# Lecture Guide. Math 90 - Intermediate Algebra. Stephen Toner. Intermediate Algebra, 2nd edition. Miller, O'Neill, & Hyde. Victor Valley College

Size: px
Start display at page:

Download "Lecture Guide. Math 90 - Intermediate Algebra. Stephen Toner. Intermediate Algebra, 2nd edition. Miller, O'Neill, & Hyde. Victor Valley College"

Transcription

1 Lecture Guide Math 90 - Intermediate Algebra to accompan Intermediate Algebra, 2nd edition Miller, O'Neill, & Hde Prepared b Stephen Toner Victor Valle College Last updated: 11/24/10 0

2 1.1 Sets of Numbers The set of rational numbers can be written as A. Tpes of Numbers Natural - Whole - Integers - Rational - an number which can be epressed as the of two numbers, provided the denominator is not zero. Aleks Problem: Classif each number below as an integer or not. Integer? Yes No Aleks Problem: Classif each number below as irrational or rational Rational Irrational Irrational - Real - B. Set Builder Notation can be written as Aleks Problem: Rewrite the Set R b listing the elements. Make sure to use the appropriate set notation. 1

3 C. Interval Notation D. Unions and Intersections Inequalit Graph Interval Notation Given:, Find each of the following: Find each union or intersection. Write our solution using interval notation

4 5. E. Words and Inequalities more than less than at least at most 6. no more than no less than 7. Aleks Problem: The sets C and D are defined as follows: Write and using interval notation. 8. Aleks Problem: Write " is less than or equal to b, and 3 is greater than b" as an algebraic epression. 3

5 1.2 Operations with Real Numbers 1.2 #84 Order of Operations We assume ou remember the rules for adding, subtracting, multipling and dividing real numbers... Evaluate: (57 of them) 1.2 #92 Order of Operations Propert: Be careful! *Evaluate each if and : a. b. 4

6 1.3 Simplifing Epressions A. Properties Aleks: A trick problem... Which propert is illustrated? Commutative Propert of addition... of multiplication Simplif: Associative Propert of addition... of multiplication 1.3 #68 Simplif: Additive Identit Multiplicative Identit 1.3 #74 Additive Inverse Multiplicative Inverse Distributive Properties 5

7 1.4 Linear Equations 1.4 #56 Solve: Solve: 1.4 #42 Solve: There are three classes of equtions: Conditional the tpe we've been doing Identit "all real numbers" is our solution Contradiction there is no solution 1.4 #72 Solve: When an equation contains fractions, it is usuall a good idea to multipl through b the least common denominator to clear the fractions. 1.4 #46 Solve: 1.4 #80 Solve: 6

8 1.5 Word Problems A. Number Problems 1.5 #16 Twice the sum of a number and three is the same as 1 subtracted from the number. Find the number. 1.5 #26 Five times the smallest of three consecutive even integers is 10 more than twice the largest. Find the integers. C. Percentage Word Problems B. Consecutive Integer Problems consecutive integers 1.5 #26 The price of a used tetbook after a 35% markdown is \$ What was the original price? consecutive odd integers consecutive even integers 1.5 #24 Four times the smaller of two consecutive odd integers is the same as 73 less than 5 times the larger. Find the integers. 1.5 #32 Robert can take out a 3-r loan at 8% simple interest or a 2-r loan at 8.5% simple interest. If he borrows \$7000, how much interest will he pa for each loan? Which option will require less interest? 7

9 D. Miture Problems 1.5 #58 A nut miute consists of almonds and cashews. Almonds are \$4.98/lb. and cashews are \$6.98/lb. How man pounds of each tpe of nut must be mied to produce 16 pounds of a miture selling for \$5.73/lb.? 1.5 #52 One fruit punch has 40% fruit juice and another is 70% fruit juice. How much of the 40% punch should be mied with 10 gallons of 70% punch to create a fruit punch that is 45% fruit juice? 1.5 #56 How man ounces of water must be added to 20 oz. of an 8% salt solution to make a 2% salt solution? 8

10 Aleks problem: Two factor plants are making TV panels. Plant A produced 3000 fewer panels than Plant B did. Five percent of the panels from Plant A and 2% of the panels from Plant B are defective. How man panels did Plant A produce, if the two plants together produced 1110 defective panels? E. Investment Problems 1.5 #44 Amanda borrowed \$6000 from two sources: her parents and a credit union. Her parents charged her 3% simple interest and the credit union charged 8%. If after 1 ear she paid \$255 in interest, how much did she borrow from each source? F. Distance Problems Aleks problem: A car travels 221 miles in 3 hours and 15 minutes. How man miles did it travel per hour? 9

11 Distance Problems- General Procedure: 1.5 #62 Two cars are 190 miles apart and travel toward each other. The meet in 2 hours. One car travels 5 miles per hour slower than the other car. What are the speeds of both cars? 1.5 #60 A woman can hike 1 mph faster down a trail than she can on the return trip uphill. It takes 3 hours to get to her destination and 6 hours to return. What is her downhill speed? 1.5 #64 Two canoes travel down a river starting at 9:00. One canoe travels twice as fast as the other. After 3.5 hours the canoes are 5.25 miles apart. Find the average rate of each canoe. 10

