POWER ALGEBRA NOTES: QUICK & EASY

Size: px

Start display at page:

Download "POWER ALGEBRA NOTES: QUICK & EASY"

Reynold Hamilton
6 years ago
Views:

1 POWER ALGEBRA NOTES: QUICK & EASY 1

2 Table of Contents Basic Algebra Terms and Concepts... 5 Number Operations... 5 Variables... 5 Order of Operation... 6 Translating Verbal and Algebraic Phrases... 7 Definition of Equations, Inequalities and Solutions... 7 Fractions and Decimals... 8 Converting Fractions/Decimals... 8 LCM/LCD... 8 Multiplying and Dividing Fractions... 9 Adding and Subtracting Fractions Real Numbers Real Number System Adding and Subtracting Real Numbers Multiplying and Dividing Real Numbers Distributive Property Combining Like Terms Equations One-Step Equations Two-Step Equations Multi-Step Equations Formulas and Literal Equations Inequalities Graphing Inequalities Verifying Solutions to Inequalities Solving an Inequality and Graphing the Solution Solve and Graph a Two-Variable Inequality

3 Graphing Linear Equations Graphing Lines with One Variable Slope of a Line Graphing Lines with Two Variables Writing the Equation of a Linear Equation Using Slope-Intercept Form (y=mx + b) Using Point-Slope Form Write the Equation of a Line Given Two Points Standard Form Best Fitting Lines Systems Solve By Graphing Substitution Method Linear Combination System of Linear Inequalities Linear Programming Absolute Value Absolute Value Definition Evaluating Absolute Value Expressions Graphing Absolute Value Equations Solving Absolute Value Equations Solving Absolute Value Inequalities Powers and Exponents Properties of Exponents Scientific Notation Compound Interest Exponential Growth and Decay Polynomials and Factoring Adding and Subtracting Polynomials Multiplying Polynomials Special Polynomial Multiplication Rules Factoring the Greatest Common Factor Factoring Quadratic Trinomials Special Factoring Rules

4 Quadratic Equations Solve by Taking Square Roots Graphing Quadratic Equations Quadratic Formula Solve Quadratic Equations by Factoring The Discriminant- Type of Roots Completing The Square Graphing Quadratic Inequalities Functions and Relations Introduction to Functions and Relations Function Operations Inverse Functions Graphing Functions Linear and Non-Linear Functions Composite Functions Special Functions Rational Expressions and Equations Ratios and Proportions Percent Direct and Inverse Variation Simplifying Rational Expressions Multiplying and Dividing Rational Expressions Adding and Subtracting Rational Expressions Solving Rational Equations Radical Expressions and Equations Simplifying Radicals Operations with Radicals Solving Radical Equations Distance and Midpoint Formulas The Pythagorean Theorem Surface Area and Volume of Basic Figures Area of Basic Figures Circles- Area and Circumference Surface Area of Basic Figures Volume of Basic Figures

5 Basic Algebra Terms and Concepts Number Operations Variables 5

6 Basic Algebra Terms and Concepts Order of Operations 6

7 Basic Algebra Terms and Concepts Translating Verbal and Algebraic Phrases Definition of Equations, Inequalities and Solutions 7

