Math Review Packet. for Pre-Algebra to Algebra 1
|
|
- Rosemary Griffin
- 5 years ago
- Views:
Transcription
1 Math Review Packet for Pre-Algebra to Algebra 1 Epressions, Equations, Eponents, Scientific Notation, Linear Functions, Proportions, Pythagorean Theorem 2016 Math in the Middle
2 Evaluating Algebraic Epressions 1. Substitute the given values for the variables in the epression 2. Evaluate the epression using the order of operations Parentheses/Brackets (inside to outside) Eponents Multiplication/Division (left to right) Addition/Subtraction (left to right) e: 9 2 4(y + z) for = -, y = 2, z = 5 9(-) 2 4(2 + 5) 9(-) 2 4(2 + 15) 9(-) = 1 The Distributive Property 1. Multiply the number outside the parentheses by each term in the parentheses. 2. Keep the addition/subtraction sign between each term. e: 5(8 ) 5(8 ) 5(8) 5() Simplifying Algebraic Epressions 1. Clear any parentheses using the Distributive Property 2. Add or subtract like terms (use the sign in front of each term to determine whether to add or subtract) e: 2( 4) ( 4)
3 Evaluate each epression for a = 9, b = -, c = -2, d = 7. Show your work. 1. a - cd 2. 2b + c 2. a + d c b 4. (a b) 2 + d(a + c) 5. 4c (b a) 6. a b - 5a 7. 2bc + d(12 5) 8. b + 0.5[8 (2c + a)] Simplify each epression using the Distributive Property. 9. 5(2g 8) 10. 7(y + ) 11. -(4w ) 12. (6r + )2 Simplify each epression, showing all work. 1. 8( + 1) w w z 15. 9n 8 + (2n 11) 16. (7 + 4y) 2(2 + y) 17. (15 + 8d)(-5) 24d + d 18. 9(b 1) c + b + c f 4(5f + 4) (h 4) h (h + 7)
4 Solving One-Step Equations 1. Cancel out the number on the same side of the equal sign as the variable using inverse operations (addition/subtraction; multiplication/division) 2. Be sure to do the same thing to both sides of the equation! e: -18 = 6j -18 = 6j = j j = - Solving Two-Step Equations 1. Undo operations one at a time with inverse operations, using the order of operations in reverse (i.e. undo addition/subtraction before multiplication/division) 2. Be sure to always do the same thing to both sides of the equation! e: a 7 12 = 9 a 7 7 X 12 = a 7 = X 7 a = 21 Solving Multi-Step Equations 1. Clear any parentheses using the Distributive Property 2. Combine like terms on each side of the equal sign. Get the variable terms on the same side of the equation by adding/subtracting a variable term to/from both sides of the equation to cancel it out on one side 4. The equation is now a two-step equation, so finish solving it as described above e: 5(2 1) = = = = = 4 = 4
5 Solve each equation, showing all work. 21. f 64 = = 2d b 12 = = m = -28 w + 8 = h 4 = = 6y = (5d 8) = r + 21 = 49r 2. -9g = -(g + 2). 5( 2) = 5(4 + 1) 4. d 4 + d = 8d (-12) 5. f 6 = -2f + (f 2) 6. -2(y 1) = 4y (y + 2)
6 Scientific Notation Standard Form to Scientific Notation: move the decimal after the first non-zero digit and eliminate any trailing zeros. Multiply by 10 to the power equal to the number of places you moved the decimal point. If the original number was greater than 1, the eponent is positive. If the number was less than 1, the eponent is negative. Scientific Notation to Standard Form: move the decimal point the number of places indicated by the eponent. If the eponent is positive, move the decimal right. If negative, move left. e: Original number < 1, so negative eponent = e:.5 10 Positive eponent, so move decimal right.500 =,500 Negative Eponents & Simplifying