12 1.6 Literal Equations & Geometr Problems A. Literal Equations 1.6 #36 Solve for. B. Geometr Problems 1.6 #8 The length of a rectangle is 4 inches less than twice the width. The perimeter is 112 inches. Find its dimensions. 1.6 #42 Solve for. 1.6 #48 Solve for h. 1.6 #10 A triangular garden has sides that can be represented b 3 consecutive integers. If the perimeter is 15 ft, what are the lengths of the sides? Solve for w. 11

13 1.6 #10 The smallest angle in a triangle is the size of the largest angle. The middle angle measures less than the largest. Find all three angle measures. 1.7 Solving Inequalities *Be careful to change the direction of the inequalit whenever ou or each side of the inequalit b a. *For each of the following, graph our solutions sets. Also write our solutions using interval notation. 1.7 # #20 Find : (+15) 1.7 #36 12

14 Ke Phraes: at most at least no more than no less than Aleks Problem: Brian is choosing between two eercise routines: In routine #1, he burns 46 calories walking. He then runs at a rate that burns 11 calories per minute. Aleks Problem: For her phone service, Kira pas a monthl fee of \$20, and she pas an additional \$0.04 per minute of use. The least she has been charged in a month is \$ What are the possible numbers of minutes she has used her phone in a month? Use for the number of minutes, and solve our inequalit for. In routine #2, he burns 22 calories walking. He then runs at a rate that burns 15 calories per minute. For what amounts of time spent running will Routine #1 burn fewer calories than Routine #2? Use for the number of minutes spent running, and solve our inequalit for. 13

15 1.8 Eponents & Scientific Notation A. Properites of Eponents 1. *Simplif each of the following: a. b. 2. c. d. 3. e. f. 4. g. 5. h. i. j. Negative eponents are NOT considered to be simplified. Do NOT leave them in final answers! 14

16 k. s. l. m. 6. ALEKS PROPLEM TYPE: Simplif: n. o. p. q. r. Multiple choice: a. b. c. d. 15

17 B. Scientific Notation Scientific notationis a shorthand notation for writing etremel small or large numbers. *Multipl. Write our answers in scientific notation: 6. Notation: 7. *Write each using scientific notation: 1. 9,374, trillion *Divide. Write our answers in scientific notation: *Write each in standard form:

18 Additional Aleks Problems (Chapter 1) 1. The properties of addition are: [1] Commutative Propert [2] Associative Propert [3] Additive Identit Propert [4] Additive Inverse Propert 3. Dale rented a truck for one da. There was a base fee of \$20.99, and there was an additional charge of 95 cents for each mile driven. Dale had to pa \$ when he returned the truck. For how man miles did he drive the truck? For each equation below, indicate the propert that justifies the equation b filling in the bo with the appropriate number. 2. Consider the following properties of real numbers: [1] Commutative Propert of Addition [2] Associative Propert of Addition [3] Additive Identit Propert [4] Additive Inverse Propert [5] Distributive Propert [6] Commutative Propert of Multiplication [7] Associative Propert of Multiplication [8] Multiplicative Identit Propert [9] Multiplicative Inverse Propert [10] Multiplication Propert of Zero 4. Raina invested her savings in two investment funds. The amount she invested in Fund A was 3 times as much as the amount she invested in Fund B. Fund A returned a 4% profit and Fund B returned a 6% profit. How much did she invest in Fund A, if the total profit from the two funds together was \$1080? For each equation below, indicate the propert that justifies the equation b filling in the bo with the appropriate number. 5. The price of an item has been reduced b 80%. The original price was \$90. What is the price of the item now? 17

19 2.1 Graphing Lines Graph: Methods for Graphing Lines: 1. The X-Y Chart Graph: Graph: 2. Horizontal and Vertical Lines 4. Graphing b Intercepts Graph: 3. The Slope-Intercept Method A. Identif and plot the -intercept. B. Identif the slope. Rise and run (to the right) from the -intercept to another point on the line. C. Draw the line. 18

20 2.2 Slope Formula: *In each equation, identif the slope and the -intercept. 3. *Find the slope of each line: *Find the slope of the line which runs through the given pair of points: *Find the slope of the graphed line (passes through and :

21 2.3 Point-Slope Form **Parallel lines have the slope. **The slopes of perpendicular lines are of each other. *Find the equation of the line (in slopeintercept form) which has has the following characteristics. a. and has -intercept *Are the following pairs of lines parallel, perpendicular, or neither? 1. b. and the line passes through Three Forms of a Line c. passes through and

22 d. passes through and is parallel to the line Aleks Problem: Consider the line. Find the equation of the line that is parallel to this line and passes through the point. Find the equation of the line that is perpendicular to this line and passes through the point. e. passes through and is perpendicular to the line Aleks Problem: Write equations for the horizontal and vertical lines passing through the point. horizontal line: vertical line: 21

