Summer Math Packet (revised 2017)


 Derek Ray
 5 years ago
 Views:
Transcription
1 Summer Math Packet (revised 07) In preparation for Honors Math III, we have prepared a packet of concepts that students should know how to do as these concepts have been taught in previous math classes. This packet does not require ou to use a calculator; in fact ou should not use a calculator on some of the problem sets where it is noted. Honors Math III builds on the concepts in this packet, and we start teaching Math III concepts on the first da of school. We epect ou to know the concepts in the packet in order to help ou be successful in Honors Math III. Although ou do not have to complete ever problem in this packet, ou will be held responsible for knowing how to complete them all and the content/skills used. Answer kes are included at the end of this packet to check our understanding. If ou are struggling with an content from this packet, get help from a friend, parent, peer, or tutor. If ou can t find someone to help ou, there are tutors available. A list of tutors can be found b calling Reagan High School or from Reagan s Student Services website. Keep in mind these tutors ma charge a fee. You can also go to outube.com and tpe in the name of the concept and watch videos of math teachers and tutors eplain the concepts for FREE!!!! You will have a graded assignment within the first two weeks of school. The graded assignment will cover the concepts/skills in the packet, but will not have the eact same problems. The graded assignment will contain a calculator inactive part so be prepared b following instructions where calculators are not allowed. You will be able to use our packet with completed problems as a resource on the assessment at the beginning of the ear so it is in our best interest to complete as needed. The packet s answer ke section ma not be used on the graded assessment. TABLE OF CONTENTS: ) Vocabular & Important Things to Remember page (KEY p. 90) ) Operations with Fractions page (KEY p. ) ) Solving Equations & Inequalities page (KEY p. ) ) Linear Equations page (KEY p. ) ) Graphing Linear Equations & Inequalities page 6 (KEY p. ) 6) Sstems of Equations page 8 (KEY p. 7) 7) Laws of Eponents page 0 (KEY p. 9) 8) Polnomial Operations page (KEY p. 0) 9) Radicals & & Rational Eponents page (KEY p. ) 0) Using Function Notation (with numbers & variables; word problems) page (KEY p. ) ) Solving Quadratic Equations (Quadratic Formula, Factoring, page (KEY p. ) Square Root Propert & Completing the Square) ) Using Midpoint & Distance Formulas page (KEY p. ) ) Proving Congruent Triangles page 6 (KEY p. ) ) Transformations (using absolute value graphs) page 7 (KEY p. 6) ) ANSWER KEYS page 8
2 ) Vocabular/Know the Difference Review. Proportions vs. multipling fractions Proportion 8 vs.. * =? vs. + =? Multipling Fractions 8. order of operations: don t be tricked b these common mistaken identities a. * vs. ( * ) b. + ( + ) c. 8 vs. (8). ( 9) vs. ( + 9) vs. ( 9)( + 9) a. ( 9) = b. ( + 9) = c. ( 9)( + 9) =. know the difference between a term, epression, equation, and inequalit term epression equation inequalit 6. know the difference between solve, evaluate and simplif simplif evaluate solve 7. know the difference between rational and irrational rational irrational 8. know the > and < smbols b name: 9. know coefficient 0. know factor. reduce factors not individual terms
3 ) Operations with Fractions DO NOT USE A CALCULATOR ) 9 ) 7 ) 6 ) 9 ) 7 6) 6 7) 9 8) 7 9) 6
4 ) Solve Equations and Inequalities DO NOT USE A CALCULATOR Clear out fractions. 7 ) 7 ) 7 ) a a a 8 6 Variables on both sides. ) ( 8 ) + ( + ) = ) 8 + ( a ) = ( a + ) 6) 6 + = Solve inequalities and graph our answer. When ou multipl or divide both sides b a negative remember to flip the inequalit. Get variable on the left. 6 8) 6 6 7) Word Problems  You must be able to write the equation or inequalit first. Then solve for the variable. 9) The greater of two numbers is 6 more than times the smaller. Their sum is. Find the numbers. 0) Find three consecutive integers whose sum is 0. ) Find three consecutive even integers whose sum is 8. ) The length of a rectangle is feet more than its width. If its perimeter is 0 feet, find the length & width. ) The second angle in a triangle is less than twice the first angle. The third angle measure 8 more than twice the first angle. Find each angle. ) Jeffer has grades of 9 and 8 on the st tests of the quarter. Progress reports go home after the rd test. If Jeffer does not have an A average on his progress report, he cannot go to the football game that week. Jeffer will have to make at least what grade on the third test to be allowed to go to the football game?
5 ) Linear Equations: Slope, Writing Linear Equations, Horizontal & Vertical, Parallel & Perpendicular Find the slope (rate of change) of the following problems., 8,.,. Da Temperature. ( F ) The cost of museum tickets is $8 for four people and $78 for 0 people. What is the cost per person? Write the equation of the line in slopeintercept form & standard form given the following.., m 6., 7 m 7., 6, 8. m =, b = 9. (, ) m = 0 0. (, ) m = undefined.. The cost for 7 dance lessons is $8. The cost for lessons is $. Write a linear equation to find the total cost C for L dance lessons. Then use the equation to find the cost of lessons.
6 . Write the equation for a vertical line that goes through the point (, ).. Write the equation for a horizontal line that goes through the point (, ). Solve the equation for if necessar, and find the slope. Then, find the slope of a line parallel and perpendicular to the original line. SLOPE PARALLEL PERPENDICULAR. + 6 = 8 6. = 7. =  Write the answers for 80 in slope intercept and standard forms. 8. Write the equation for the line parallel to the given line = 9 and and through the point (, ). 9. Write the equation for the line perpendicular to the given line = 9 and through the point (8, ). 0. Given a line through (, ) and (8, ), find the equation of the line perpendicular to that line through the midpoint of those points.