Monomials Zero Eponent: power equals 1 Any number raised to the zero Negative Eponent: Move the base to the opposite side of the fraction line and make the eponent positive Monomial Monomial: Multiply the coefficients and add the eponents of like bases Monomial Monomial: Divide the coefficients and subtract the eponents of like bases Power of a Monomial: Raise each base (including the coefficient) to that power. If a base already has an eponent, multiply the two eponents Power of a Quotient: Raise each base (including the coefficient) to that power. If a base already has an eponent, multiply the two eponents e: y 0 = 1 e: -4 = 1 4 e: (4 )(2 5 ) = 8 8 e: a a 6 = a 5 = 1 a 5 e: (-2fg 5 ) = -8f g 15 e: 5d c 2 = 25d6 c 2
7 Convert each number to Scientific Notation ,000,000, ,201,000,000,000,000 Convert each number to Standard Form Simplify each epression. Write your answers using only positive eponents. 45. w m f5 f 48. m 2 h 2 g 49. (a 5 ) b 51. z r 6 r 2r p 2 q 54. 8d 2cd (g 4 h) 2 (2g h -1 ) (6a) (-n 2 k 4 ) w y w 2 y ( ) ( )
8 Slope & Rate of Change Finding the Slope Given Two Points: Use the coordinates from the points in the slope formula: Slope (m) = y 2 y Finding the Rate of Change From a Table: Determine the amount the dependent variable (y) is changing and the amount the independent variable () is changing. Rate of Change = change in y change in Finding the Slope From a Graph: Choose 2 points on the graph. Find the vertical change (rise) and horizontal change (run) between the 2 points and write it as a fraction rise run. (Up is positive, down is negative, right is positive, and left is negative). y e: (4, -2), (-, 8) m = 8 ( 2) 4 = 10 7 = 10 7 e: m 1 y 1 2 y 2 # months Cost ($) = = 25 dollars/month rise = +1 run = -2 m = 1 2 = 1 2 Graphing Linear Equations Slope-Intercept Form: y = m + b e: y = 2-4 slope y-intercept y-intercept: -4 How To Graph: 1. Make a point on the y-ais at the y-intercept. 2. Use the slope to determine where to make the net point. The numerator tells you the rise (how far up/down) and the denominator tells you the run (how far right/left) to make the net point.. Repeat to make more points and then connect the points with a line. slope: 2 = 2 1 rise run
9 Find the slope of the line that passes through the points. Show your work. 61. (-5, ), (2, 1) 62. (8, 4), (11, 6) 6. (9, ), (9, -1) 64. (-4, -2), (-6, 4) Find the rate of change. Show your work Number of Hours Distance (in miles) Number of Weeks Pounds Find the slope of the line Graph the line. 70. y = y = y = y = y = y = 1 4
10 Solving Proportions 1. Set the two cross-products equal to each other 2. Solve the equation for the variable e: m 4 = 5 5m = m = 2.4 Similar Figures 1. To find a missing side length, set up a proportion, matching up corresponding sides. 2. Solve the proportion using the steps above. e: 9 mm 1.5 = mm = 2.45 mm 1.5 mm The Pythagorean Theorem *** The Pythagorean Theorem applies to right triangles only ** The sides net to the right angle (a & b) are legs e: 12 cm The side across from the right angle (c) is the hypotenuse b = leg a = leg Pythagorean Theorem: a 2 + b 2 = c 2 To find the hypotenuse: add the squares of the legs and then find the square root of the sum To find a leg: subtract the square of the given leg from the square of the hypotenuse and then find the square root of the difference 15 cm is the hypotenuse = = 2 69 = 2 = cm e: a =?, b =, c = 6 a is a leg a = 6 2 a = 6 a 2 = 6 9 = 27 a =
