The American School of Marrakesh. Algebra 2 Algebra 2 Summer Preparation Packet
|
|
- Nathaniel Golden
- 5 years ago
- Views:
Transcription
1 The American School of Marrakesh Algebra Algebra Summer Preparation Packet Summer 016
2 Algebra Summer Preparation Packet This summer packet contains eciting math problems designed to ensure our readiness for Algebra. The topics covered in this packet are concepts that should have been mastered in courses before entering Algebra. You are laing the groundwork for success net ear b keeping important concepts fresh, and making sure ou identif the important concepts needed to build upon for success in Algebra. Show all work that leads ou to each solution. Use separate paper, if necessar. You ma get help with this packet from friends, a tutor, the internet, or a teacher, but please understand that help means having someone eplain how to solve the problem, not just simpl suppling the answer or coping the work someone else did. YOU are responsible for understanding the material contained in this packet, and for being able to emplo the skills necessar to solve each problem. All work should be completed and read to turn in on the first da of school. This packet will count as part of our first term grade and will be graded on completeness and correctness. You will not be given credit for problems in this packet if no work is shown. A Summer Math Packet test will be given the first full week of school. Do a little of our Summer Math Packet each week. You are not epected to do all of it on the first da or the last week. Your Summer Math Packet will be used to analze our strengths and weaknesses, and assist our teacher in helping ou grow mathematicall throughout the ear. Students should tr to answer all of the questions. However, a minimum of 105 of the questions must be answered to receive full credit. So, if ou reall can t answer certain questions, ou ma write the word pass on up to 10 of the questions without penalt. (The purpose of this option is to allow students to show what the know on certain concepts while informing the teacher of concepts that ma need to be reviewed with students after school starts.) Honor and integrit are at the heart of all students at The American School of Marrakesh. True Warriors never cheat. You are onl hurting ourself b attempting to cop someone else s work. This packet is to help ou be read for Algebra, and help our teachers know what ou can do. Thank ou and have a great summer! If ou are receiving this packet, please provide the following information to me through to corense@asm.ac.ma Name: Phone: ing this information acknowledges receipt of the packet, and an understanding that completion of this prerequisite packet is a requirement for the Algebra course. The packet is due on the first da of class.
3 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 to simplif an algebraic epression. Simplif polnomial epressions using addition and subtraction. Multipl a monomial and polnomial. B. Solving Equations Objectives: The student will be able to: Solve multi-step equations. Solve a literal equation for a specific variable, and use formulas to solve problems. C. Rules of Eponents Objectives: The student will be able to: Simplif epressions using the laws of eponents. Evaluate powers that have zero or negative eponents. D. Binomial Multiplication Objectives: The student will be able to: Multipl two binomials. E. Factoring Objectives: The student will be able to: Identif the greatest common factor of the terms of a polnomial epression. Epress a polnomial as a product of a monomial and a polnomial. Find all factors of the quadratic epression a + b + c b factoring and graphing. F. Radicals Objectives: The student will be able to: Simplif radical epressions. G. Graphing Lines Objectives: The student will be able to: Identif and calculate the slope of a line. Graph linear equations using a variet of methods. Determine the equation of a line. H. Regression and Use of the Graphing Calculator Objectives: The student will be able to: Draw a scatter plot, find the line of best fit, and use it to make predictions. Graph and interpret real-world situations using linear models. 4
