ALGEBRA 2 Summer Review Assignments Graphing

Size: px
Start display at page:

Download "ALGEBRA 2 Summer Review Assignments Graphing"

Transcription

1 ALGEBRA 2 Summer Review Assignments Graphing To be prepared for algebra two, and all subsequent math courses, you need to be able to accurately and efficiently find the slope of any line, be able to write the equation of a line given some basic information, and also be able to graph a line when given some basic information, or an equation in any form. Complete each of the following by filling in the blanks. 1. What is slope-intercept formula? y = mx + b. In this formula, m stands for slope, b stands for the y-intercept, and (x, y) stands for any point on the line. 2. What is point-slope formula? y y 1 = m(x x 1 ) In this formula, m stands for the slope and (x 1, y 1 ) stands for a specific point on the line, while (x, y) stands for a generic point on the line. 3. All horizontal lines have equations in the form of y = a constant value 4. All vertical lines have equations in the form of x = a constant value 5. The x-intercept is the point where the graph intersects the x-axis, and is the point where y equals The y-intercept is the point where the graph intersects the y-axis, and is the point where x equals 0. Note: Finding both the x and y intercept can allow us to graph a linear equation very quickly since it is an application of using the number 0. If we can find both the x and intercepts quickly, we can plot them, connect with a line, and finish the graph, making sure to label all important features! 7. Slope can be described in many different ways. In equations, we always represent slope by the variable m. Slope is seen to be the steepness of the line. The slope of a line tells which direction it rises or falls. There are four different types of slope: positive, negative, undefined, and zero. 8. The formula for slope when given two points is: m = y 2 y 1 /x 2 x 1 which tells us that slope is constant and can be described using the phrase RISE over RUN. Note: If we are asked to graph an equation and are given the slope and a point on the graph, we can now do this without solving for the x and y intercepts and without the need to make an x/y table. We would start our graph at the y intercept and then move to other points on the graph by using the slope be thinking about rise over run. Finally we need to complete the graph by connecting the points with a line, making sure to label all important features! 9. Parallel lines are defined as two lines in the same plane that never intersect. Algebraically, we see that these lines have equal slopes.

2 10. Perpendicular lines are defined as two lines that intersect to form right angles. Algebraically, we see that these lines have opposite reciprocal slopes. Note: A relation is a set of ordered pairs. A function is a relation in which no X value is repeated. In order for a relation to be a function its graph must past the vertical line test. In using this test, if you can draw ANY vertical line that passes through more than one point on the graph, then the relation is not a function! 11. Use the vertical line test to determine if each relation is a function or not. a) b) c) Note: The domain of a relation is the set of all x-coordinates in the relation. The range of a relation is the set of all y-coordinates in the relation. In both of these cases, the values should be written in numeric order, with no x or y values repeated. 12. For the relation {(2, 5) (-3, 7) (2, 3)} a. determine the domain of the relation: b. determine the range of the relation: c. determine if the relation is a function: Note: f(x) =4x 2 15, is an example of a function that is written in function notation. f(x) is really another way of expressing Y. If we were to evaluate f(-2) for the function f(x) = 4x 2 15, we would do so like this: f(-2) = 4x 2 15 = 4(-2) 2 15 = 4*4 15 = = Now, still using the function 4x 2 15, find each of the following values: a. Find f(8) b. Find 4[f(-10)] c. Find f(f(3))

3 For exercises 14 16, complete your graphs by finding the x and y intercepts first and then using that information to graph the lines ON GRAPH PAPER. Be sure to label the x and y axis, the key ordered pairs of the graph, and to put arrows on both the x and y axis and the ends of the graphed line itself y + 2x = x = y = 14 x-intercept = x-intercept = x-intercept = y-intercept = y-intercept = y-intercept = For exercises 17 21, find the slope of the line containing the following points. 17. (-5, -3) (4, 7) 18. (3, -5) (-4, -5) 19. (-7, -1) (-7, 3) Slope = Slope = Slope = 20. (4, 6) (-8, 2) 21. (-5, -6) (2, -8) Slope = Slope = 22. Given a line with a slope of 5/7, determine the slope of a line that is parallel to this line. 23. Given a line with a slope of -5, determine the slope of a line that is perpendicular to this line. For exercises 24 30, graph each equation on a separate piece of graph paper, using any method y 4x = x + ½ y = x = y + 4y = y = -11 For exercises 31 38, graph each line remembering special facts about parallel and perpendicular lines slopes. Be sure to label the x and y axis, the key ordered pairs of the graph, and to put arrows on both the x and y axis and the ends of the graphed line itself. 29. Graph a line passing through (-6, -5) that is parallel to a line with a slope of Graph a line passing through (3, -2) that is parallel to a line with the equation x = Graph a line passing through (-5, 1) that is perpendicular to a line with a slope of 5/ Graph a line passing through (-4, 2) that is perpendicular to a line with an equation of y = 5

4 For exercises 39 57, write an equation of the line and put your answer in slope-intercept form, if possible. Do this work on a separate piece of paper. 33. Write an equation of the line in slope-intercept form that has slope 1/17 and a y-intercept of Write an equation of the line in slope-intercept form that passes through (-4, 2) and has slope Write an equation of the line in slope-intercept form that passes through the points (6, 10) and (5, -3) 36. Write an equation of the line in slope-intercept form that passes through the points (4, -5) and (3,3) 36b. Write an equation of the line in slope-intercept form whose slope is undefined and passes through (-6, -2) 37. Write an equation of the line in slope-intercept form that passes through (4, 6) and has a slope of zero 38. Write an equation of the line in slope-intercept form that passes through (-2, 4) and is parallel to the line with equation y = 3x Write an equation of the line in slope-intercept form that has a y-intercept of 7 and is perpendicular to the line with equation x = Write an equation of the line in slope-intercept form that has an x-intercept of 2 and is parallel to the line with equation x = Write an equation of the line in slope-intercept form that passes through (1, 7) and is perpendicular to the line with equation -2x + 8y = Write an equation of the line in slope-intercept form that has an x-intercept of 3 and a y-intercept of Also on a separate piece of paper, show whether the graphs of the lines y = 3/5 x 7 and 5y 3x = 45 are parallel, perpendicular, or neither? Explain your reasoning. 44. Also on a separate piece of paper, show whether the graphs of the lines y 5 = 2(x + 8) and 8y 4x = 24 are parallel, perpendicular, or neither? Explain your reasoning.