23 2.4 Word Problems 2.4 #8 Ale is a sales representative and earns a base salar of \$1000 per month plus a 4% commission on his sales for the month. a. Write a linear equation that epresses Ale s monthl salar in terms of his sales. 2.4 #14 Let represent the average number of miles driven per ear for passenger cars in the United States since Let =0 represent the ear where corresponds to 1980, =1 corresponds to 1981, and so on. The average earl mileage for passenger cars can be approimated b the equation = where. b. Graph the equation. a. Use the linear equation to approimate the average earl mileage for passenger cars in the United States in the ear c. What is the -intercept and what does it represent in the contet of this problem? d. What is the slope of the line and what does it represent in the contet of this problem? b. Use the linear equation to approimate the average mileage for the ear 1985, and compare it with the actual value of 9700 mi. e. How much will Ale make if his sales for a given month are \$30,000? c. What is the slope of the line and what does it mean in the contet of this problem? d. What is the -intercept and what does it mean in the contet of this problem? 22

24 Aleks Problem: Owners of a recreation area are filling a small pond with water. The are adding water at a rate of 35 liters per minute. There are 700 liters in the pond to start. Aleks Problem: The monthl cost (in dollars) of a long-distance phone plan is a linear function of the total calling time (in minutes), as shown in the figure below. Let W represent the amount of water in the pond (in liters), and let T represent the number of minutes that water has been added. Write an equation relating W to T, and then graph our equation using the aes below. The monthl cost for 51 minutes of calls is \$17.52 and the monthl cost for 79 minutes is \$ What is the monthl cost for 69 minutes of calls? 23

25 Aleks Problem: Suppose that the credit remaining on a phone card (in dollars) is a linear function of the total calling time (in minutes). When graphed, the function gives a line with a slope of. See the figure below. There is \$25.04 in credit remaining on the card after 42 minutes of calls. How much credit was there after 29 minutes of calls? 2.5 Domain and Range The domain of an epression is the set of values which substituted into the epression. The range of an epression is the set of values which can the epression. Eample: domain: range: To find the domain, start with a "default" domain of and then take awa -values which... ** ** ** *Find the domain of each: 24

26 To determine the domain from a graph, look at where the graph etends, left to right. To determine the range from a graph, look at where the graph etends verticall. *Find the domain and range of each graph: *Find the domain and range of each: 25

27 2.6 Functions A function is a rule which assigns a -value in the range to each value in its domain. *Do the following relations represent functions? When we write, we mean Given,, find the following: 1. A graph is that of a function if it passes the 2. *Are the following graphs those of functions? Notation: is pronounced Antime ou see., ou can replace it with 8. 26

28 *Find the requested values from the graph: 2.6 #57 The graph of is given. *Find the domain of each function. Write the answers in interval notation. 2.6 #64 a. Find. b. Find 2.6 #65 c. Find d. For what value(s) of is e. For what value(s) of is 2.6 #68 f. Write the domain of. g. Write the range of. 2.6 # #58 The graph of is given. a. Find. 2.6 #73 b. Find 2.6 #76 c. Find d. For what value(s) of is e. For what value(s) of is A. h ( ) 1 5 f. Write the domain of. g. Write the range of. 27

29 2.7 Graphs of Basic Functions Graph each of the following. Then state the domain and range of each. 4. Absolute Value Function 1. Linear Function 5. Square Root Function 2. Quadratic Function 6. Reciprocal Function 3. Cubic Function 28

30 Graph the parabola points on its graph.. Indicate five Review: Solve the following equation for : Graph the cubic function three points on its graph.. Indicate Simplif: Aleks Problem: For each function below, choose the correct description of its graph: 29

### Intermediate Algebra Review for Exam 1 - Spring 2005

Intermediate Algebra Review for Eam - Spring 00 Use mathematical smbols to translate the phrase. ) a) 9 more than half of some number b) 0 less than a number c) 37 percent of some number Evaluate the epression.

### Lecture Guide. Math 42 - Elementary Algebra. Stephen Toner. Introductory Algebra, 3rd edition. Miller, O'Neill, Hyde. Victor Valley College

Lecture Guide Math 42 - Elementar Algebra to accompan Introductor Algebra, 3rd edition Miller, O'Neill, Hde Prepared b Stephen Toner Victor Valle College Accompaning videos can be found at www.mathvideos.net.

### Lecture Guide. Math 50 - Elementary Algebra. Stephen Toner. Introductory Algebra, 2nd edition. Miller, O'Neil, Hyde. Victor Valley College

Lecture Guide Math 50 - Elementar Algebra to accompan Introductor Algebra, 2nd edition Miller, O'Neil, Hde Prepared b Stephen Toner Victor Valle College Last updated: 12/27/10 1 1.1 - Sets of Numbers and

### Identify the domain and the range of the relation from the graph. 8)

INTERMEDIATE ALGEBRA REVIEW FOR TEST Use the given conditions to write an equation for the line. 1) a) Passing through (, -) and parallel to = - +. b) Passing through (, 7) and parallel to - 3 = 10 c)

### Lecture Guide. Math College Algebra. Stephen Toner. College Algebra, 2nd edition. John Coburn. Victor Valley College. to accompany.