4 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: E. : -8h + 10h 3-1h - 15h 3-8h + 10h 3-1h - 15h 3-0h - 5h 3 II. Appling the Distributive Propert - Ever term inside the parentheses is multiplied b the term outside of the parentheses. E. 1: 3(9 " 4) 3# 9 " 3# 4 7 "1 E. : 4 ( ) 4 " " III. Combining Like Terms AND the Distributive Propert (Problems with a Mi!) - Sometimes problems will require ou to distribute AND combine like terms!! E. 1: 3(4 " ) +13 3# 4 " 3# " " 6 E. : 3(1 " 5) " 9("7 +10) 3#1 " 3# 5" 9("7) " 9(10) 36 "15+ 63" 90 "
5 PRACTICE SET 1 Simplif. 1. 8! ! n! (3! 4n) 4.! (11b! 3) q ( ) 6.! ( 5! 6) 7. 3(18z! 4w) + (10z! 6w) 8. ( 8c + 3) + 1(4c! 10)! 9. 9(6! )! 3(9 3) 10.! (! ) + 6(5 + 7) 6
6 I. Solving Two-Step Equations B. Solving Equations A couple of hints: 1. To solve an equation, UNDO the order of operations and work in the reverse order.. REMEMBER! Addition is undone b subtraction, and vice versa. Multiplication is undone b division, and vice versa. E. 1: 4 " = = = 8 E. : 87 = " " 1 " 1 66 = "11 "11 "11 " 6 = II. Solving Multi-step Equations With Variables on Both Sides of the Equal Sign - When solving equations with variables on both sides of the equal sign, be sure to get all terms with variables on one side and all the terms without variables on the other side. E. 3: = " 4 " 4 8 = " 4 " 4 4 = = 6 III. Solving Equations that need to be simplified first - In some equations, ou will need to combine like terms and/or use the distributive propert to simplif each side of the equation, and then begin to solve it. E. 4 : 5(4 " 7) = " 35 = "10 "10 10 " 35 = = = 8 7
7 PRACTICE SET Solve each equation. You must show all work. 1. 5! = = (3! 4) = ! = = 4(1! 9) = ! 68 7.! 131 =! 5(3! 8) ! 7! 10 = ! 15 =! (3! 8) 10.! ( 1! 6) = IV. Solving Literal Equations - A literal equation is an equation that contains more than one variable. - You can solve a literal equation for one of the variables b getting that variable b itself (isolating the specified variable). E.1: 3 =18, Solve for. 3 3 = 18 3 = 6 E. : 5a "10b = 0, Solve for a. +10b =+10b 5a = 0 +10b 5a 5 = b 5 a = 4 + b 8
8 PRACTICE SET 3 Solve each equation for the specified variable. 1. Y + V = W, for V. 9wr = 81, for w 3. d 3f = 9, for f 4. d + t = 10, for 5. P = (g 9)180, for g h = 10 + u, for 9
9 C. Rules of Eponents Multiplication: Recall ( m )( n ) ( m+ n) = E: (3 4 )(4 5 )=(3" 4)( 4 " 1 )( " 5 )=1 5 7 Division: Recall m ( m n)! n 5 5 4m j ' 4 $ ' m $ ' j $ = E: = 14m j 3 % " =! 3 1 3m j 3 % m " % j "! &! #& #& # Powers: Recall ( m ) n ( m! n) = E: (! a bc ) = (! ) ( a ) ( b ) ( c ) =! 8a b c 0 Power of Zero: Recall = 1,! 0 E: = (5)(1)( ) = 5 PRACTICE SET 4 Simplif each epression m 1. ( c )( c)( c ). 3 m 3. (k 4 ) d 5. ( q )( p q ) p z 3 5 z (! t 7 ) g f 9. (4h k )(15k h ) a b 36ab c 11. ( 3 n m ) 4 1. ) 0 ( (! 5a b)(ab c)(! 3b) ( ) ( 3 )( ) 3 10
10 I. Reviewing the Distributive Propert D. Binomial Multiplication The distributive propert is used when ou want to multipl a single term b an epression. E 1: 8(5 8 " 5 40! 9) + 8 " (! 9)! 7 II. Multipling Binomials the FOIL method When multipling two binomials (an epression with two terms), we use the FOIL method. The FOIL method uses the distributive propert twice! FOIL is the order in which ou will multipl our terms. First Outer Inner Last E. 1: ( + 6)( + 10) FIRST OUTER First " > ( + 6)( + 10) Outer Inner > > 6 INNER LAST Last > (After combining like terms) 11
11 Recall: 4 = 4 4 = E. ( + 5) ( + 5) = ( + 5)(+5) Now ou can use the FOIL method to get a simplified epression. PRACTICE SET 5 Multipl. Write our answer in simplest form. 1. ( + 10)( 9). ( + 7)( 1) 3. ( 10)( ) 4. ( 8)( + 81) 5. ( 1)(4 + 3) 6. (- + 10)(-9 + 5) 7. (-3 4)( + 4) 8. ( + 10) 9. (- + 5) 10. ( 3) 1
12 E. Factoring I. Using the Greatest Common Factor (GCF) to Factor. Alwas determine whether there is a greatest common factor (GCF) first. E ! In this eample the GCF is3. So when we factor, we have 3 (! ). Now we need to look at the polnomial remaining in the parentheses. Can this trinomial be factored into two binomials? In order to determine this make a list of all of the factors of Since = -11 and (-5)(-6) = 30 we should choose -5 and -6 in order to factor the epression. The epression factors into 3 (! 5)(! 6) Note: Not all epressions will have a GCF. If a trinomial epression does not have a GCF, proceed b tring to factor the trinomial into two binomials. II. Appling the difference of squares: a! b = ( a! b)( a + b) E. 4 3 "100 ( ) 4 " 5 ( )( + 5) 4 " 5 Since and 5 are perfect squares separated b a subtraction sign, ou can appl the difference of two squares formula. 13
