1. f(x) = f(x) = 3. y 2-3y p - 4 8p2. Math 0312 EXAM 3 Review Questions. Name. Find all numbers not in the domain of the function.

Size: px
Start display at page:

Download "1. f(x) = f(x) = 3. y 2-3y p - 4 8p2. Math 0312 EXAM 3 Review Questions. Name. Find all numbers not in the domain of the function."

Transcription

1 Name Find all numbers not in the domain of the function. 1. f(x) = 8 x - 5 Find all numbers that are not in the domain of the function. Then give the domain using set notation f(x) = x x + 24 Express the rational expression in lowest terms. 3. y 2-3y - 10 y2-4y - 12 Write the rational expression in lowest terms. (y - 6)(y - 4) 4. (4 - y)(6 + y) Perform the indicated operation and express in lowest terms. 5. 4p - 4 8p2 p 6p - 6 1

2 6. z z + 36 z2 + 16z + 63 z2 + 4z z2-2z x x Assume that the expressions given are denominators of fractions. Find the least common denominator. 8. 7a + 21, a2 + 3a Add or subtract as indicated. Write the answer in lowest terms y2-3y y x 4 y xy 11. 2ab a2 - b2 - b a - b + 4 2

3 Simplify the complex fraction. x x x x Without actually solving the equation, list all possible numbers that would have to be rejected if they appeared as potential solutions x x - 9 = 0 Solve the equation w w - 8 = -41 3w w

4 Graph the rational function. Give the equations of the vertical and horizontal asymptotes. 16. f(x) = 5 x Solve the problem. 17. The speed of a stream is 5 mph. If a boat travels 52 miles downstream in the same time that it takes to travel 26 miles upstream, what is the speed of the boat in still water? 4

5 Suppose the triangles shown are similar, with angle A = angle D, angle B = angle E, and angle C = angle F. Answer the question. 18. E B A 2x - 7 C D 2x + 4 F What is the value of x? Solve the problem. Round your answer, as needed. 19. Doug and Inga can deliver 100 papers in 4 hours. How long would it take them to deliver 95 papers? Solve the problem. 20. Frank can type a report in 2 hours and James takes 5 hours. How long will it take the two of them typing together? 5

6 Find the root if it is a real number Graph the function and give its domain and its range. 23. f(x) = x - 3 Simplify the root. 24. x 10 Solve the problem. 25. The cost of manufacturing clocks is given by c = 121 n + 16, where c is the total cost and n is the number produced. What is the cost when no clocks are produced? Simplify the expression involving rational exponents / /2 Write with radicals. Assume that all variables represent positive real numbers. 28. (3m + n) 5/6 6

7 Simplify by first converting to rational exponents. Assume that all variables represent positive real numbers u 7 u 3 Use the rules of exponents to simplify the expression. Write the answer with positive exponents. Assume that all variables represent positive real numbers. x /4 y x1/2 x 3/10 x 2/5 (x 2 ) -1/2 Solve the problem. 32. In an economics study, three quantities m, p, and q have been found to be related by the equation m = p 1/2 q 1/2. Find m, if p = 9 and q = 36. Multiply using the product rule xy 3 9xy Simplify the radical. Assume that all variables represent positive real numbers x x 4 2x 7

8 Express the radical in simplified form Express the radical in simplified form. Assume that all variables represent positive real numbers a 8 b y 22 8 Simplify the radical. Assume that all variables represent positive real numbers Simplify by first writing the radicals with the same index. Then multiply Find the unknown length in the right triangle. Simplify the answer if necessary. 41. b

9 Find the distance between the pair of points. 42. (-1, -2) and (1, -6) Simplify. Assume that all variables represent positive real numbers x x x x 7-2x 4 x Solve the problem. Give the answer as a simplified radical expression. 47. Find the perimeter of a lot with sides measuring 3 18, 3 50, 5 8, and 2 27 yards. Multiply, then simplify the product. Assume that all variables represent positive real numbers. 48. ( 5x + 6)( 6x + 4) 9

10 Rationalize the denominator. Assume that all variables represent positive real numbers x 3 y5 Simplify. Assume that all variables represent positive real numbers x2 Rationalize the denominator. Assume that all variables represent positive real numbers and that the denominator is not zero x 8 + x Write the expression in lowest terms. Assume that all variables represent positive real numbers Solve the equation q - 2 = 2 10

11 56. p 2-5p + 16 = p s + 6 = 4 8s 58. 2x x + 1 = 1 Rewrite the expressions with rational exponents as radical expressions, and then solve the equation. 59. (x 2 + 2) 1/2 - (2x + 5) 1/2 = 0 Solve the formula for the indicated variable. S 60. r = 4 for S Write the number as a product of a real number and i. Simplify the radical expression

