1. The dosage in milligrams D of a heartworm preventive for a dog who weighs X pounds is given by D x. Substitute 28 in place of x to get:

Size: px
Start display at page:

Download "1. The dosage in milligrams D of a heartworm preventive for a dog who weighs X pounds is given by D x. Substitute 28 in place of x to get:"

Transcription

1 1. The dosage in milligrams D of a heartworm preventive for a dog who weighs X pounds is given by D x 28 pounds. ( ) = 136 ( ). Find the proper dosage for a dog that weighs 25 x Substitute 28 in place of x to get: ( ) = 136 ( ) = D The dosage is milligrams. 2. Find the domain of the rational function. C( x) = x 1 x 2 25 The restrictions on the domain of the function will involve values of x for which the denominator of the function, x 2 25, is equal to zero, since dividing by zero is not defined. To determine these values, set the denominator equal to zero and solve for x: x 2 25 = 0 x 2 = 25 x = 25 x = 5, 5 The domain is {x x is a real number and x 5, -5} (All that you need to enter is 5, -5)

2 3. Find the root. Assume that the variable represents a positive number. 100x 2 By inspection, the roots are 10x and -10x. Since there is no specific instruction about separating answers by a comma, it s possible that they are only expecting you to enter 10x, and to disregard the negative root. 4. Simplify the rational expression: x 2 8x 48 x + 4 The numerator can be factored as (x + 4)(x 12). The expression can then be rewritten as: ( x + 4) x 12 x + 4 ( ) The term x + 4 can then be canceled from both the numerator and the denominator, leaving just: x Subtract: ( 5y 2 8y + 7) ( 4y 2 8y + 4) Rewrite this as: 5y 2 4y 2 8y (-8y) Then simplify by combining like terms: 5y 2 4y 2 8y + 8y (5 4)y 2 + (8 8)y y 2 + 3

3 6. Solve 3x 2 5 = 0 Add 5 to both sides to get: 3x = x 2 = 5 Square both sides to get: ( 3x 2 ) 2 = ( 5) 2 3x 2 = 25 Add 2 to both sides to get: 3x = x = 27 Divide both sides by 3 to get: 3x 3 = 27 3 x = 9

4 7. Solve the compound inequality: 5 4x 5 19 Separate the compound inequality into two separate inequalities: -5 4x 5 and 4x 5 19 Add 5 to both sides of both inequalities to get: x and 4x x and 4x 24 Divide both sides of both inequalities by 4 to get: 0 4 4x 4 and 4x x and x 6 The solution as a compound inequality is then: 0 x 6 The solution in interval notation is [0, 6] 8. Find the slope and y-intercept of the line: 2x 7y = -14 By rearranging the equation of the line into the form y = mx + b, the slope and y-intercept can be determined by inspection: 2x 7y + 7y = y 2x + 14 = y 2x + 14 = 7y 7y = 2x + 14

5 y = 2 7 x y = 2 7 x + 2 In this case, the slope is 2, and the y-intercept as an ordered pair is (0, 2) Solve the equation: 6( x 4) + x = 7( x 4) + 4 Distribute the 6 on the left side of the equation to get: 6x 24 + x = 7(x 4) + 4 Distribute the 7 on the right side of the equation to get: 6x 24 + x = 7x Subtract 7x from both sides, in order to collect all of the x terms on the left side: 6x 24 + x 7x = 7x 7x x 24 + x 7x = Add 24 to both sides, in order to collect all of the constant terms on the right side: 6x x 7x = x + x 7x = Combine like terms to get: 0x = 0 Any value of x will satisfy this equation, so the solution set is all real numbers. B. The solution is all real numbers.

6 10. Simplify the expression: ( 7x 6 y 6 )( 9x 3 y 7 ) Simplify this by multiplying -7 and 9 to get -63. Simplify the x and y terms by adding the exponents: ( 7x 6 y 6 )( 9x 3 y 7 ) = ( 7 *9)( x 6 * x 3 )( y 6 * y 7 ) = 63( x 6+3 )( y 6+7 ) = 63( x 9 )( y 13 ) = 63x 9 y A principal of $5000 is invested in an account paying an annual rate of 5%. Find the amount in the account after 4 years if the account is compounded semiannually, quarterly, and monthly. The formula for compound interest is: where: FV = PV ( ) 1+ r n nt FV is the future value, PV is the present value, ( principal ) r is the annual interest rate, expressed as a decimal value n is the number of compounding periods per year t is the number of years.