Lecture Guide Math 105 - College Algebra to accompan College Algebra, 2nd edition John Coburn Prepared b Stephen Toner Victor Valle College Last updated: 10/7/10 1 ALEKS Review Topics Simplif: 1.1 Linear

### Math 154A Elementary Algebra Fall 2014 Final Exam Study Guide

Math A Elementar Algebra Fall 0 Final Eam Stud Guide The eam is on Tuesda, December 6 th from 6:00pm 8:0pm. You are allowed a scientific calculator and a " b 6" inde card for notes. On our inde card be

### Review for Intermediate Algebra (MATD 0390) Final Exam Oct 2009

Review for Intermediate Algebra (MATD 090) Final Eam Oct 009 Students are epected to know all relevant formulas, including: All special factoring formulas Equation of a circle All formulas for linear equations

### Intermediate Algebra / MAT 135 Spring 2017 Master ( Master Templates)

Test 1 Review #1 Intermediate Algebra / MAT 135 Spring 017 Master ( Master Templates) Student Name/ID: 1. Solve for. = 8 18. Solve for. = + a b 3. Solve for. a b = L 30. Two trains leave stations miles

### Math Intermediate Algebra

Math 095 - Intermediate Algebra Final Eam Review Objective 1: Determine whether a relation is a function. Given a graphical, tabular, or algebraic representation for a function, evaluate the function and

### Test 1 Review #5. Intermediate Algebra / MAT 135 Fall 2016 Master (Prof. Fleischner)

Test 1 Review #5 Intermediate Algebra / MAT 135 Fall 016 Master (Prof. Fleischner) Student Name/ID: 1. Solve for n. d = m + 9n. Solve for b. r = 5 b + a 3. Solve for C. A = 7 8 B + C ALEKS Test 1 Review

### REVIEW PACKET FOR END OF COURSE EXAM

Math H REVIEW PACKET FOR END OF COURSE EXAM DO NOT WRITE ON PACKET! Do on binder paper, show support work. On this packet leave all fractional answers in improper fractional form (ecept where appropriate

### Diaz Math 080 Midterm Review: Modules A-F Page 1 of 7

Diaz Math 080 Midterm Review: Modules A-F Page 1 of 7 1. Use the rule for order of operations to simplif the epression: 11 9 7. Perform the indicated operations and simplif: 7( + ) 6(5 9) 3. If a = 3,

### Review of Elementary Algebra Content

Review of Elementar Algebra Content 0 1 Table of Contents Fractions...1 Integers...5 Order of Operations...9 Eponents...11 Polnomials...18 Factoring... Solving Linear Equations...1 Solving Linear Inequalities...

### Advanced Algebra Scope and Sequence First Semester. Second Semester

Last update: April 03 Advanced Algebra Scope and Sequence 03-4 First Semester Unit Name Unit : Review of Basic Concepts and Polynomials Unit : Rational and Radical Epressions Sections in Book 0308 SLOs

### Diaz Math 080 Midterm Review: Modules A-F Page 1 of 7

Diaz Math 080 Midterm Review: Modules A-F Page 1 of 7 1. Use the rule for order of operations to simplif the epression: 11 9 7. Perform the indicated operations and simplif: 7(4 + 4) 6(5 9) 3. If a = 3,

### Chapter 4 Page 1 of 16. Lecture Guide. Math College Algebra Chapter 4. to accompany. College Algebra by Julie Miller

Chapter 4 Page 1 of 16 Lecture Guide Math 105 - College Algebra Chapter 4 to accompan College Algebra b Julie Miller Corresponding Lecture Videos can be found at Prepared b Stephen Toner & Nichole DuBal

### Math 0210 Common Final Review Questions (2 5 i)(2 5 i )

Math 0 Common Final Review Questions In problems 1 6, perform the indicated operations and simplif if necessar. 1. ( 8)(4) ( )(9) 4 7 4 6( ). 18 6 8. ( i) ( 1 4 i ) 4. (8 i ). ( 9 i)( 7 i) 6. ( i)( i )

### Topic 1: Writing and Solving Equations and Inequalities

Topic 1: Writing and Solving Equations and Inequalities In #1 3, solve each equation. Use inverse operations. 1. 8 21 5 = 15 2. 3 10 = 2(4 5) 3. 2( + 2) = 2 + 1 4. The rectangle and square have equivalent

### MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. C) C) 31.

Eam Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Write the sentence as a mathematical statement. 1) Negative twent-four is equal to negative

### Intermediate Algebra. Exam 1 Review (Chapters 1, 2, and 3)

Eam Review (Chapters,, and ) Intermediate Algebra Name. Epress the set in roster form. { N and 7}. Epress the set in set builder form. {-, 0,,,, }. Epress in set builder notation each set of numbers that

### MATH 103 Sample Final Exam Review

MATH 0 Sample Final Eam Review This review is a collection of sample questions used b instructors of this course at Missouri State Universit. It contains a sampling of problems representing the material

### Math 115 Spring Break Homework Package Name. . List all

Math Spring Break Homework Package Name Show all work neatl and sstematicall for full credit. Total points: 00 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the

### math0320 FALL interactmath sections developmental mathematics sullivan 1e

Eam final eam review 180 plus 234 TSI questions for intermediate algebra m032000 013014 NEW Name www.alvarezmathhelp.com math0320 FALL 201 1400 interactmath sections developmental mathematics sullivan

### LESSON #12 - FORMS OF A LINE COMMON CORE ALGEBRA II

LESSON # - FORMS OF A LINE COMMON CORE ALGEBRA II Linear functions come in a variet of forms. The two shown below have been introduced in Common Core Algebra I and Common Core Geometr. TWO COMMON FORMS