12 Multiply or divide as indicated Add or subtract as indicated. Write your answer in the form a + bi. 65. (2-4i) + (9 + 2i) Multiply. 66. (8-2i)(7 + 4i) 67. i(5-5i)(6-8i) Write the expression in the form a + bi i 5 + 2i Find the power of i. 69. i 13 Simplify. 70. i 21 12

13 Answer Key Testname: MATH EXAM 3 - REVIEW QUESTIONS 1. 5 Objective: (6.1) Find Numbers Not in Domain 2. -8, -3; {x x -8, -3} Objective: (6.1) Give Domain of Rational Function 3. y - 5 y - 6 Objective: (6.1) Write Rational Expression in Lowest Terms y 6 + y Objective: (6.1) Write Rational Exprn in Lowest Terms (Recognize Factor of -1) 5. 16p 3 Objective: (6.1) Multiply or Divide Rational Expressions I 6. z - 9 z 7. Objective: (6.1) Multiply or Divide Rational Expressions I 10 17x Objective: (6.2) Add or Subtract Rational Expressions (Common Denom) 8. 7a(a + 3) Objective: (6.2) Find Least Common Denominator x 10y - 11 (y - 1)(y + 1)(y - 2) Objective: (6.2) Add or Subtract Rational Expressions I 1-44x 3 y 12x 4 y 2 Objective: (6.2) Add or Subtract Rational Expressions I 4a + 5b a + b Objective: (6.2) ^Add or Subtract Rational Expressions II x(x + 4) 56 Objective: (6.3) Simplify Complex Fraction Objective: (6.3) Simplify Complex Fraction , 9 Objective: (6.4) List Impossible Values for Solutions 15. Objective: (6.4) Solve Rational Equation 16. x = 0; y = 0 Objective: (6.4) Graph Rational Function and Give Eqn of Vertical Asymptote mph Objective: (6.5) Solve Apps: Distance, Rate, and Time Objective: (6.5) Solve Apps: Geometry hours Objective: (6.5) Solve Apps: Proportions hr Objective: (6.5) Solve Apps: Work Objective: (7.1) Find Square Root Objective: (7.1) Find Higher Roots 1

14 Answer Key Testname: MATH EXAM 3 - REVIEW QUESTIONS 23. [3, ); [0, ) x 2 Objective: (7.3) Use Quotient Rule for Radicals to Simplify Expression 35. 2x Objective: (7.3) Use Quotient Rule for Radicals to Simplify Expression Objective: (7.3) Express Radical in Simplified Form I 24. x 5 Objective: (7.1) Graph Radical Function; Give Domain and Range Objective: (7.1) Simplify Root Objective: (7.1) Solve Apps: Equations with Radical Expressions Objective: (7.2) Simplify Expression Involving Rational Exponent I Objective: (7.2) Simplify Expression Involving Rational Exponent II (3m + n) 5 Objective: (7.2) Write Exponential Expression with Radicals u 16 Objective: (7.2) Simplify Radical Expression II 30. xy 2 Objective: (7.2) Use Rules of Exponents to Simplify Expression I 31. x 11/5 Objective: (7.2) Use Rules of Exponents to Simplify Expression II Objective: (7.2) Solve Apps: Rational Exponents x 2 y 2 Objective: (7.3) Use Product Rule for Radicals to Simplify Expression a 2 b 3 a 2 b 2 Objective: (7.3) Express Radical in Simplified Form II 38. y7 3 y 2 Objective: (7.3) Express Radical in Simplified Form II Objective: (7.3) Simplify Radical by Using Smaller Index Objective: (7.3) Multiply Radicals with Different Indexes Objective: (7.3) Find Unknown Length in Right Triangle Objective: (7.3) Find Distance Between Pair of Points Objective: (7.4) Simplify Sum or Difference of Radicals (Index = 2) x Objective: (7.4) Simplify Sum or Difference of Radicals (Index = 2) 45. 9x 4 x 3 Objective: (7.4) Simplify Sum or Difference of Radicals (Index > 2) Objective: (7.4) Simplify Sum or Difference of Radicals (Fractions) yards Objective: (7.4) Solve Apps: Geometry 48. x x + 6 6x + 24 Objective: (7.5) Multiply and Simplify Radical Expressions