7 a) Compounded semiannually (n = 2) for 4 years (t = 4): ( ) FV = *4 FV = ( 5000) ( ) 8 FV = 6, The amount in the account after 4 years if the account is compounded semiannually is $ b) Compounded quarterly (n = 4) for 4 years (t = 4): ( ) FV = *4 FV = ( 5000) ( ) 16 FV = 6, The amount in the account after 4 years if the account is compounded quarterly is $ c) Compounded monthly (n = 12) for 4 years (t = 4): ( ) FV = *4 FV = ( 5000) ( ) 48 FV = 6, The amount in the account after 4 years if the account is compounded monthly is $

8 12. Perform the indicated operation: x 4 x + 3 x + 3 x 3 The least common denominator of the two terms will be (x + 3)(x 3). Multiplying the first term by x 3 x + 3, and multiply the second term by x 3 x + 3 x 4 x 3 x + 3 x 3 x + 3 x + 3 x 3 x + 3 ( x 4) x 3 x + 3 ( ) ( )( x 3) ( x + 3) ( x + 3) ( x + 3) ( x 3) to get: x 2 4x 3x +12 x 2 9 x 2 7x +12 x 2 9 x2 + 3x + 3x + 9 x 2 9 x2 + 6x + 9 x 2 9 x 2 7x +12 x 2 6x 9 x 2 9 x 2 x 2 7x 6x x x + 3 x In 2006, the population of the country was 31.4 million. This represented an increase in population of 2.4% since What was the population of the country in 2001? Round to the nearest hundredth of a million. Let x represent the population in 2001 in millions. Then: x(1.024) = 31.4

9 x = 31.4 / x = In 2001, the population of the country was million. 14. Use the quadratic formula to solve the equation: x 2 + 7x + 3 = 0 This equation is in the form ax 2 + bx + c = 0, with a = 1, b = 7, and c = 3. The quadratic formula is: x = b ± b2 4ac 2a Substituting the values for a, b, and c gives: ( )( 3) ( ) x = 7 ± x = 7 ± x = 7 ± 37 2 The solutions are: x = ,

10 15. Simplify: 2x 7 y 2 4 2x 7 y 2 4 ( ) 4 ( y 2 ) 4 ( = 2) 4 * x 7 ( x 7 ) 4 = ( 2) 4 * y 2 ( ) 4 = x28 16y Find the product: (8x + 7) 2 (8x + 7) 2 = (8x + 7)(8x + 7) = 64x x + 56x + 49 = 64x x + 49

11 17. Solve the equation and check: 11t 30 t 6 = 1 Multiply each term in the equation by 30 to get: 11t ( ) t 6 30 ( ) = 1( 30) 11t 5t = 30 6t = 30 t = 30 6 t = 5 Then, as a check: 11( 5) = = = = 1 1 = 1 The solution checks. A. t = 5

12 18. In 2006, the median price of an existing home in some country was approximately $222,100. In 2001 the median price of an existing home was $152,000. Let y be the median price of an existing home in the year x, where x = 0 represents a. Write a linear equation that models the median existing home price in terms of the year x. The slope of the linear equation will be: m = 222, , = 14,020 The y-intercept will be the median price in year 0, or 152,000. Substituting these values into the form y = mx + b, the linear equation that models the median existing home price is: y = 14020x + 152,000 b. Use this equation to predict the median existing home price for the year In the year 2010, the value of x will be 9. y = 14020(9) + 152,000 y = $278,180 c. Interpret the slope of the equation found in part a: C. Every year, the median price of a home increases by $14, Rationalize the denominator: =

13 20. The amount P of pollution varies directly with the population N of people. City A has a population of 494,000 and produces 260,000 tons of pollutants. Find how many tons of pollution we should expect City B to produce, if we know that its population is 350, , ,000 = 350,000 x 494,000x = ( 350,000) ( 260,000) ( )( 260,000) x = 350, ,000 x = 184,211 City B produces 184,211 tons of pollution. 21. Solve the equation: 4t 2 5 = 11t Multiplying each term in the equation by 10 gives: 4t 2 ( ) = 11t ( ) + 13 ( ) t 2 = 22t +13 8t 2 22t 13 = 0 Using the Quadratic Formula, with a = 8, b = -22, and c = -13 gives:

14 ( ) ± 22 2( 8) t = 22 ( )2 4 8 ( )( 13) t = t = t = t = 22 ± ± = = 13 4 = 8 16 = 1 2 A. The solutions are t = 13 4, Find an equation of the line. Write the equation using function notation. Through (6, -3); Perpendicular to 5y = x 10 Divide the equation 5y = x 10 through by 5 to put it in y = mx + b form: 5y = x 10 y = 1 5 x 2 The slope of this line is 1/5. The slope of a line perpendicular to the given line will be the negative reciprocal of 1/5, or -5. The equation of the perpendicular line will then have the form y = -5x + b. Use the given point, (6, -3) to solve for the unknown, b: -3 = -5(6) + b -3 = b

15 = b b = 27 The equation of the perpendicular line is f(x) = -5x Simplify and write using positive exponents only. 2a 4 b 7 10a 2 b 4 Rewrite this expression by moving factors with negative exponents to the other side of the fraction bar, and changing the sign of the exponent. In other words, move a -4 in the numerator to the denominator and write it as a 4. Similarly, move b -4 in the denominator to the numerator and write is as b 4. This gives: 2a 4 b 7 10a 2 b 4 = 2b7 b 4 10a 2 a 4 Next, combine the b terms in the numerator by adding their exponents. Similarly, combine the a terms in the denominator by adding their exponents. This gives: = 2b7 b 4 10a 2 a = 2b a 10a = 2b11 Finally, factor a 2 from the numerator and the denominator, leaving: b 11 5a 6