### Algebra 2 Unit 1 Practice

Algebra Unit Practice LESSON - Use this information for Items. Aaron has \$ to rent a bike in the cit. It costs \$ per hour to rent a bike. The additional fee for a helmet is \$ for the entire ride.. Write

### 118 Intermediate Algebra Fall Intermediate Algebra FNMT Time: 6:30-9:35 pm, Thursday. Room 228

118 Intermediate Algebra Fall 2018 Intermediate Algebra - 40428 - FNMT 118-122 Time: 6:30-9:3 pm, Thursda Room 228 SYLLABUS Catalog description. Real numbers, polnomials, rational epressions, algebraic

### In order to prepare for the final exam, you need to understand and be able to work problems involving the following topics:

MATH 080: Review for the Final Exam In order to prepare for the final exam, you need to understand and be able to work problems involving the following topics: I. Simplifying Expressions: Do you know how

### Algebra 1 Midterm Name

Algebra 1 Midterm 01-013 Name Stud Guide Date: Period: THIS REVIEW WILL BE COLLECTED JANUARY 4 th or Januar 7 th. One problem each page will be graded! You ma not turn this eam review in after the due

### West Campus State Math Competency Test Info and Practice

West Campus State Math Competenc Test Info and Practice Question Page Skill A Simplif using order of operations (No grouping/no eponents) A Simplif using order of operations (With grouping and eponents)

### MATH 110: FINAL EXAM REVIEW

MATH 0: FINAL EXAM REVIEW Can you solve linear equations algebraically and check your answer on a graphing calculator? (.) () y y= y + = 7 + 8 ( ) ( ) ( ) ( ) y+ 7 7 y = 9 (d) ( ) ( ) 6 = + + Can you set

### Practice « «3. ` «- -2« 5. ` « « « \$ «\$ -7« \$ 16.!2 \$

Practice - Properties of Real Numbers Simplif.. - 4.«. - 6«. ` 7 4. «- -«6 `. ` 6. 0. -6«7. 4-8«8. -0.0«` Replace each \$ with the smbol R, S,or to make the sentence true. 9.!6 \$!0 0. \$.. 0.06 \$ 0.6. 4

### Analytic Geometry 300 UNIT 9 ANALYTIC GEOMETRY. An air traffi c controller uses algebra and geometry to help airplanes get from one point to another.

UNIT 9 Analtic Geometr An air traffi c controller uses algebra and geometr to help airplanes get from one point to another. 00 UNIT 9 ANALYTIC GEOMETRY Copright 00, K Inc. All rights reserved. This material

### LESSON #11 - FORMS OF A LINE COMMON CORE ALGEBRA II

LESSON # - FORMS OF A LINE COMMON CORE ALGEBRA II Linear functions come in a variet of forms. The two shown below have been introduced in Common Core Algebra I and Common Core Geometr. TWO COMMON FORMS

### Math Review Part C Advanced Level (Up to end of MAT 053)

Math Review Part C Advanced Level (Up to end of MAT 05) A scientific calculator is allowed. Answers provided in the final section. Math Review Part C Advanced Level Advanced Level Algebra ALGEBRAIC EXPRESSIONS

### THIS IS A CLASS SET - DO NOT WRITE ON THIS PAPER

THIS IS A CLASS SET - DO NOT WRITE ON THIS PAPER ALGEBRA EOC PRACTICE Which situation can be represented b =? A The number of eggs,, in dozen eggs for sale after dozen eggs are sold B The cost,, of buing

### INTERMEDIATE ALGEBRA REVIEW FOR TEST 1

INTERMEDIATE ALGEBRA REVIEW FOR TEST 1 Write the set using the roster method. 1) a) { is a counting number less than 7} b) { is a whole number between 4 and 8} Let A = {0, 2, 4, 6, 8, }, B = {0,, 6, 9},

### Elementary Algebra FALL 2005 Review for Exam 2

Elementar Algebra FALL 200 Review for Eam 2 1) In a surve of 60 students, the students showed these preferences for instructional materials. Answer the questions. Graph the equation. 6) = 4 + 3 7) 3 +

### Algebra 2 Chapter 2 Page 1

Mileage (MPGs) Section. Relations and Functions. To graph a relation, state the domain and range, and determine if the relation is a function.. To find the values of a function for the given element of

### 3 when n = x Summer Math Packet Moving from Algebra 1 Academic to Advanced Geometry. Name:

01 Summer Math Packet Moving from Algebra 1 Academic to Advanced Geometry Name: This packet provides insight to the topics that were either not covered in Algebra 1, but were covered in Algebra 1 Advanced,

### b(n) = 4n, where n represents the number of students in the class. What is the independent

Which situation can be represented b =? A The number of eggs,, in dozen eggs for sale after dozen eggs are sold B The cost,, of buing movie tickets that sell for \$ each C The cost,, after a \$ discount,

### North Carolina Community College System Diagnostic and Placement Test Sample Questions

North Carolina Communit College Sstem Diagnostic and Placement Test Sample Questions 0 The College Board. College Board, ACCUPLACER, WritePlacer and the acorn logo are registered trademarks of the College

### (c) ( 5) 2. (d) 3. (c) 3(5 7) 2 6(3) (d) (9 13) ( 3) Question 4. Multiply using the distributive property and collect like terms if possible.