15 Answer Key Testname: MATH EXAM 3 - REVIEW QUESTIONS Objective: (7.5) Rationalize Denominator (Index = 2) 3x 5xy y 3 Objective: (7.5) Rationalize Denominator (Index = 2) 3 15x 3x Objective: (7.5) Rationalize Denominator (Index > 2) Objective: (7.5) Rationalize Binomial Denominator 53. 3x 8 + x 8 + x Objective: (7.5) Rationalize Binomial Denominator Objective: (7.5) Write Radical Expression in Lowest Terms 55. {2} Objective: (7.6) Solve Radical Equation Using Power Rule 56. {5} Objective: (7.6) Solve Radical Equation by Squaring Binomial Objective: (7.6) Solve Radical Equation Using Power Rule (Index > 2) 58. {3, -1} Objective: (7.6) Solve Radical Equation Using Power Rule Twice 59. {3, -1} Objective: (7.6) Solve Eqn with Rational Exponents for Indicated Variable 60. S = 4 r 2 Objective: (7.6) Use Power Rule to Solve Formula for Indicated Variable 61. 2i Objective: (7.7) Write Radical as Product of Real Number and i i 2 Objective: (7.7) Write Radical as Product of Real Number and i Objective: (7.7) Multiply or Divide Radicals Objective: (7.7) Multiply or Divide Radicals i Objective: (7.7) Add or Subtract Complex Numbers i Objective: (7.7) Multiply Complex Numbers i Objective: (7.7) Multiply Complex Numbers i Objective: (7.7) Divide Complex Numbers 69. i Objective: (7.7) Find Power of i 70. i Objective: (7.8) Chapter Test

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

MATH98 Intermediate Algebra Practice Test Form B

MATH98 Intermediate Algebra Practice Test Form B MATH98 Intermediate Algebra Practice Test Form B MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the equation. 1) (y - 4) - (y + 9) = y 1) -

More information

MATH98 Intermediate Algebra Practice Test Form A

MATH98 Intermediate Algebra Practice Test Form A MATH98 Intermediate Algebra Practice Test Form A MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the equation. 1) (y - 4) - (y + ) = 3y 1) A)

More information

Final Exam Review for DMAT 0310

Final Exam Review for DMAT 0310 Final Exam Review for DMAT 010 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Factor the polynomial completely. What is one of the factors? 1) x

More information

Math 120 online. Practice Midterm Exam #2 Prof. Kinoshita. Fall (Actual midterm will have 100 pts)

Math 120 online. Practice Midterm Exam #2 Prof. Kinoshita. Fall (Actual midterm will have 100 pts) Note: The format of this practice midterm will be similar to the real midterm. However, the actual midterm will have less questions and be worth 100 points. There will also be more room to work on the

More information

Chapter 4: Radicals and Complex Numbers

Chapter 4: Radicals and Complex Numbers Chapter : Radicals and Complex Numbers Section.1: A Review of the Properties of Exponents #1-: Simplify the expression. 1) x x ) z z ) a a ) b b ) 6) 7) x x x 8) y y y 9) x x y 10) y 8 b 11) b 7 y 1) y

More information

Math 110 Final Exam Review Revised October 2018

Math 110 Final Exam Review Revised October 2018 Math 110 Final Exam Review Revised October 2018 Factor out the GCF from each polynomial. 1) 60x - 15 2) 7x 8 y + 42x 6 3) x 9 y 5 - x 9 y 4 + x 7 y 2 - x 6 y 2 Factor each four-term polynomial by grouping.

More information

Radical Expressions and Graphs 8.1 Find roots of numbers. squaring square Objectives root cube roots fourth roots

Radical Expressions and Graphs 8.1 Find roots of numbers. squaring square Objectives root cube roots fourth roots 8. Radical Expressions and Graphs Objectives Find roots of numbers. Find roots of numbers. The opposite (or inverse) of squaring a number is taking its square root. Find principal roots. Graph functions

More information

ALGEBRA 2 FINAL EXAM REVIEW

ALGEBRA 2 FINAL EXAM REVIEW Class: Date: ALGEBRA 2 FINAL EXAM REVIEW Multiple Choice Identify the choice that best completes the statement or answers the question.. Classify 6x 5 + x + x 2 + by degree. quintic c. quartic cubic d.

More information

Final Exam Review Part 1 #4

Final Exam Review Part 1 #4 Final Exam Review Part #4 Intermediate Algebra / MAT 35 Fall 206 Master (Prof. Fleischner) Student Name/ID:. Solve the compound inequality. 5 < 2x 3 3 Graph the solution on the number line. - -0-9 -8-7

More information

MATH 125 ELAC SPRING 2018 TEST 2 REVIEW SHEET NAME: SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

MATH 125 ELAC SPRING 2018 TEST 2 REVIEW SHEET NAME: SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. MATH 125 ELAC SPRING 2018 TEST 2 REVIEW SHEET NAME: SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Solve. 1) 5x + 5 + 3 = 12 1) 2) 3 5x + 4 + 5 = 0 2)

More information

Math 110 Final Exam Review Revised December 2015

Math 110 Final Exam Review Revised December 2015 Math 110 Final Exam Review Revised December 2015 Factor out the GCF from each polynomial. 1) 60x - 15 2) 7x 8 y + 42x 6 3) x 9 y 5 - x 9 y 4 + x 7 y 2 - x 6 y 2 Factor each four-term polynomial by grouping.

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

Math 100 Final Exam Review

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.