7 ) Graphing Linear Equations and Inequalities DO NOT USE A CALCULATOR Graph each of the following lines. ) slope:,, through, ) slope:, through ) slope:, intercept: ) slope:, intercept: ) 6) 7) 6 8) 9) 7 0) ) 6 ) 0 6
8 ) ) 7 ) 6) 7) no slope; through (, ) 8) slope: 0 through (, 7) Write each of the following in slopeintercept form: ( m b) 9) A computer technician charges $7 for a consultation plus $ per hour. 0) The population of Pine Bluff is 679 and is decreasing at the rate of 7 per ear. ) A video store charges $0 for a rental card plus a $ per rental. Graph each inequalit. Remember to use either a solid or dotted line, then SHADE. ) < ) > ) < 7
9 8 6) Sstems of Equations IF THE LINES INTERSECT ONCE, ANSWER IS THE ORDERED PAIR. IF THE LINES DO NOT INTERSECT (PARALLEL), ANSWER IS. IF THE LINES ALWAYS TOUCH (ARE THE SAME LINE), ANSWER IS INFINITLY MANY. Solve b graphing. ) 6 ) 0 ) 8 ) ) 6) 8 6 9
10 9 Solve using Substitution or Elimination. 7) 8) 9) 0) ) 7 ) 6 ) 6 ) 0
11 7) Laws of Eponents (negative eponents should alwas be simplified) (Remember: a b ab, a b ab ( ), a b ab, 0 and a a ) a b a 7 b ) z z ) a b b c a c ) ) 0 ) c c 7) ac bc ab 6) 8) a b 9) 6 0 a b 0 0) ) ) 0 () ) a b ab 7 8 8a b ) 0 a b ) ) 0 7) 7 8) 9) 6 0) 6 ) a 9 8 ) 7 ) ) ( 0 ) 0
12 8) Polnomial Operations Simplif. ) (6 ) ) ab ab a b ) 6 ( 7 ) ) 8 ) 6) 6 7) 8) n 8n 8 9) 6w w 7w 0) 8 ) m mp 6 p m mp p
13 9) Radical & Rational Eponents Simplif a a a 9. z z... Rational Eponents See these as eamples of rational eponents: DO NOT USE A CALCULATOR = = 8 = 8 Simplif the following Write as a rational eponent:
14 0) Using Function Notation State whether each set is a function. Answer es or no. Find the domain and the range. ) {(, ), (, 6), (, 6), (, 8)} Domain: Range: ) {(, ), (8, ), (, 8), (, )} Domain: Range: Use the vertical line test to determine whether each graph is the graph of a function. Answer es or no. ) ) ) 6) f g Use and 7) f 8) to find each value. g 7 9) f f 8 0) ) f c ) gw 7 ) f m ) g ) The temperature of the atmosphere decreases about o F for ever 000 feet increase in altitude. Thus, if the temperature at ground level is 77 o F, the temperature t at a given altitude is found b using the equation t 77.00h, where h is the height in feet. a) Write the equation in function notation where t is a function of h [f() is meant as f is a function of ]. b) Find t(00) and eplain its meaning in this problem. g 6) The function 60. models the weight gain of a basketball plaer as he starts a workout program where g is the weight in pounds after weeks. a) Eplain the meaning of 60 in the contet of this problem. b) Eplain the meaning of. in the contet of this problem. c) Evaluate g 6 and eplain its meaning.
15 ) Solving Quadratic Equations Should be able to use: Square Root Propert Factoring (Remember when equation must be set = 0 before solving) Completing the Square [ a + b + c = 0 ] Quadratic Formula Solve using Square Root Propert: (best when onl term is present or polnomial is squared) ) ) ( ) 9 7 Solve using Factoring: (best when equation can be easil factored; equation must be set = 0 to begin) ) ( )( ) 9 ) ( 8)( ) 0 ) ( ) 7 6) ( ) Solve using Complete the Square: (best when b is even but a must be = before using) 7) 7 0 8) 6 6 Solve using Quadratic Formula: (this method alwas works but is time consuming; set equation =0) b b ac 9) 6 0 0) 0 a
16 ) Using Midpoint & Distance Formulas Midpoint Formula: ( +, + ) Find the midpoint of the segments with endpoints at the given coordinates. ), and 0, ), 8 and 0,6 ), 0 and 0, 0 ) 9,.7 and,. Distance Formula: d = ( ) + ( ) Find the distance between each pair of points with the given coordinates. Simplif radicals. ),7 and, 6), and, 7), and 6,9 8) 0, and,
17 ) Proving Congruent Triangles 6
18 ) Transformations f ( ) a h k DO NOT USE A CALCULATOR How does the graph of change to produce each of the following graphs? Write the equation of the absolute value functions with the following shifts: 0. Up 7 and left 0.. Down, Reflects over ais, Vertical shrink of.. Right 6, Vertical stretch of. 7
19 ANSWER KEYS 8
20 ) Vocabular/Know the difference Review KEY. Proportions vs. multipling fractions (cross multipling for a proportion vs. multipling numerators and multipling denominators when multipling fractions) Proportion 8 = 8 = vs.. * = vs. + = Multipling Fractions 8 (8) 6 () 6. order of operations: don t be tricked b these common mistaken identities 9 a. * vs. ( * ) b. + ( + ) c. 8 vs. (8) * 8 = 0 0 = not 8( + )  * 6 = 6 (8)(8) = 6. ( 9) vs. ( + 9) vs. ( 9)( + 9) a. ( 9) = = b. ( + 9) = = c. ( 9)( + 9) = = 8. know the difference between a term, epression, equation, and inequalit term number, variable, or product of numbers and variables (e:,, or ) epression terms with mathematical smbols (e:,, +, ) equation epressions set equal to one another (e: =, + = ) inequalit epressions not equal to one another (e: >, + ) 6. know the difference between solve, evaluate and simplif simplif to rewrite an epression in simplest form possible where nothing else can be performed (includes no parentheses or negative eponents; all fractions have been reduced) evaluate to find the value of (once the value has been found, the final result should be written in simplest form) solve to work out the solution to the problem 7. know the difference between rational and irrational rational real number that can be written as a fraction (e:0,,,, 0.) [repeating or terminating decimals] irrational real number that can t be written as a fraction [nonrepeating, nonterminating decimals] (e:,, ) 8. know the smbols b name: > as greater than vs. < as less than 9