16 24. Use the quotient rule to simplify: 10a 5 b 7 c 8 5a 3 b 4 c 6 To simplify this expression using the quotient rule, subtract the value of the exponent in the denominator from the value of the exponent in the numerator for each variable: 10a 5 b 7 c 8 5a 3 b 4 c 6 = 10a5 3 b 7 4 c = 10a2 b 3 c 2 5 Finally, factor a 5 from both the numerator and the denominator to get: 2a 2 b 3 c Match the graph with the equation is most closely resembles. The slope of the graph shown is -1, which means that m = -1 The y-intercept is (0, -1), which means that b = -1 Substituting these into the y = mx + b form of the equation of a line gives: y = (-1)x 1 y = -x 1 This matches with answer B. y = -x - 1

Mock Final Exam Name. Solve and check the linear equation. 1) (-8x + 8) + 1 = -7(x + 3) A) {- 30} B) {- 6} C) {30} D) {- 28}

Mock Final Exam Name. Solve and check the linear equation. 1) (-8x + 8) + 1 = -7(x + 3) A) {- 30} B) {- 6} C) {30} D) {- 28} Mock Final Exam Name Solve and check the linear equation. 1) (-8x + 8) + 1 = -7(x + 3) 1) A) {- 30} B) {- 6} C) {30} D) {- 28} First, write the value(s) that make the denominator(s) zero. Then solve the

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

Review Problems for the Final

Review Problems for the Final Review Problems for the Final Math 0-08 008 These problems are provided to help you study The presence of a problem on this handout does not imply that there will be a similar problem on the test And the

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

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

PAP Geometry Summer Work- Show your work

PAP Geometry Summer Work- Show your work PRE- PAP Geometry Summer Work- Show your work Solve the equation. Check your solution. 1. 2. Solve the equation. 3. 4. 5. Describe the values of c for which the equation has no solution. Write the sentence

More information

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

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. MAC 1105 Fall 2007 - Final Exam Dr. Schnackenberg If you do not agree with the given answers, answer "E" for "None of the above". MULTIPLE CHOICE. Choose the one alternative that best completes the statement

More information

Inverse Functions. Definition 1. The exponential function f with base a is denoted by. f(x) = a x

Inverse Functions. Definition 1. The exponential function f with base a is denoted by. f(x) = a x Inverse Functions Definition 1. The exponential function f with base a is denoted by f(x) = a x where a > 0, a 1, and x is any real number. Example 1. In the same coordinate plane, sketch the graph of

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

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 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

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

College Algebra and College Algebra with Review Final Review

College Algebra and College Algebra with Review Final Review The final exam comprises 30 questions. Each of the 20 multiple choice questions is worth 3 points and each of the 10 open-ended questions is worth 4 points. Instructions for the Actual Final Exam: Work

More information

Final Exam A Name. 20 i C) Solve the equation by factoring. 4) x2 = x + 30 A) {-5, 6} B) {5, 6} C) {1, 30} D) {-5, -6} -9 ± i 3 14

Final Exam A Name. 20 i C) Solve the equation by factoring. 4) x2 = x + 30 A) {-5, 6} B) {5, 6} C) {1, 30} D) {-5, -6} -9 ± i 3 14 Final Exam A Name First, write the value(s) that make the denominator(s) zero. Then solve the equation. 1 1) x + 3 + 5 x - 3 = 30 (x + 3)(x - 3) 1) A) x -3, 3; B) x -3, 3; {4} C) No restrictions; {3} D)

More information

Intermediate Algebra Chapter 12 Review

Intermediate Algebra Chapter 12 Review Intermediate Algebra Chapter 1 Review Set up a Table of Coordinates and graph the given functions. Find the y-intercept. Label at least three points on the graph. Your graph must have the correct shape.

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 III: Blizzard Bag #1 Exponential and Logarithm Functions

Algebra III: Blizzard Bag #1 Exponential and Logarithm Functions NAME : DATE: PERIOD: Algebra III: Blizzard Bag #1 Exponential and Logarithm Functions Students need to complete the following assignment, which will aid in review for the end of course exam. Look back

More information

Subtract 6 to both sides Divide by 2 on both sides. Cross Multiply. Answer: x = -9

Subtract 6 to both sides Divide by 2 on both sides. Cross Multiply. Answer: x = -9 Subtract 6 to both sides Divide by 2 on both sides Answer: x = -9 Cross Multiply. = 3 Distribute 2 to parenthesis Combine like terms Subtract 4x to both sides Subtract 10 from both sides x = -20 Subtract

More information

Exponential Functions and Their Graphs (Section 3-1)

Exponential Functions and Their Graphs (Section 3-1) Exponential Functions and Their Graphs (Section 3-1) Essential Question: How do you graph an exponential function? Students will write a summary describing the steps for graphing an exponential function.