13 PRACTICE SET 6 Factor each epression a b! 16ab + 8ab c 3.! 5 4. n + 8n g! 9g d + 3d! 8 7. z! 7z! m + 18m ! k + 30k!
14 F. Radicals To simplif a radical, we need to find the greatest perfect square factor of the number under the radical sign (the radicand) and then take the square root of that number. E. 1: 7 36 " 6 E. : " 9 " 10 4 " 3" E. 3: OR E. 3: " " 3 This is not simplified completel because 1 is divisible b 4 (another perfect square) 4 3 PRACTICE SET 7 Simplif each radical
15 G. Graphing Lines I. Finding the Slope of the Line that Contains each Pair of Points. Given two points with coordinates ( 1, 1) and (, ) the line containing the points is! m = 1.! E. (, 5) and (4, 1) E. (-3, ) and (, 3) 1! 5! 4 3! 1 m = = =! m = = 4!! (! 3) 5 1 The slope is -. The slope is 5 1, the formula for the slope, m, of PRACTICE SET 8 1. (-1, 4) and (1, -). (3, 5) and (-3, 1) 3. (1, -3) and (-1, -) 4. (, -4) and (6, -4) 5. (, 1) and (-, -3) 6. (5, -) and (5, 7) 16
16 II. Using the Slope Intercept Form of the Equation of a Line. The slope-intercept form for the equation of a line with slope m and -intercept b is 3 E. = 3! 1 E. =! Slope: 3 -intercept: -1 Slope:! -intercept: 4 = m + b. Place a point on the -ais at -1. Place a point on the -ais at. Slope is 3 or 3/1, so travel up 3 on Slope is -3/4 so travel down 3 on the the -ais and over 1 to the right. -ais and over 4 to the right. Or travel up 3 on the -ais and over 4 to the left. PRACTICE SET = + 5. =! 3 Slope: -intercept: Slope: -intercept: 17
17 3. =! =! 3 Slope: Slope: -intercept: -intercept 5. =! + 6. = Slope: Slope: -intercept: -intercept 18
18 III. Using Standard Form to Graph a Line. An equation in standard form can be graphed using several different methods. Two methods are eplained below. a. Re-write the equation in = m + b form, identif the -intercept and slope, then graph as in Part II above. b. Solve for the - and - intercepts. To find the -intercept, let = 0 and solve for. To find the -intercept, let = 0 and solve for. Then plot these points on the appropriate aes and connect them with a line. E.! 3 = 10 a. Solve for. OR b. Find the intercepts:! 3 =! + 10 let = 0 : let = 0:! + 10 =! 3! 3(0) = 10 (0)! 3 = =! 3 3 = 10! 3 = 10 = 5 10 =! 3 So -intercept is (5, 0) & 10 # So -intercept is $ 0,'! % 3 " On the -ais place a point at On the -ais place a point at! 3 Connect the points with the line. =!
19 PRACTICE SET = = = ! 3 = 9 0
20 5.! + 6 = 1 6. =! 3 1
21 H. Regression and Use of the Graphing Calculator Note: For guidance in using our calculator to graph a scatterplot and finding the equation of the linear regression (line of best fit), please see the calculator direction sheet included in the back of the review packet. PRACTICE SET The following table shows the math and science test scores for a group of ninth graders. Math Test Scores Science Test Scores Let's find out if there is a relationship between a student's math test score and his or her science test score. a. Fill in the table below. Remember, the variable quantities are the two variables ou are comparing, the lower bound is the minimum, the upper bound is the maimum, and the interval is the scale for each ais. Variable Quantit Lower Bound Upper Bound Interval b. Create the scatter plot of the data on our calculator. c. Write the equation of the line of best fit. d. Based on the line of best fit, if a student scored an 8 on his math test, what would ou epect his science test score to be? Eplain how ou determined our answer. Use words, smbols, or both. e. Based on the line of best fit, if a student scored a 53 on his science test, what would ou epect his math test score to be? Eplain how ou determined our answer. Use words, smbols, or both.