11 Solve each proportion, showing all work = m 5 = k 78. h 7 = n = = c Assume each pair of figures is similar. Find the missing side length, showing all work cm in 8. ft 2 cm 1 in n 14 cm 6 in 8 ft r 2 ft mm mm y 18 in 12 in 9 mm 18 in j 2 mm 24 in f 10 cm 5 cm 8 cm Find the missing side length in each right triangle to the nearest tenth. Show your work! 87. a = 6, b = 8, c =? 88. a =?, b = 9 cm, c = 1 cm 89. a = 7, b =?, c = a = 14 in, b = 14 in, c =? in mm 5 in 10 mm in ft ft 52 in 20 cm 24 cm Determine whether or not you can form a right triangle from the given side lengths. Eplain , 22, , 12, 1
12 Evaluate each epression for a = 9, b = -, c = -2, d = 7. Show your work. 1. a - cd 2. 2b + c 2. a + d c b (a b) 2 + d(a + c) 5. 4c (b a) 6. a b - 5a 7. 2bc + d(12 5) 8. b + 0.5[8 (2c + a)] Simplify each epression using the Distributive Property. 9. 5(2g 8) 10. 7(y + ) 11. -(4w ) 12. (6r + )2 10g y w r + 6 Simplify each epression, showing all work. 1. 8( + 1) w w z 15. 9n 8 + (2n 11) 16. (7 + 4y) 2(2 + y) w - z n y 17. (15 + 8d)(-5) 24d + d 18. 9(b 1) c + b + c f 4(5f + 4) (h 4) h (h + 7) -6d b h - 9
13 Solve each equation, showing all work. 21. f 64 = = 2d 2. b 12 = = m + 21 f = 41 d = - 7 / 2 = -.5 b = 72 m = = w + 8 = h 4 = = 6y + 7 = -5 w = 19 h = 84 y = 5 / 2 = = (5d 8) = r + 21 = 49r 2. -9g = -(g + 2) = 1 = - 2 / 5 = -0.4 r = 1 / 2 = 0.5 no solution. 5( 2) = 5(4 + 1) 4. d 4 + d = 8d (-12) 5. f 6 = -2f + (f 2) 6. -2(y 1) = 4y (y + 2) = - d = -4 all real numbers y = 4 / 5 = 0.8
14 Convert each number to Scientific Notation ,000,000, ,201,000,000,000, Convert each number to Standard Form ,000, Simplify each epression. Write your answers using only positive eponents. 45. w m f5 f 48. m 2 1 w 9 m f 8 h 6 h 2 g g 49. (a 5 ) b 51. z r 6 r 2r 2 a 10 b 1 24r p 2 q q 54. 8d 2cd 2 p 2 4d 5 c 55. (g 4 h) 2 (2g h -1 ) (6a) 0 4g (-n 2 k 4 ) w 5 2 y 59. w 2 y 4 9n 4 k 8 w ( ) ( ) 9 y
15 Find the slope of the line that passes through the points. Show your work. 61. (-5, ), (2, 1) 62. (8, 4), (11, 6) 6. (9, ), (9, -1) 64. (-4, -2), (-6, 4) m = m = 2 m = undefined m = - Find the rate of change. Show your work Number of Hours Distance (in miles) Number of Weeks Pounds miles per hour -2 pounds per week Find the slope of the line m = - m = 0 m = 2 Graph the line. 70. y = y = y = y = y = y = 1 4
16 Solve each proportion, showing all work = m 5 = k 78. h 7 = n = = c m = 4.6 k = 7.2 h = 28 h = 88 h = Assume each pair of figures is similar. Find the missing side length to the nearest tenth cm in 8. ft 2 cm 1 in n 14 cm 6 in 8 ft = 4 cm = 4 in = 5. ft r 2 ft mm mm y 10 cm 18 in 12 in 9 mm 18 in f j 2 mm 24 in j 18. mm y = 1.5 in f = 6.25 cm 5 cm 8 cm Find the missing side length in each right triangle to the nearest tenth. Show your work! 87. a = 6, b = 8, c =? 88. a =?, b = 9 cm, c = 1 cm 89. a = 7, b =?, c = a = 14 in, b = 14 in, c =? c = 10 units a 9.4 cm b 12.1 units c 19.8 in in mm 5 in 10 mm = 4 units 14.1 mm 8.6 in 8.7 units in ft ft 52 in 19.8 units 116. in.5 ft 24 cm 20 cm 1. cm Determine whether or not you can form a right triangle from the given side lengths. Eplain , 22, , 12, 1 No; Yes; = 1 2
Summer 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 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 informationIndicate the answer choice that best completes the statement or answers the question.
