# TSI College Level Math Practice Test

Size: px
Start display at page:

Transcription

1 TSI College Level Math Practice Test Tutorial Services Mission del Paso Campus. Factor the Following Polynomials 4 a. 6 8 b. c. 7 d. ab + a + b + 6 e. 9 f Perform the indicated operation a. ( +7y) + (4 + 7) + (y ) d. (4 6y + 9y ) (8 6y - y ) yb b. ( -4)( + 9) e. 7 9y c. (-a + 4b) f Simplify the following Epressions a. ( 7) 4 c b. 6 d Solve Each Linear Equation a. ( + ) = + c. P = L + W solve for W m 4 m b. d. 4. Solve each word problem a. Maria rode her bicycle at an average speed of 8 mph on level roads and then slowed down to 0mph on the hilly roads of the trip. The entire trip covered 98 miles. How long did the entire trip take if traveling the level roads took the same time as traveling the hilly roads? {Remember, d = r t } b. The bottom of Jim s backpack contains 0 coins in nickels and dimes. If the coins have a total value of \$.8, find the number of each type of coin. c. The sum of three consecutive integers is more than twice the smallest integer. Find the integers. d. Laura invested \$4,000 in two accounts: a mutual fund paying 8% annual interest and a CD paying 9% annual interest. If her annual interest was \$,00 how much did she invest in each account? Saved C: Accuplacer College Level Math Assessment Page of 7

2 6. Solve the Following Quadratic Equations a. m m 6 0 b. ( + )( ) = c. 8 d Solve the following Radical Equations a. 9 b. c. 4 d. 8. Rational Epressions: Perform the indicated operation 4 a. b c. a 9 a a 6 a a 6 a 6 d. a 4a 8 a a 9. Rational Epressions: Solve the following equations a. 6 a c. 6 4 d. 0. Solve the following absolute value equations a. b. c. 7 d. 8. Eponents & Radicals: Simplify 49 a. b. 4 c. 8a b d. 6. Eponents & Radical: Perform the indicated operation a. 4 b. 6 c. 8 y y d. 8 Saved C: Accuplacer College Level Math Assessment Page of 7

3 . Imaginary Numbers (i): Perform the indicated operation a. 4 b. (4-7i) + ( + i) c. 6i( i) d. ( i)( i) 7 8 e. f. i g. (7i)(-9i) h. (6 - i)( + i) 4 i 4. Simplify the following comple fractions. a. b. c. d.. Functions: Perform the indicated operation Let f() = and let g() = a. (f + g)() b. (f g)() c. (f g)() d. f () g 6. Functions: Find the following Let f() = and let g() = + a. ( f g)( ) b. ( g f )() 7. Sequence & Series: Evaluate 6 i a. i0 b. i i c. Find the sum of the first si terms of the arithmetic sequence,, 8,, 4, 7 n S n ( a an ) d. Find the sum of the first si terms of the geometric sequence, 0, 0, 40, 80, 60 n a r S n ( ) r 8. Logarithmic & Eponential Functions: Perform the indicated operation a. Find the inverse of the given function f() = 6 + b. Find the inverse of the given function f() = 4 c. Solve: 4 = 64 d. Solve: 9 e. Solve: log ( ) 4 f. Write the equation using logarithmic notation: 49 = 7 g. Write the equation using eponential notation: log 6 4 h. Write as a single log: log 8 log 4 i. Write as a sum, difference, or multiple: j. Solve: ln () = Saved C: Accuplacer College Level Math Assessment Page of 7 log

4 9. Solve the following inequalities a. + < 8 c. < 4 < 7 b. d. - < 6 0. Graphing Linear Equations: Perform the indicated operation a. Find the slope of the line containing the following points (, ) (8, ) b. Find the equation of the line for the given points (, ) (-, 4) and graph c. Find the equation of the line through (, 8) and parallel to y = 4 d. Write the equation of the following line, vertical through (, 6) e. Write the equation of the following line, horizontal through (0, ) f. Find the and y intercepts and the slope of the following equation 6 + y = 0. Which equation is represented by this graph? a. y > b. y + c. y + d. y +. Graphing Relations, Domain & Range: For the following relation: f() = a. State if it is a function b. State the domain and range c. Graph it. Find the Verte, and the -intercepts a. y = -( ) - c. y = ( + ) + b. y = + 4 d. y = - 4. Identify the conic section and put in standard form a. Find the equation of the circle with center (-7, ) and radius 0 b. Write in standard form y 4 8y 6 Saved C: Accuplacer College Level Math Assessment Page 4 of 7

5 . Systems of Equations and Matrices: Perform the indicated operation y z 8 y 4 0 a. Solve the system b. Solve the system y z 0 y y z 0 c. Multiply d. Find the determinant: e. Find the inverse f. Perform the indicated operation: 6 6. Use the graph below to answer the question that follows. Which of the following equations represents line AB? A. y = + B. y = + C. y = + D. y = + 7. Use the graph below to answer the question that follows. Which of the following inequalities describes the shaded region? A. y < 4 B. C. y 4 D. y 4 Saved C: Accuplacer College Level Math Assessment Page of 7

6 8. Which of the following graphs shows the solution of y + + = 0 and y = A. B. C. D. 9. Use the diagram below to answer the question that follows. A window is rectangular with a triangular top section. What is the total area of glass needed for the window? A. 4 square feet B. 0 square feet C. 6 square feet D. 48 square feet Saved C: Accuplacer College Level Math Assessment Page 6 of 7