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

Exponential and Logarithmic Functions

Exponential and Logarithmic Functions Exponential and Logarithmic Functions Learning Targets 1. I can evaluate, analyze, and graph exponential functions. 2. I can solve problems involving exponential growth & decay. 3. I can evaluate expressions

More information

PERT Practice Test #2

PERT Practice Test #2 Class: Date: PERT Practice Test #2 Multiple Choice Identify the choice that best completes the statement or answers the question. Ê 1. What is the quotient of 6y 6 9y 4 + 12y 2 ˆ Ê 3y 2 ˆ? a. 2y 4 + 3y

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

Intermediate Algebra Semester Summary Exercises. 1 Ah C. b = h

Intermediate Algebra Semester Summary Exercises. 1 Ah C. b = h . Solve: 3x + 8 = 3 + 8x + 3x A. x = B. x = 4 C. x = 8 8 D. x =. Solve: w 3 w 5 6 8 A. w = 4 B. w = C. w = 4 D. w = 60 3. Solve: 3(x ) + 4 = 4(x + ) A. x = 7 B. x = 5 C. x = D. x = 4. The perimeter of

More information

nt and A = Pe rt to solve. 3) Find the accumulated value of an investment of $10,000 at 4% compounded semiannually for 5 years.

nt and A = Pe rt to solve. 3) Find the accumulated value of an investment of $10,000 at 4% compounded semiannually for 5 years. Exam 4 Review Approximate the number using a calculator. Round your answer to three decimal places. 1) 2 1.7 2) e -1.4 Use the compound interest formulas A = P 1 + r n nt and A = Pe rt to solve. 3) Find

More information

Final Exam Study Guide Mathematical Thinking, Fall 2003

Final Exam Study Guide Mathematical Thinking, Fall 2003 Final Exam Study Guide Mathematical Thinking, Fall 2003 Chapter R Chapter R contains a lot of basic definitions and notations that are used throughout the rest of the book. Most of you are probably comfortable

More information

Final Exam C Name i D) 2. Solve the equation by factoring. 4) x2 = x + 72 A) {1, 72} B) {-8, 9} C) {-8, -9} D) {8, 9} 9 ± i

Final Exam C Name i D) 2. Solve the equation by factoring. 4) x2 = x + 72 A) {1, 72} B) {-8, 9} C) {-8, -9} D) {8, 9} 9 ± i Final Exam C Name First, write the value(s) that make the denominator(s) zero. Then solve the equation. 7 ) x + + 3 x - = 6 (x + )(x - ) ) A) No restrictions; {} B) x -, ; C) x -; {} D) x -, ; {2} Add

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

ASU Mathematics Placement Test Sample Problems June, 2000

ASU Mathematics Placement Test Sample Problems June, 2000 ASU Mathematics Placement Test Sample Problems June, 000. Evaluate (.5)(0.06). Evaluate (.06) (0.08). Evaluate ( ) 5. Evaluate [ 8 + ( 9) ] 5. Evaluate 7 + ( ) 6. Evaluate ( 8) 7. Evaluate 5 ( 8. Evaluate

More information

Logarithmic and Exponential Equations and Inequalities College Costs

Logarithmic and Exponential Equations and Inequalities College Costs Logarithmic and Exponential Equations and Inequalities ACTIVITY 2.6 SUGGESTED LEARNING STRATEGIES: Summarize/ Paraphrase/Retell, Create Representations Wesley is researching college costs. He is considering

More information

Basic Fraction and Integer Operations (No calculators please!)

Basic Fraction and Integer Operations (No calculators please!) P1 Summer Math Review Packet For Students entering Geometry The problems in this packet are designed to help you review topics from previous mathematics courses that are important to your success in Geometry.

More information

Algebra Readiness. Curriculum (445 topics additional topics)

Algebra Readiness. Curriculum (445 topics additional topics) Algebra Readiness This course covers the topics shown below; new topics have been highlighted. Students navigate learning paths based on their level of readiness. Institutional users may customize the

More information

My Math Plan Assessment #3 Study Guide

My Math Plan Assessment #3 Study Guide My Math Plan Assessment # Study Guide 1. Identify the vertex of the parabola with the given equation. f(x) = (x 5) 2 7 2. Find the value of the function. Find f( 6) for f(x) = 2x + 11. Graph the linear

More information

Florida Math Curriculum (433 topics)

Florida Math Curriculum (433 topics) Florida Math 0028 This course covers the topics shown below. Students navigate learning paths based on their level of readiness. Institutional users may customize the scope and sequence to meet curricular

More information

Final Exam Review: Study Guide Math 3

Final Exam Review: Study Guide Math 3 Final Exam Review: Study Guide Math 3 Name: Day 1 Functions, Graphing, Regression Relation: Function: Domain: Range: Asymptote: Hole: Graphs of Functions f(x) = x f(x) = f(x) = x f(x) = x 3 Key Ideas Key