8 Fractions and Decimals Converting Fractions/Decimals LCM/LCD 8

9 Fractions and Decimals Multiplying and Dividing Fractions 9

10 Fractions and Decimals Adding and Subtracting Fractions 10

11 Real Numbers Real Number System Adding and Subtracting Real Numbers 11

12 Real Numbers Multiplying and Dividing Real Numbers Distributive Property Combining Like Terms 12

13 Equations One-Step Equations Two-Step Equations 13

14 Equations Multi-Step Equations 14

15 Equations Formulas and Literal Equations 15

16 Inequalities Graphing Inequalities Verifying Solutions to Inequalities 16

17 Inequalities Solving an Inequality and Graphing the Solution 17

18 Inequalities Solve and Graph a Two-Variable Inequality 18

19 Graphing Linear Equations Graphing Lines with One Variable 19

20 Graphing Linear Equations Slope of a Line 20

21 Graphing Linear Equations Graphing Lines with Two Variables 21

22 Graphing Linear Equations 22

23 Graphing Linear Equations 23

24 Graphing Linear Equations 24

25 Writing the Equation of a Linear Equation Using Slope-Intercept Form (y=mx + b) Using Point-Slope Form 25

26 Writing the Equation of a Linear Equation Write the Equation of a Line Given Two Points 26

27 Writing the Equation of a Linear Equation Standard Form Best Fitting Lines 27

28 Systems Solve By Graphing 28

29 Systems Substitution Method 29

30 Systems Linear Combination 30

31 Systems System of Linear Inequalities 31

32 Systems Linear Programming 32

33 Absolute Value Absolute Value Definition Evaluating Absolute Value Expressions 33

34 Absolute Value Graphing Absolute Value Equations 34

35 Absolute Value 35

36 Absolute Value Solving Absolute Value Equations 36

37 Absolute Value Solving Absolute Value Inequalities 37

38 Powers and Exponents Properties of Exponents 38

39 Powers and Exponents Scientific Notation 39

40 Powers and Exponents Compound Interest Exponential Growth and Decay 40

41 Polynomials and Factoring Adding and Subtracting Polynomials 41

42 Polynomials and Factoring Multiplying Polynomials 42

43 Polynomials and Factoring Special Polynomial Multiplication Rules Factoring the Greatest Common Factor 43

44 Polynomials and Factoring Factoring Quadratic Trinomials 44

45 Polynomials and Factoring Special Factoring Rules 45

46 Quadratic Equations Solve by Taking Square Roots 46

47 Quadratic Equations Graphing Quadratic Equations 47

48 Quadratic Equations Quadratic Formula 48

49 Quadratic Equations Solve Quadratic Equations by Factoring The Discriminant- Type of Roots 49

50 Quadratic Equations Completing the Square 50

51 Quadratic Equations Graphing Quadratic Inequalities 51

52 Functions and Relations Introduction to Functions and Relations 52

53 Functions and Relations Introduction to Functions and Relations 53

54 Functions and Relations Function Operations Inverse Functions 54

55 55

56 Functions and Relations Graphing Functions Linear and Non-Linear Functions Composite Functions 56

57 Functions and Relations Special Functions Rational Expressions and Equations Ratios and Proportions 57

58 Rational Expressions and Equations Percent 58

59 Rational Expressions and Equations Direct and Inverse Variation 59

60 Rational Expressions and Equations Simplifying Rational Expressions Multiplying and Dividing Rational Expressions 60

61 Rational Expressions and Equations Adding and Subtracting Rational Expressions 61

62 Rational Expressions and Equations Solving Rational Equations 62

63 63

64 Radical Expressions and Equations Simplifying Radicals Operations with Radicals 64

65 Radical Expressions and Equations Solving Radical Equations 65

66 Radical Expressions and Equations Distance and Midpoint Formulas 66

67 Radical Expressions and Equations Distance and Midpoint Formulas Radical Expressions and Equations The Pythagorean Theorem 67