7 0. Use the diagram below to answer the question that follows. The drawing above represents a race track. The ends are semicircular. What is the approimate distance in meters a runner runs in 8 laps around the track? A. 60 m B m C m D. 70 m. An observatory dome is hemispherical in shape with a radius of 8 meters and is built using equal sections. Which of the following formulas describes the surface area of each section? A. B. C. D.. Use the diagram below to answer the question that follows. A ramp feet long is leaning against a raised platform which is feet above the ground. What is the distance from the ramp's contact point with the ground and the base of the platform? A. 7 feet B. 8. feet C. feet D. feet. Figure ABCDE is similar to figure FGHIJ. If AE =, FJ = 0, and BC = 40, what is GH? A. 0 B. C. 4 D If pentagon ABCDE is similar to pentagon GHIDF, and DI = 0, CD = 0, and DE = 4, what is DF? A.. B. C. 8 D. Saved C: Accuplacer College Level Math Assessment Page 7 of 7

8 . Use the diagram below to answer the question that follows. Line AB is parallel to line CD. What is the sum of the measure of angle k and the measure of angle y? A. 90 B. 00 C. 80 D Use the diagram below to answer the question that follows. If ABD is an equilateral triangle, and line BD is parallel to line CE, what is the measure of angle? A. 60 B. 90 C. 0 D Use the diagram below to answer the question that follows. A rectangular bo has dimensions feet feet feet. What is the length of the longest object that can be put in the bo, if the object can be placed in any position? A..6 feet B..9 feet C. 6. feet D.. feet Saved C: Accuplacer College Level Math Assessment Page 8 of 7

9 8. Use the pie charts below to answer the question that follows. The first pie chart represents a company's ependitures, and the second pie chart shows a breakdown of the company's advertising ependitures. What percent of the company's ependitures is spent on radio advertising? A. 6.% B..7% C. 8.0% D..0% 9. The SINE of angle B is? A a. BC AC b. AC AB c. AB BC d. AB AC C B 40. Which equation is represented by this graph? a. y > b. y > c. y d. y + 4 Saved C: Accuplacer College Level Math Assessment Page 9 of 7

10 Graphing Formulas Slope-Intercept y = m + b slope y-intercept Point-Slope y - y = m( - ) Two-Point Formula y y For finding the equation of the line {You can use this formula, when you don t Know the slope, to find the equation of the line} y y Slope-Formula m = y - y - ( ) Standard Form a + by = c of a linear equation y-intercept = c Slope = -a b b Standard Form of a + b + c = 0 or f() = a( - h) + k a quadratic equation where (h,k) is the verte Quadratic Formula = -b b - 4ac a Verte Formula = -b a Circle Formula ( - h) + (y - k) = r where (h,k) is the center and (,y) is any point on the circle Midpoint Formula y +y, Distance Formula d = ( - ) (y - y ) Saved C: Accuplacer College Level Math Assessment Page 0 of 7

11 Geometric Figures & Formulas Square Area = Perimeter = 4s Rectangle Area = w Perimeter = + w Triangle Area = bh Right triangle Pythagorean formula: Circle Area = Circumference = Diameter = r r Sphere Surface area = 4 Volume = Cube Surface area = Volume = Rectangular solid Surface area = w + h + wh Volume = wh Right circular cylinder Surface area = rh + Volume = h Saved C: Geometric Figures Microsoftword Saved C: Accuplacer College Level Math Assessment Page of 7

12 BASIC ALGEBRA RULES Order of Division Multiplication & Division Addition & Subtraction Order of Operations a (-)(+) = - b = a b = b a (-)(-) = + (+) (-) = - (-) (+) = = + 8 = 8 + = +8 = + P (innermost) E (eponents) M & D (left right) A & S (left right) a + 0 = a Addition by zero identity a + b = b + a Commutative property of addition (a + b) + c = a + (b + c) Associate property of addition a + (-a) = -a + a = 0 Inverse property of addition a 0 = 0 a = 0 Multiplication by zero identity a = a = a Multiplication by one identity a b = b a Commutative property of multiplication a a = a a = = Multiplicative inverse (reciprocal) (a b) c = a (b c) Associate property of multiplication Eponent Rules 6 ( ) 0 a = 0 a a = a 0 = undefined a = a = a b = a b ab = a b a = aa = a > < X X X = = = 4 = 8 = 9 = = = 64 = = = = = = = = = = = = 000 = = = 44 = 78 = 69 = = = 744 = = 7 Saved C: Accuplacer College Level Math Assessment Page of 7

13 ANSWER KEY. Factor the following Polynomials {p. 0 #, } & {p.8 #,,} & {p.6 EX# } Sum of Two Cubes Difference of Two Cubes ( a b )( a ab b ) ( a b )( a ab b ) a. ( 4 ) b. ( )( + ) c. ( + )( + 9) d. (a + )(b + ) e. ( - )( + ) f. ( + )( + ) a. Perform the indicated operation {p.96 #48, 49, 6, 6, 8, 8} a. 4 8y 6 d. 4 0y b. 6 e. b 6 y 4 9 c. 9 a 4ab 6b f Simplify the following Epressions { p. #, 7} &{p.7 #9, 4} a. 48 c. 4 b. - d. 4. Solve each linear equation {p.6 #8,, 6} & {p.44 #} a. {-} c. w = p b. /6 d. {-8}. Solve each word problem {p.48 E#, 4} & {p. #, } & {p.8 #49} a. distance level distance + hilly distance 98 = = b. money in nickels + money in dimes = total money (0 ) =.8 = {number of nickels} c. + ( + ) + ( + ) = + = 0 d. \$4,000 at 8% and \$0,000 at 9% 6. Solve the following Quadratic Equations {p.8 #, 7, 6, } a. {-6, } b. {, - + } c. {-0, } d , 7. Solve the following Radical Equations {p.6 EX#,, 4, } a. = 4 b. = -9 c. = d. = /9 Saved C: Accuplacer College Level Math Assessment Page of 7