5 NOTES: We use a scatter plot for showing a set of data points. The points do not usually form a line but they may approximate a linear relationship. Through these points, we draw a line to show the linear relationship. We call this line the best-fit line. The prediction equation is used to determine the equation of a line knowing two points. It is used to estimate or predict one variable when knowing the other. To write this equation, first plot the points of the scatter plot. Then, decide where to draw the best-fit line. Then choose two ordered pairs on that line, and use them to find the slope of the equation. Finally, use the slope that you found and one of the two points that you just used to write the prediction equation. 45. Draw a scatter plot and find a prediction equation to show how keyboarding speed and experience are related. Predict the keyboarding speed in words per minute of a student who has 17 weeks of experience. Let x represent the weeks of experience, and y represent the speed in words per minute. Weeks of experience Speed (WPM) Make a scatter plot on a piece of graph paper. Label the axis, the ordered pairs, and show your best fit line. Choose two ordered pairs on the best fit line (, ) (, ). Find the slope of these points: Find the prediction equation: Use the prediction equation to predict the keyboarding speed of a student who has 17 weeks of experience. 46. Draw a scatter plot and find a prediction equation to show how the number of salespersons and total sales are related. # of salespersons Total sales Company A 12 $250 Company B 33 $699 Company C 17 $350 Company D 22 $460 Company E 24 $501 Company F 8 $162 Identify the independent variable: Identify the dependent variable: Make a scatter plot on a piece of graph paper. Label the axis, the ordered pairs, and show your best fit line. Choose two ordered pairs on the best fit line (, ) (, ). Find the slope of these points: Find the prediction equation: If this relationship holds true, predict the total sales for company G that employs 58 salespeople. If this relationship holds true, how many salespeople would be required to generate $1800 in sales for the month? NOTE: The definition to a solution of a linear equation is an ordered pair that satisfies the equation.

6 In problems 47 48, determine which of the ordered pairs listed are solutions of the equation x = 2y 1 a. (1, -2) b. (-1, -1) c. (-2, -2.5) d. (0, -½) 48. 2y = x + 3 a. (1, -2) b. (-1, -1) c. (-3, 0) d. (0, -3/2) NOTE: If you are asked to solve the equation for the given domain, this tells you that you should make an x/y table, plug the given domain values in for x, and find the corresponding y value for each. In problems 49 50, solve the equation if the domain is {-2, -1, 0, 3, 8}. 49. y = 4x x y = 6

7 ALGEBRA 2 Summer Review Assignments Monomials and Polynomials To be prepared for your subsequent math courses, you need to be able to accurately and efficiently add, subtract, multiply, and divide monomials and polynomials. Additionally, you need to be aware of all of the rules of exponents, including those for negative exponents. NOTES: A monomial is a number, a variable, or a product of a number and one or more variables. Examples of monomials would include: 6 3x 4xy A polynomial is a monomial or a sum of monomials. 3 7x 6 9y A binomial is the sum of 2 monomials. A trinomial is the sum of 3 monomials. Examples of: Monomials Binomials Trinomials 3 4x x 2 4x x 3 4x x 8 x x 1 When multiplying monomials with like bases, add the exponents of like bases. x a x b x a b The denominator in a fraction can be written in the numerator if the sign of the exponent changes. Any base (other than 0) with an exponent of 0 is equal to 1. x a x x a a ab When raising a term to an exponent, multiply all of the inside exponents by the outside exponent. b x x When dividing terms with like bases, subtract the exponents of like bases. x x a b x a b For all problems in this assignment, simplify each expression using the rules of exponents for monomials and polynomials. Provide answers with positive exponents only and in descending order. 1. ( ) ( ) 2. 3(xy) 3 (4xz 2 ) + z(4xy)(5x 3 y 2 z) 3. (-6x xy + 9xy 2 ) (5xy 4x 2 y + 9xy 2 ) 4. (3x 3 4ax + 9a 2 ) + (-5x 3 8ax + 4a 2 ) 5. (3x 2 5)(4x 2 + 7) 6. (x + 3)(2x 2 5x + 4) 7. (9a 2 3c)(5a 2 + 3c) 8. (x 5) 3 9. ( ) ( )

8 12. ( ) ( ) 13. ( ) 14. ( ) 15. ( ) ( ) ( ) 18. ( )( ) 19. ( )( ) 20. ( ) ( ) ( ) 23. ( ) 24. ( ) 25. ( )( ) 26. ( )( ) 27. ( ) 28. ( ) ( ) (5x 5 y 7 z) (-6x 4 y 2 z 15 ) 31. (-2x 4 y 5 z) 3 (3x 3 yz 5 ) 32. x 3 + x x 2-2x 3x (5a 2 7)(-8a 2 + 4) 35. (3xy 5 ) (-5x 4 y 3 8x 2 y 2 + 4x 3 y 4 ) (-8x 2 y 2 + 5x 4 y 3 + 4x 3 y 4 )

9 ALGEBRA 2 Summer Review Assignments Factoring Polynomials To be prepared for your subsequent math courses, you need to be able to accurately and efficiently factor some basic polynomials. This will include finding a GCF, factoring a difference of perfect squares, and factoring a trinomial both with a lead coefficient of one, and also a lead coefficient other than one. Factor out the GCF that is the only step for exercises 1 and a 3 20a 2. 8x 4 y 2 12x 2 y x 3 y 3 For exercises 3 32, factor each expression completely. Remember to look for a GCF first! 3. w x 2 4x y y 2 3y x 2 + 8x x 2 y x 2 y 2 + 4x 2 y 9. 12y 3 3y x 2 14x y 2 5ay 6a w 2 64 m x x r 2 27w x 2 3x r 3 + 3r 2 54r 17. 6n 2 11n k 3 2k 2 r 3kr x 6 4x x 4 13x

10 NOTE: We can now solve quadratic equations is by factoring. To use this method, we must use the zero product property, which says that for any real numbers a and b, if a*b = 0, then either a=0, b=0, or BOTH a AND b each = 0 So, in order to solve an equation by factoring, the equation must be first set equal to 0! When we have factored, we can find the solutions of the equation by setting each of the factors equal to 0 and then solving each of those little equations for the variable. For problems 33 38, solve each of the equations by factoring. 21. x 2 25 = x 2 42x = x 2 10x 24 = x 2 25x 18 = x 2 + 8x + 21 = x 3 48x = 0