More information

MAT 1033 Final Review for Intermediate Algebra (Revised April 2013)

MAT 1033 Final Review for Intermediate Algebra (Revised April 2013) 1 This review corresponds to the Charles McKeague textbook. Answers will be posted separately. Section 2.1: Solve a Linear Equation in One Variable 1. Solve: " = " 2. Solve: "# = " 3. Solve: " " = " Section

More information

Answers of the MATH97 Practice Test Form A

Answers of the MATH97 Practice Test Form A Answers of the MATH97 Practice Test Form A A1) Answer B Section 1.2: concepts of solution of the equations. Pick the pair which satisfies the equation 4x+y=10. x= 1 and y=6 A2) Answer A Section 1.3: select

More information

Math Exam Jam Solutions. Contents. 1 Linear Inequalities and Absolute Value Equations 2

Math Exam Jam Solutions. Contents. 1 Linear Inequalities and Absolute Value Equations 2 Math 11100 Exam Jam Solutions Contents 1 Linear Inequalities and Absolute Value Equations 2 2 Linear Equations, Graphing and Solving Systems of Equations 4 3 Polynomials and Rational Expressions 13 4 Radical

More information

Alg 1B Chapter 7 Final Exam Review

Alg 1B Chapter 7 Final Exam Review Name: Class: Date: ID: A Alg B Chapter 7 Final Exam Review Please answer all questions and show your work. Simplify ( 2) 4. 2. Simplify ( 4) 4. 3. Simplify 5 2. 4. Simplify 9x0 y 3 z 8. 5. Simplify 7w0

More information

Chapter 7 Review Sections labeled at the start of the related problems

Chapter 7 Review Sections labeled at the start of the related problems Chapter 7 Review Sections labeled at the start of the related problems.6 State whether the equation is an example of the product rule, the quotient rule, the power rule, raising a product to a power, or

More information

Math 100 Final Exam Review

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.

More information

Reteach Multiplying and Dividing Rational Expressions

Reteach Multiplying and Dividing Rational Expressions 8-2 Multiplying and Dividing Rational Expressions Examples of rational expressions: 3 x, x 1, and x 3 x 2 2 x 2 Undefined at x 0 Undefined at x 0 Undefined at x 2 When simplifying a rational expression:

More information

Math 100 Exam 4 Review (Chapters 7-8) Name

Math 100 Exam 4 Review (Chapters 7-8) Name Math 100 Eam 4 Review (Chapters 7-8) Name The problems included in this review involve the important concepts covered in chapters 7 and 8. Be prepared to write soltuions on the board if called upon. Find

More information

Functions: Polynomial, Rational, Exponential

Functions: Polynomial, Rational, Exponential Functions: Polynomial, Rational, Exponential MATH 151 Calculus for Management J. Robert Buchanan Department of Mathematics Spring 2014 Objectives In this lesson we will learn to: identify polynomial expressions,

More information

Chapter 4: Radicals and Complex Numbers

Chapter 4: Radicals and Complex Numbers Section 4.1: A Review of the Properties of Exponents #1-42: Simplify the expression. 1) x 2 x 3 2) z 4 z 2 3) a 3 a 4) b 2 b 5) 2 3 2 2 6) 3 2 3 7) x 2 x 3 x 8) y 4 y 2 y 9) 10) 11) 12) 13) 14) 15) 16)

More information

1. Write in symbols: (a) The quotient of -6 and the sum of 2 and -8. (b) Now Simplify the expression in part a. 2. Simplify. x 4, given x=-2 and y=4

1. Write in symbols: (a) The quotient of -6 and the sum of 2 and -8. (b) Now Simplify the expression in part a. 2. Simplify. x 4, given x=-2 and y=4 Sample problems for common Final Exam Math 115 LASC Directions: To receive credit show enough work so that your method of solution is clear. Box answers. Show all work on this test form. No Work=No Credit.

More information

My Math Plan Assessment #1 Study Guide

My Math Plan Assessment #1 Study Guide My Math Plan Assessment #1 Study Guide 1. Find the x-intercept and the y-intercept of the linear equation. 8x y = 4. Use factoring to solve the quadratic equation. x + 9x + 1 = 17. Find the difference.

More information

Math 46 Final Exam Review Packet

Math 46 Final Exam Review Packet Math 46 Final Exam Review Packet Question 1. Perform the indicated operation. Simplify if possible. 7 x x 2 2x + 3 2 x Question 2. The sum of a number and its square is 72. Find the number. Question 3.