14 ANSWER KEY 8. Rational Epressions: Perform the indicated operation {p.80 #47, 0,, 7} 0 a. b. ( )( ) c. a 4a a d. a 8 4aa ( ) 9. Rational Epressions: Solve the following equations {p.79#,,, 7} a. = 7 b. = - c. = d. = - 0. Solve the following absolute value equations {p.6 EX#, 4, 7, 8} a. {4, -0} b. The absolute value of any epression is never negative. c. {-, } d. {/4, }. Eponentials & Radicals: Simplify the following epressions {p.4 #, 49, 64, 87} a. 4 b. 7 c. ab 7 d.. Eponents & Radicals: Perform the indicated operation {p.6 #4, 8} & {p.0 #, 6} a. 0 b. c. y y d Imaginary Numbers (i): Perform the indicated operation {p.7#, 9,, 8,, 7, 4, 49} Note: to simplify imaginary eponents use the chart below. Remainder = Answer 0 = = i = - = -i Step Divide the eponent by 4 Step The remainder gives you the answer. a. i 6 b. 6 4i c. 8 + i d. 0 8 e. i f. g. 6 h Simplify the following comple fractions {purplemath.com} a. 4 b. y c. 4 t d. t. Functions: Perform the indicated operation {p. 90 E# } a. 4 b. c. - + d. all real numbers ecept 6. Functions: Find the Following {p.9 EX# 4} a. b. Saved C: Accuplacer College Level Math Assessment Page 4 of 7

15 The linked image cannot be displayed. The file may have been moved, renamed, or deleted. Verify that the link points to the correct file and location. 7. Sequence & Series: Evaluate {p. E#} & {p.9 E# } & {p. EX#4} 6 i a. = 0 4 i0 Answer Key 6 = ( ) = 7 0 b. i i 4 = = = 6 n c. S n ( a an ) = ( ) ( ) d. S n a( r r n 6 ) ( ) ( 6) = S 6 8. Logarithmic & Eponential Functions: Perform the indicated operation{p.07 #7,, 4,, 6, 8, 40, 46, 4, 68} To find the inverse Step Replace f() with y Step Interchange and y Step Solve the equation for y ( 4) a. f ( ) b. f ( ) 6 f. log 7 49 g. 4 c. { } d. {-} e. 7 6 h. log i. log log ( ) j. e 9. Solve the following inequalities {p.6 E#} & {p. 69 EX#,, } 9 a. b. 9 c. d. 0. Graphing Linear Equations {p. #,} & {p.0 #9, 4, 4} a. 9 b. y c. 4 y = 4 d. = e. y = f. -intercept (, 0) y-intercept (0, 6) slope = 6 Saved C: Accuplacer College Level Math Assessment Page of 7

16 . C. y + {Taken from internet Site Purple Math.com } Answer Key. Graphing Relations: Find the Domain and Range {purplemath.com } a. yes b. Domain [/, ) & Range [0, ) c.. Find the verte, and the intercepts {p.87 #6,,, } a. verte (, -) there are no -intercepts b. verte (-, -9) and the -intercepts are = - and = c. verte (-, ) there are no -intercepts d. verte (, -6) and the -intercepts are = and = - 4. Identify the conic section and put in standard form {p.86 EX# 7, 8} a. ( h) ( y k) r ( 7) ( y ) 00 b. You must complete the square, to get the equation in standard form. ( ) ( y 4) 6. Systems of Equations and Matrices: Perform the indicated operation {p.44 # 7,,} & Aims Ditto y z 8 y 4 0 a. answer is {, } b. y z 0 answer is {6, -, 4} y y z c. Multiply The Answer is = 4 0 d. Find the determinant 7 ad bc = (7) ()(-) = + = 6 e. Find the inverse of The Answer is = A 7. C 8. C 9. B f. Perform the indicated operation 6 The Answer is = -8 4 Saved C: Accuplacer College Level Math Assessment Page 6 of 7

17 Answer Key 0. C. Step Step Find the perimeter of the rectangle Find the circumference of the circle P = L + W C = d P = (00) + (0) C =.4(0) P = C = 7. D. C. D 4. C. C 6. C P = 400 Step (400 8 laps) + (7 8 laps) = 446 Note: When finding the perimeter of composite figures you must delete the side they share from one of the equations, it you don t you ll end up counting that side twice, and your answer will be wrong. That s why, 00 was deleted from the perimeter of the rectangle. The rectangle and the circle share that side, so it was deleted from one of the formulas. 7. B Step This is an unusual problem to solve because you are dealing with the concept of -dimensions, which usually isn t covered in great detail until you reach calculus II or III. Since, we are trying to squeeze the object into the bo, we are trying to find the longest diagonal line within the bo. So, to solve this problem you need to use the following formula: D +y +z You can also write your formula this way D = l w h D +y +z D = () () (.) D D. D =.9 feet 8. A. Step You have to find 8% of %, so make % your base. 8% of is what? 8 a 00 a = 6. A 9. D. SINE = opposite hypotenuse The answer is SINE = AC AB opposite hypotenuse C Adjacent B 40. B. {do not pick choice C the inequality sign is incorrect} Problems taken from Math 00 Tetbook Intermediate Algebra by K. Elayn Martin-Gay99, & Purplemath.com, and THEA Test Saved C: Accuplacer College Level Math Assessment Page 7 of 7