11 ALGEBRA 2 Summer Review Assignments Radicals To be prepared for your subsequent math courses, you need to be able to accurately and efficiently simplify a radical statement. This includes adding, subtracting, all forms of multiplying, and dividing. As you will see at several times in mathematics, you will also ALWAYS need to check your work when solving a radical equation. NOTES: In the expression, 25 the is called the radical sign, the 25 is referred to as the radicand and the whole expression is called a radical. When the square root of a number is taken, the two answers are called the principal and negative square roots. In the expression, n x a, the n is the root index. If no root index is shown, then it is assumed to be 2, and the root is called a square root. When the root index is even, the radicand must be positive for the value to be real. The directions to problems in this section will only say to simplify. While that seems like a harmless little word, it carries much weight here. A radical expression has been completely simplified, only if each of the following are all completed: 1. All radicals that can be combined by addition, subtraction, or multiplication have been combined. 2. There are no perfect square factors in the radicand. 3. There are no radicals in the denominator 4. All fractions have been reduced. 5. The root index is as small as possible. Radicals are like variables. You may only multiply and divide numbers if they both have the square root, or both don t have the square root. OK: or NOT OK: or The product property of radicals shows that: This property allows us to simplify a radical expression by finding the largest perfect square that is a factor of the radicand, separating it into two radical expressions, then simplifying the perfect root factor. For example, 24 = 4 6 = 2 6 To simplify an expression such as 20 x, we would divide the exponent of the radicand by the root index (in this case, 2. To simplify an expression such as, 3 x 20, divide the exponent of the radicand by the root index (in this case, 3; leave the quotient as a power on the outside and the remainder as a power under the radical. The rules for adding and subtracting radicals are like those for combining like terms We can only add or subtract radicals when the radicands AND root indexes are alike. When we add or subtract radicals, remember do NOT add or subtract the radicands OR root indexes. Also, remember, NEVER COMBINE unlike radicals. If a radicand is a fraction, it can be rewritten into two separate radicals. To rationalize the denominator, we need to multiply by a value of 1. We can do this because any number times 1 equals itself. The value can be expressed by some radical divided by itself. We will know what radicand to use by the radical in the denominator.

12 For problems 1 19, simplify each radical expression completely ± For problems 20 35, use the rules/properties of multiplication to simplify each radical expression completely. 20. (5 6)(5 6) 21. (3 5 )(-2 2 ) ( ) ( ) ( ) 34. ( ) For problems 36 41, use the rules of adding/subtracting to simplify each radical expression completely For problems 42 61, use the rules/properties of division to simplify each radical expression completely

13 ALGEBRA 2 Summer Review Assignments Systems of Equations To be prepared for algebra two, and all subsequent math courses, you need to be able to accurately solve and classify a system of linear equations. You will need to be able to solve using all three methods graphing, substitution, and elimination. (Elimination is also called linear combination, as well as addition ) NOTES: A system of equations is two or more equations containing the same variables. The solution to a system of equations is the ordered pair that satisfies every equation in the system. On a graph, the solution is where lines intersect. A system of equations that has exactly one solution is defined to be consistent and independent. The graph of a system of equations that has exactly one solution looks like intersecting lines. The equations of a system that has exactly one solution must have different slopes, but we do not know anything about their y-intercepts A system of equations that has no solution is defined as inconsistent. The graph of a system of equations that has no solution looks like parallel lines. The equations of a system that does not have a solution must have the same slopes, and different y-intercepts. A system of equations that has an infinite number of solutions is defined to be consistent and dependent. The graph of a system of equations that an infinite number of solutions looks like overlapping lines. The equations of a system that has an infinite number of solutions must have the same slopes, and the same y-intercepts. For numbers 1 5, solve each of the following systems by graphing. Complete your graphs on GRAPH PAPER ONLY and use a RULER! As of May 2013, this website is still a good place to go if you need to print your own graph paper: If the site closes, there are dozens like it on the internet. On your graphs, be sure to label all important information What do you notice about the graphs of the equations in #3? Therefore, what is the classification of this system? 7. What do you notice about the graphs of the equations in #1? Therefore, what is the classification of this system? 8. What do you notice about the graphs of the equations in #4? Therefore, what is the classification of this system?

14 NOTE: To solve a system of equations by substitution, these are the steps: 1. Solve one equation for one variable. 2. Substitute (for the variable solved) into the other equation. 3. Solve for the remaining variable. 4. Substitute this solution into an equation to solve for the other variable. For numbers 9 12, use substitution to solve each system of equations. Leave all answers as simplified fractions. There may be one solution, no solution, or infinitely many solutions NOTE: To solve a system of equations by elimination using multiplication, these are the steps: 1. Arrange the terms so that all variables are on the same side of the equation and in the same order. Arrange them as columns. 2. Multiply one or both equations so that the coefficients of one variable are the same. 3. Add or subtract the columns so that one variable has a coefficient of zero. 4. Solve the equation remaining for the variable remaining. 5. Substitute this solution into an original equation to find the other variable. For numbers 13 17, use elimination using multiplication to solve each system of equations. Leave all answers as simplified fractions. There may be one solution, no solution, or infinitely many solutions

Study Guide for Math 095

Study Guide for Math 095 Study Guide for Math 095 David G. Radcliffe November 7, 1994 1 The Real Number System Writing a fraction in lowest terms. 1. Find the largest number that will divide into both the numerator and the denominator.

More information

Geometry 21 Summer Work Packet Review and Study Guide

Geometry 21 Summer Work Packet Review and Study Guide Geometry Summer Work Packet Review and Study Guide This study guide is designed to accompany the Geometry Summer Work Packet. Its purpose is to offer a review of the ten specific concepts covered in the

More information

Herndon High School Geometry Honors Summer Assignment

Herndon High School Geometry Honors Summer Assignment Welcome to Geometry! This summer packet is for all students enrolled in Geometry Honors at Herndon High School for Fall 07. The packet contains prerequisite skills that you will need to be successful in

More information

Never leave a NEGATIVE EXPONENT or a ZERO EXPONENT in an answer in simplest form!!!!!

Never leave a NEGATIVE EXPONENT or a ZERO EXPONENT in an answer in simplest form!!!!! 1 ICM Unit 0 Algebra Rules Lesson 1 Rules of Exponents RULE EXAMPLE EXPLANANTION a m a n = a m+n A) x x 6 = B) x 4 y 8 x 3 yz = When multiplying with like bases, keep the base and add the exponents. a

More information

Algebra I Unit Report Summary

Algebra I Unit Report Summary Algebra I Unit Report Summary No. Objective Code NCTM Standards Objective Title Real Numbers and Variables Unit - ( Ascend Default unit) 1. A01_01_01 H-A-B.1 Word Phrases As Algebraic Expressions 2. A01_01_02

More information

Solving Equations Quick Reference

Solving Equations Quick Reference Solving Equations Quick Reference Integer Rules Addition: If the signs are the same, add the numbers and keep the sign. If the signs are different, subtract the numbers and keep the sign of the number

More information

Algebra 1 Seamless Curriculum Guide

Algebra 1 Seamless Curriculum Guide QUALITY STANDARD #1: REAL NUMBERS AND THEIR PROPERTIES 1.1 The student will understand the properties of real numbers. o Identify the subsets of real numbers o Addition- commutative, associative, identity,

More information

Algebra 31 Summer Work Packet Review and Study Guide

Algebra 31 Summer Work Packet Review and Study Guide Algebra Summer Work Packet Review and Study Guide This study guide is designed to accompany the Algebra Summer Work Packet. Its purpose is to offer a review of the ten specific concepts covered in the

More information

MA.8.1 Students will apply properties of the real number system to simplify algebraic expressions and solve linear equations.