68 Radical Expressions and Equations The Pythagorean Theorem 68

69 Surface Area and Volume of Basic Figures Area of Basic Figures 69

70 Surface Area and Volume of Basic Figures Circles- Area and Circumference 70

71 Surface Area and Volume of Basic Figures Surface Area of Basic Figures 71

72 Surface Area and Volume of Basic Figures Surface Area of Basic Figures 72

73 Surface Area and Volume of Basic Figures Volume of Basic Figures 73

74 Surface Area and Volume of Basic Figures Volume of Basic Figures 74

75 Avoiding Common Mistakes and Instilling Good Habits (by John Zimmerman) Experience is the best teacher. As such I want to share with you lessons that I have learned over the years when it comes to teaching young people mathematics. Knowing what to look for in your child s math work can help you encourage good habits and correct common problems. Areas to pay special attention to: Fractions: many young people have trouble with fractions. It s an absolute must that your child understands fractions and their respective operations. Often students ignore fractions because they have a calculator don t fall into this trap! If you re weak in fractions you will have a difficult time with algebra and beyond. Integers: students that have not mastered working with positive and negative numbers will have a very difficult time in middle and high school math. Once again, don t let your child rely on a calculator they must know and memorized the rules of integers. Order of Operations: often, many students have a false sense of security that they are following the proper order of operations when simplifying a numeric expression. Weakness in this area if not corrected early will undermine success in mathematics. So, please ensure that your child understands and thoroughly practices the order of operations, also known as PEMDAS (Please Excuse My Dear Aunt Sally). Distributive Property: many students tend to make distributive property errors especially when solving equations. If you see a pattern of your child not correctly applying the distributive property it is imperative that you go back and review the distributive property section until the skill is mastered. Neatness: Mathematics is a language. To clearly understand what we are saying in math it s vital that we write out steps in a neat and orderly manner. Again, students tend to get over confident in thinking that writing out each step is a waste of time, only to find out that they made an error that could have been caught if they had carefully written out the steps (I called this the, I knew that mistake). To instill neatness and logic in problem solving, have students model their work to the steps shown in the videos. Pencil not pen: no one writes out all the steps in math perfectly the first time so students must be prepared to erase mistakes. This seems obvious, but many students like to work in pen and their work gets messy fast; if your child likes using a pen insist on using a pencil. Enough space: another tendency students have is that they like to conserve space on their paper while working on problems. This noble conservation unfortunately leads to crowded work that does not show all the steps of a problem solving process. Avoid this tendency by encouraging your child to use whatever amount of paper it takes to show all the steps. Also, if your child writes very small try to encourage them to write a bit larger so they can see all their work clearly.

GET THE INSIDE SECRETS FROM MATH TEACHERS EASY THINGS THAT CAN RAISE YOUR ALGEBRA TEST SCORES DRAMATICALLY!

As a middle and high school math teacher I graded thousands of math tests and all along the way I had to determine how many points I would reward a student for their efforts.

Of course each teacher will grade tests slightly different, but I can assure you most math teachers are looking for certain indicators before they award points.

How teachers determine grades and how to maximize your scores: 1. Correct answer Clearly the sure fire way to increase your math test score is answer as many questions with the right answer!

76 GET THE INSIDE SECRETS FROM MATH TEACHERS EASY THINGS THAT CAN RAISE YOUR ALGEBRA TEST SCORES DRAMATICALLY! By understanding how your teacher grades tests you can significantly raise your math grades even if you have not completely mastered the concepts. As a middle and high school math teacher I graded thousands of math tests and all along the way I had to determine how many points I would reward a student for their efforts. The process was fairly subjective and I often used my gut or best judgment to make a decision on how many points I would award a student for the work on their test. Of course each teacher will grade tests slightly different, but I can assure you most math teachers are looking for certain indicators before they award points. Students can really help improve their grade if they know what their teacher is looking for and it s much more than the correct answer. How teachers determine grades and how to maximize your scores: 1. Correct answer Clearly the sure fire way to increase your math test score is answer as many questions with the right answer! So study and be as ready as possible for tests and quizzes. However, let me give you an inside tip to make your study time even more effective. Before your test ask your teacher as many questions about what will be on the test you will be surprised on how many details you can find out if you pester your teacher for inside information on a test! Knowing more about what will be on a test can focus your efforts to study the right material. Also, you can almost be certain that 70% of the test questions on a test will be a version of a homework problem or lecture problem covered in class review your notes and homework problems because these problems will be repackaged as the test questions. One last point to stress, even if you answer a question right make sure you show the supporting work. Most math teachers don t trust magically appearing right answers without evidence that you understood how you arrived at the solution. Many teachers will give you NO credit for correct solutions without supporting work! Be smart show off what you know!