### Review of Intermediate Algebra Content

Review of Intermediate Algebra Content Table of Contents Page Factoring GCF and Trinomials of the Form + b + c... Factoring Trinomials of the Form a + b + c... Factoring Perfect Square Trinomials... 6

### Math 0980 Chapter Objectives. Chapter 1: Introduction to Algebra: The Integers.

Math 0980 Chapter Objectives Chapter 1: Introduction to Algebra: The Integers. 1. Identify the place value of a digit. 2. Write a number in words or digits. 3. Write positive and negative numbers used

### Students Currently in Algebra 2 Maine East Math Placement Exam Review Problems

Students Currently in Algebra Maine East Math Placement Eam Review Problems The actual placement eam has 100 questions 3 hours. The placement eam is free response students must solve questions and write

### MEMORANDUM. All students taking the CLC Math Placement Exam PLACEMENT INTO CALCULUS AND ANALYTIC GEOMETRY I, MTH 145:

MEMORANDUM To: All students taking the CLC Math Placement Eam From: CLC Mathematics Department Subject: What to epect on the Placement Eam Date: April 0 Placement into MTH 45 Solutions This memo is an

### MATH 60 NOTEBOOK CERTIFICATIONS

MATH 60 NOTEBOOK CERTIFICATIONS Chapter #1: Integers and Real Numbers 1.1a 1.1b 1.2 1.3 1.4 1.8 Chapter #2: Algebraic Expressions, Linear Equations, and Applications 2.1a 2.1b 2.1c 2.2 2.3a 2.3b 2.4 2.5

### MATHCOUNTS TOOLBOX Facts, Formulas and Tricks

MATHCOUNTS TOOLBOX Facts, Formulas and Tricks MATHCOUNTS Coaching Kit 40 I. PRIME NUMBERS from 1 through 100 (1 is not prime!) 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97 II.

### of surface, 569-571, 576-577, 578-581 of triangle, 548 Associative Property of addition, 12, 331 of multiplication, 18, 433

Absolute Value and arithmetic, 730-733 defined, 730 Acute angle, 477 Acute triangle, 497 Addend, 12 Addition associative property of, (see Commutative Property) carrying in, 11, 92 commutative property

### 3 e) x f) 2. Precalculus Worksheet P.1. 1. Complete the following questions from your textbook: p11: #5 10. 2. Why would you never write 5 < x > 7?

Precalculus Worksheet P.1 1. Complete the following questions from your tetbook: p11: #5 10. Why would you never write 5 < > 7? 3. Why would you never write 3 > > 8? 4. Describe the graphs below using

### Expression. Variable Equation Polynomial Monomial Add. Area. Volume Surface Space Length Width. Probability. Chance Random Likely Possibility Odds

Isosceles Triangle Congruent Leg Side Expression Equation Polynomial Monomial Radical Square Root Check Times Itself Function Relation One Domain Range Area Volume Surface Space Length Width Quantitative

### Mathematics Placement Examination (MPE)

Practice Problems for Mathematics Placement Eamination (MPE) Revised August, 04 When you come to New Meico State University, you may be asked to take the Mathematics Placement Eamination (MPE) Your inital

### MATH 095, College Prep Mathematics: Unit Coverage Pre-algebra topics (arithmetic skills) offered through BSE (Basic Skills Education)

MATH 095, College Prep Mathematics: Unit Coverage Pre-algebra topics (arithmetic skills) offered through BSE (Basic Skills Education) Accurately add, subtract, multiply, and divide whole numbers, integers,

### Higher Education Math Placement

Higher Education Math Placement Placement Assessment Problem Types 1. Whole Numbers, Fractions, and Decimals 1.1 Operations with Whole Numbers Addition with carry Subtraction with borrowing Multiplication

### SUNY ECC. ACCUPLACER Preparation Workshop. Algebra Skills

SUNY ECC ACCUPLACER Preparation Workshop Algebra Skills Gail A. Butler Ph.D. Evaluating Algebraic Epressions Substitute the value (#) in place of the letter (variable). Follow order of operations!!! E)

### COMPETENCY TEST SAMPLE TEST. A scientific, non-graphing calculator is required for this test. C = pd or. A = pr 2. A = 1 2 bh

BASIC MATHEMATICS COMPETENCY TEST SAMPLE TEST 2004 A scientific, non-graphing calculator is required for this test. The following formulas may be used on this test: Circumference of a circle: C = pd or

### Graphing Trigonometric Skills

Name Period Date Show all work neatly on separate paper. (You may use both sides of your paper.) Problems should be labeled clearly. If I can t find a problem, I ll assume it s not there, so USE THE TEMPLATE

### Summer Math Exercises. For students who are entering. Pre-Calculus

Summer Math Eercises For students who are entering Pre-Calculus It has been discovered that idle students lose learning over the summer months. To help you succeed net fall and perhaps to help you learn

### MATH 100 PRACTICE FINAL EXAM

MATH 100 PRACTICE FINAL EXAM Lecture Version Name: ID Number: Instructor: Section: Do not open this booklet until told to do so! On the separate answer sheet, fill in your name and identification number