MA.8.1 Students will apply properties of the real number system to simplify algebraic expressions and solve linear equations. Focus Statement: Students will solve multi-step linear, quadratic, and compound equations and inequalities using the algebraic properties of the real number system. They will also graph linear and quadratic

More information

Bishop Kelley High School Summer Math Program Course: Algebra 2 A

Bishop Kelley High School Summer Math Program Course: Algebra 2 A 06 07 Bishop Kelley High School Summer Math Program Course: Algebra A NAME: DIRECTIONS: Show all work in packet!!! The first 6 pages of this packet provide eamples as to how to work some of the problems

More information

Algebra 2 Summer Work Packet Review and Study Guide

Algebra 2 Summer Work Packet Review and Study Guide Algebra Summer Work Packet Review and Study Guide This study guide is designed to accompany the Algebra Summer Work Packet. Its purpose is to offer a review of the nine specific concepts covered in the

More information

Beginning Algebra. 1. Review of Pre-Algebra 1.1 Review of Integers 1.2 Review of Fractions

Beginning Algebra. 1. Review of Pre-Algebra 1.1 Review of Integers 1.2 Review of Fractions 1. Review of Pre-Algebra 1.1 Review of Integers 1.2 Review of Fractions Beginning Algebra 1.3 Review of Decimal Numbers and Square Roots 1.4 Review of Percents 1.5 Real Number System 1.6 Translations:

More information

2017 SUMMER REVIEW FOR STUDENTS ENTERING GEOMETRY

2017 SUMMER REVIEW FOR STUDENTS ENTERING GEOMETRY 2017 SUMMER REVIEW FOR STUDENTS ENTERING GEOMETRY The following are topics that you will use in Geometry and should be retained throughout the summer. Please use this practice to review the topics you

More information

Course Number 420 Title Algebra I Honors Grade 9 # of Days 60

Course Number 420 Title Algebra I Honors Grade 9 # of Days 60 Whitman-Hanson Regional High School provides all students with a high- quality education in order to develop reflective, concerned citizens and contributing members of the global community. Course Number

More information

Basic ALGEBRA 2 SUMMER PACKET

Basic ALGEBRA 2 SUMMER PACKET Name Basic ALGEBRA SUMMER PACKET This packet contains Algebra I topics that you have learned before and should be familiar with coming into Algebra II. We will use these concepts on a regular basis throughout

More information

Algebra 2 Honors: Final Exam Review

Algebra 2 Honors: Final Exam Review Name: Class: Date: Algebra 2 Honors: Final Exam Review Directions: You may write on this review packet. Remember that this packet is similar to the questions that you will have on your final exam. Attempt

More information

Evaluate algebraic expressions for given values of the variables.

Evaluate algebraic expressions for given values of the variables. Algebra I Unit Lesson Title Lesson Objectives 1 FOUNDATIONS OF ALGEBRA Variables and Expressions Exponents and Order of Operations Identify a variable expression and its components: variable, coefficient,

More information

SOLUTIONS FOR PROBLEMS 1-30

SOLUTIONS FOR PROBLEMS 1-30 . Answer: 5 Evaluate x x + 9 for x SOLUTIONS FOR PROBLEMS - 0 When substituting x in x be sure to do the exponent before the multiplication by to get (). + 9 5 + When multiplying ( ) so that ( 7) ( ).

More information

OBJECTIVES UNIT 1. Lesson 1.0

OBJECTIVES UNIT 1. Lesson 1.0 OBJECTIVES UNIT 1 Lesson 1.0 1. Define "set," "element," "finite set," and "infinite set," "empty set," and "null set" and give two examples of each term. 2. Define "subset," "universal set," and "disjoint

More information

COUNCIL ROCK HIGH SCHOOL MATHEMATICS. A Note Guideline of Algebraic Concepts. Designed to assist students in A Summer Review of Algebra

COUNCIL ROCK HIGH SCHOOL MATHEMATICS. A Note Guideline of Algebraic Concepts. Designed to assist students in A Summer Review of Algebra COUNCIL ROCK HIGH SCHOOL MATHEMATICS A Note Guideline of Algebraic Concepts Designed to assist students in A Summer Review of Algebra [A teacher prepared compilation of the 7 Algebraic concepts deemed

More information

MA094 Part 2 - Beginning Algebra Summary

MA094 Part 2 - Beginning Algebra Summary MA094 Part - Beginning Algebra Summary Page of 8/8/0 Big Picture Algebra is Solving Equations with Variables* Variable Variables Linear Equations x 0 MA090 Solution: Point 0 Linear Inequalities x < 0 page

More information

Algebra 2 Segment 1 Lesson Summary Notes

Algebra 2 Segment 1 Lesson Summary Notes Algebra 2 Segment 1 Lesson Summary Notes For each lesson: Read through the LESSON SUMMARY which is located. Read and work through every page in the LESSON. Try each PRACTICE problem and write down the

More information

Part 2 - Beginning Algebra Summary

Part 2 - Beginning Algebra Summary Part - Beginning Algebra Summary Page 1 of 4 1/1/01 1. Numbers... 1.1. Number Lines... 1.. Interval Notation.... Inequalities... 4.1. Linear with 1 Variable... 4. Linear Equations... 5.1. The Cartesian

More information

Chetek-Weyerhaeuser High School

Chetek-Weyerhaeuser High School Chetek-Weyerhaeuser High School Unit 1 Variables and Expressions Math RtI Units and s Math RtI A s 1. I can use mathematical properties to evaluate expressions. I can use mathematical properties to evaluate

More information

Variables and Expressions

Variables and Expressions Variables and Expressions A variable is a letter that represents a value that can change. A constant is a value that does not change. A numerical expression contains only constants and operations. An algebraic

More information

Polynomials. Exponents. End Behavior. Writing. Solving Factoring. Graphing. End Behavior. Polynomial Notes. Synthetic Division.