22 . Use the chart below of winning times for the women's 00-meter run in the Olmpics below to answer the following questions. Year Time (Seconds) a. Fill in the table below. Remember, the variable quantities are the two variables ou are comparing, the lower bound is the minimum, the upper bound is the maimum, and the interval is the scale for each ais. Variable Quantit Lower Bound Upper Bound Interval b. Create a scatter plot of the data on our calculator. c. Write the equation of the regression line (line of best fit) below. Eplain how ou determined our equation. d. The Summer Olmpics will be held in London, England, in 01. According to the line of best fit equation, what would be the winning time for the women's 00- meter run during the 01 Olmpics? Does this answer make sense? Wh or wh not? 3
23 graph a function Press the Y= ke, Enter the function directl using the X, T,!, n ke to input. Press the GRAPH ke to view the function. Use the WINDOW ke to change the dimensions TI-83 Plus/TI-84 Graphing Calculator Tips How to and scale of the graph. Pressing TRACE lets ou move the cursor along the function with the arrow kes to displa eact coordinates. find the -value of an -value Once ou have graphed the function, press CALC nd TRACE and select 1:value. Enter the - value. The corresponding -value is displaed and the cursor find the maimum value of a function Once ou have graphed the function, press CALC nd TRACE and select 4:maimum. You can set the left and right boundaries of the area to be eamined and guess the maimum value either b entering values find the zero of a function Once ou have graphed the function, press CALC nd TRACE and select :zero. You can set the left and right boundaries of the root to be eamined and guess the value either b entering values find the intersection of two functions Once ou have graphed the function, press CALC nd TRACE and select 5:intersect. Use the up and down arrows to move among functions and press ENTER to select two. Net, enter lists of data Press the STAT ke and select 1:Edit. Store ordered pairs b entering the coordinates in L1 and the coordinates in L. You can calculate new lists. To moves to that point on the function. directl or b moving the cursor along the function and pressing ENTER. The -value and -value of the point with the maimum -value are then displaed. directl or b moving the cursor along the function and pressing ENTER. The -value displaed is the root. enter a guess for the point of intersection or move the cursor to an estimated point and press ENTER. The -value and -value of the intersection are then displaed. create a list that is the sum of two previous lists, for eample, move the cursor onto the L3 heading. Then enter the formula L1+L at the L3 prompt. 4
24 plot data Once ou have entered our data into lists, press STAT PLOT nd Y= and select Plot1. Select On and choose the tpe of graph ou want, e.g. scatterplot (points not connected) or connected dot for graph a linear regression of data Once ou have graphed our data, press STAT and move right to select the CALC menu. Select 4:LinReg(a+b). Tpe in the parameters L1, L, Y1. To enter Y1, press VARS draw the inverse of a function Once ou have graphed our function, press DRAW nd PRGM and select 8:DrawInv. Then enter Y1 if our function is in Y1, or just enter the function itself. create a matri From the home screen, press nd -1 to select MATRX and move right to select the EDIT menu. Select 1:[A] and enter the number of rows and the number of columns. Then fill in the matri b entering a value in each element. solve a sstem of equations Once ou have entered the matri containing the coefficients of the variables and the constant terms for a particular sstem, press MATRX (nd -1, move to MATH, and select B:rref. generate lists of random integers From the home screen, press MATH and move left to select the PRB menu. Select 5:RandInt and enter the lower integer bound, the upper integer bound, and the number of trials, separated b two variables, histogram for one variable. Press ZOOM and select 9:ZoomStat to resize the window to fit our data. Points on a connected dot graph or histogram are plotted in the listed order. and move right to select the Y-VARS menu. Select 1:Function and then 1:Y1. Press ENTER to displa the linear regression equation and Y= to displa the function. You ma move among elements with the arrow kes. When finished, press QUIT nd MODE to return to the home screen. To insert the matri into calculations on the home screen, press nd -1 to select MATRX and select NAMES and select 1:[A]. Then enter the name of the matri and press ENTER. The solution to the sstem of equations is found in the last column of the matri. commas, in that order. Press STO and L1 to store the generated numbers in List 1. Repeat substituting L to store a second set of integers in List. 5
H.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 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 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 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 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: 5-7 + 10 +
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 informationRAMAPO&INDIAN*HILLS*SCHOOL*DISTRICT*
1 * * Algebra 2 CP Summer Packet RAMAPO&INDIAN*HILLS*SCHOOL*DISTRICT* DearRamapo*IndianHillsStudent: Pleasefindattachedthesummerpacketforourupcomingmathcourse.Thepurposeof thesummerpacketistoprovideouwithanopportunittoreviewprerequisiteskillsand
More informationJAMES WOOD HIGH SCHOOL 161 Apple Pie Ridge Road Winchester, VA (540) FAX (540)
JAMES WOOD HIGH SCHOOL 161 Apple Pie Ridge Road Winchester, VA 603-4118 (540) 667-56 FAX (540) 667-3154 Summer Math Packet Ms. K. Hill hillk@fcpsk1.net Honors Algebra Name N School o Welcome to Honors
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 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 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 informationNorthwood High School Algebra 2/Honors Algebra 2 Summer Review Packet
Northwood High School Algebra 2/Honors Algebra 2 Summer Review Packet This assignment should serve as a review of the Algebra 1 skills necessary for success. Our hope is that this review will keep your
More informationSummer Math Packet (revised 2017)
Summer Math Packet (revised 07) In preparation for Honors Math III, we have prepared a packet of concepts that students should know how to do as these concepts have been taught in previous math classes.