### Algebra Geometry Glossary. 90 angle

lgebra Geometry Glossary 1) acute angle an angle less than 90 acute angle 90 angle 2) acute triangle a triangle where all angles are less than 90 3) adjacent angles angles that share a common leg Example:

### ( ) ( ) Math 0310 Final Exam Review. # Problem Section Answer. 1. Factor completely: 2. 2. Factor completely: 3. Factor completely:

Math 00 Final Eam Review # Problem Section Answer. Factor completely: 6y+. ( y+ ). Factor completely: y+ + y+ ( ) ( ). ( + )( y+ ). Factor completely: a b 6ay + by. ( a b)( y). Factor completely: 6. (

### Math Placement Test Study Guide. 2. The test consists entirely of multiple choice questions, each with five choices.

Math Placement Test Study Guide General Characteristics of the Test 1. All items are to be completed by all students. The items are roughly ordered from elementary to advanced. The expectation is that

### Midterm 2 Review Problems (the first 7 pages) Math 123-5116 Intermediate Algebra Online Spring 2013

Midterm Review Problems (the first 7 pages) Math 1-5116 Intermediate Algebra Online Spring 01 Please note that these review problems are due on the day of the midterm, Friday, April 1, 01 at 6 p.m. in

### SAT Subject Math Level 2 Facts & Formulas

Numbers, Sequences, Factors Integers:..., -3, -2, -1, 0, 1, 2, 3,... Reals: integers plus fractions, decimals, and irrationals ( 2, 3, π, etc.) Order Of Operations: Arithmetic Sequences: PEMDAS (Parentheses

### MTH 100 College Algebra Essex County College Division of Mathematics Sample Review Questions 1 Created June 6, 2011

MTH 00 College Algebra Essex County College Division of Mathematics Sample Review Questions Created June 6, 0 Math 00, Introductory College Mathematics, covers the mathematical content listed below. In

### SAT Math Hard Practice Quiz. 5. How many integers between 10 and 500 begin and end in 3?

SAT Math Hard Practice Quiz Numbers and Operations 5. How many integers between 10 and 500 begin and end in 3? 1. A bag contains tomatoes that are either green or red. The ratio of green tomatoes to red

### Anchorage School District/Alaska Sr. High Math Performance Standards Algebra

Anchorage School District/Alaska Sr. High Math Performance Standards Algebra Algebra 1 2008 STANDARDS PERFORMANCE STANDARDS A1:1 Number Sense.1 Classify numbers as Real, Irrational, Rational, Integer,

### Scope and Sequence KA KB 1A 1B 2A 2B 3A 3B 4A 4B 5A 5B 6A 6B

Scope and Sequence Earlybird Kindergarten, Standards Edition Primary Mathematics, Standards Edition Copyright 2008 [SingaporeMath.com Inc.] The check mark indicates where the topic is first introduced

### ACT Math Vocabulary. Altitude The height of a triangle that makes a 90-degree angle with the base of the triangle. Altitude

ACT Math Vocabular Acute When referring to an angle acute means less than 90 degrees. When referring to a triangle, acute means that all angles are less than 90 degrees. For eample: Altitude The height

### Algebra and Geometry Review (61 topics, no due date)

Course Name: Math 112 Credit Exam LA Tech University Course Code: ALEKS Course: Trigonometry Instructor: Course Dates: Course Content: 159 topics Algebra and Geometry Review (61 topics, no due date) Properties

### Exponential and Logarithmic Functions

Chapter 6 Eponential and Logarithmic Functions Section summaries Section 6.1 Composite Functions Some functions are constructed in several steps, where each of the individual steps is a function. For eample,

### A Quick Algebra Review

1. Simplifying Epressions. Solving Equations 3. Problem Solving 4. Inequalities 5. Absolute Values 6. Linear Equations 7. Systems of Equations 8. Laws of Eponents 9. Quadratics 10. Rationals 11. Radicals

### How To Understand And Solve Algebraic Equations

College Algebra Course Text Barnett, Raymond A., Michael R. Ziegler, and Karl E. Byleen. College Algebra, 8th edition, McGraw-Hill, 2008, ISBN: 978-0-07-286738-1 Course Description This course provides

### CSU Fresno Problem Solving Session. Geometry, 17 March 2012

CSU Fresno Problem Solving Session Problem Solving Sessions website: http://zimmer.csufresno.edu/ mnogin/mfd-prep.html Math Field Day date: Saturday, April 21, 2012 Math Field Day website: http://www.csufresno.edu/math/news

### Students will be able to simplify and evaluate numerical and variable expressions using appropriate properties and order of operations.

Outcome 1: (Introduction to Algebra) Skills/Content 1. Simplify numerical expressions: a). Use order of operations b). Use exponents Students will be able to simplify and evaluate numerical and variable

### Geometry and Measurement

The student will be able to: Geometry and Measurement 1. Demonstrate an understanding of the principles of geometry and measurement and operations using measurements Use the US system of measurement for

### 1) (-3) + (-6) = 2) (2) + (-5) = 3) (-7) + (-1) = 4) (-3) - (-6) = 5) (+2) - (+5) = 6) (-7) - (-4) = 7) (5)(-4) = 8) (-3)(-6) = 9) (-1)(2) =

Extra Practice for Lesson Add or subtract. ) (-3) + (-6) = 2) (2) + (-5) = 3) (-7) + (-) = 4) (-3) - (-6) = 5) (+2) - (+5) = 6) (-7) - (-4) = Multiply. 7) (5)(-4) = 8) (-3)(-6) = 9) (-)(2) = Division is