Name: 9th Grade Final Test Review160 pts Class: Date: Indicate the answer choice that best completes the statement or answers the question. Use the Distributive Property to write each expression as an
More informationGeometry A & Geometry B & Honors Geometry Summer Packet
Geometry A & Geometry B & Honors Geometry Summer Packet RADICALS Radical expressions contain numbers and/or variables under a radical sign,. A radical sign tells you to take the square root of the value
More informationAlgebra I Part B. Help Pages & Who Knows
Algebra I Part B & Who Knows 83 Vocabulary General Absolute Value the distance between a number,, and zero on a number line; written as. Eample: 5 = 5 reads The absolute value of 5 is 5. -7 = 7 reads The
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 informationPAP Geometry Summer Assignment 2017
PAP Geometry Summer Assignment 2017 Name This assignment should be completed without the use of a calculator or an EOC chart. Show all work on separate paper for credit. A. Solve. Leave answers as improper
More informationMA 22000, Lesson 2 Functions & Addition/Subtraction Polynomials Algebra section of text: Sections 3.5 and 5.2, Calculus section of text: Section R.
MA 000, Lesson Functions & Addition/Subtraction Polynomials Algebra section of tet: Sections.5 and 5., Calculus section of tet: Section R.1 Definition: A relation is any set of ordered pairs. The set of
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 informationSummer Packet Pre-AP Algebra
Name: (5/11/17) Summer Packet Pre-AP Algebra 1-2018-19 To receive credit all work must be shown. There will be a test the first week back from summer on this packet. Any work done on additional paper must
More information( ) ( 4) ( ) ( ) Final Exam: Lessons 1 11 Final Exam solutions ( )
Show all of your work in order to receive full credit. Attach graph paper for your graphs.. Evaluate the following epressions. a) 6 4 6 6 4 8 4 6 6 6 87 9 b) ( 0) if ( ) ( ) ( ) 0 0 ( 8 0) ( 4 0) ( 4)
More informationRAMAPO&INDIAN*HILLS*SCHOOL*DISTRICT*
1 * * Algebra 2 CP Summer Packet RAMAPO&INDIAN*HILLS*SCHOOL*DISTRICT* DearRamapo*IndianHillsStudent: Pleasefindattachedthesummerpacketforourupcomingmathcourse.Thepurposeof thesummerpacketistoprovideouwithanopportunittoreviewprerequisiteskillsand
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 informationA 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
More informationEby, MATH 0310 Spring 2017 Page 53. Parentheses are IMPORTANT!! Exponents only change what they! So if a is not inside parentheses, then it
Eby, MATH 010 Spring 017 Page 5 5.1 Eponents Parentheses are IMPORTANT!! Eponents only change what they! So if a is not inside parentheses, then it get raised to the power! Eample 1 4 b) 4 c) 4 ( ) d)
More informationMy Math Plan Assessment #1 Study Guide
My Math Plan Assessment #1 Study Guide 1. Find the x-intercept and the y-intercept of the linear equation. 8x y = 4. Use factoring to solve the quadratic equation. x + 9x + 1 = 17. Find the difference.
More informationNote-Taking Guides. How to use these documents for success
1 Note-Taking Guides How to use these documents for success Print all the pages for the module. Open the first lesson on the computer. Fill in the guide as you read. Do the practice problems on notebook
More informationNew Rochelle High School Geometry Summer Assignment
NAME - New Rochelle High School Geometry Summer Assignment To all Geometry students, This assignment will help you refresh some of the necessary math skills you will need to be successful in Geometry and
More informationAlgebra Review C H A P T E R. To solve an algebraic equation with one variable, find the value of the unknown variable.