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 U-shaped graph
More informationRising HONORS Algebra 2 TRIG student Summer Packet for 2016 (school year )
Rising HONORS Algebra TRIG student Summer Packet for 016 (school ear 016-17) Welcome to Algebra TRIG! To be successful in Algebra Trig, ou must be proficient at solving and simplifing each tpe of problem
More informationChapter 5: Quadratic Equations and Functions 5.1 Modeling Data With Quadratic Functions Quadratic Functions and Their Graphs
Ch 5 Alg Note Sheet Ke Chapter 5: Quadratic Equations and Functions 5.1 Modeling Data With Quadratic Functions Quadratic Functions and Their Graphs Definition: Standard Form of a Quadratic Function The
More information+ = + + = x = + = + = 36x
Ch 5 Alg L Homework Worksheets Computation Worksheet #1: You should be able to do these without a calculator! A) Addition (Subtraction = add the opposite of) B) Multiplication (Division = multipl b the
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 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 informationCh 5 Alg 2 L2 Note Sheet Key Do Activity 1 on your Ch 5 Activity Sheet.
Ch Alg L Note Sheet Ke Do Activit 1 on our Ch Activit Sheet. Chapter : Quadratic Equations and Functions.1 Modeling Data With Quadratic Functions You had three forms for linear equations, ou will have
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 informationUNIT 2 QUADRATIC FUNCTIONS AND MODELING Lesson 2: Interpreting Quadratic Functions Instruction
Prerequisite Skills This lesson requires the use of the following skills: knowing the standard form of quadratic functions using graphing technolog to model quadratic functions Introduction The tourism
More informationGlossary. Also available at BigIdeasMath.com: multi-language glossary vocabulary flash cards. An equation that contains an absolute value expression
Glossar This student friendl glossar is designed to be a reference for ke vocabular, properties, and mathematical terms. Several of the entries include a short eample to aid our understanding of important
More informationOHS Algebra 2 Summer Packet
OHS Algebra 2 Summer Packet Good Luck to: Date Started: (please print student name here) Geometry Teacher s Name: Complete each of the following exercises in this formative assessment. To receive full
More informationWestside Algebra 2 PreAP
Westside Algebra 2 PreAP Name Period IMPORTANT INSTRUCTIONS FOR STUDENTS!!! We understand that students come to Algebra II with different strengths and needs. For this reason, students have options for
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 informationBishop Kelley High School Summer Math Program Course: Algebra 2 A
015 016 Bishop Kelley High School Summer Math Program Course: Algebra A NAME: DIRECTIONS: Show all work in packet!!! The first 16 pages of this packet provide eamples as to how to work some of the problems
More informationWestside. Algebra 2 PreAP
Westside Algebra 2 PreAP Name Period IMPORTANT INSTRUCTIONS FOR STUDENTS!!! We understand that students come to Algebra II with different strengths and needs. For this reason, students have options for
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 informationUnit 3 NOTES Honors Common Core Math 2 1. Day 1: Properties of Exponents
Unit NOTES Honors Common Core Math Da : Properties of Eponents Warm-Up: 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 informationAre You Ready For Math Analysis?
This is a District-Wide 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 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 informationAlgebra 2 Prep. Name Period
Algebra 2 Prep Name Period IMPORTANT INSTRUCTIONS FOR STUDENTS!!! We understand that students come to Algebra II with different strengths and needs. For this reason, students have options for completing
More informationAre You Ready For Math Analysis?