Name: Chapter 1 Question 1. Evaluate the following epressions. (a) 5 (c) ( 5) (b) 5 (d) ( 1 ) 3 3 Question. Evaluate the following epressions. (a) 0 5() 3 4 (c) 3(5 7) 6(3) (b) 9 + (8 5) (d) (9 13) + 15

### Name Date. and y = 5.

Name Date Chapter Fair Game Review Evaluate the epression when = and =.... 0 +. 8( ) Evaluate the epression when a = 9 and b =.. ab. a ( b + ) 7. b b 7 8. 7b + ( ab ) 9. You go to the movies with five

### SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Math 1 Final Eam Review Name SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Solve. 1) - - 6 = - + 7 1) ) 6 + 7(- - ) = -8 - ) ) - t + t = 6 t + 1 ) Solve

### a. In the statement "Height is a function of weight," which is the independent variable and which is the dependent variable?

1. The weights and heights of si mathematics students are given in the table. Answer parts a through e. Weight (lb.) Height (cm) 157 19 11 155 1 11 175 17 157 15 17 17 a. In the statement "Height is a

### MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Practice Test 1-0312-Chap. 2.4,2.7, 3.1-3.6,4.1,.4,. Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Write an inequalit statement involving the

### Name: Period: QVMS GTA FALL FINAL EXAM REVIEW PRE-AP ALGEBRA 1

Name: Period: QVMS GTA FALL FINAL EXAM REVIEW PRE-AP ALGEBRA ) When simplifing an epression, ou perform operations inside grouping smbols first. a. alwas b. sometimes c. never ) The opposite of a negative

### LESSON #1 - BASIC ALGEBRAIC PROPERTIES COMMON CORE ALGEBRA II

1 LESSON #1 - BASIC ALGEBRAIC PROPERTIES COMMON CORE ALGEBRA II Mathematics has developed a language all to itself in order to clarif concepts and remove ambiguit from the analsis of problems. To achieve

### Algebra I End of Course Review

Algebra I End of Course Review Properties and PEMDAS 1. Name the property shown: a + b + c = b + a + c (Unit 1) 1. Name the property shown: a(b) = b(a). Name the property shown: m + 0 = m. Name the property

### 1. Simplify each expression and write all answers without negative exponents. for variable L.

MATH 0: PRACTICE FINAL Spring, 007 Chapter # :. Simplif each epression and write all answers without negative eponents. ( ab ) Ans. b 9 7a 6 Ans.. Solve each equation. 5( ) = 5 5 Ans. man solutions + 7

### 9 (0, 3) and solve equations to earn full credit.

Math 0 Intermediate Algebra II Final Eam Review Page of Instructions: (6, ) Use our own paper for the review questions. For the final eam, show all work on the eam. (-6, ) This is an algebra class do not

### Intermediate Algebra 100A Final Exam Review Fall 2007

1 Basic Concepts 1. Sets and Other Basic Concepts Words/Concepts to Know: roster form, set builder notation, union, intersection, real numbers, natural numbers, whole numbers, integers, rational numbers,

### Math 030 Review for Final Exam Revised Fall 2010 RH/ DM 1

Math 00 Review for Final Eam Revised Fall 010 RH/ DM 1 1. Solve the equations: (-1) (7) (-) (-1) () 1 1 1 1 f. 1 g. h. 1 11 i. 9. Solve the following equations for the given variable: 1 Solve for. D ab

### A C B D. 2. Which table corresponds to the equation y = 3x 2? A B C D. 3. Which function table represents the equation y = 2x + 1?

1. Jessie will be going on a hiking trip and plans to leave her cat at Pet Palace while she is awa. If Pet Palace charges an initial \$20 registration fee and \$7 per da of care, which table BEST represents

### MATH 021 UNIT 1 HOMEWORK ASSIGNMENTS

MATH 01 UNIT 1 HOMEWORK ASSIGNMENTS General Instructions You will notice that most of the homework assignments for a section have more than one part. Usuall, the part (A) questions ask for eplanations,

### Diagnostic Tests Study Guide

California State Universit, Sacramento Department of Mathematics and Statistics Diagnostic Tests Stud Guide Descriptions Stud Guides Sample Tests & Answers Table of Contents: Introduction Elementar Algebra

### Honors and Regular Algebra II & Trigonometry Summer Packet

Honors and Regular Algebra II & Trigonometry Summer Packet Hello Students, Parents, and Guardians! I hope everyone is enjoying the summer months and the time to rela and recoup. To add to your summer fun,

### Glossary. Also available at BigIdeasMath.com: multi-language glossary vocabulary flash cards. An equation that contains an absolute value expression

Glossar This student friendl glossar is designed to be a reference for ke vocabular, properties, and mathematical terms. Several of the entries include a short eample to aid our understanding of important

### 2. Which of the following expressions represents the product of four less than three times x and two more than x?

Algebra Topics COMPASS Review You will be allowed to use a calculator on the COMPASS test. Acceptable calculators are: basic calculators, scientific calculators, and graphing calculators up through the

### 1.1. Use a Problem Solving Plan. Read a problem and make a plan. Goal p Use a problem solving plan to solve problems. VOCABULARY. Formula.