Polynomials. Exponents. End Behavior. Writing. Solving Factoring. Graphing. End Behavior. Polynomial Notes. Synthetic Division. Polynomials Polynomials 1. P 1: Exponents 2. P 2: Factoring Polynomials 3. P 3: End Behavior 4. P 4: Fundamental Theorem of Algebra Writing real root x= 10 or (x+10) local maximum Exponents real root x=10

More information

Math 75 Mini-Mod Due Dates Spring 2016

Math 75 Mini-Mod Due Dates Spring 2016 Mini-Mod 1 Whole Numbers Due: 4/3 1.1 Whole Numbers 1.2 Rounding 1.3 Adding Whole Numbers; Estimation 1.4 Subtracting Whole Numbers 1.5 Basic Problem Solving 1.6 Multiplying Whole Numbers 1.7 Dividing

More information

SCIE 4101 Fall Math Review Packet #2 Notes Patterns and Algebra I Topics

SCIE 4101 Fall Math Review Packet #2 Notes Patterns and Algebra I Topics SCIE 4101 Fall 014 Math Review Packet # Notes Patterns and Algebra I Topics I consider Algebra and algebraic thought to be the heart of mathematics everything else before that is arithmetic. The first

More information

Module 2 Study Guide. The second module covers the following sections of the textbook: , 4.1, 4.2, 4.5, and

Module 2 Study Guide. The second module covers the following sections of the textbook: , 4.1, 4.2, 4.5, and Module 2 Study Guide The second module covers the following sections of the textbook: 3.3-3.7, 4.1, 4.2, 4.5, and 5.1-5.3 Sections 3.3-3.6 This is a continuation of the study of linear functions that we

More information

SCIE 4101 Spring Math Review Packet #2 Notes Algebra I

SCIE 4101 Spring Math Review Packet #2 Notes Algebra I SCIE 4101 Spring 011 Math Review Packet # Notes Algebra I I consider Algebra and algebraic thought to be the heart of mathematics everything else before that is arithmetic. The first characteristic of

More information

Bishop Kelley High School Summer Math Program Course: Algebra 2 A

Bishop Kelley High School Summer Math Program Course: Algebra 2 A 015 016 Bishop Kelley High School Summer Math Program Course: Algebra A NAME: DIRECTIONS: Show all work in packet!!! The first 16 pages of this packet provide eamples as to how to work some of the problems

More information

Westside Algebra 2 PreAP

Westside Algebra 2 PreAP Westside Algebra 2 PreAP Name Period IMPORTANT INSTRUCTIONS FOR STUDENTS!!! We understand that students come to Algebra II with different strengths and needs. For this reason, students have options for

More information

MATH 8. Unit 1: Rational and Irrational Numbers (Term 1) Unit 2: Using Algebraic Properties to Simplify Expressions - Probability

MATH 8. Unit 1: Rational and Irrational Numbers (Term 1) Unit 2: Using Algebraic Properties to Simplify Expressions - Probability MATH 8 Unit 1: Rational and Irrational Numbers (Term 1) 1. I CAN write an algebraic expression for a given phrase. 2. I CAN define a variable and write an equation given a relationship. 3. I CAN use order

More information

Booker T. Washington Summer Math Packet 2015 Completed by Thursday, August 20, 2015 Each student will need to print the packet from our website.

Booker T. Washington Summer Math Packet 2015 Completed by Thursday, August 20, 2015 Each student will need to print the packet from our website. BTW Math Packet Advanced Math Name Booker T. Washington Summer Math Packet 2015 Completed by Thursday, August 20, 2015 Each student will need to print the packet from our website. Go to the BTW website

More information

SUMMER REVIEW PACKET. Name:

SUMMER REVIEW PACKET. Name: Wylie East HIGH SCHOOL SUMMER REVIEW PACKET For students entering Regular PRECALCULUS Name: Welcome to Pre-Calculus. The following packet needs to be finished and ready to be turned the first week of the

More information

Westside. Algebra 2 PreAP

Westside. Algebra 2 PreAP Westside Algebra 2 PreAP Name Period IMPORTANT INSTRUCTIONS FOR STUDENTS!!! We understand that students come to Algebra II with different strengths and needs. For this reason, students have options for

More information

Chapter R - Basic Algebra Operations (94 topics, no due date)

Chapter R - Basic Algebra Operations (94 topics, no due date) Course Name: Math 00024 Course Code: N/A ALEKS Course: College Algebra Instructor: Master Templates Course Dates: Begin: 08/15/2014 End: 08/15/2015 Course Content: 207 topics Textbook: Barnett/Ziegler/Byleen/Sobecki:

More information

Rising 8th Grade Math. Algebra 1 Summer Review Packet

Rising 8th Grade Math. Algebra 1 Summer Review Packet Rising 8th Grade Math Algebra 1 Summer Review Packet 1. Clear parentheses using the distributive property. 2. Combine like terms within each side of the equal sign. Solving Multi-Step Equations 3. Add/subtract

More information

ALGEBRA I CURRICULUM OUTLINE

ALGEBRA I CURRICULUM OUTLINE ALGEBRA I CURRICULUM OUTLINE 2013-2014 OVERVIEW: 1. Operations with Real Numbers 2. Equation Solving 3. Word Problems 4. Inequalities 5. Graphs of Functions 6. Linear Functions 7. Scatterplots and Lines

More information

Gaithersburg High School Summer 2018 Math Packet For Rising Algebra 2/Honors Algebra 2 Students

Gaithersburg High School Summer 2018 Math Packet For Rising Algebra 2/Honors Algebra 2 Students Gaithersburg High School Math Packet For Rising Algebra 2/Honors Algebra 2 Students 1 This packet is an optional review of the skills that will help you be successful in Algebra 2 in the fall. By completing

More information

Algebra 1. Math Review Packet. Equations, Inequalities, Linear Functions, Linear Systems, Exponents, Polynomials, Factoring, Quadratics, Radicals

Algebra 1. Math Review Packet. Equations, Inequalities, Linear Functions, Linear Systems, Exponents, Polynomials, Factoring, Quadratics, Radicals Algebra 1 Math Review Packet Equations, Inequalities, Linear Functions, Linear Systems, Exponents, Polynomials, Factoring, Quadratics, Radicals 2017 Math in the Middle 1. Clear parentheses using the distributive

More information

Algebra 1 Khan Academy Video Correlations By SpringBoard Activity and Learning Target

Algebra 1 Khan Academy Video Correlations By SpringBoard Activity and Learning Target Algebra 1 Khan Academy Video Correlations By SpringBoard Activity and Learning Target SB Activity Activity 1 Investigating Patterns 1-1 Learning Targets: Identify patterns in data. Use tables, graphs,

More information

Solving Multi-Step Equations

Solving Multi-Step Equations 1. Clear parentheses using the distributive property. 2. Combine like terms within each side of the equal sign. Solving Multi-Step Equations 3. Add/subtract terms to both sides of the equation to get the

More information

Summer Packet for Students Taking Introduction to Calculus in the Fall

Summer Packet for Students Taking Introduction to Calculus in the Fall Summer Packet for Students Taking Introduction to Calculus in the Fall Algebra 2 Topics Needed for Introduction to Calculus Need to know: à Solve Equations Linear Quadratic Absolute Value Polynomial Rational

More information

MATH 7 HONORS. Unit 1: Rational and Irrational Numbers (Term 1) Unit 2: Using Algebraic Properties to Simplify Expressions - Probability

MATH 7 HONORS. Unit 1: Rational and Irrational Numbers (Term 1) Unit 2: Using Algebraic Properties to Simplify Expressions - Probability MATH 7 HONORS Unit 1: Rational and Irrational Numbers (Term 1) 1. I CAN write an algebraic expression for a given phrase. 2. I CAN define a variable and write an equation given a relationship. 3. I CAN