More information

= (Type exponential notation with positive exponents)

= (Type exponential notation with positive exponents) 1. Subtract. Simplify by collecting like radical terms if possible. 2 2 = (Simplify your answer) 2. Add. Simplify if possible. = (Simplify your answer) 3. Divide and simplify. = (Type exponential notation

More information

Five-Minute Check (over Lesson 8 3) CCSS Then/Now New Vocabulary Key Concept: Vertical and Horizontal Asymptotes Example 1: Graph with No Horizontal

Five-Minute Check (over Lesson 8 3) CCSS Then/Now New Vocabulary Key Concept: Vertical and Horizontal Asymptotes Example 1: Graph with No Horizontal Five-Minute Check (over Lesson 8 3) CCSS Then/Now New Vocabulary Key Concept: Vertical and Horizontal Asymptotes Example 1: Graph with No Horizontal Asymptote Example 2: Real-World Example: Use Graphs

More information

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. C) 2 1 3

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. C) 2 1 3 Exam Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. ) Subtract the mixed numbers. ) 4-2 A) 2 4 B) 2 C) 2 D) 4 2) If oak flooring, including

More information

MATH 0312 FINAL EXAM REVIEW ITEMS

MATH 0312 FINAL EXAM REVIEW ITEMS MATH 012 FINAL EXAM REVIEW ITEMS Name The items on this review are representative of the items that ou might see on our course final eam. No formul sheets are allowed and calculators are not allowed on

More information

DIVIDING BY ZERO. Rational Expressions and Equations. Note Package. Name: 1: Simplifying Rational Expressions 2: Multiplying and Dividing

DIVIDING BY ZERO. Rational Expressions and Equations. Note Package. Name: 1: Simplifying Rational Expressions 2: Multiplying and Dividing MAT30S Mr. Morris Rational Expressions and Equations Lesson 1: Simplifying Rational Expressions 2: Multiplying and Dividing 3: Adding and Subtracting 4: Solving Rational Equations Note Package Extra Practice

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

Assignment #1 MAT121 Summer 2015 NAME:

Assignment #1 MAT121 Summer 2015 NAME: Assignment #1 MAT11 Summer 015 NAME: Directions: Do ALL of your work on THIS handout in the space provided! Circle your final answer! On problems that your teacher would show work on be sure that you also

More information

John L. Lehet

John L. Lehet New! Android App! SAT Mathematics Review Algebra John L. Lehet jlehet@mathmaverick.com www.mathmaverick.com SAT Math Daily Question Android App - new question each day - archive of over 200 questions -

More information

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

P.1 Prerequisite skills Basic Algebra Skills

P.1 Prerequisite skills Basic Algebra Skills P.1 Prerequisite skills Basic Algebra Skills Topics: Evaluate an algebraic expression for given values of variables Combine like terms/simplify algebraic expressions Solve equations for a specified variable

More information

6.1 Polynomial Functions

6.1 Polynomial Functions 6.1 Polynomial Functions Definition. A polynomial function is any function p(x) of the form p(x) = p n x n + p n 1 x n 1 + + p 2 x 2 + p 1 x + p 0 where all of the exponents are non-negative integers and

More information

Math 155 Intermediate Algebra Practice Exam on Chapters 6 & 8 Name

Math 155 Intermediate Algebra Practice Exam on Chapters 6 & 8 Name Math 155 Intermediate Algebra Practice Eam on Chapters 6 & 8 Name Find the function value, provided it eists. 1) f() = 7-8 8 ; f(-3) Simplify by removing a factor equal to 1. ) 5 + 0 + 3) m - m - m Find

More information

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

Review Topics. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Review Topics MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. On the real number line, label the points with the given coordinates. 1) 11,- 11 1)

More information

Math 2 Variable Manipulation Part 2 Powers & Roots PROPERTIES OF EXPONENTS:

Math 2 Variable Manipulation Part 2 Powers & Roots PROPERTIES OF EXPONENTS: Math 2 Variable Manipulation Part 2 Powers & Roots PROPERTIES OF EXPONENTS: 1 EXPONENT REVIEW PROBLEMS: 2 1. 2x + x x + x + 5 =? 2. (x 2 + x) (x + 2) =?. The expression 8x (7x 6 x 5 ) is equivalent to?.

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

Final Exam Review Calculators Not Allowed

Final Exam Review Calculators Not Allowed Math 35 Final Exam Review Calculators Not Allowed From the Chapter 2 and 3 Test: (Refer to the White Ch. 2/3 Test answer key.) Solve this literal equation for the variable requested. 4. y = mx + b (solve

More information

Answers to Sample Exam Problems

Answers to Sample Exam Problems Math Answers to Sample Exam Problems () Find the absolute value, reciprocal, opposite of a if a = 9; a = ; Absolute value: 9 = 9; = ; Reciprocal: 9 ; ; Opposite: 9; () Commutative law; Associative law;

More information

MATH 125 FALL 2018 ELAC TEST 3 TAKE HOME Name: SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

MATH 125 FALL 2018 ELAC TEST 3 TAKE HOME Name: SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. MATH 125 FALL 2018 ELAC TEST 3 TAKE HOME Name: SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Determine whether the functions f and g are inverses of

More information

30 Wyner Math Academy I Fall 2015

30 Wyner Math Academy I Fall 2015 30 Wyner Math Academy I Fall 2015 CHAPTER FOUR: QUADRATICS AND FACTORING Review November 9 Test November 16 The most common functions in math at this level are quadratic functions, whose graphs are parabolas.