21 9. know coefficient numerical factor of a monomial [number being multiplied b a variable] 0. know factor two or more numbers that multipl to produce another number [ and are factors of 0]. reduce entire factors not parts of a factor (individual terms)  ou can reduce 0 = 0 b rewriting the numerator in factored form first:  ou can t reduce 0 b tring to reduce just 0 0
22 ) Operations with Fractions DO NOT USE A CALCULATOR KEY ) 9 = 0 9 ) 7 = 9 0 ) 6 = ) 9 = 8 7 ) 7 = 7 6) = 6 8 7) = 9 8) 7 = 6 9) = 6 9
23 ) Solve Equations and Inequalities DO NOT USE A CALCULATOR KEY Clear out fractions. 7 ) 7 ) 7 ) a a a 8 6 = 8 = 7 a = / Variables on both sides. ) ( 8 ) + ( + ) = ) 8 + ( a ) = ( a + ) 6) 6 + = a 7 Solve Inequalities and graph our answer. When ou multipl or divide both sides b a negative remember to flip the inequalit. Get variable on the left. 8) 6 6 7) Word Problems  You must be able to write the equation or inequalit first. Then solve for the variable. 9) The greater of two numbers is 6 more than times the smaller. Their sum is. Find the numbers. 6 7 and,,6 0) Find three consecutive integers whose sum is 0. 0, 6, 8 ) Find three consecutive even integers whose sum is 8. 8 ) The length of a rectangle is feet more than its width. If its perimeter is 0 feet, find the length and width. 0 w w Length: Width: 9 ) The second angle in a triangle is less than twice the first angle. The third angle measure 8 more than twice the first angle. Find each angle. 8 80, 67, 78 ) Jeffer has grades of 9 and 8 on the first two tests of the quarter. Progress reports will go home after the third test. If Jeffer does not have an A average on his progress report, he cannot go to the football game that week. Jeffer will have to make at least what grade on the third test to be allowed to go to the football game?
24 ) Linear Equations  Slope, Writing Linear Equations, Horizontal & Vertical, Parallel & Perpendicular KEY Find the slope (rate of change) of the following problems., 8,., 7 8. Da Temperature. ( F ) The cost of museum tickets is $8 for four people and $78 for 0 people. What is the cost per person? $ per person Write the equation of the line in slopeintercept form & standard form given the following.., m 6., 7 m 7., 6, 8. m =, b = (, ) m = 0 0. (, ) m = undefined.. The cost for 7 dance lessons is $8. The cost for lessons is $. Write a linear equation to find the total cost C for L dance lessons. Then use the equation to find the cost of lessons. C 0L $
25 . Write the equation for a vertical line that goes through the point (, ). =. Write the equation for a horizontal line that goes through the point (, ). = Solve the equation for if necessar, and find the slope. Then, find the slope of a line parallel and perpendicular to the original line. SLOPE PARALLEL PERPENDICULAR. + 6 = 8 6. = undefined/none undefined/none 0 7. = undefined/none Write the answers for 80 in slope intercept and standard forms. 8. Write the equation for the line parallel to the given line = 9 and through the point (, ). 9. Write the equation for the line perpendicular to the given line = 9 and through the point (8, ). 0. Given a line through (, ) and (8, ), find the equation of the line perpendicular to that line through the midpoint of those points. 9 9
26 ) Graphing Linear Equations and Inequalities DO NOT USE A CALCULATOR KEY
27 9) 7 0) ) 0 ) ) ) 6
28 7 6) Sstems of Equations KEY ) 6 ) 0,, ) 8 ), 7, ) 6) infinitel man
29 7) 8) KEY,, 9) 0), ) 7 ) 6,, ) 6 ) 0 infinitel man 0, 8
30 7) Laws of Eponents KEY ) a b a 7 b ) z z ) a b b c a c ) 0 a b 6 z a 6 b c 6 ) c c 7) ac bc ab 6) 8) 0 8c 7 0 a b c 0 a b 8 0 a b 9) 6 0 0) ) ) 0 () 8b a ) a b ab 7 8 8a b ) 0 a b ) ) 0 a b 7 a b ) 7 8) 9) 6 0) ) a 9 8 ) 7 ) a 6 ) ( 6 0 ) 9
31 8) Polnomial Operations KEY Simplif. ) (6 ) ) ab ab a b ) 6 ( 7 ) 0 0 a b 0a b 6 6 ) 8 ) 6) 6 0 7) 8) n 8n 8 9) 6w w 7w n 7 8w 6w 0 0) 8 ) m mp 6 p m mp p 8 8m 7mp 7 p 0
32 9) Radicals & Rational Eponents KEY i i i a a a a 9. z z 0a 6a z 6 0 z... 6 ( ) Rational Eponents See these as eamples of rational eponents: = = 8 = 8 Simplif the following Write as a rational eponent:
33 0) Using Function Notation KEY State whether each set is a function. Answer es or no. Find the domain and the range. ) {(, ), (, 6), (, 6), (, 8)} no Domain:,, 6,,6,8 Range: ) {(, ), (8, ), (, 8), (, )} es Domain:,,,8 Range:,,,8 Use the vertical line test to determine whether each graph is the graph of a function. Answer es or no. ) no ) es ) es 6) no f g Use and 7) f 6 8) to find each value. g 7 9 9) f 9 f 8 0) 0 ) f c ) gw 7 ) f m ) g 9c 9 w m m ) The temperature of the atmosphere decreases about o F for ever 000 feet increase in altitude. Thus, if the temperature at ground level is 77 o F, the temperature t at a given altitude is found b using the equation t 77.00h, where h is the height in feet. a) Write the equation in function notation where t is a function of h. [f() is meant as f is a function of ] t( h) h 76. b) Find t(00) and eplain its meaning in this problem. 6) The function g 60. models the weight gain of a basketball plaer as he starts a workout program where g is the weight in pounds after weeks. a) Eplain the meaning of 60 in the contet of this problem. Starting/initial weight (intercept) b) Eplain the meaning of. in the contet of this problem. # of pounds added per week (slope) c) Evaluate g 6 and eplain its meaning. 69; weight 6 weeks after starting
34 ) Solving Quadratic Equations Should be able to use: Square Root Propert KEY Factoring (Remember when equation must be set = 0 before solving) Completing the Square [ a + b + c = 0 ] Quadratic Formula Solve using Square Root Propert: (best when onl term is present or polnomial is squared) ) ) ( ) 9 7 =,, Solve using Factoring: (best when equation can be easil factored; equation must be set = 0 to begin) ) ( )( ) 9 ) ( 8)( ) 0 6,, ) ( ) 7 6) ( ) 9, 8 9, Solve using Complete the Square: (best when b is even but a must be = before using) 7) 7 0 8) 6 6 i i Solve using Quadratic Formula: (this method alwas works but is time consuming; set equation =0) b b ac 9) 6 0 0) 0 a i 8 7
35 ) Using Midpoint & Distance Formulas KEY Midpoint Formula: ( +, + ) Find the midpoint of the segments with endpoints at the given coordinates. ), and 0, ), 8 and 0,6 (7, 8) (6, ) ), 0 and 0, 0 ) 9,.7 and,. (, ) ( 0, ) Distance Formula: d = ( ) + ( ) Find the distance between each pair of points with the given coordinates. Simplif radicals. ),7 and, 6), and, 0 7), and 6,9 8) 0, and,
36 ) Proving Congruent Triangles KEY
37 ) Transformations f ( ) a h k DO NOT USE A CALCULATOR KEY How does the graph of change to produce each of the following graphs?.. up.. left. 9. right 9.. reflect over ais; vertical stretch _.. down vertical shrink left ; down vertical stretch; right _ reflect over ais; vertical shrink; up Write the equation of the absolute value functions with the following shifts: f ( ) 0. Up 7 and left Down, Reflects over ais, Vertical shrink of. _ f ( ). Right 6, Vertical stretch of. f ( ) 6 6
Math 030 Review for Final Exam Revised Fall 2010 RH/ DM 1
Math 00 Review for Final Eam Revised Fall 010 RH/ DM 1 1. Solve the equations: (1) (7) () (1) () 1 1 1 1 f. 1 g. h. 1 11 i. 9. Solve the following equations for the given variable: 1 Solve for. D ab
More informationPRECALCULUS Summer Math Packet
PRECALCULUS Summer Math Packet In preparation for PreCalculus, we have prepared a packet of concepts that students should know how to do. These concepts have been taught in previous math classes. This
More informationNorthwest High School s Algebra 2/Honors Algebra 2
Northwest High School s Algebra /Honors Algebra Summer Review Packet 0 DUE Frida, September, 0 Student Name This packet has been designed to help ou review various mathematical topics that will be necessar
More informationAlgebra 1 Skills Needed for Success in Math
Algebra 1 Skills Needed for Success in Math A. Simplifing Polnomial Epressions Objectives: The student will be able to: Appl the appropriate arithmetic operations and algebraic properties needed to simplif
More informationAn assessment of these skills will occur the first week of school.
Fort Zumwalt West High School PreAP Algebra SUMMER REVIEW PACKET Name: * This packet is to be handed in to our Pre AP Algebra teacher on the first da of the school ear. *All work must be shown in the
More informationThe American School of Marrakesh. Algebra 2 Algebra 2 Summer Preparation Packet
The American School of Marrakesh Algebra Algebra Summer Preparation Packet Summer 016 Algebra Summer Preparation Packet This summer packet contains eciting math problems designed to ensure our readiness
More informationRising HONORS Algebra 2 TRIG student Summer Packet for 2016 (school year )
Rising HONORS Algebra TRIG student Summer Packet for 016 (school ear 01617) Welcome to Algebra TRIG! To be successful in Algebra Trig, ou must be proficient at solving and simplifing each tpe of problem
More informationCourse 15 Numbers and Their Properties
Course Numbers and Their Properties KEY Module: Objective: Rules for Eponents and Radicals To practice appling rules for eponents when the eponents are rational numbers Name: Date: Fill in the blanks.