Advanced GMAT Math Questions Version Quantitative Fractions and Ratios 1. The current ratio of boys to girls at a certain school is to 5. If 1 additional boys were added to the school, the new ratio of

### Algebra I Credit Recovery

Algebra I Credit Recovery COURSE DESCRIPTION: The purpose of this course is to allow the student to gain mastery in working with and evaluating mathematical expressions, equations, graphs, and other topics,

### Algebra. Exponents. Absolute Value. Simplify each of the following as much as possible. 2x y x + y y. xxx 3. x x x xx x. 1. Evaluate 5 and 123

Algebra Eponents Simplify each of the following as much as possible. 1 4 9 4 y + y y. 1 5. 1 5 4. y + y 4 5 6 5. + 1 4 9 10 1 7 9 0 Absolute Value Evaluate 5 and 1. Eliminate the absolute value bars from

### Factoring Polynomials

UNIT 11 Factoring Polynomials You can use polynomials to describe framing for art. 396 Unit 11 factoring polynomials A polynomial is an expression that has variables that represent numbers. A number can

### McDougal Littell California:

McDougal Littell California: Pre-Algebra Algebra 1 correlated to the California Math Content s Grades 7 8 McDougal Littell California Pre-Algebra Components: Pupil Edition (PE), Teacher s Edition (TE),

### 1.1 Practice Worksheet

Math 1 MPS Instructor: Cheryl Jaeger Balm 1 1.1 Practice Worksheet 1. Write each English phrase as a mathematical expression. (a) Three less than twice a number (b) Four more than half of a number (c)

### GRADES 7, 8, AND 9 BIG IDEAS

Table 1: Strand A: BIG IDEAS: MATH: NUMBER Introduce perfect squares, square roots, and all applications Introduce rational numbers (positive and negative) Introduce the meaning of negative exponents for

### 135 Final Review. Determine whether the graph is symmetric with respect to the x-axis, the y-axis, and/or the origin.

13 Final Review Find the distance d(p1, P2) between the points P1 and P2. 1) P1 = (, -6); P2 = (7, -2) 2 12 2 12 3 Determine whether the graph is smmetric with respect to the -ais, the -ais, and/or the

### Algebra 1 Course Title

Algebra 1 Course Title Course- wide 1. What patterns and methods are being used? Course- wide 1. Students will be adept at solving and graphing linear and quadratic equations 2. Students will be adept

### Answer Key for California State Standards: Algebra I

Algebra I: Symbolic reasoning and calculations with symbols are central in algebra. Through the study of algebra, a student develops an understanding of the symbolic language of mathematics and the sciences.

### Administrative - Master Syllabus COVER SHEET

Administrative - Master Syllabus COVER SHEET Purpose: It is the intention of this to provide a general description of the course, outline the required elements of the course and to lay the foundation for

### Charlesworth School Year Group Maths Targets

Charlesworth School Year Group Maths Targets Year One Maths Target Sheet Key Statement KS1 Maths Targets (Expected) These skills must be secure to move beyond expected. I can compare, describe and solve

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

North Carolina Community College System Diagnostic and Placement Test Sample Questions 01 The College Board. College Board, ACCUPLACER, WritePlacer and the acorn logo are registered trademarks of the College

### EQUATIONS and INEQUALITIES

EQUATIONS and INEQUALITIES Linear Equations and Slope 1. Slope a. Calculate the slope of a line given two points b. Calculate the slope of a line parallel to a given line. c. Calculate the slope of a line

### Polynomial Degree and Finite Differences

CONDENSED LESSON 7.1 Polynomial Degree and Finite Differences In this lesson you will learn the terminology associated with polynomials use the finite differences method to determine the degree of a polynomial

### Prentice Hall Mathematics: Algebra 2 2007 Correlated to: Utah Core Curriculum for Math, Intermediate Algebra (Secondary)

Core Standards of the Course Standard 1 Students will acquire number sense and perform operations with real and complex numbers. Objective 1.1 Compute fluently and make reasonable estimates. 1. Simplify

### Lesson 18 Pythagorean Triples & Special Right Triangles

Student Name: Date: Contact Person Name: Phone Number: Teas Assessment of Knowledge and Skills Eit Level Math Review Lesson 18 Pythagorean Triples & Special Right Triangles TAKS Objective 6 Demonstrate

### Algebra 2 Year-at-a-Glance Leander ISD 2007-08. 1st Six Weeks 2nd Six Weeks 3rd Six Weeks 4th Six Weeks 5th Six Weeks 6th Six Weeks

Algebra 2 Year-at-a-Glance Leander ISD 2007-08 1st Six Weeks 2nd Six Weeks 3rd Six Weeks 4th Six Weeks 5th Six Weeks 6th Six Weeks Essential Unit of Study 6 weeks 3 weeks 3 weeks 6 weeks 3 weeks 3 weeks

### Vocabulary Words and Definitions for Algebra

Name: Period: Vocabulary Words and s for Algebra Absolute Value Additive Inverse Algebraic Expression Ascending Order Associative Property Axis of Symmetry Base Binomial Coefficient Combine Like Terms

### How do you compare numbers? On a number line, larger numbers are to the right and smaller numbers are to the left.

The verbal answers to all of the following questions should be memorized before completion of pre-algebra. Answers that are not memorized will hinder your ability to succeed in algebra 1. Number Basics

### Mathematics Placement

Mathematics Placement The ACT COMPASS math test is a self-adaptive test, which potentially tests students within four different levels of math including pre-algebra, algebra, college algebra, and trigonometry.