More information

Course Name: MAT 135 Spring 2017 Master Course Code: N/A. ALEKS Course: Intermediate Algebra Instructor: Master Templates

Course Name: MAT 135 Spring 2017 Master Course Code: N/A. ALEKS Course: Intermediate Algebra Instructor: Master Templates Course Name: MAT 135 Spring 2017 Master Course Code: N/A ALEKS Course: Intermediate Algebra Instructor: Master Templates Course Dates: Begin: 01/15/2017 End: 05/31/2017 Course Content: 279 Topics (207

More information

MATH Spring 2010 Topics per Section

MATH Spring 2010 Topics per Section MATH 101 - Spring 2010 Topics per Section Chapter 1 : These are the topics in ALEKS covered by each Section of the book. Section 1.1 : Section 1.2 : Ordering integers Plotting integers on a number line

More information

ACCUPLACER MATH 0311 OR MATH 0120

ACCUPLACER MATH 0311 OR MATH 0120 The University of Teas at El Paso Tutoring and Learning Center ACCUPLACER MATH 0 OR MATH 00 http://www.academics.utep.edu/tlc MATH 0 OR MATH 00 Page Factoring Factoring Eercises 8 Factoring Answer to Eercises

More information

Secondary Math 2H Unit 3 Notes: Factoring and Solving Quadratics

Secondary Math 2H Unit 3 Notes: Factoring and Solving Quadratics Secondary Math H Unit 3 Notes: Factoring and Solving Quadratics 3.1 Factoring out the Greatest Common Factor (GCF) Factoring: The reverse of multiplying. It means figuring out what you would multiply together

More information

Chapter R - Review of Basic Algebraic Concepts (26 topics, no due date)

Chapter R - Review of Basic Algebraic Concepts (26 topics, no due date) Course Name: Math 00023 Course Code: N/A ALEKS Course: Intermediate Algebra Instructor: Master Templates Course Dates: Begin: 08/15/2014 End: 08/15/2015 Course Content: 245 topics Textbook: Miller/O'Neill/Hyde:

More information

evaluate functions, expressed in function notation, given one or more elements in their domains

evaluate functions, expressed in function notation, given one or more elements in their domains Describing Linear Functions A.3 Linear functions, equations, and inequalities. The student writes and represents linear functions in multiple ways, with and without technology. The student demonstrates

More information

( )( ) Algebra I / Technical Algebra. (This can be read: given n elements, choose r, 5! 5 4 3! ! ( 5 3 )! 3!(2) 2

( )( ) Algebra I / Technical Algebra. (This can be read: given n elements, choose r, 5! 5 4 3! ! ( 5 3 )! 3!(2) 2 470 Algebra I / Technical Algebra Absolute Value: A number s distance from zero on a number line. A number s absolute value is nonnegative. 4 = 4 = 4 Algebraic Expressions: A mathematical phrase that can

More information

Intermediate Algebra with Applications

Intermediate Algebra with Applications Lakeshore Technical College 10-804-118 Intermediate Algebra with Applications Course Outcome Summary Course Information Alternate Title Description Total Credits 4 Total Hours 72 Pre/Corequisites Prerequisite

More information

College Algebra Through Problem Solving (2018 Edition)

College Algebra Through Problem Solving (2018 Edition) City University of New York (CUNY) CUNY Academic Works Open Educational Resources Queensborough Community College Winter 1-25-2018 College Algebra Through Problem Solving (2018 Edition) Danielle Cifone

More information

Review for Mastery. Integer Exponents. Zero Exponents Negative Exponents Negative Exponents in the Denominator. Definition.

Review for Mastery. Integer Exponents. Zero Exponents Negative Exponents Negative Exponents in the Denominator. Definition. LESSON 6- Review for Mastery Integer Exponents Remember that means 8. The base is, the exponent is positive. Exponents can also be 0 or negative. Zero Exponents Negative Exponents Negative Exponents in

More information

MATH 0960 ELEMENTARY ALGEBRA FOR COLLEGE STUDENTS (8 TH EDITION) BY ANGEL & RUNDE Course Outline

MATH 0960 ELEMENTARY ALGEBRA FOR COLLEGE STUDENTS (8 TH EDITION) BY ANGEL & RUNDE Course Outline MATH 0960 ELEMENTARY ALGEBRA FOR COLLEGE STUDENTS (8 TH EDITION) BY ANGEL & RUNDE Course Outline 1. Real Numbers (33 topics) 1.3 Fractions (pg. 27: 1-75 odd) A. Simplify fractions. B. Change mixed numbers

More information

HONORS GEOMETRY Summer Skills Set

HONORS GEOMETRY Summer Skills Set HONORS GEOMETRY Summer Skills Set Algebra Concepts Adding and Subtracting Rational Numbers To add or subtract fractions with the same denominator, add or subtract the numerators and write the sum or difference

More information

Geometry Summer Assignment 2018

Geometry Summer Assignment 2018 Geometry Summer Assignment 2018 The following packet contains topics and definitions that you will be required to know in order to succeed in Geometry this year. You are advised to be familiar with each

More information

Day 131 Practice. What Can You Do With Polynomials?

Day 131 Practice. What Can You Do With Polynomials? Polynomials Monomial - a Number, a Variable or a PRODUCT of a number and a variable. Monomials cannot have radicals with variables inside, quotients of variables or variables with negative exponents. Degree

More information

correlated to the Utah 2007 Secondary Math Core Curriculum Algebra 1

correlated to the Utah 2007 Secondary Math Core Curriculum Algebra 1 correlated to the Utah 2007 Secondary Math Core Curriculum Algebra 1 McDougal Littell Algebra 1 2007 correlated to the Utah 2007 Secondary Math Core Curriculum Algebra 1 The main goal of Algebra is to

More information

Finite Mathematics : A Business Approach

Finite Mathematics : A Business Approach Finite Mathematics : A Business Approach Dr. Brian Travers and Prof. James Lampes Second Edition Cover Art by Stephanie Oxenford Additional Editing by John Gambino Contents What You Should Already Know

More information

Sections 7.2, 7.3, 4.1

Sections 7.2, 7.3, 4.1 Sections 7., 7.3, 4.1 Section 7. Multiplying, Dividing and Simplifying Radicals This section will discuss the rules for multiplying, dividing and simplifying radicals. Product Rule for multiplying radicals

More information

8th Grade Math Definitions

8th Grade Math Definitions 8th Grade Math Definitions Absolute Value: 1. A number s distance from zero. 2. For any x, is defined as follows: x = x, if x < 0; x, if x 0. Acute Angle: An angle whose measure is greater than 0 and less

More information

= 9 = x + 8 = = -5x 19. For today: 2.5 (Review) and. 4.4a (also review) Objectives:

= 9 = x + 8 = = -5x 19. For today: 2.5 (Review) and. 4.4a (also review) Objectives: Math 65 / Notes & Practice #1 / 20 points / Due. / Name: Home Work Practice: Simplify the following expressions by reducing the fractions: 16 = 4 = 8xy =? = 9 40 32 38x 64 16 Solve the following equations

More information

CURRICULUM UNIT MAP 1 ST QUARTER. COURSE TITLE: Applied Algebra 1 GRADE: 9

CURRICULUM UNIT MAP 1 ST QUARTER. COURSE TITLE: Applied Algebra 1 GRADE: 9 1 ST QUARTER Unit 1: Exploring Rational Numbers WEEK 1-3 Objectives: Write equations and formulas to solve application problems Compare order and plot rational and irrational numbers, including square

More information

ALGEBRA 2. Background Knowledge/Prior Skills Knows what operation properties hold for operations with matrices

ALGEBRA 2. Background Knowledge/Prior Skills Knows what operation properties hold for operations with matrices ALGEBRA 2 Numbers and Operations Standard: 1 Understands and applies concepts of numbers and operations Power 1: Understands numbers, ways of representing numbers, relationships among numbers, and number

More information

An equation is a statement that states that two expressions are equal. For example:

An equation is a statement that states that two expressions are equal. For example: Section 0.1: Linear Equations Solving linear equation in one variable: An equation is a statement that states that two expressions are equal. For example: (1) 513 (2) 16 (3) 4252 (4) 64153 To solve the

More information

Index I-1. in one variable, solution set of, 474 solving by factoring, 473 cubic function definition, 394 graphs of, 394 x-intercepts on, 474

Index I-1. in one variable, solution set of, 474 solving by factoring, 473 cubic function definition, 394 graphs of, 394 x-intercepts on, 474 Index A Absolute value explanation of, 40, 81 82 of slope of lines, 453 addition applications involving, 43 associative law for, 506 508, 570 commutative law for, 238, 505 509, 570 English phrases for,

More information

Lake Elsinore Unified School District Pacing Guide & Benchmark Assessment Schedule Algebra 1 Essentials

Lake Elsinore Unified School District Pacing Guide & Benchmark Assessment Schedule Algebra 1 Essentials 1.0 Students identify and use the arithmetic properties of subsets of integers, including closure properties for the four basic arithmetic operations where applicable: 1.1 Students use properties of numbers

More information

SUMMER MATH PACKET ALGEBRA TWO COURSE 229

SUMMER MATH PACKET ALGEBRA TWO COURSE 229 SUMMER MATH PACKET ALGEBRA TWO COURSE 9 MATH SUMMER PACKET INSTRUCTIONS MATH SUMMER PACKET INSTRUCTIONS Attached you will find a packet of exciting math problems for your enjoyment over the summer. The

More information

Prerequisite: Qualification by assessment process or completion of Mathematics 1050 or one year of high school algebra with a grade of "C" or higher.

Prerequisite: Qualification by assessment process or completion of Mathematics 1050 or one year of high school algebra with a grade of C or higher. Reviewed by: D. Jones Reviewed by: B. Jean Reviewed by: M. Martinez Text update: Spring 2017 Date reviewed: February 2014 C&GE Approved: March 10, 2014 Board Approved: April 9, 2014 Mathematics (MATH)

More information

Pacing Guide Algebra 1

Pacing Guide Algebra 1 Pacing Guide Algebra Chapter : Equations and Inequalities (one variable) Section Section Title Learning Target(s) I can. Evaluate and Simplify Algebraic Expressions. Evaluate and simplify numeric and algebraic

More information

8th Grade Curriculum. Unit 1 - Equations. Quality Questions. Learning Targets. Skills

8th Grade Curriculum. Unit 1 - Equations. Quality Questions. Learning Targets. Skills Unit 1 - Equations How can you use reasoning to explain order of operations? Why does it make sense to use inverse operations to isolate variables in multistep equations? How can we utilze equations to

More information

Radicals: To simplify means that 1) no radicand has a perfect square factor and 2) there is no radical in the denominator (rationalize).

Radicals: To simplify means that 1) no radicand has a perfect square factor and 2) there is no radical in the denominator (rationalize). Summer Review Packet for Students Entering Prealculus Radicals: To simplify means that 1) no radicand has a perfect square factor and ) there is no radical in the denominator (rationalize). Recall the

More information

Chapter 1A -- Real Numbers. iff. Math Symbols: Sets of Numbers

Chapter 1A -- Real Numbers. iff. Math Symbols: Sets of Numbers Fry Texas A&M University! Fall 2016! Math 150 Notes! Section 1A! Page 1 Chapter 1A -- Real Numbers Math Symbols: iff or Example: Let A = {2, 4, 6, 8, 10, 12, 14, 16,...} and let B = {3, 6, 9, 12, 15, 18,

More information

Algebra 1 S1 Lesson Summaries. Lesson Goal: Mastery 70% or higher

Algebra 1 S1 Lesson Summaries. Lesson Goal: Mastery 70% or higher Algebra 1 S1 Lesson Summaries For every lesson, you need to: Read through the LESSON REVIEW which is located below or on the last page of the lesson and 3-hole punch into your MATH BINDER. Read and work

More information

Accessible Topic - Topics accessible to visually impaired students using a screen reader.

Accessible Topic - Topics accessible to visually impaired students using a screen reader. Course Name: Winter 2018 Math 95 - Course Code: ALEKS Course: Developmental Math Instructor: Course Dates: Begin: 01/07/2018 End: 03/23/2018 Course Content: 390 Topics (172 goal + 218 prerequisite) / 334

More information

Math 0320 Final Exam Review

Math 0320 Final Exam Review Math 0320 Final Exam Review SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Factor out the GCF using the Distributive Property. 1) 6x 3 + 9x 1) Objective:

More information

Algebra I. AIR Study Guide

Algebra I. AIR Study Guide Algebra I AIR Study Guide Table of Contents Topic Slide Topic Slide Formulas not on formula sheet 3 Polynomials 20 What is Algebra 4 Systems of Equations 21 Math Operator Vocabulary 5 FOIL (double distribution)

More information

STUDY GUIDE Math 20. To accompany Intermediate Algebra for College Students By Robert Blitzer, Third Edition

STUDY GUIDE Math 20. To accompany Intermediate Algebra for College Students By Robert Blitzer, Third Edition STUDY GUIDE Math 0 To the students: To accompany Intermediate Algebra for College Students By Robert Blitzer, Third Edition When you study Algebra, the material is presented to you in a logical sequence.