More informationREVIEW PACKET FOR END OF COURSE EXAM
Math H REVIEW PACKET FOR END OF COURSE EXAM DO NOT WRITE ON PACKET! Do on binder paper, show support work. On this packet leave all fractional answers in improper fractional form (ecept where appropriate
More informationReview Packet For Math III
Review Packet For Math III Student Name: The problems in this packet are designed to help ou review topics from previous mathematics courses that are important to our success this coming ear. I hope that
More informationAlgebra 2 Honors Summer Packet 2018
Algebra Honors Summer Packet 018 Solving Linear Equations with Fractional Coefficients For these problems, ou should be able to: A) determine the LCD when given two or more fractions B) solve a linear
More informationSummer Review For Students Entering Algebra 2
Summer Review For Students Entering Algebra Teachers and administrators at Tuscarora High School activel encourage parents and communit members to engage in children s learning. This Summer Review For
More informationA. Simplifying Polynomial Expressions
A. Simplifing Polnomial Epressions I. Combining Like Terms  You can add or subtract terms that are considered "like", or terms that have the same variable(s) with the same eponent(s). E. 1: 57 + 10 +
More informationPreCalculus. Ocean Township High School Mathematics Department
PreCalculus Summer Assignment Name Period Date Ocean Township High School Mathematics Department These are important topics from previous courses that ou must be comfortable doing before ou can be successful
More informationSystems of Linear Equations: Solving by Graphing
8.1 Sstems of Linear Equations: Solving b Graphing 8.1 OBJECTIVE 1. Find the solution(s) for a set of linear equations b graphing NOTE There is no other ordered pair that satisfies both equations. From
More informationAlgebra 2 CPA Summer Assignment 2018
Algebra CPA Summer Assignment 018 This assignment is designed for ou to practice topics learned in Algebra 1 that will be relevant in the Algebra CPA curriculum. This review is especiall important as ou
More informationAlgebra 1 Skills Needed to be Successful in Algebra 2
Algebra 1 Skills Needed to be Successful in Algebra A. Simplifing Polnomial Epressions Objectives: The student will be able to: Appl the appropriate arithmetic operations and algebraic properties needed
More informationBRONX COMMUNITY COLLEGE of the City University of New York DEPARTMENT OF MATHEMATICS & COMPUTER SCIENCE. MTH 05 Review Sheet
BRONX COMMUNITY COLLEGE of the Cit Universit of New York DEPARTMENT OF MATHEMATICS & COMPUTER SCIENCE MTH 05 Review Sheet Go to http://www.cun.edu/testing for more information on the CUNY Elementar Algebra
More informationGeometry and Honors Geometry Summer Review Packet 2014
Geometr and Honors Geometr Summer Review Packet 04 This will not be graded. It is for our benefit onl. The problems in this packet are designed to help ou review topics from previous mathematics courses
More informationH.Algebra 2 Summer Review Packet
H.Algebra Summer Review Packet 1 Correlation of Algebra Summer Packet with Algebra 1 Objectives A. Simplifing Polnomial Epressions Objectives: The student will be able to: Use the commutative, associative,
More informationGlossary. Also available at BigIdeasMath.com: multilanguage glossary vocabulary flash cards. An equation that contains an absolute value expression
Glossar This student friendl glossar is designed to be a reference for ke vocabular, properties, and mathematical terms. Several of the entries include a short eample to aid our understanding of important
More informationMath Analysis/Honors Math Analysis Summer Assignment
Math Analysis/Honors Math Analysis Summer Assignment To be successful in Math Analysis or Honors Math Analysis, a full understanding of the topics listed below is required prior to the school year. To
More informationChapter 9. WorkedOut Solutions. Check. Chapter 9 Maintaining Mathematical Proficiency (p. 477) y = 2 x 2. y = 1. = (x + 5) 2 4 =?
Maintaining Mathematical Proficienc (p. ). x + 0x + x + (x)() + (x + ). x 0x + 00 x (x)(0) + 0 (x 0). x + x + x + (x)() + (x + ). x x + x (x)(9) + 9 (x 9). x + x + x + (x)() + (x + ) Check x x +? ()? ()
More informationEOC Review. Algebra I
EOC Review Algebra I Order of Operations PEMDAS Parentheses, Eponents, Multiplication/Division, Add/Subtract from left to right. A. Simplif each epression using appropriate Order of Operations.. 5 6 +.
More informationName: Richard Montgomery High School Department of Mathematics. Summer Math Packet. for students entering. Algebra 2/Trig*
Name: Richard Montgomer High School Department of Mathematics Summer Math Packet for students entering Algebra 2/Trig* For the following courses: AAF, Honors Algebra 2, Algebra 2 (Please go the RM website
More informationAre You Ready For Math Analysis?
Are You Read For Math Analsis? This is a DistrictWide Summer Assignment for students taking Math Analsis in September 018. The Math Analsis teachers in all UCVTS programs will be using this for evaluation
More informationreview math0410 (1174) and math 0320 ( ) aafinm mg
Eam Name review math04 (1174) and math 0320 (17243) 03201700aafinm0424300 mg MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Simplif. 1) 7 23 A)
More informationMath 0308 Final Exam Review(answers) Solve the given equations. 1. 3x 14 8x 1
Math 8 Final Eam Review(answers) Solve the given equations.. 8.. 9.. 9 9 8 8.. 8 8 all real numbers 8. 9. all real numbers no solution 8 8 9 9 9 Solve the following inequalities. Graph our solution on
More informationReview Topics for MATH 1400 Elements of Calculus Table of Contents
Math 1400  Mano Table of Contents  Review  page 1 of 2 Review Topics for MATH 1400 Elements of Calculus Table of Contents MATH 1400 Elements of Calculus is one of the Marquette Core Courses for Mathematical
More informationINTRODUCTION GOOD LUCK!
INTRODUCTION The Summer Skills Assignment for has been developed to provide all learners of our St. Mar s Count Public Schools communit an opportunit to shore up their prerequisite mathematical skills
More informationa 2 x y 1 y SOL AII.1a
SOL AII.a The student, given rational, radical, or polnomial epressions, will a) add, subtract, multipl, divide, and simplif rational algebraic epressions; Hints and Notes Rules for fractions: ) Alwas
More informationMath Intermediate Algebra
Math 095  Intermediate Algebra Final Eam Review Objective 1: Determine whether a relation is a function. Given a graphical, tabular, or algebraic representation for a function, evaluate the function and
More informationAre You Ready For Math Analysis?
This is a DistrictWide Summer Assignment for students taking Math Analsis in September 014. The Math Analsis teachers in all UCVTS programs will be using this for evaluation in their classes. Are ou read
More informationMath 115 Spring Break Homework Package Name. . List all
Math Spring Break Homework Package Name Show all work neatl and sstematicall for full credit. Total points: 00 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the
More informationAlgebra II Notes Unit Five: Quadratic Functions. Syllabus Objectives: 5.1 The student will graph quadratic functions with and without technology.