C H A P T E R 6 Algebra Review This chapter reviews key skills and concepts of algebra that you need to know for the SAT. Throughout the chapter are sample questions in the style of SAT questions. Each
More informationACCUPLACER MATH 0310
The University of Teas at El Paso Tutoring and Learning Center ACCUPLACER MATH 00 http://www.academics.utep.edu/tlc MATH 00 Page Linear Equations Linear Equations Eercises 5 Linear Equations Answer to
More informationOBJECTIVES UNIT 1. Lesson 1.0
OBJECTIVES UNIT 1 Lesson 1.0 1. Define "set," "element," "finite set," and "infinite set," "empty set," and "null set" and give two examples of each term. 2. Define "subset," "universal set," and "disjoint
More informationAlgebra 1 FINAL EXAM REVIEW Spring Semester Material (by chapter)
Name: Per.: Date: Algebra 1 FINAL EXAM REVIEW Spring Semester Material (by chapter) Your Algebra 1 Final will be on at. You will need to bring your tetbook and number 2 pencils with you to the final eam.
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 informationExample: x 10-2 = ( since 10 2 = 100 and [ 10 2 ] -1 = 1 which 100 means divided by 100)
Scientific Notation When we use 10 as a factor 2 times, the product is 100. 10 2 = 10 x 10 = 100 second power of 10 When we use 10 as a factor 3 times, the product is 1000. 10 3 = 10 x 10 x 10 = 1000 third
More informationOne of your primary goals in mathematics should be to become a good problem solver. It helps to approach a problem with a plan.
PROBLEM SOLVING One of our primar goals in mathematics should be to become a good problem solver. It helps to approach a problem with a plan. Step Step Step Step Understand the problem. Read the problem
More informationIntermediate Algebra 100A Final Exam Review Fall 2007
1 Basic Concepts 1. Sets and Other Basic Concepts Words/Concepts to Know: roster form, set builder notation, union, intersection, real numbers, natural numbers, whole numbers, integers, rational numbers,
More informationRising 7th Grade Math. Pre-Algebra Summer Review Packet
Rising 7th Grade Math Pre-Algebra Summer Review Packet Operations with Integers Adding Integers Negative + Negative: Add the absolute values of the two numbers and make the answer negative. ex: -5 + (-9)
More informationMath 75 Mini-Mod Due Dates Spring 2016
Mini-Mod 1 Whole Numbers Due: 4/3 1.1 Whole Numbers 1.2 Rounding 1.3 Adding Whole Numbers; Estimation 1.4 Subtracting Whole Numbers 1.5 Basic Problem Solving 1.6 Multiplying Whole Numbers 1.7 Dividing
More informationSTA Summer Review for Students Entering Algebra 3
Alg Summer Review STA Summer Review for Students Entering Algebra This packet will be collected and graded the first week of school. There will also be a test over this material the first week of school.
More informationSolving Equations. Solving Equations - decimal coefficients and constants. 2) Solve for x: 3(3x 6) = 3(x -2) 1) Solve for x: 5 x 2 28 x
Level C Review Packet This packet briefly reviews the topics covered on the Level A Math Skills Assessment. If you need additional study resources and/or assistance with any of the topics below, please
More informationPrecalculus Summer Assignment 2015
Precalculus Summer Assignment 2015 The following packet contains topics and definitions that you will be required to know in order to succeed in CP Pre-calculus this year. You are advised to be familiar
More informationSummer Work for students entering PreCalculus
Summer Work for students entering PreCalculus Name Directions: The following packet represent a review of topics you learned in Algebra 1, Geometry, and Algebra 2. Complete your summer packet on separate
More informationName: Geometry & Intermediate Algebra Summer Assignment
Name: Geometry & Intermediate Algebra Summer Assignment Instructions: This packet contains material that you have seen in your previous math courses (Pre- Algebra and/or Algebra 1). We understand that
More informationVisit us at: for a wealth of information about college mathematics placement testing!