More information

California Algebra 1

California Algebra 1 California Algebra 1 This course covers the topics shown below. Students navigate learning paths based on their level of readiness. Institutional users may customize the scope and sequence to meet curricular

More information

Chapter 14: Basics of Functions

Chapter 14: Basics of Functions Math 91 Final Exam Study Guide Name Chapter 14: Basics of Functions Find the domain and range. 1) {(5,1), (5,-4), (6,7), (3,4), (-9,-6)} Find the indicated function value. 2) Find f(3) when f(x) = x2 +

More information

Middle School Math Course 2

Middle School Math Course 2 Middle School Math Course 2 This course covers the topics shown below. Students navigate learning paths based on their level of readiness. Institutional users may customize the scope and sequence to meet

More information

8.1 Apply Exponent Properties Involving Products. Learning Outcome To use properties of exponents involving products

8.1 Apply Exponent Properties Involving Products. Learning Outcome To use properties of exponents involving products 8.1 Apply Exponent Properties Involving Products Learning Outcome To use properties of exponents involving products Product of Powers Property Let a be a real number, and let m and n be positive integers.

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

Algebra I+ Pacing Guide. Days Units Notes Chapter 1 ( , )

Algebra I+ Pacing Guide. Days Units Notes Chapter 1 ( , ) Algebra I+ Pacing Guide Days Units Notes Chapter 1 (1.1-1.4, 1.6-1.7) Expressions, Equations and Functions Differentiate between and write expressions, equations and inequalities as well as applying order

More information

x 1 2 i 1 5 2i 11 9x 9 3x 3 1 y 2 3y 4 y 2 1 Poudre School District s College Algebra Course Review

x 1 2 i 1 5 2i 11 9x 9 3x 3 1 y 2 3y 4 y 2 1 Poudre School District s College Algebra Course Review . Perform the indicated operations and simplify the result. Leave the answer in factored form. 9x 9 x a. b. 9x 9 x x. Solve: x 7x x 0. a. x., b. x 0,., x,0,. x.,0,. Find the quotient and the remainder

More information

A is any of ordered pairs. The set of all. components of the pairs is called the of the

A is any of ordered pairs. The set of all. components of the pairs is called the of the Section 8.1: INTRODUCTION TO FUNCTIONS When you are done with your homework you should be able to Find the domain and range of a relation Determine whether a relation is a function Evaluate a function

More information

Algebra 2 Summer Math Answer Section

Algebra 2 Summer Math Answer Section Algebra 2 Summer Math Answer Section 1. ANS: A PTS: 1 DIF: Level B REF: MALG0064 STA: SC.HSCS.MTH.00.AL1.A1.I.C.4 TOP: Lesson 1.1 Evaluate Expressions KEY: word volume cube area solid 2. ANS: C PTS: 1

More information

Chapter 7 - Exponents and Exponential Functions

Chapter 7 - Exponents and Exponential Functions Chapter 7 - Exponents and Exponential Functions 7-1: Multiplication Properties of Exponents 7-2: Division Properties of Exponents 7-3: Rational Exponents 7-4: Scientific Notation 7-5: Exponential Functions

More information

ID: ID: ID: of 39 1/18/ :43 AM. Student: Date: Instructor: Alfredo Alvarez Course: 2017 Spring Math 1314

ID: ID: ID: of 39 1/18/ :43 AM. Student: Date: Instructor: Alfredo Alvarez Course: 2017 Spring Math 1314 1 of 39 1/18/017 10:43 AM Student: Date: Instructor: Alfredo Alvarez Course: 017 Spring Math 1314 Assignment: Practice Final 1. Graph the equation. y= x 3 ID: 1.1-11. Perform the multiplication and write

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

9.5. Polynomial and Rational Inequalities. Objectives. Solve quadratic inequalities. Solve polynomial inequalities of degree 3 or greater.

9.5. Polynomial and Rational Inequalities. Objectives. Solve quadratic inequalities. Solve polynomial inequalities of degree 3 or greater. Chapter 9 Section 5 9.5 Polynomial and Rational Inequalities Objectives 1 3 Solve quadratic inequalities. Solve polynomial inequalities of degree 3 or greater. Solve rational inequalities. Objective 1

More information

4 Exponential and Logarithmic Functions

4 Exponential and Logarithmic Functions 4 Exponential and Logarithmic Functions 4.1 Exponential Functions Definition 4.1 If a > 0 and a 1, then the exponential function with base a is given by fx) = a x. Examples: fx) = x, gx) = 10 x, hx) =

More information

Section September 6, If n = 3, 4, 5,..., the polynomial is called a cubic, quartic, quintic, etc.