### What are the place values to the left of the decimal point and their associated powers of ten?

The verbal answers to all of the following questions should be memorized before completion of algebra. Answers that are not memorized will hinder your ability to succeed in geometry and algebra. (Everything

### Algebra Cheat Sheets

Sheets Algebra Cheat Sheets provide you with a tool for teaching your students note-taking, problem-solving, and organizational skills in the context of algebra lessons. These sheets teach the concepts

### POLYNOMIAL FUNCTIONS

POLYNOMIAL FUNCTIONS Polynomial Division.. 314 The Rational Zero Test.....317 Descarte s Rule of Signs... 319 The Remainder Theorem.....31 Finding all Zeros of a Polynomial Function.......33 Writing a

### CRLS Mathematics Department Algebra I Curriculum Map/Pacing Guide

Curriculum Map/Pacing Guide page 1 of 14 Quarter I start (CP & HN) 170 96 Unit 1: Number Sense and Operations 24 11 Totals Always Include 2 blocks for Review & Test Operating with Real Numbers: How are

Academic Content Standards Grade Eight and Grade Nine Ohio Algebra 1 2008 Grade Eight STANDARDS Number, Number Sense and Operations Standard Number and Number Systems 1. Use scientific notation to express

### Algebra I. In this technological age, mathematics is more important than ever. When students

In this technological age, mathematics is more important than ever. When students leave school, they are more and more likely to use mathematics in their work and everyday lives operating computer equipment,

### Definition 8.1 Two inequalities are equivalent if they have the same solution set. Add or Subtract the same value on both sides of the inequality.

8 Inequalities Concepts: Equivalent Inequalities Linear and Nonlinear Inequalities Absolute Value Inequalities (Sections 4.6 and 1.1) 8.1 Equivalent Inequalities Definition 8.1 Two inequalities are equivalent

### Algebra I Vocabulary Cards

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

### 10.1. Solving Quadratic Equations. Investigation: Rocket Science CONDENSED

CONDENSED L E S S O N 10.1 Solving Quadratic Equations In this lesson you will look at quadratic functions that model projectile motion use tables and graphs to approimate solutions to quadratic equations

### Brunswick High School has reinstated a summer math curriculum for students Algebra 1, Geometry, and Algebra 2 for the 2014-2015 school year.

Brunswick High School has reinstated a summer math curriculum for students Algebra 1, Geometry, and Algebra 2 for the 2014-2015 school year. Goal The goal of the summer math program is to help students

### MATH 0110 Developmental Math Skills Review, 1 Credit, 3 hours lab

MATH 0110 Developmental Math Skills Review, 1 Credit, 3 hours lab MATH 0110 is established to accommodate students desiring non-course based remediation in developmental mathematics. This structure will

### Thnkwell s Homeschool Precalculus Course Lesson Plan: 36 weeks

Thnkwell s Homeschool Precalculus Course Lesson Plan: 36 weeks Welcome to Thinkwell s Homeschool Precalculus! We re thrilled that you ve decided to make us part of your homeschool curriculum. This lesson

### MPE Review Section III: Logarithmic & Exponential Functions

MPE Review Section III: Logarithmic & Eponential Functions FUNCTIONS AND GRAPHS To specify a function y f (, one must give a collection of numbers D, called the domain of the function, and a procedure

### 1. Mathematics Content/Alignment with the Standards Correlation to California Algebra Readiness Standards

PROGRAM DESCRIPTION The goal of Prentice Hall Connecting to Algebra is to fully prepare students for success in Algebra 1 by thoroughly covering the Algebra Readiness standards outlined by the California

### SAT Math Facts & Formulas Review Quiz

Test your knowledge of SAT math facts, formulas, and vocabulary with the following quiz. Some questions are more challenging, just like a few of the questions that you ll encounter on the SAT; these questions

### CAMI Education linked to CAPS: Mathematics

- 1 - TOPIC 1.1 Whole numbers _CAPS curriculum TERM 1 CONTENT Mental calculations Revise: Multiplication of whole numbers to at least 12 12 Ordering and comparing whole numbers Revise prime numbers to

### Algebra 1 Course Information

Course Information Course Description: Students will study patterns, relations, and functions, and focus on the use of mathematical models to understand and analyze quantitative relationships. Through

### Indicator 2: Use a variety of algebraic concepts and methods to solve equations and inequalities.

3 rd Grade Math Learning Targets Algebra: Indicator 1: Use procedures to transform algebraic expressions. 3.A.1.1. Students are able to explain the relationship between repeated addition and multiplication.

### Math 0306 Final Exam Review

Math 006 Final Exam Review Problem Section Answers Whole Numbers 1. According to the 1990 census, the population of Nebraska is 1,8,8, the population of Nevada is 1,01,8, the population of New Hampshire

### MATD 0390 - Intermediate Algebra Review for Pretest

MATD 090 - Intermediate Algebra Review for Pretest. Evaluate: a) - b) - c) (-) d) 0. Evaluate: [ - ( - )]. Evaluate: - -(-7) + (-8). Evaluate: - - + [6 - ( - 9)]. Simplify: [x - (x - )] 6. Solve: -(x +

### IV. ALGEBRAIC CONCEPTS

IV. ALGEBRAIC CONCEPTS Algebra is the language of mathematics. Much of the observable world can be characterized as having patterned regularity where a change in one quantity results in changes in other

### Sample Test Questions

mathematics College Algebra Geometry Trigonometry Sample Test Questions A Guide for Students and Parents act.org/compass Note to Students Welcome to the ACT Compass Sample Mathematics Test! You are about