More information

Math 9 Practice Final Exam #1

Math 9 Practice Final Exam #1 Class: Date: Math Practice Final Exam #1 Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Determine the value of 0.64. a. 0.8 b. 0.08 0.4 d. 0.1 2. Which

More information

INTERMEDIATE ALGEBRA REVIEW FOR TEST 3

INTERMEDIATE ALGEBRA REVIEW FOR TEST 3 INTERMEDIATE ALGEBRA REVIEW FOR TEST 3 Evaluate the epression. ) a) 73 (-4)2-44 d) 4-3 e) (-)0 f) -90 g) 23 2-4 h) (-2)4 80 i) (-2)5 (-2)-7 j) 5-6 k) 3-2 l) 5-2 Simplify the epression. Write your answer

More information

5.1 Multiplying and Dividing Radical Expressions

5.1 Multiplying and Dividing Radical Expressions Practice 5. Multiplying and Dividing Radical Expressions Multiply, if possible. Then simplify. To start, identify the index of each radical.. 4 # 6. 5 # 8. 6 # 4 9 index of both radicals is 4 # 6 Simplify.

More information

5.3. Polynomials and Polynomial Functions

5.3. Polynomials and Polynomial Functions 5.3 Polynomials and Polynomial Functions Polynomial Vocabulary Term a number or a product of a number and variables raised to powers Coefficient numerical factor of a term Constant term which is only a

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

Chapter 7 Rational Expressions, Equations, and Functions

Chapter 7 Rational Expressions, Equations, and Functions Chapter 7 Rational Expressions, Equations, and Functions Section 7.1: Simplifying, Multiplying, and Dividing Rational Expressions and Functions Section 7.2: Adding and Subtracting Rational Expressions

More information

Chapter 5: Exponents and Polynomials

Chapter 5: Exponents and Polynomials Chapter 5: Exponents and Polynomials 5.1 Multiplication with Exponents and Scientific Notation 5.2 Division with Exponents 5.3 Operations with Monomials 5.4 Addition and Subtraction of Polynomials 5.5

More information

MATH 190 KHAN ACADEMY VIDEOS

MATH 190 KHAN ACADEMY VIDEOS MATH 10 KHAN ACADEMY VIDEOS MATTHEW AUTH 11 Order of operations 1 The Real Numbers (11) Example 11 Worked example: Order of operations (PEMDAS) 7 2 + (7 + 3 (5 2)) 4 2 12 Rational + Irrational Example

More information

B) 75k k D) 75k k C) 3 5

B) 75k k D) 75k k C) 3 5 Fall 018 Preview Exam Math 110 This is only provided to you are a resource to help you practice and prepare for an upcoming exam. It is not a contract of inclusion and/or exclusion. You are still responsible

More information

My Math Plan Assessment #2 Study Guide

My Math Plan Assessment #2 Study Guide My Math Plan Assessment #2 Study Guide 1. Find the x-intercept and the y-intercept of the linear equation. 8x y = 4 2. Use factoring to solve the quadratic equation. x 2 + 9x + 1 = 17. Multiply and simplify

More information

Math 108, Solution of Midterm Exam 3

Math 108, Solution of Midterm Exam 3 Math 108, Solution of Midterm Exam 3 1 Find an equation of the tangent line to the curve x 3 +y 3 = xy at the point (1,1). Solution. Differentiating both sides of the given equation with respect to x,

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

Section 1.3 Review of Complex Numbers

Section 1.3 Review of Complex Numbers 1 Section 1. Review of Complex Numbers Objective 1: Imaginary and Complex Numbers In Science and Engineering, such quantities like the 5 occur all the time. So, we need to develop a number system that

More information

Remember, you may not use a calculator when you take the assessment test.

Remember, you may not use a calculator when you take the assessment test. Elementary Algebra problems you can use for practice. Remember, you may not use a calculator when you take the assessment test. Use these problems to help you get up to speed. Perform the indicated operation.

More information

Rational Numbers, Irrational Numbers, Whole Numbers, Integers, Natural Numbers

Rational Numbers, Irrational Numbers, Whole Numbers, Integers, Natural Numbers College Readiness Math Semester Eam Review Write the set using interval notation and graph the inequality on the number line. 1) { -6 < < 9} Use the order of operations to simplify the epression. 4 (8

More information

Chapter 8 RADICAL EXPRESSIONS AND EQUATIONS

Chapter 8 RADICAL EXPRESSIONS AND EQUATIONS Name: Instructor: Date: Section: Chapter 8 RADICAL EXPRESSIONS AND EQUATIONS 8.1 Introduction to Radical Expressions Learning Objectives a Find the principal square roots and their opposites of the whole

More information

FLC Ch 6. Simplify. State any restrictions (if necessary). a) b) Simplify each. List all restrictions on the domain. Next, graph the function f.