. Georgia Performance Standard(s) MMPd, MMPa Your Notes Use a Problem Solving Plan Goal p Use a problem solving plan to solve problems. VOCABULARY Formula A PROBLEM SOLVING PLAN Step Read the problem carefull.

### Intermediate Algebra Math 097. Evaluates/Practice Tests. For solutions, refer to the back of the PAN.

Intermediate Algebra Math 097 Evaluates/Practice Tests For solutions, refer to the back of the PAN. Page of 8 Take this practice test to be sure that ou are prepared for the final quiz in Evaluate.. Solve

### Algebra 1 Honors First Semester Review

Permitted resources: Algebra 1 Honors First Semester Review TI-108 (or similar basic four function calculator) Algebra 1 and Geometr EOC Reference Sheet 4. Identif the mapping diagram that represents the

### Chapter 9 Rational Expressions and Equations Lesson 9-1 Multiplying and Dividing Rational Expressions Pages

Chapter 9 Rational Epressions and Equations Lesson 9- Multipling and Dividing Rational Epressions Pages 76 78. Sample answer: 3. Never; solving the equation using cross products leads to 5 0, which is

### Ready To Go On? Skills Intervention 2-1 Solving Linear Equations and Inequalities

A Read To Go n? Skills Intervention -1 Solving Linear Equations and Inequalities Find these vocabular words in Lesson -1 and the Multilingual Glossar. Vocabular equation solution of an equation linear

### Woodland Community College: Math Practice Test

Woodland Communit College: Math Practice Test Elementar Algebra Math Test The following problems are recommended practice problems for the elementar algebra section of the placement test. Some of the problems

### On a video game, Jacob got 1685 points and earned two bonuses worth 193 and 270 points. What is his total score? Answer: 2148 points

Chapter Numerical Expressions and Factors Information Frame 9. Sample answers are given.. Ke Words: the sum of, the total of Real-Life Application : On a video game, Jacob got 68 points and earned two

### State whether the following statements are true or false: 27.

Cumulative MTE -9 Review This packet includes major developmental math concepts that students ma use to prepare for the VPT Math (Virginia Placement Test for Math or for students to use to review essential

### Advanced Algebra 2 Final Review Packet KG Page 1 of Find the slope of the line passing through (3, -1) and (6, 4).

Advanced Algebra Final Review Packet KG 0 Page of 8. Evaluate (7 ) 0 when and. 7 7. Solve the equation.. Solve the equation.. Solve the equation. 6. An awards dinner costs \$ plus \$ for each person making

### CHAPTER 2 Solving Equations and Inequalities

CHAPTER Solving Equations and Inequalities Section. Linear Equations and Problem Solving........... 8 Section. Solving Equations Graphically............... 89 Section. Comple Numbers......................

### Chapter 5: Systems of Equations

Chapter : Sstems of Equations Section.: Sstems in Two Variables... 0 Section. Eercises... 9 Section.: Sstems in Three Variables... Section. Eercises... Section.: Linear Inequalities... Section.: Eercises.

### Equations and Inequalities

Equations and Inequalities Figure 1 CHAPTER OUTLINE 1 The Rectangular Coordinate Systems and Graphs Linear Equations in One Variable Models and Applications Comple Numbers Quadratic Equations 6 Other Types

### Mourning Sr. High. Pre-Calculus 2017 Summer Assignment. 2. Write the final answer on the line provided.

Mourning Sr. High Directions: 1. Show all of our work. Pre-Calculus 017 Summer Assignment. Write the final answer on the line provided. This assignment will be collected the first da of school. You will

### Summer Math Packet (revised 2017)

Summer Math Packet (revised 07) In preparation for Honors Math III, we have prepared a packet of concepts that students should know how to do as these concepts have been taught in previous math classes.

### TOLLESON UNION HIGH SCHOOL DISTRICT 8 th Grade Algebra 1 Study Guide. 1. Which of these graphs correctly represents the inequality

TOLLESON UNION HIGH SCHOOL DISTRICT 8 th Grade Algebra 1 Stud Guide 1. Which of these graphs correctl represents the inequalit? C. D.. Which method represents a correct wa to solve the equation? Method

### Unit 2: Rational Expressions

Rational Epressions Pure Math 0 Notes Unit : Rational Epressions -: Simplifing Rational Epressions Rational Epressions: - fractions with polnomials as numerator and / or denominator. To Simplif (Reduce)

### State whether the following statements are true or false: 30. 1

Cumulative MTE -9 Review This packet includes major developmental math concepts that students ma use to prepare for the VPT Math (Virginia Placement Test for Math or for students to use to review essential

### MATH 410 Notes Simplifying Algebraic Expressions

MATH 410 Notes 2016 1.9 - Simplifying Algebraic Expressions Commutative Property: a + b = b + a and a b = b a Associative Property: a + (b + c) = (a + b) + c and a (b c) = (a b) c Distributive Property:

### Ready To Go On? Skills Intervention 5-1 Using Transformations to Graph Quadratic Functions

Read To Go On? Skills Intervention 5-1 Using Transformations to Graph Quadratic Functions Find these vocabular words in Lesson 5-1 and the Multilingual Glossar. Vocabular quadratic function parabola verte

### Name Period Date. Practice FINAL EXAM Intro to Calculus (50 points) Show all work on separate sheet of paper for full credit!