Are You Read For Math Analsis? This is a District-Wide 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 informationChapter 1 Functions and Models
Chapter 1 Functions and Models 1.2 Mathematical Models: A catalog of Essential Functions A mathematical model is a mathematical description of a real world situations such as the size of a population,
More informationSummer Packet Geometry PAP
Summer Packet Geometry PAP IMPORTANT INSTRUCTIONS FOR STUDENTS!!! We understand that students come to Geometry with different strengths and needs. For this reason, students have options for completing
More information12x y (4) 2x y (4) 5x y is the same as
Name: Unit #6 Review Quadratic Algebra Date: 1. When 6 is multiplied b the result is 0 1 () 9 1 () 9 1 () 1 0. When is multiplied b the result is 10 6 1 () 7 1 () 7 () 10 6. Written without negative eponents
More informationTopic: Expressions & Operations AII.1
Topic: Epressions & Operations AII.1 AII.1 The student will identify field properties, aioms of equality and inequality, and properties of order that are valid for the set of real numbers and its subsets,
More informationJune Mr. Brown
June 06 Hello, future Algebra II students: The packet attached to this letter contains a series of problems that will overview the Algebra I skills you must have mastered in order to have a good start
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 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 informationUNIT 6 MODELING GEOMETRY Lesson 1: Deriving Equations Instruction
Prerequisite Skills This lesson requires the use of the following skills: appling the Pthagorean Theorem representing horizontal and vertical distances in a coordinate plane simplifing square roots writing
More information3.7 Linear and Quadratic Models
3.7. Linear and Quadratic Models www.ck12.org 3.7 Linear and Quadratic Models Learning Objectives Identif functions using differences and ratios. Write equations for functions. Perform eponential and quadratic
More informationMath 154 :: Elementary Algebra
Math :: Elementar Algebra Section. Section. Section. Section. Section. Section. Math :: Elementar Algebra Section. Eponents. When multipling like-bases, ou can add the eponents to simplif the epression..
More informationLESSON #24 - POWER FUNCTIONS COMMON CORE ALGEBRA II
1 LESSON #4 - POWER FUNCTIONS COMMON CORE ALGEBRA II Before we start to analze polnomials of degree higher than two (quadratics), we first will look at ver simple functions known as power functions. The
More informationAlgebra(2(Honors( Summer(Packet( ( ( Work(on(this(packet(during(the(summer.( ( ( There(will(be(an(in=class(quiz(on(the(material(the(
Algebra((Honors( Summer(Packet( ( ( Work(on(this(packet(during(the(summer.( ( ( There(will(be(an(in=class(quiz(on(the(material(the( first(week(of(school.( ( ( Please(visit(the(CHS(website(to(view(answers(to(
More informationAttributes of Polynomial Functions VOCABULARY
8- Attributes of Polnomial Functions TEKS FCUS Etends TEKS ()(A) Graph the functions f () =, f () =, f () =, f () =, f () = b, f () =, and f () = log b () where b is,, and e, and, when applicable, analze
More informationAlgebra/Pre-calc Review
Algebra/Pre-calc Review The following pages contain various algebra and pre-calculus topics that are used in the stud of calculus. These pages were designed so that students can refresh their knowledge
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 informationLESSON #42 - INVERSES OF FUNCTIONS AND FUNCTION NOTATION PART 2 COMMON CORE ALGEBRA II
LESSON #4 - INVERSES OF FUNCTIONS AND FUNCTION NOTATION PART COMMON CORE ALGEBRA II You will recall from unit 1 that in order to find the inverse of a function, ou must switch and and solve for. Also,
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 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 informationHerndon High School Geometry Honors Summer Assignment
Welcome to Geometry! This summer packet is for all students enrolled in Geometry Honors at Herndon High School for Fall 07. The packet contains prerequisite skills that you will need to be successful in
More informationHonors Algebra
Honors Algebra 08-09 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 informationf(x) = 2x 2 + 2x - 4
4-1 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 information2015 SUMMER MATH PACKET
Name: Date: 05 SUMMER MATH PACKET College Algebra Trig. - I understand that the purpose of the summer packet is for my child to review the topics they have already mastered in previous math classes and
More informationSUMMER MATH PACKET ALGEBRA TWO COURSE 229
SUMMER MATH PACKET ALGEBRA TWO COURSE 9 MATH SUMMER PACKET INSTRUCTIONS MATH SUMMER PACKET INSTRUCTIONS Attached you will find a packet of exciting math problems for your enjoyment over the summer. The
More informationLESSON #28 - POWER FUNCTIONS COMMON CORE ALGEBRA II
1 LESSON #8 - POWER FUNCTIONS COMMON CORE ALGEBRA II Before we start to analze polnomials of degree higher than two (quadratics), we first will look at ver simple functions known as power functions. The
More informationMath 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 informationCOUNCIL ROCK HIGH SCHOOL MATHEMATICS. A Note Guideline of Algebraic Concepts. Designed to assist students in A Summer Review of Algebra
COUNCIL ROCK HIGH SCHOOL MATHEMATICS A Note Guideline of Algebraic Concepts Designed to assist students in A Summer Review of Algebra [A teacher prepared compilation of the 7 Algebraic concepts deemed
More informationx Radical Sign: Radicand: the number beneath the radical sign
Sllabus Objective: 9.4 The student will solve quadratic equations using graphic and algebraic techniques to include the quadratic formula, square roots, factoring, completing the square, and graphing.