FLC Ch 6. Simplify. State any restrictions (if necessary). a) b) Simplify each. List all restrictions on the domain. Next, graph the function f. Math 0 Intermediate Algebra Defn Sec 6.: Rational Expressions and Functions: Multiplying and Dividing A polynomial divided by another nonzero polynomial is called a rational expression. If P and Q are

More information

Quiz # 6 Date: Name. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Quiz # 6 Date: Name. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Quiz # 6 Date: Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find all numbers not in the domain of the function. ) f(x) = x + None - 0 ) )

More information

Introductory Algebra Chapter 9 Review

Introductory Algebra Chapter 9 Review Introductory Algebra Chapter 9 Review Objective [9.1a] Find the principal square roots and their opposites of the whole numbers from 0 2 to 2 2. The principal square root of a number n, denoted n,is the

More information

7.1 Introduction to Rational Expressions. The " 1" Technique: Reduce: Simplify:

7.1 Introduction to Rational Expressions. The  1 Technique: Reduce: Simplify: 77 7.1 Introduction to Rational Expressions The " 1" Technique: Reduce: 5 10 Simplify: 48a2 b 3 8a 7 b When simplifying rational expressions, you are actually dividing both the numerator and the denominaror

More information

Intermediate Algebra Sample Final Exam Fall 2016

Intermediate Algebra Sample Final Exam Fall 2016 Intermediate Algebra Sample Final Exam Fall 2016 You will have 2 hours to complete this exam. You may use a calculator (TI-84 or lower, no cell phones) but must show all algebraic work in the space provided

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

Intermediate Algebra

Intermediate Algebra Intermediate Algebra George Voutsadakis 1 1 Mathematics and Computer Science Lake Superior State University LSSU Math 102 George Voutsadakis (LSSU) Intermediate Algebra August 2013 1 / 40 Outline 1 Radicals

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

Chapter 5B - Rational Functions

Chapter 5B - Rational Functions Fry Texas A&M University Math 150 Chapter 5B Fall 2015 143 Chapter 5B - Rational Functions Definition: A rational function is The domain of a rational function is all real numbers, except those values

More information

Sect Complex Numbers

Sect Complex Numbers 161 Sect 10.8 - Complex Numbers Concept #1 Imaginary Numbers In the beginning of this chapter, we saw that the was undefined in the real numbers since there is no real number whose square is equal to a

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

Math Review for Incoming Geometry Honors Students

Math Review for Incoming Geometry Honors Students Solve each equation. 1. 5x + 8 = 3 + 2(3x 4) 2. 5(2n 3) = 7(3 n) Math Review for Incoming Geometry Honors Students 3. Victoria goes to the mall with $60. She purchases a skirt for $12 and perfume for $35.99.

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

Advanced Algebra 2 - Assignment Sheet Chapter 1

Advanced Algebra 2 - Assignment Sheet Chapter 1 Advanced Algebra - Assignment Sheet Chapter #: Real Numbers & Number Operations (.) p. 7 0: 5- odd, 9-55 odd, 69-8 odd. #: Algebraic Expressions & Models (.) p. 4 7: 5-6, 7-55 odd, 59, 6-67, 69-7 odd,

More information

Basic Property: of Rational Expressions

Basic Property: of Rational Expressions Basic Properties of Rational Expressions A rational expression is any expression of the form P Q where P and Q are polynomials and Q 0. In the following properties, no denominator is allowed to be zero.

More information

Ron Paul Curriculum Mathematics 8 Lesson List

Ron Paul Curriculum Mathematics 8 Lesson List Ron Paul Curriculum Mathematics 8 Lesson List 1 Introduction 2 Algebraic Addition 3 Algebraic Subtraction 4 Algebraic Multiplication 5 Week 1 Review 6 Algebraic Division 7 Powers and Exponents 8 Order

More information

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

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Math 170 Final Exam Review Name SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Evaluate the function at the given value of the independent variable and

More information

Natural Numbers Positive Integers. Rational Numbers

Natural Numbers Positive Integers. Rational Numbers Chapter A - - Real Numbers Types of Real Numbers, 2,, 4, Name(s) for the set Natural Numbers Positive Integers Symbol(s) for the set, -, - 2, - Negative integers 0,, 2,, 4, Non- negative integers, -, -

More information

124b End of Semester Practice Problems. Simplify the radical. 1) ) ) ) 4) ) 5) 5 (-3)5 5)