Sllabus Objectives:.1 The student will graph quadratic functions with and without technolog. Quadratic Function: a function that can be written in the form are real numbers Parabola: the Ushaped graph
More informationreview for math TSI 55 practice aafm m
Eam TSI Name review for math TSI practice 01704041700aafm042430m www.alvarezmathhelp.com MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the
More informationHonors Algebra
Honors Algebra 0809 Honors Algebra is a rigorous course that requires the use of Algebra skills. The summer work is designed to maintain and reinforce these prerequisite skills so as to prepare ou for
More informationmath FALL developmental mathematics sullivan 1e
TSIpractice eam review 1 131 180 plus 34 TSI questions for elementar and intermediate algebra m0300004301 aaa Name www.alvarezmathhelp.com math0300004301 FALL 01 100 interactmath developmental mathematics
More informationCan a system of linear equations have no solution? Can a system of linear equations have many solutions?
5. Solving Special Sstems of Linear Equations Can a sstem of linear equations have no solution? Can a sstem of linear equations have man solutions? ACTIVITY: Writing a Sstem of Linear Equations Work with
More informationObjectives To solve quadratic equations using the quadratic formula To find the number of solutions of a quadratic equation
96 The Quadratic Formula and the Discriminant Content Standards A.REI..a Use the method of completing the square to transform an quadratic equation in into an equation of the form ( p) 5 q... Derive the
More informationReview of Elementary Algebra Content
Review of Elementar Algebra Content 0 1 Table of Contents Fractions...1 Integers...5 Order of Operations...9 Eponents...11 Polnomials...18 Factoring... Solving Linear Equations...1 Solving Linear Inequalities...
More informationCoached Instruction Supplement
Practice Coach PLUS Coached Instruction Supplement Mathematics 8 Practice Coach PLUS, Coached Instruction Supplement, Mathematics, Grade 8 679NASP Triumph Learning Triumph Learning, LLC. All rights reserved.
More informationMATH 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 informationa 2 x y 1 x 1 y SOL AII.1a
SOL AII.a The student, given rational, radical, or polnomial epressions, will a) add, subtract, multipl, divide, and simplif rational algebraic epressions; Hints and Notes Rules for fractions: ) Alwas
More informationSystems of Linear Inequalities
. Sstems of Linear Inequalities sstem of linear inequalities? How can ou sketch the graph of a ACTIVITY: Graphing Linear Inequalities Work with a partner. Match the linear inequalit with its graph. + Inequalit
More informationMath 154A Elementary Algebra Fall 2014 Final Exam Study Guide
Math A Elementar Algebra Fall 0 Final Eam Stud Guide The eam is on Tuesda, December 6 th from 6:00pm 8:0pm. You are allowed a scientific calculator and a " b 6" inde card for notes. On our inde card be
More informationAlgebra 2 Semester Exam Review
Algebra Semester Eam Review 7 Graph the numbers,,,, and 0 on a number line Identif the propert shown rs rs r when r and s Evaluate What is the value of k k when k? Simplif the epression 7 7 Solve the equation
More informationFINAL EXAM REVIEW ITEMS Math 0312: Intermediate Algebra Name
FINAL EXAM REVIEW ITEMS Math 0312: Intermediate Algebra Name 1) Find the SUM of the solutions of the equation. 82 + 0 = 16 Use the quadratic formula to solve the equation. (All solutions are real numbers.)
More information5. Perform the indicated operation and simplify each of the following expressions:
Precalculus Worksheet.5 1. What is  1? Just because we refer to solutions as imaginar does not mean that the solutions are meaningless. Fields such as quantum mechanics and electromagnetism depend on
More informationMATH 60 Review Problems for Final Exam
MATH 60 Review Problems for Final Eam Scientific Calculators Onl  Graphing Calculators Not Allowed NO CLASS NOTES PERMITTED Evaluate the epression for the given values. m 1) m + 3 for m = 3 2) m 2  n2
More informationMATH 115: Final Exam Review. Can you find the distance between two points and the midpoint of a line segment? (1.1)
MATH : Final Eam Review Can ou find the distance between two points and the midpoint of a line segment? (.) () Consider the points A (,) and ( 6, ) B. (a) Find the distance between A and B. (b) Find the
More informationSummer Packet Honors PreCalculus
Summer Packet Honors PreCalculus Honors PreCalculus is a demanding course that relies heavily upon a student s algebra, geometry, and trigonometry skills. You are epected to know these topics before entering
More informationx. 4. 2x 10 4x. 10 x
CCGPS UNIT Semester 1 COORDINATE ALGEBRA Page 1 of Reasoning with Equations and Quantities Name: Date: Understand solving equations as a process of reasoning and eplain the reasoning MCC91.A.REI.1 Eplain
More informationSummer Assignment for students ENTERING: Algebra 2 Trigonometry Honors
Summer Assignment for students ENTERING: Algebra Trigonometry Honors Please have the following worksheets completed and ready to be handed in on the first day of class, August 1, 017. Make sure you show
More informationModule 3, Section 4 Analytic Geometry II
Principles of Mathematics 11 Section, Introduction 01 Introduction, Section Analtic Geometr II As the lesson titles show, this section etends what ou have learned about Analtic Geometr to several related
More informationDiagnostic Tests Study Guide
California State Universit, Sacramento Department of Mathematics and Statistics Diagnostic Tests Stud Guide Descriptions Stud Guides Sample Tests & Answers Table of Contents: Introduction Elementar Algebra
More informationCh 3 Alg 2 Note Sheet.doc 3.1 Graphing Systems of Equations
Ch 3 Alg Note Sheet.doc 3.1 Graphing Sstems of Equations Sstems of Linear Equations A sstem of equations is a set of two or more equations that use the same variables. If the graph of each equation =.4
More informationRELATIONS AND FUNCTIONS through
RELATIONS AND FUNCTIONS 11.1.2 through 11.1. Relations and Functions establish a correspondence between the input values (usuall ) and the output values (usuall ) according to the particular relation or
More informationmath0320 FALL interactmath sections developmental mathematics sullivan 1e
Eam final eam review 180 plus 234 TSI questions for intermediate algebra m032000 013014 NEW Name www.alvarezmathhelp.com math0320 FALL 201 1400 interactmath sections developmental mathematics sullivan
More information(2.5) 1. Solve the following compound inequality and graph the solution set.
