principal
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Section 2
Combination & Permutation
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Probability of an Event P(E) = Event/Total Number of Outcomes
*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
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Section 3
Probability
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Section 4
Probability with Two Outcomes
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Section 5
Probability with Two Outcomes: At Least/At Most
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Section 6
Binomial Expansion
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Section 7
Finding a Single Term
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Chapter 12
Sequences
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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, 128 …..
Geometric Sequence – has a common multiple(same # being multiplied over and over). Common Multiple r = 2
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Section 1
Sequences
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Section 2
Arithmetic Sequences
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Section 3
Geometric Sequences
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Section 4
Sigma Notation
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Section 5
Arithmetic Series Sheet
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Section 6
Geometric Series Sheet
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Section 7
Recursive Sequences
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Chapter 13
Remaining Topics
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Trigonometry of the Right Triangle
Angles and Quadrants
Quadrant Angles
Radian Measure
Unit Circle
Special Angles
Calculator for Trig Functions
Reducing Trig Functions
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
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
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Section 1
Worksheets