124b End of Semester Practice Problems. Simplify the radical. 1) ) ) ) 4) ) 5) 5 (-3)5 5) 124b End of Semester Practice Problems Name Simplify the radical. 1) 3 1 27 1) 2) 4 256 2) 3) 4-16 3) 4) 3 83 4) 5) 5 (-3)5 5) 1 6) 3 (x + 2)3 6) Evaluate the expression, if possible. 7) 641/2 7) 8) 27

More information

Recognize the appropriate method for factoring a polynomial Use a general strategy for factoring polynomials

Recognize the appropriate method for factoring a polynomial Use a general strategy for factoring polynomials Section 6.5: A GENERAL FACTORING STRATEGY When you are done with your homework you should be able to Recognize the appropriate method for factoring a polynomial Use a general strategy for factoring polynomials

More information

Math 0312 EXAM 2 Review Questions

Math 0312 EXAM 2 Review Questions Name Decide whether the ordered pair is a solution of the given system. 1. 4x + y = 2 2x + 4y = -20 ; (2, -6) Solve the system by graphing. 2. x - y = 6 x + y = 16 Solve the system by substitution. If

More information

Section 2.4: Add and Subtract Rational Expressions

Section 2.4: Add and Subtract Rational Expressions CHAPTER Section.: Add and Subtract Rational Expressions Section.: Add and Subtract Rational Expressions Objective: Add and subtract rational expressions with like and different denominators. You will recall

More information

Algebra One As of: September 2014 Teacher Contact: Ms.Zinn (CVHS-NGC)

Algebra One As of: September 2014 Teacher Contact: Ms.Zinn (CVHS-NGC) Algebra One As of: September 2014 Teacher Contact: Ms.Zinn (CVHS-NGC) CCSS Unit Theme SKILLS ASSESSMENT & PRODUCTS Translate sentences into equations such as, The length of a rectangle is ten less than

More information

27 Wyner Math 2 Spring 2019

27 Wyner Math 2 Spring 2019 27 Wyner Math 2 Spring 2019 CHAPTER SIX: POLYNOMIALS Review January 25 Test February 8 Thorough understanding and fluency of the concepts and methods in this chapter is a cornerstone to success in the

More information

SUMMER MATH ASSIGNMENTS School Year. General Information for all Math students. Pre -Algebra IXL ASSIGNMENTS:

SUMMER MATH ASSIGNMENTS School Year. General Information for all Math students. Pre -Algebra IXL ASSIGNMENTS: SUMMER MATH ASSIGNMENTS 2018-2019 School Year General Information for all Math students All assignments are to be completed between May 25, 2018 and September 1, 2018. The assignments are based on the

More information

CUNY Elementary Algebra Final Exam (CEAFE) Fall 2012 Item Results and Learning Outcomes Correspondence

CUNY Elementary Algebra Final Exam (CEAFE) Fall 2012 Item Results and Learning Outcomes Correspondence 1 CUNY Elementary Algebra Final Exam (CEAFE) Fall 2012 Item Results and Learning Outcomes Correspondence Purpose of Exam: Students enrolled in any CUNY Elementary Algebra developmental courses, workshops

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

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

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

College Algebra. Chapter 5 Review Created by: Lauren Atkinson. Math Coordinator, Mary Stangler Center for Academic Success

College Algebra. Chapter 5 Review Created by: Lauren Atkinson. Math Coordinator, Mary Stangler Center for Academic Success College Algebra Chapter 5 Review Created by: Lauren Atkinson Math Coordinator, Mary Stangler Center for Academic Success Note: This review is composed of questions from the chapter review at the end of

More information

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

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Math 170 Final Exam Review Name SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Evaluate the function at the given value of the independent variable and

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

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

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

TABLE OF CONTENTS. Introduction to Finish Line Indiana Math 10. UNIT 1: Number Sense, Expressions, and Computation. Real Numbers

TABLE OF CONTENTS. Introduction to Finish Line Indiana Math 10. UNIT 1: Number Sense, Expressions, and Computation. Real Numbers TABLE OF CONTENTS Introduction to Finish Line Indiana Math 10 UNIT 1: Number Sense, Expressions, and Computation LESSON 1 8.NS.1, 8.NS.2, A1.RNE.1, A1.RNE.2 LESSON 2 8.NS.3, 8.NS.4 LESSON 3 A1.RNE.3 LESSON

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

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

Chapter 2. Polynomial and Rational Functions. 2.6 Rational Functions and Their Graphs. Copyright 2014, 2010, 2007 Pearson Education, Inc.

Chapter 2. Polynomial and Rational Functions. 2.6 Rational Functions and Their Graphs. Copyright 2014, 2010, 2007 Pearson Education, Inc. Chapter Polynomial and Rational Functions.6 Rational Functions and Their Graphs Copyright 014, 010, 007 Pearson Education, Inc. 1 Objectives: Find the domains of rational functions. Use arrow notation.

More information