Intermediate Algebra Practice Final Math 0 (7 th ed.) (Ch. ) (.5). Solve the following compound inequalit and graph the solution set. 0 and and > or or (.7). Solve the following absolute value inequalities.
More informationC) x m A) 260 sq. m B) 26 sq. m C) 40 sq. m D) 364 sq. m. 7) x x  (6x + 24) = 4 A) 0 B) all real numbers C) 4 D) no solution
Sample Departmental Final  Math 46 Perform the indicated operation. Simplif if possible. 1) 7   22 + 3 2  A) +  2 B)  + 42 C) + 42 D)  +  2 Solve the problem. 2) The sum of a number and its
More informationMaintaining Mathematical Proficiency
Name Date Chapter 3 Maintaining Mathematical Proficienc Plot the point in a coordinate plane. Describe the location of the point. 1. A( 3, 1). B (, ) 3. C ( 1, 0). D ( 5, ) 5. Plot the point that is on
More informationUnit 3 NOTES Honors Common Core Math 2 1. Day 1: Properties of Exponents
Unit NOTES Honors Common Core Math Da : Properties of Eponents WarmUp: Before we begin toda s lesson, how much do ou remember about eponents? Use epanded form to write the rules for the eponents. OBJECTIVE
More informationAlgebra Concepts Equation Solving Flow Chart Page 1 of 6. How Do I Solve This Equation?
Algebra Concepts Equation Solving Flow Chart Page of 6 How Do I Solve This Equation? First, simplify both sides of the equation as much as possible by: combining like terms, removing parentheses using
More informationName Period Date. Practice FINAL EXAM Intro to Calculus (50 points) Show all work on separate sheet of paper for full credit!
Name Period Date Practice FINAL EXAM Intro to Calculus (0 points) Show all work on separate sheet of paper for full credit! ) Evaluate the algebraic epression for the given value or values of the variable(s).
More informationALGEBRA 2 NY STATE COMMON CORE
ALGEBRA NY STATE COMMON CORE Kingston High School 017018 emathinstruction, RED HOOK, NY 1571, 015 Table of Contents U n i t 1  Foundations of Algebra... 1 U n i t  Linear Functions, Equations, and their
More informationAnswers. Chapter Warm Up. Sample answer: The graph of h is a translation. 3 units right of the parent linear function.
Chapter. Start Thinking As the string V gets wider, the points on the string move closer to the ais. This activit mimics a vertical shrink of a parabola... Warm Up.. Sample answer: The graph of f is a
More information(c) ( 5) 2. (d) 3. (c) 3(5 7) 2 6(3) (d) (9 13) ( 3) Question 4. Multiply using the distributive property and collect like terms if possible.
Name: Chapter 1 Question 1. Evaluate the following epressions. (a) 5 (c) ( 5) (b) 5 (d) ( 1 ) 3 3 Question. Evaluate the following epressions. (a) 0 5() 3 4 (c) 3(5 7) 6(3) (b) 9 + (8 5) (d) (9 13) + 15
More informationUNCORRECTED SAMPLE PAGES. 3Quadratics. Chapter 3. Objectives
Chapter 3 3Quadratics Objectives To recognise and sketch the graphs of quadratic polnomials. To find the ke features of the graph of a quadratic polnomial: ais intercepts, turning point and ais of smmetr.
More informationALGEBRA 2 HONORS SUMMER WORK. June Dear Algebra 2 Students,
ALGEBRA HONORS SUMMER WORK June 0 Dear Algebra Students, Attached you will find the Summer Math Packet for Algebra. The purpose of this packet is to review and sharpen your Algebra skills so that when
More informationElementary Algebra FALL 2005 Review for Exam 2
Elementar Algebra FALL 200 Review for Eam 2 1) In a surve of 60 students, the students showed these preferences for instructional materials. Answer the questions. Graph the equation. 6) = 4 + 3 7) 3 +
More informationCitrus Valley High School
Citrus Valle High School Dear Math I Honors Student, Familiarit with prehigh school math concepts is essential for success in the Integrated Math I Honors class. The majorit of the questions in Math I
More informationBishop Kelley High School Summer Math Program Course: Algebra 2 A
06 07 Bishop Kelley High School Summer Math Program Course: Algebra A NAME: DIRECTIONS: Show all work in packet!!! The first 6 pages of this packet provide eamples as to how to work some of the problems
More informationBasic 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 informationMath Departmental Exit Assessment Review (Student Version)
Math 03  Departmental Eit Assessment Review (Student Version) Factor completel. (Factoring Review) ) 66  0 ) 3343 3) 3  + 840 4)  36 ) +  6 + 9 + 8  + + Add or subtract as indicated. Simplif completel.
More informationACCUPLACER MATH 0311 OR MATH 0120
The University of Teas at El Paso Tutoring and Learning Center ACCUPLACER MATH 0 OR MATH 00 http://www.academics.utep.edu/tlc MATH 0 OR MATH 00 Page Factoring Factoring Eercises 8 Factoring Answer to Eercises
More information02. 2) Plot the points and connect them. X
1) Pam s Pie Pantry had 2 backorders for cherry pies. Pam can bake 3 pies every hour. Fill in the blanks. Hours 02 Pies Practice 6C 2) Plot the points and connect them. 3) Write an equation for the line.
More informationName Date. and y = 5.