$EASY THINGS THAT CAN RAISE YOUR ALGEBRA TEST SCORES DRAMATICALLY! 2. Simplified solution Give me the correct answer as the fraction and I will take points off!$ $Examples of correct solutions that are not simplified are unreduced fractions, answers that don t have the proper of units of measure (like an area or volume problem) and variable or number$

77 EASY THINGS THAT CAN RAISE YOUR ALGEBRA TEST SCORES DRAMATICALLY! 2. Simplified solution Give me the correct answer as the fraction and I will take points off! Every math teacher I know will deduct points for correct answers that are not simplified. Examples of correct solutions that are not simplified are unreduced fractions, answers that don t have the proper of units of measure (like an area or volume problem) and variable or number expressions that are not finished. So when it comes to racking up easy points on your tests, finishing and simplifying your solutions go a long way. 3. How much work you show The best thing a student can do for their grade beyond getting the correct answer is show as much work as possible even if you don t know what you re doing! Of course the work you show has to be a serious effort at trying to figure out the problem, but if you provide written evidence that you really tried to answer a question you will most likely earn some charity points it all adds up in the end and can make a major difference in your overall grade. 4. How many questions you attempt Never, never, never leave a question blank this is the kiss of death for your math test score! I would like to stress a few points here. When taking a test, first invest the majority of time on the problems you feel that you can answer correctly. However, you always need to leave a little time to attempt questions that you doubt you can figure out. I d like to refer you back to my 3 rd point how much work you show as what you need to be focusing on with these last ditch problems. Always try your best to leave no question blank. If you show your teacher that you at least tried each problem, often you will discover they will kick you a few extra points for your effort.

For example, let s say you re working on an equation and wrote each step correctly until you were stumped. Guess what you have earned some points!

78 EASY THINGS THAT CAN RAISE YOUR ALGEBRA TEST SCORES DRAMATICALLY! 5. How much understanding you demonstrated If you show that you understand some parts of a problem your teacher will reward you even if you re not able to complete the problem. For example, let s say you re working on an equation and wrote each step correctly until you were stumped. Guess what you have earned some points! Now let s take the same problem with the attitude, I can t do this, so it s a waste of my time this approach will always yield in no points. The main factor in collecting points on your test score is demonstrating what you know even if you can t get the problem right! Partial credit is what I m talking about and as teacher I can tell you that partial credit can often be the difference between a B- and an A-. Be smart and get credit for what you know! 6. Whether your work is clear, neat and understandable Even if your work is correct if your teacher can t understand it, you re at risk of not getting points! Neatness is a struggle for many students, but overcoming sloppiness can result in big points. A way to get on a teacher s good side (which will always improve your score) is to write your work so neatly that it s easy to read and understand. Now, frustrate your teacher by complicated chicken scratch and they won t be as motivated to stick around and find points from your answer. Remember that increasing your math test scores will be the sum of a lot of little things you do and writing neatly is definitely one of them! 7. Your attitude and effort Talk in class, disrupt a lesson, and don t do your homework I guarantee your teachers will not be extra creative to find points on your tests. Teachers will absolutely help those that help themselves and often that means the difference between a 69% (D) and 70% (C). Of course if you re interested in getting better math grades than you need to act like it in class, your teacher can tell if you re trying. Ask questions, ask for help and do your best that alone will yield more points and could very well be the difference between passing and failing.

Instructors Manual Algebra and Trigonometry, 2e Cynthia Y. Young

Dear Instructor, Instructors Manual Algebra and Trigonometry, 2e Cynthia Y. Young I hope that when you read my Algebra and Trigonometry book it will be seamless with how you teach. My goal when writing