Section September 6, If n = 3, 4, 5,..., the polynomial is called a cubic, quartic, quintic, etc. Section 2.1-2.2 September 6, 2017 1 Polynomials Definition. A polynomial is an expression of the form a n x n + a n 1 x n 1 + + a 1 x + a 0 where each a 0, a 1,, a n are real numbers, a n 0, and n is a

More information

MATH 236 ELAC FALL 2017 TEST 3 NAME: SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

MATH 236 ELAC FALL 2017 TEST 3 NAME: SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. MATH 6 ELAC FALL 7 TEST NAME: SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Evaluate the integral using integration by parts. ) 9x ln x dx ) ) x 5 -

More information

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

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Exam Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Decide if the function is an exponential function. If it is, state the initial value and

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

Check boxes of Edited Copy of Sp Topics (was 145 for pilot) Beginning Algebra, 3rd Ed. [open all close all] Course Readiness and

Check boxes of Edited Copy of Sp Topics (was 145 for pilot) Beginning Algebra, 3rd Ed. [open all close all] Course Readiness and Check boxes of Edited Copy of 10021 Sp 11 152 Topics (was 145 for pilot) Beginning Algebra, 3rd Ed. [open all close all] Course Readiness and Additional Topics Appendix Course Readiness Multiplication

More information

Evaluate the expression if x = 2 and y = 5 6x 2y Original problem Substitute the values given into the expression and multiply

Evaluate the expression if x = 2 and y = 5 6x 2y Original problem Substitute the values given into the expression and multiply Name EVALUATING ALGEBRAIC EXPRESSIONS Objective: To evaluate an algebraic expression Example Evaluate the expression if and y = 5 6x y Original problem 6() ( 5) Substitute the values given into the expression

More information

Honors Advanced Algebra Chapter 8 Exponential and Logarithmic Functions and Relations Target Goals

Honors Advanced Algebra Chapter 8 Exponential and Logarithmic Functions and Relations Target Goals Honors Advanced Algebra Chapter 8 Exponential and Logarithmic Functions and Relations Target Goals By the end of this chapter, you should be able to Graph exponential growth functions. (8.1) Graph exponential

More information

Algebra I Chapter 4 Curriculum and IXL

Algebra I Chapter 4 Curriculum and IXL Chapter 4 Curriculum and IXL C4L1 Functions and Non-Functions Represent relations as mappings, sets of points, and graphs: WS Determine whether a relation is a function or not: WS C4L2 Linear and Non-Linear

More information

What kind of number is? Write the number in scientific notation ,000

What kind of number is? Write the number in scientific notation ,000 Chapter 1: 1.1, 1.2, 1.3, 1.4 Chapter 2: 2.1, 2.2, 2.3, 2.4 Chapter 3: 3.1, 3.2, 3.3, 3.4 Chapter 4: 4.1, 4.2, 4.3, 4.5, 4.7 Chapter 5: 5.1, 5.2, 5.3, 5.4, 5.6, 5.7 Chapter 6: 6.1 1.1 What kind of number

More information

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

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Algebraic Concepts Review MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the inequality. ) - - 0x - -x - ) A) x > -0 B) x < -0 C) x 0 D) x

More information

Example. Determine the inverse of the given function (if it exists). f(x) = 3

Example. Determine the inverse of the given function (if it exists). f(x) = 3 Example. Determine the inverse of the given function (if it exists). f(x) = g(x) = p x + x We know want to look at two di erent types of functions, called logarithmic functions and exponential functions.

More information

Course Readiness and Skills Review Handbook (Topics 1-10, 17) (240 topics, due. on 09/11/2015) Course Readiness (55 topics)

Course Readiness and Skills Review Handbook (Topics 1-10, 17) (240 topics, due. on 09/11/2015) Course Readiness (55 topics) Course Name: Gr. 8 Fall 2015 Course Code: C6HNH-TEK9E ALEKS Course: Middle School Math Course 3 Instructor: Mr. Fernando Course Dates: Begin: 08/31/2015 End: 06/17/2016 Course Content: 642 Topics (637

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

Pre Algebra. Curriculum (634 topics)

Pre Algebra. Curriculum (634 topics) Pre Algebra This course covers the topics shown below. Students navigate learning paths based on their level of readiness. Institutional users may customize the scope and sequence to meet curricular needs.

More information

Chapter 11 Logarithms

Chapter 11 Logarithms Chapter 11 Logarithms Lesson 1: Introduction to Logs Lesson 2: Graphs of Logs Lesson 3: The Natural Log Lesson 4: Log Laws Lesson 5: Equations of Logs using Log Laws Lesson 6: Exponential Equations using

More information

Final Exam Study Guide Dynamics of Algebra 2. Chapter Section Example

Final Exam Study Guide Dynamics of Algebra 2. Chapter Section Example Final Exam Study Guide- 011-01 Dynamics of Algebra Chapter Section Example Chapter What is a function? Properties of a function Is it a function? Explain. Finding the Slope Slope y y m = x x 1 1 Find the

More information

Math Literacy. Curriculum (457 topics)