Name Date Chapter Fair Game Review Evaluate the epression when = and =.... 0 +. 8( ) Evaluate the epression when a = 9 and b =.. ab. a ( b + ) 7. b b 7 8. 7b + ( ab ) 9. You go to the movies with five
More informationChapter 6: Systems of Equations and Inequalities
Chapter 6: Sstems of Equations and Inequalities 61: Solving Sstems b Graphing Objectives: Identif solutions of sstems of linear equation in two variables. Solve sstems of linear equation in two variables
More informationFor questions 58, solve each inequality and graph the solution set. You must show work for full credit. (2 pts each)
Alg Midterm Review Practice Level 1 C 1. Find the opposite and the reciprocal of 0. a. 0, 1 b. 0, 1 0 0 c. 0, 1 0 d. 0, 1 0 For questions , insert , or = to make the sentence true. (1pt each) A. 5
More informationGlossary. Also available at BigIdeasMath.com: multilanguage glossary vocabulary flash cards
Glossar This student friendl glossar is designed to be a reference for ke vocabular, properties, and mathematical terms. Several of the entries include a short eample to aid our understanding of important
More informationCHAPTER 6: LINEAR SYSTEMS AND THEIR GRAPHS
Name: Date: Period: CHAPTER : LINEAR SYSTEMS AND THEIR GRAPHS Notes #: Section.: Solving Linear Sstems b Substitution The solution to a sstem of equations represents the where the. It would be great if
More informationSample Problems For Grade 9 Mathematics. Grade. 1. If x 3
Sample roblems For 9 Mathematics DIRECTIONS: This section provides sample mathematics problems for the 9 test forms. These problems are based on material included in the New York Cit curriculum for 8.
More informationMaths A Level Summer Assignment & Transition Work
Maths A Level Summer Assignment & Transition Work The summer assignment element should take no longer than hours to complete. Your summer assignment for each course must be submitted in the relevant first
More informationKeira Godwin. Time Allotment: 13 days. Unit Objectives: Upon completion of this unit, students will be able to:
Keira Godwin Time Allotment: 3 das Unit Objectives: Upon completion of this unit, students will be able to: o Simplif comple rational fractions. o Solve comple rational fractional equations. o Solve quadratic
More informationClasswork #40: Final Review: Solving Equations, Word Problems, Linear Equations, Systems of Linear Equations
Classwork #0: Final Review: Solving Equations, Word Problems, Linear Equations, Sstems of Linear Equations Solving Equations: Isolate the variable! Things to watch for: when ou have parentheses the inequalit
More information3.1 Graph Quadratic Functions
3. Graph Quadratic Functions in Standard Form Georgia Performance Standard(s) MMA3b, MMA3c Goal p Use intervals of increase and decrease to understand average rates of change of quadratic functions. Your
More informationUnit 2 Notes Packet on Quadratic Functions and Factoring
Name: Period: Unit Notes Packet on Quadratic Functions and Factoring Notes #: Graphing quadratic equations in standard form, verte form, and intercept form. A. Intro to Graphs of Quadratic Equations: a
More informationShrine Catholic High School Required Summer Math Quiz. Designed for Students entering Algebra 2 & Honors Algebra 2
Shrine Catholic High School Required Summer Math Quiz Designed for Students entering Algebra & Honors Algebra Dear Parents and Students: Summer work, such as math packets and novel reading, can be useful
More information8.4. If we let x denote the number of gallons pumped, then the price y in dollars can $ $1.70 $ $1.70 $ $1.70 $ $1.
8.4 An Introduction to Functions: Linear Functions, Applications, and Models We often describe one quantit in terms of another; for eample, the growth of a plant is related to the amount of light it receives,
More informationAlgebra II Notes Unit Six: Polynomials Syllabus Objectives: 6.2 The student will simplify polynomial expressions.
Algebra II Notes Unit Si: Polnomials Sllabus Objectives: 6. The student will simplif polnomial epressions. Review: Properties of Eponents (Allow students to come up with these on their own.) Let a and
More informationALGEBRA 1 CP FINAL EXAM REVIEW
ALGEBRA CP FINAL EXAM REVIEW Alg CP Sem Eam Review 0 () Page of 8 Chapter 8: Eponents. Write in rational eponent notation. 7. Write in radical notation. Simplif the epression.. 00.. 6 6. 7 7. 6 6 8. 8
More informationCalifornia State University, Northridge
California State Universit, Northridge MATH 09 HYBRID WORKBOOKS Spring 00 Chapter Equations, Inequalities and Applications. The Addition Propert of Equalit Learning Objectives:. Use the Addition Propert
More informationLearning Goals. College of Charleston Department of Mathematics Math 101: College Algebra Final Exam Review Problems 1
College of Charleston Department of Mathematics Math 0: College Algebra Final Eam Review Problems Learning Goals (AL) Arithmetic of Real and Comple Numbers: I can classif numbers as natural, integer,
More informationMath Review Packet. for PreAlgebra to Algebra 1
Math Review Packet for PreAlgebra to Algebra 1 Epressions, Equations, Eponents, Scientific Notation, Linear Functions, Proportions, Pythagorean Theorem 2016 Math in the Middle Evaluating Algebraic Epressions
More informationLinear Equation Theory  2
Algebra Module A46 Linear Equation Theor  Copright This publication The Northern Alberta Institute of Technolog 00. All Rights Reserved. LAST REVISED June., 009 Linear Equation Theor  Statement of Prerequisite
More informationALLEN 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 This summer packet is intended to be completed by the FIRST DAY of school. This packet will be
More informationf(x) = 2x 2 + 2x  4
41 Graphing Quadratic Functions What You ll Learn Scan the tet under the Now heading. List two things ou will learn about in the lesson. 1. Active Vocabular 2. New Vocabular Label each bo with the terms
More informationAlgebra/Precalc Review
Algebra/Precalc Review The following pages contain various algebra and precalculus topics that are used in the stud of calculus. These pages were designed so that students can refresh their knowledge
More information