North Carolina Early Mathematics Placement Testing Program, 9--4. Multiply: A. 9 B. C. 9 9 9 D. 9 E. 9 Solution and Answer to Question # will be provided net Monday, 9-8-4 North Carolina Early Mathematics
More informationAnswer the following questions using a fraction and a percent (round to the nearest tenth of a percent).
ALGEBRA 1 Ch 10 Closure Solving Comple Equations Name: Two-Way Tables: A simple random sample of adults in a metropolitan area was selected and a survey was administered to determine the relationship between
More informationSUMMER REVIEW PACKET. Name:
Wylie East HIGH SCHOOL SUMMER REVIEW PACKET For students entering Regular PRECALCULUS Name: Welcome to Pre-Calculus. The following packet needs to be finished and ready to be turned the first week of the
More informationSummer Work for students entering PreCalculus
Summer Work for students entering PreCalculus Name Directions: The following packet represent a review of topics you learned in Algebra 1, Geometry, and Algebra 2. Complete your summer packet on separate
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 informationEquations and Inequalities. College Algebra
Equations and Inequalities College Algebra Radical Equations Radical Equations: are equations that contain variables in the radicand How to Solve a Radical Equation: 1. Isolate the radical expression on
More informationGeometry 263 Prerequisites
Name Geometry 6 Prerequisites Dear Incoming Geometry Student, Listed below are fifteen skills that we will use throughout Geometry 6. You have likely learned and practiced these skills in previous math
More information6. The braking distance (in feet) for a car traveling 50 miles per hour on a wet uphill road is given by
MATH 34 - College Algebra Review for Test 3 Section 4.6. Let f ( ) = 3 5 + 4. (a) What is the domain? (b) Give the -intercept(s), if an. (c) Give the -intercept(s), if an. (d) Give the equation(s) of the
More informationElementary Algebra Study Guide Some Basic Facts This section will cover the following topics
Elementary Algebra Study Guide Some Basic Facts This section will cover the following topics Notation Order of Operations Notation Math is a language of its own. It has vocabulary and punctuation (notation)
More informationIntroductory Algebra Chapter 9 Review
Introductory Algebra Chapter 9 Review Objective [9.1a] Find the principal square roots and their opposites of the whole numbers from 0 2 to 2 2. The principal square root of a number n, denoted n,is the
More 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 informationRegina Summer Math Review. For students who will be taking. Algebra 2. Completed review packet due the first day of classes
Regina Summer Math Review For students who will be taking Algebra 2 Completed review packet due the first day of classes Algebra 2 Summer Review Packet Welcome to Algebra 2! In the following pages, you
More informationAlgebra 1 S1 Lesson Summaries. Lesson Goal: Mastery 70% or higher
Algebra 1 S1 Lesson Summaries For every lesson, you need to: Read through the LESSON REVIEW which is located below or on the last page of the lesson and 3-hole punch into your MATH BINDER. Read and work
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 informationWhich Mathematics Course Should You Take? August 22, 2018 Which mathematics course you should take depends on your current mathematics skill level
Which Mathematics Course Should You Take? August, 018 Which mathematics course you should take depends on your current mathematics skill level and your intended major. This is a conversation you should
More information( )( ) Algebra I / Technical Algebra. (This can be read: given n elements, choose r, 5! 5 4 3! ! ( 5 3 )! 3!(2) 2
470 Algebra I / Technical Algebra Absolute Value: A number s distance from zero on a number line. A number s absolute value is nonnegative. 4 = 4 = 4 Algebraic Expressions: A mathematical phrase that can
More informationDay 3: Section P-6 Rational Expressions; Section P-7 Equations. Rational Expressions
1 Day : Section P-6 Rational Epressions; Section P-7 Equations Rational Epressions A rational epression (Fractions) is the quotient of two polynomials. The set of real numbers for which an algebraic epression
More informationAlgebra One Dictionary
Algebra One Dictionary Page 1 of 17 A Absolute Value - the distance between the number and 0 on a number line Algebraic Expression - An expression that contains numbers, operations and at least one variable.