More informationPolynomial and Rational Functions
Name Date Chapter Polnomial and Rational Functions Section.1 Quadratic Functions Objective: In this lesson ou learned how to sketch and analze graphs of quadratic functions. Important Vocabular Define
More informationQUADRATIC FUNCTION REVIEW
Name: Date: QUADRATIC FUNCTION REVIEW Linear and eponential functions are used throughout mathematics and science due to their simplicit and applicabilit. Quadratic functions comprise another ver important
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 informationChapter 2 Linear Relations and Functions
Chapter Linear Relations and Functions I. Relations and Functions A. Definitions 1. Relation. Domain the variable ( ) 3. Range the variable ( ). Function a) A relationship between ( ) and ( ). b) The output
More informationVocabulary. Term Page Definition Clarifying Example degree of a monomial. degree of a polynomial. end behavior. leading coefficient.
CHAPTER 6 Vocabular The table contains important vocabular terms from Chapter 6. As ou work through the chapter, fill in the page number, definition, and a clarifing eample. Term Page Definition Clarifing
More informationThe grade on this summer packet will count as your first journal grade and points will be deducted for late submissions.
Welcome to Honors Algebra 2, May 2018 Hello, and Welcome to Honors Algebra 2. Honors Algebra 2 is the next course in your path to college-level mathematics. If you are entering Honors Algebra 2, then you
More informationParenthesis and other grouping symbols. Exponential expressions. Multiplication & Division Addition & Subtraction.
NAME SADDLE BROOK HIGH SCHOOL HONORS ALGEBRA II SUMMER PACKET To maintain a high quality program, students entering Honors Algebra II are expected to remember the basics of the mathematics taught in their
More informationamt Algebra 1 Skills Needed to be Successful in Algebra 2 E. Factoring F. Radicals
amt Algebra 1 Skills Needed to be Successful in Algebra 2 A. Simplifying Polynomial Expressions Apply the appropriate arithmetic operations and algebraic properties needed to simplify an algebraic expression.
More information3.2 LOGARITHMIC FUNCTIONS AND THEIR GRAPHS
Section. Logarithmic Functions and Their Graphs 7. LOGARITHMIC FUNCTIONS AND THEIR GRAPHS Ariel Skelle/Corbis What ou should learn Recognize and evaluate logarithmic functions with base a. Graph logarithmic
More informationAlg2/Trig Summer Assignment 2018
Alg/Trig Summer Assignment 018 This assignment is for you to practice topics learned in Algebra 1 that will be relevant in the Algebra /Trig curriculum. This review is especially important as you have
More informationLESSON #1 - BASIC ALGEBRAIC PROPERTIES COMMON CORE ALGEBRA II
1 LESSON #1 - BASIC ALGEBRAIC PROPERTIES COMMON CORE ALGEBRA II Mathematics has developed a language all to itself in order to clarif concepts and remove ambiguit from the analsis of problems. To achieve
More informationdue date: third day of class estimated time: 10 hours (for planning purposes only; work until you finish)
Honors Algebra II Summer Work 0 due date: third da of class estimated time: 0 hours (for planning purposes onl; work until ou finish) Dear Honors Algebra II Students, This assignment is designed for ou
More information15.2 Graphing Logarithmic
_ - - - - - - Locker LESSON 5. Graphing Logarithmic Functions Teas Math Standards The student is epected to: A.5.A Determine the effects on the ke attributes on the graphs of f () = b and f () = log b
More informationReady To Go On? Skills Intervention 6-1 Polynomials
6A Read To Go On? Skills Intervention 6- Polnomials Find these vocabular words in Lesson 6- and the Multilingual Glossar. Vocabular monomial polnomial degree of a monomial degree of a polnomial leading
More informationReview of Essential Skills and Knowledge
Review of Essential Skills and Knowledge R Eponent Laws...50 R Epanding and Simplifing Polnomial Epressions...5 R 3 Factoring Polnomial Epressions...5 R Working with Rational Epressions...55 R 5 Slope
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 informationAlgebra 2 Chapter 2 Page 1
Mileage (MPGs) Section. Relations and Functions. To graph a relation, state the domain and range, and determine if the relation is a function.. To find the values of a function for the given element of
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 informationAlgebra II Summer Packet. Summer Name:
Algebra II Summer Packet Summer 2017 Name: NAME ALGEBRA II & TRIGONOMETRY SUMMER REVIEW PACKET To maintain a high quality program, students entering Algebra II are expected to remember the basics of the
More informationWest Campus State Math Competency Test Info and Practice
West Campus State Math Competenc Test Info and Practice Question Page Skill A Simplif using order of operations (No grouping/no eponents) A Simplif using order of operations (With grouping and eponents)
More informationGearing Up for Geometry!