Name Period Date Practice FINAL EXAM Intro to Calculus (0 points) Show all work on separate sheet of paper for full credit! ) Evaluate the algebraic epression for the given value or values of the variable(s).

### Los Angeles Mission College

Los Angeles Mission College Math : Elementar Algebra Common Final Practice Set This practice set is a compilation of 0 questions that are similar in content to those on the common final. Since the content

### L What are the properties that should be used to isolate the variable in the equation? 3x + 11 = 5

lgebra Name: MITERM REVIEW Part Hour: ate: L... What are the properties that should be used to isolate the variable in the equation? x + = 5 additive identit and multiplicative identit additive inverse

### [ ] 4. Math 70 Intermediate Algebra II Final Exam Review Page 1 of 19. Instructions:

Math Intermediate Algebra II Final Eam Review Page of 9 Instructions: Use our own paper for the review questions. For the final eam, show all work on the eam. This is an algebra class do not guess! Write

### MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Math 1 Chapter 1 Practice Test Bro. Daris Howard MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) When going more than 38 miles per hour, the gas

### IM1 Summative Practice #1 Show all your Work

IM1 Summative Practice #1 Name: Show all your Work Period: Simplify each expression below. 1. 5x (7 3x) 2. 5(x 12) + 15(x + y) 3. 8 2(x 2 3x) (9 3x 2 ) Solve each equation. Justify each step with a property

### ( 3x. Chapter Review. Review Key Vocabulary. Review Examples and Exercises 6.1 Properties of Square Roots (pp )

6 Chapter Review Review Ke Vocabular closed, p. 266 nth root, p. 278 eponential function, p. 286 eponential growth, p. 296 eponential growth function, p. 296 compound interest, p. 297 Vocabular Help eponential

### STA Summer Review for Students Entering Algebra 3

Alg Summer Review STA Summer Review for Students Entering Algebra This packet will be collected and graded the first week of school. There will also be a test over this material the first week of school.

### Lecture Guide. Math 90 - Intermediate Algebra. Stephen Toner. Intermediate Algebra, 3rd edition. Miller, O'Neill, & Hyde. Victor Valley College

Lecture Guide Math 90 - Intermediate Algebra to accompany Intermediate Algebra, 3rd edition Miller, O'Neill, & Hyde Prepared by Stephen Toner Victor Valley College Last updated: 7/21/14 6.1 Introduction

### Math 100 Final Exam Review

Math 0 Final Eam Review Name The problems included in this review involve the important concepts covered this semester. Work in groups of 4. If our group gets stuck on a problem, let our instructor know.

### Math Departmental Exit Assessment Review (Student Version)

Math 008 - Departmental Eit Assessment Review (Student Version) Solve the equation. (Section.) ) ( + ) - 8 = 6-80 - 0 ) + - - 7 = 0-60 - 0 ) 8 + 9 = 9 - - ) - = 60 0-0 -60 ) 0.0 + 0.0(000 - ) = 0.0 0 6000

### 2.4 Library of Functions; Piecewise-defined Functions. 1 Graph the Functions Listed in the Library of Functions

80 CHAPTER Functions and Their Graphs Problems 8 88 require the following discussion of a secant line. The slope of the secant line containing the two points, f and + h, f + h on the graph of a function

### Math 0240 Final Exam Review Questions 11 ( 9) 6(10 4)

11 ( 9) 6(10 4) 1. Simplif: 4 8 3 + 8 ( 7). Simplif: 34 3. Simplif ( 5 7) 3( ) 8 6 4. Simplif: (4 3 ) 9 5. Simplif: 4 7 3 6. Evaluate 3 4 5 when and 3 Write each of the values below in decimal or standard

### Section Use properties of equality to solve each of the equations. Show your steps.

MTH00 Review Problems for Final Eam - MLC This is not a sample test. These problems are designed to get ou started on our review for the test. Stud the homework from the tetbook and our class notes for

### Lesson 5: Solving Linear Systems Problem Solving Assignment solutions

Write inequalities to represent the following problem, and then solve to answer the question. 1. The Rent-A-Lemon Car Rental Company charges \$60 a day to rent a car and an additional \$0.40 per mile. Alex

### I. ORDER OF OPERATIONS

ALGEBRA II HONORS REVIEW PACKET NAME This packet contains all of the material that you should have mastered in Algebra I. You are responsible for reviewing this material over the summer and expect an assessment

### Practice Algebra 1 SCP Midterm 2015

Practice Algebra 1 SCP Midterm 01 Multiple Choice Identif the choice that best completes the statement or answers the question. Solve the equation. 1. = m 0 7 7 7 7. 0 7 60. x 6 = 7 8 19 1 1 19 1..1x +.

### Algebra 1 Unit 3 Practice

Lesson 1-1 Use the table for Items 1 and. Canoe Rental Days Cost (\$) 1 5 3 78 5 1 7 13 1. Use function notation to write a linear function that gives the cost C in dollars of renting a canoe for t days.

### Math 115 Sample Final

Math Sample Final Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Factor completel. If the polnomial is prime, state this. ) + 8-0 ( - )( + )