More information

Pre-Calculus Summer Packet

Pre-Calculus Summer Packet 2013-2014 Pre-Calculus Summer Packet 1. Complete the attached summer packet, which is due on Friday, September 6, 2013. 2. The material will be reviewed in class on Friday, September 6 and Monday, September

More information

COURSE OUTLINE MATH 050 INTERMEDIATE ALGEBRA 147 HOURS 6 CREDITS

COURSE OUTLINE MATH 050 INTERMEDIATE ALGEBRA 147 HOURS 6 CREDITS COURSE OUTLINE INTERMEDIATE ALGEBRA 147 HOURS 6 CREDITS PREPARED BY: Annie-Claude Letendre, Instructor DATE: June 28, 2018 APPROVED BY: DATE: APPROVED BY ACADEMIC COUNCIL: RENEWED BY ACADEMIC COUNCIL:

More information

Which one of the following is the solution to the equation? 1) 4(x - 2) + 6 = 2x ) A) x = 5 B) x = -6 C) x = -5 D) x = 6

Which one of the following is the solution to the equation? 1) 4(x - 2) + 6 = 2x ) A) x = 5 B) x = -6 C) x = -5 D) x = 6 Review for Final Exam Math 124A (Flatley) Name Which one of the following is the solution to the equation? 1) 4(x - 2) + 6 = 2x - 14 1) A) x = 5 B) x = -6 C) x = -5 D) x = 6 Solve the linear equation.

More information

PETERS TOWNSHIP HIGH SCHOOL

PETERS TOWNSHIP HIGH SCHOOL PETERS TOWNSHIP HIGH SCHOOL COURSE SYLLABUS: ALG EBRA 2 HONORS Course Overview and Essential Skills This course is an in-depth study of the language, concepts, and techniques of Algebra that will prepare

More information

Algebra I Vocabulary Cards

Algebra I Vocabulary Cards Algebra I Vocabulary Cards Table of Contents Expressions and Operations Natural Numbers Whole Numbers Integers Rational Numbers Irrational Numbers Real Numbers Order of Operations Expression Variable Coefficient

More information

A field trips costs $800 for the charter bus plus $10 per student for x students. The cost per student is represented by: 10x x

A field trips costs $800 for the charter bus plus $10 per student for x students. The cost per student is represented by: 10x x LEARNING STRATEGIES: Activate Prior Knowledge, Shared Reading, Think/Pair/Share, Note Taking, Group Presentation, Interactive Word Wall A field trips costs $800 for the charter bus plus $10 per student

More information

A Correlation of. Pearson. Mathematical Ideas. to the. TSI Topics

A Correlation of. Pearson. Mathematical Ideas. to the. TSI Topics A Correlation of Pearson 2016 to the A Correlation of 2016 Table of Contents Module M1. Linear Equations, Inequalities, and Systems... 1 Module M2. Algebraic Expressions and Equations (Other Than Linear)...

More information

Keystone Exams: Algebra

Keystone Exams: Algebra KeystoneExams:Algebra TheKeystoneGlossaryincludestermsanddefinitionsassociatedwiththeKeystoneAssessmentAnchorsand Eligible Content. The terms and definitions included in the glossary are intended to assist

More information

Algebra I Vocabulary Cards

Algebra I Vocabulary Cards Algebra I Vocabulary Cards Table of Contents Expressions and Operations Natural Numbers Whole Numbers Integers Rational Numbers Irrational Numbers Real Numbers Absolute Value Order of Operations Expression

More information

Algebra Final Exam Review Packet

Algebra Final Exam Review Packet Algebra 1 00 Final Eam Review Packet UNIT 1 EXPONENTS / RADICALS Eponents Degree of a monomial: Add the degrees of all the in the monomial together. o Eample - Find the degree of 5 7 yz Degree of a polynomial:

More information

Module 1: Whole Numbers Module 2: Fractions Module 3: Decimals and Percent Module 4: Real Numbers and Introduction to Algebra

Module 1: Whole Numbers Module 2: Fractions Module 3: Decimals and Percent Module 4: Real Numbers and Introduction to Algebra Course Title: College Preparatory Mathematics I Prerequisite: Placement with a score below 20 on ACT, below 450 on SAT, or assessing into Basic Applied Mathematics or Basic Algebra using Accuplacer, ASSET

More information

Algebra I. Course Outline

Algebra I. Course Outline Algebra I Course Outline I. The Language of Algebra A. Variables and Expressions B. Order of Operations C. Open Sentences D. Identity and Equality Properties E. The Distributive Property F. Commutative

More information

PETERS TOWNSHIP HIGH SCHOOL

PETERS TOWNSHIP HIGH SCHOOL PETERS TOWNSHIP HIGH SCHOOL COURSE SYLLABUS: ALGEBRA 1 ACADEMIC Course Overview and Essential Skills This course is a study of the language, concepts, and techniques of Algebra that will prepare students

More information

MathB65 Ch 4 IV, V, VI.notebook. October 31, 2017

MathB65 Ch 4 IV, V, VI.notebook. October 31, 2017 Part 4: Polynomials I. Exponents & Their Properties II. Negative Exponents III. Scientific Notation IV. Polynomials V. Addition & Subtraction of Polynomials VI. Multiplication of Polynomials VII. Greatest

More information

West Windsor-Plainsboro Regional School District Math A&E Grade 7

West Windsor-Plainsboro Regional School District Math A&E Grade 7 West Windsor-Plainsboro Regional School District Math A&E Grade 7 Page 1 of 24 Unit 1: Introduction to Algebra Content Area: Mathematics Course & Grade Level: A&E Mathematics, Grade 7 Summary and Rationale

More information

College Algebra with Corequisite Support: A Compressed Approach

College Algebra with Corequisite Support: A Compressed Approach College Algebra with Corequisite Support: A Compressed Approach 978-1-63545-059-0 To learn more about all our offerings Visit Knewton.com Source Author(s) (Text or Video) Title(s) Link (where applicable)

More information

UNIT 4: RATIONAL AND RADICAL EXPRESSIONS. 4.1 Product Rule. Objective. Vocabulary. o Scientific Notation. o Base

UNIT 4: RATIONAL AND RADICAL EXPRESSIONS. 4.1 Product Rule. Objective. Vocabulary. o Scientific Notation. o Base UNIT 4: RATIONAL AND RADICAL EXPRESSIONS M1 5.8, M2 10.1-4, M3 5.4-5, 6.5,8 4.1 Product Rule Objective I will be able to multiply powers when they have the same base, including simplifying algebraic expressions

More information

Algebra One Dictionary

Algebra One Dictionary Algebra One Dictionary Page 1 of 17 A Absolute Value - the distance between the number and 0 on a number line Algebraic Expression - An expression that contains numbers, operations and at least one variable.

More information

Reference Material /Formulas for Pre-Calculus CP/ H Summer Packet

Reference Material /Formulas for Pre-Calculus CP/ H Summer Packet Reference Material /Formulas for Pre-Calculus CP/ H Summer Packet Week # 1 Order of Operations Step 1 Evaluate expressions inside grouping symbols. Order of Step 2 Evaluate all powers. Operations Step

More information