Gearing Up for Geometry! Geometry is right around the corner and you need to make sure you are ready! Many of the concepts you learned in Algebra I will be used in Geometry and you will be epected to remember
More informationWatertown Public Schools Algebra 2 Summer Packet
Name Date Teacher Watertown Public Schools Algebra 2 Summer Packet Summer 2017 Attn: In coming Algebra II Cohort, Honors, College Prep Students & Parents/Guardians This packet contains topics that you
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 informationIntermediate Algebra Summary - Part I
Intermediate Algebra Summary - Part I This is an overview of the key ideas we have discussed during the first part of this course. You may find this summary useful as a study aid, but remember that the
More informationMassey Hill Classical High School
Massey Hill Classical High School AB Calculus AP Prerequisite Packet To: From: AP Calculus AB Students and Parents Carolyn Davis, AP Calculus Instructor The AP Course: AP Calculus AB is a college level
More informationBasic ALGEBRA 2 SUMMER PACKET
Name Basic ALGEBRA SUMMER PACKET This packet contains Algebra I topics that you have learned before and should be familiar with coming into Algebra II. We will use these concepts on a regular basis throughout
More informationreview math0410 (1-174) and math 0320 ( ) aafinm mg
Eam Name review math04 (1-174) and math 0320 (17-243) 03201700aafinm0424300 mg MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Simplif. 1) 7 2-3 A)
More informationModule 2, Section 2 Solving Equations
Principles of Mathematics Section, Introduction 03 Introduction Module, Section Solving Equations In this section, you will learn to solve quadratic equations graphically, by factoring, and by applying
More informationCherry Creek High School Summer Assignment for students entering: Accelerated CP Geometry
Cherry Creek High School Summer Assignment for students entering: Accelerated CP Geometry Please have the following worksheets completed and ready to be handed in on the first day of class in the fall.
More informationAdvanced Calculus BC Summer Work Due: 1 st Day of School
Dear Calculus BC student, I hope that ou re all enjoing our first few das of summer! Here s something that will make it a little more fun! Enclosed ou will find a packet of review questions that ou should
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 informationAlgebra Final Exam Review Packet
Algebra 1 00 Final Eam Review Packet UNIT 1 EXPONENTS / RADICALS Eponents Degree of a monomial: Add the degrees of all the in the monomial together. o Eample - Find the degree of 5 7 yz Degree of a polynomial:
More informationSUMMER MATH PACKET ADVANCED ALGEBRA A COURSE 215
SUMMER MATH PACKET ADVANCED ALGEBRA A COURSE 5 Updated May 0 MATH SUMMER PACKET INSTRUCTIONS Attached you will find a packet of exciting math problems for your enjoyment over the summer. The purpose of
More informationSystems of Linear and Quadratic Equations. Check Skills You ll Need. y x. Solve by Graphing. Solve the following system by graphing.
NY- Learning Standards for Mathematics A.A. Solve a sstem of one linear and one quadratic equation in two variables, where onl factoring is required. A.G.9 Solve sstems of linear and quadratic equations
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 information9.1. Solving Quadratic Equations. Investigation: Rocket Science CONDENSED LESSON
CONDENSED LESSON 9.1 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 solve
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 informationALGEBRA 2 NY STATE COMMON CORE
ALGEBRA NY STATE COMMON CORE Kingston High School 017-018 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 information