Math Literacy. Curriculum (457 topics) Math Literacy This course covers the topics shown below. Students navigate learning paths based on their level of readiness. Institutional users may customize the scope and sequence to meet curricular

More information

Exponential and Logarithmic Functions. 3. Pg #17-57 column; column and (need graph paper)

Exponential and Logarithmic Functions. 3. Pg #17-57 column; column and (need graph paper) Algebra 2/Trig Unit 6 Notes Packet Name: Period: # Exponential and Logarithmic Functions 1. Worksheet 2. Worksheet 3. Pg 483-484 #17-57 column; 61-73 column and 76-77 (need graph paper) 4. Pg 483-484 #20-60

More information

INTERNET MAT 117. Solution for the Review Problems. (1) Let us consider the circle with equation. x 2 + 2x + y 2 + 3y = 3 4. (x + 1) 2 + (y + 3 2

INTERNET MAT 117. Solution for the Review Problems. (1) Let us consider the circle with equation. x 2 + 2x + y 2 + 3y = 3 4. (x + 1) 2 + (y + 3 2 INTERNET MAT 117 Solution for the Review Problems (1) Let us consider the circle with equation x 2 + y 2 + 2x + 3y + 3 4 = 0. (a) Find the standard form of the equation of the circle given above. (i) Group

More information

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. B) 6x + 4

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. B) 6x + 4 Math1420 Review Comprehesive Final Assessment Test Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Add or subtract as indicated. x + 5 1) x2

More information

Chapter 1: Precalculus Review

Chapter 1: Precalculus Review : Precalculus Review Math 115 17 January 2018 Overview 1 Important Notation 2 Exponents 3 Polynomials 4 Rational Functions 5 Cartesian Coordinates 6 Lines Notation Intervals: Interval Notation (a, b) (a,

More information

11) 12) ) ) ) )

11) 12) ) ) ) ) Math 155 Course Review Questions 1-38 can be used as a study plan for the midterm. All questions should be studied for the final exam. Use the order of operations to find the value of the expression. 1)

More information

ALLEN PARK HIGH SCHOOL S u m m er A s s e s s m e n t

ALLEN PARK HIGH SCHOOL S u m m er A s s e s s m e n t ALLEN PARK HIGH SCHOOL S u m m er A s s e s s m e n t F o r S t u d e n t s E n t e r i n g A l g e b r a Allen Park High School Summer Assignment Algebra Show all work for all problems on a separate sheet

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

2015 2nd Semester Exam Review

2015 2nd Semester Exam Review Algebra 2 2015 2nd Semester Exam Review 1. Write a function whose graph is a translation of the graph of the function in two directions. Describe the translation. 2. What are the solutions to the equation?

More information

Section 1.4. Meaning of Slope for Equations, Graphs, and Tables

Section 1.4. Meaning of Slope for Equations, Graphs, and Tables Section 1.4 Meaning of Slope for Equations, Graphs, and Tables Finding Slope from a Linear Equation Finding Slope from a Linear Equation Example Find the slope of the line Solution Create a table using

More information

Academic Algebra 2. Algebra 1 Review

Academic Algebra 2. Algebra 1 Review Academic Algebra On the following pages you will find a review of the Algebra concepts needed to successfully complete Academic Algebra. Concepts such as fractions, solving equations, inequalities, absolute

More information

Foundations of High School Math

Foundations of High School Math Foundations of High School Math This course covers the topics shown below. Students navigate learning paths based on their level of readiness. Institutional users may customize the scope and sequence to

More information

Unit 3 Exam Review Questions MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Unit 3 Exam Review Questions MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Unit Eam Review Questions MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Some Useful Formulas: Compound interest formula: A=P + r nt n Continuously

More information

MA Lesson 14 Notes Summer 2016 Exponential Functions

MA Lesson 14 Notes Summer 2016 Exponential Functions Solving Eponential Equations: There are two strategies used for solving an eponential equation. The first strategy, if possible, is to write each side of the equation using the same base. 3 E : Solve:

More information

Elementary Algebra

Elementary Algebra Elementary Algebra 978-1-63545-008-8 To learn more about all our offerings Visit Knewton.com/highered Source Author(s) (Text or Video) Title(s) Link (where applicable) Flatworld Text John Redden Elementary

More information

CP Algebra 2. Summer Packet. Name:

CP Algebra 2. Summer Packet. Name: CP Algebra Summer Packet 018 Name: Objectives for CP Algebra Summer Packet 018 I. Number Sense and Numerical Operations (Problems: 1 to 4) Use the Order of Operations to evaluate expressions. (p. 6) Evaluate

More information

MATH 035 and MATH 043 REVIEW for FINAL EXAM

MATH 035 and MATH 043 REVIEW for FINAL EXAM MATH 03 and MATH 043 REVIEW for FINAL EXAM MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) Solve and graph: -20 8x - 4 and 2x + 7 < 11 1) (-2,