### Section 1.1 Linear Equations: Slope and Equations of Lines

Section. Linear Equations: Slope and Equations of Lines Slope The measure of the steepness of a line is called the slope of the line. It is the amount of change in y, the rise, divided by the amount of

### SAT Subject Math Level 1 Facts & Formulas

Numbers, Sequences, Factors Integers:..., -3, -2, -1, 0, 1, 2, 3,... Reals: integers plus fractions, decimals, and irrationals ( 2, 3, π, etc.) Order Of Operations: Aritmetic Sequences: PEMDAS (Parenteses

### SAT Math Strategies Quiz

When you are stumped on an SAT or ACT math question, there are two very useful strategies that may help you to get the correct answer: 1) work with the answers; and 2) plug in real numbers. This review

### Florida Math 0028. Correlation of the ALEKS course Florida Math 0028 to the Florida Mathematics Competencies - Upper

Florida Math 0028 Correlation of the ALEKS course Florida Math 0028 to the Florida Mathematics Competencies - Upper Exponents & Polynomials MDECU1: Applies the order of operations to evaluate algebraic

### Biggar High School Mathematics Department. National 5 Learning Intentions & Success Criteria: Assessing My Progress

Biggar High School Mathematics Department National 5 Learning Intentions & Success Criteria: Assessing My Progress Expressions & Formulae Topic Learning Intention Success Criteria I understand this Approximation

### Teacher Page Key. Geometry / Day # 13 Composite Figures 45 Min.

Teacher Page Key Geometry / Day # 13 Composite Figures 45 Min. 9-1.G.1. Find the area and perimeter of a geometric figure composed of a combination of two or more rectangles, triangles, and/or semicircles

### Glencoe. correlated to SOUTH CAROLINA MATH CURRICULUM STANDARDS GRADE 6 3-3, 5-8 8-4, 8-7 1-6, 4-9

Glencoe correlated to SOUTH CAROLINA MATH CURRICULUM STANDARDS GRADE 6 STANDARDS 6-8 Number and Operations (NO) Standard I. Understand numbers, ways of representing numbers, relationships among numbers,

### IOWA End-of-Course Assessment Programs. Released Items ALGEBRA I. Copyright 2010 by The University of Iowa.

IOWA End-of-Course Assessment Programs Released Items Copyright 2010 by The University of Iowa. ALGEBRA I 1 Sally works as a car salesperson and earns a monthly salary of \$2,000. She also earns \$500 for

9.3 Solving Quadratic Equations by Using the Quadratic Formula 9.3 OBJECTIVES 1. Solve a quadratic equation by using the quadratic formula 2. Determine the nature of the solutions of a quadratic equation

### Unit 1: Integers and Fractions

Unit 1: Integers and Fractions No Calculators!!! Order Pages (All in CC7 Vol. 1) 3-1 Integers & Absolute Value 191-194, 203-206, 195-198, 207-210 3-2 Add Integers 3-3 Subtract Integers 215-222 3-4 Multiply

### FCAT FLORIDA COMPREHENSIVE ASSESSMENT TEST. Mathematics Reference Sheets. Copyright Statement for this Assessment and Evaluation Services Publication

FCAT FLORIDA COMPREHENSIVE ASSESSMENT TEST Mathematics Reference Sheets Copyright Statement for this Assessment and Evaluation Services Publication Authorization for reproduction of this document is hereby

### The GED math test gives you a page of math formulas that

Math Smart 643 The GED Math Formulas The GED math test gives you a page of math formulas that you can use on the test, but just seeing the formulas doesn t do you any good. The important thing is understanding

### Quick Reference ebook

This file is distributed FREE OF CHARGE by the publisher Quick Reference Handbooks and the author. Quick Reference ebook Click on Contents or Index in the left panel to locate a topic. The math facts listed

### 13. Write the decimal approximation of 9,000,001 9,000,000, rounded to three significant

æ If 3 + 4 = x, then x = 2 gold bar is a rectangular solid measuring 2 3 4 It is melted down, and three equal cubes are constructed from this gold What is the length of a side of each cube? 3 What is the

### http://www.castlelearning.com/review/teacher/assignmentprinting.aspx 5. 2 6. 2 1. 10 3. 70 2. 55 4. 180 7. 2 8. 4

of 9 1/28/2013 8:32 PM Teacher: Mr. Sime Name: 2 What is the slope of the graph of the equation y = 2x? 5. 2 If the ratio of the measures of corresponding sides of two similar triangles is 4:9, then the

### MATH 21. College Algebra 1 Lecture Notes

MATH 21 College Algebra 1 Lecture Notes MATH 21 3.6 Factoring Review College Algebra 1 Factoring and Foiling 1. (a + b) 2 = a 2 + 2ab + b 2. 2. (a b) 2 = a 2 2ab + b 2. 3. (a + b)(a b) = a 2 b 2. 4. (a

### ALGEBRA I (Common Core) Tuesday, June 3, 2014 9:15 a.m. to 12:15 p.m., only

ALGEBRA I (COMMON CORE) The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION ALGEBRA I (Common Core) Tuesday, June 3, 2014 9:15 a.m. to 12:15 p.m., only Student Name: School Name: The

### ACT Math Facts & Formulas

Numbers, Sequences, Factors Integers:..., -3, -2, -1, 0, 1, 2, 3,... Rationals: fractions, tat is, anyting expressable as a ratio of integers Reals: integers plus rationals plus special numbers suc as