More information

x y x y ax bx c x Algebra I Course Standards Gap 1 Gap 2 Comments a. Set up and solve problems following the correct order of operations (including proportions, percent, and absolute value) with rational

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

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

Course Readiness and Skills Review Handbook (83 topics) Course Readiness (21 topics) Course Name: Algebra Course Code: UY6JA-RATXM

Course Readiness and Skills Review Handbook (83 topics) Course Readiness (21 topics) Course Name: Algebra Course Code: UY6JA-RATXM Course Name: Algebra 1 2014-15 Course Code: UY6JA-RATXM ALEKS Course: Algebra 1A Instructor: Ms. Dalton Course Dates: Begin: 11/18/2014 End: 06/18/2015 Course Content: 335 Topics (334 goal + 1 prerequisite)

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

Algebra 1 Standards Curriculum Map Bourbon County Schools. Days Unit/Topic Standards Activities Learning Targets ( I Can Statements) 1-19 Unit 1

Algebra 1 Standards Curriculum Map Bourbon County Schools. Days Unit/Topic Standards Activities Learning Targets ( I Can Statements) 1-19 Unit 1 Algebra 1 Standards Curriculum Map Bourbon County Schools Level: Grade and/or Course: Updated: e.g. = Example only Days Unit/Topic Standards Activities Learning Targets ( I 1-19 Unit 1 A.SSE.1 Interpret

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

Algebra 1 Hour Final Exam Review Days. Complete and On Time 5 points

Algebra 1 Hour Final Exam Review Days. Complete and On Time 5 points Semester Final Exam Review Packet Name Algebra 1 Hour Final Exam Review Days Assigned on Assignment 6/1 Unit 5 and Unit 6, 1-39 Complete and On Time 5 points Complete and Late 4 points At Least 50% Complete.5

More information

Junior PSAT Training Packet Math Department Answer Key

Junior PSAT Training Packet Math Department Answer Key Junior PSAT Training Packet 2016-17 Math Department Answer Key Section 3: Math Test No Calculator QUESTION 1. Choice C is correct. Subtracting 6 from each side of 5x + 6 = 10 yields 5x = 4. Dividing both

More information

Pre-AP Algebra II Summer Packet 2014

Pre-AP Algebra II Summer Packet 2014 Pre-AP Algebra II Summer Packet 014 Name: Period: PLEASE READ THE FOLLOWING!!!!!!! Wait until a few weeks before school starts to work through this packet so that the material will be fresh when you begin

More information

Function: State whether the following examples are functions. Then state the domain and range. Use interval notation.

Function: State whether the following examples are functions. Then state the domain and range. Use interval notation. Name Period Date MIDTERM REVIEW Algebra 31 1. What is the definition of a function? Functions 2. How can you determine whether a GRAPH is a function? State whether the following examples are functions.

More information

Math 1 Unit 1 EOC Review

Math 1 Unit 1 EOC Review Math 1 Unit 1 EOC Review Name: Solving Equations (including Literal Equations) - Get the variable to show what it equals to satisfy the equation or inequality - Steps (each step only where necessary):

More information

Algebra I Assessment. Eligible Texas Essential Knowledge and Skills

Algebra I Assessment. Eligible Texas Essential Knowledge and Skills Algebra I Assessment Eligible Texas Essential Knowledge and Skills STAAR Algebra I Assessment Mathematical Process Standards These student expectations will not be listed under a separate reporting category.

More information

ALGEBRA 2 CP MIDTERM REVIEW

ALGEBRA 2 CP MIDTERM REVIEW ALGEBRA CP MIDTERM REVIEW Algebra II CP MIDTERM REVIEW Name CHAPTER 4 QUADRATICS Add or subtract the following polynomials. (Distribute if necessary, and then combine like terms) x y x y 7 7x 6 x x 7x

More information

Algebra 2. Curriculum (524 topics additional topics)

Algebra 2. Curriculum (524 topics additional topics) Algebra 2 This course covers the topics shown below. Students navigate learning paths based on their level of readiness. Institutional users may customize the scope and sequence to meet curricular needs.

More information

Review of Exponential Relations

Review of Exponential Relations Review of Exponential Relations Integrated Math 2 1 Concepts to Know From Video Notes/ HW & Lesson Notes Zero and Integer Exponents Exponent Laws Scientific Notation Analyzing Data Sets (M&M Lab & HW/video

More information

Prep for the CSU ELM

Prep for the CSU ELM Prep for the CSU ELM This course covers the topics shown below. Students navigate learning paths based on their level of readiness. Institutional users may customize the scope and sequence to meet curricular

More information

8.1 Multiplication Properties of Exponents Objectives 1. Use properties of exponents to multiply exponential expressions.

8.1 Multiplication Properties of Exponents Objectives 1. Use properties of exponents to multiply exponential expressions. 8.1 Multiplication Properties of Exponents Objectives 1. Use properties of exponents to multiply exponential expressions. 2. Use powers to model real life problems. Multiplication Properties of Exponents

More information