More informationMath 0210 Common Final Review Questions (2 5 i)(2 5 i )
Math 0 Common Final Review Questions In problems 1 6, perform the indicated operations and simplif if necessar. 1. ( 8)(4) ( )(9) 4 7 4 6( ). 18 6 8. ( i) ( 1 4 i ) 4. (8 i ). ( 9 i)( 7 i) 6. ( i)( i )
More informationALGEBRA 2 Summer Review Assignments Graphing
ALGEBRA 2 Summer Review Assignments Graphing To be prepared for algebra two, and all subsequent math courses, you need to be able to accurately and efficiently find the slope of any line, be able to write
More informationSection 1.1 Real Numbers and Number Operations
Section. Real Numbers and Number Operations Objective(s): Differentiate among subsets of the real number system. Essential Question: What is the difference between a rational and irrational number? Homework:
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 information2.3.2 Evaluate Variable Expressions Involving Multiplication of Rational Numbers
Section Anchors Skills 1.1 Using Variables A1.1.1.3.1 1.1.1 Write a Variable Expression to Represent a Given Situation 1.1.2 Given a Table of Values, Write a Variable Expression 1.2 Exponents and Order
More informationSummer Solutions Common Core Mathematics 8. Common Core. Mathematics. Help Pages
8 Common Core Mathematics 6 6 Vocabulary absolute value additive inverse property adjacent angles the distance between a number and zero on a number line. Example: the absolute value of negative seven
More informationSummer Work Packet for MPH Math Classes
Summer Work Packet for MPH Math Classes Students going into Algebra II/Trig AC Sept. 018 Name: This packet is designed to help students stay current with their math skills. Each math class expects a certain
More informationFundamentals of Algebra, Geometry, and Trigonometry. (Self-Study Course)
Fundamentals of Algebra, Geometry, and Trigonometry (Self-Study Course) This training is offered eclusively through the Pennsylvania Department of Transportation, Business Leadership Office, Technical
More informationMATH 110: FINAL EXAM REVIEW
MATH 0: FINAL EXAM REVIEW Can you solve linear equations algebraically and check your answer on a graphing calculator? (.) () y y= y + = 7 + 8 ( ) ( ) ( ) ( ) y+ 7 7 y = 9 (d) ( ) ( ) 6 = + + Can you set
More informationLevel 1: Simplifying (Reducing) Radicals: 1 1 = 1 = 2 2 = 4 = 3 3 = 9 = 4 4 = 16 = 5 5 = 25 = 6 6 = 36 = 7 7 = 49 =
Name Period Date Unit 5:Special Right Triangles and TrigonometryNotes Packet #1 Section 7.2/7.3: Radicals, Pythagorean Theorem, Special Right Triangles (PA) CRS NCP 24-27 Work with squares and square roots
More informationMATH 0960 ELEMENTARY ALGEBRA FOR COLLEGE STUDENTS (8 TH EDITION) BY ANGEL & RUNDE Course Outline
MATH 0960 ELEMENTARY ALGEBRA FOR COLLEGE STUDENTS (8 TH EDITION) BY ANGEL & RUNDE Course Outline 1. Real Numbers (33 topics) 1.3 Fractions (pg. 27: 1-75 odd) A. Simplify fractions. B. Change mixed numbers
More informationAlgebra/Trigonometry Review Notes
Algebra/Trigonometry Review Notes MAC 41 Calculus for Life Sciences Instructor: Brooke Quinlan Hillsborough Community College ALGEBRA REVIEW FOR CALCULUS 1 TOPIC 1: POLYNOMIAL BASICS, POLYNOMIAL END BEHAVIOR,
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 information1 of 7 8/11/2014 10:27 AM Units: Teacher: PacedAlgebraPartA, CORE Course: PacedAlgebraPartA Year: 2012-13 The Language of Algebra What is the difference between an algebraic expression and an algebraic
More informationEquations and Inequalities
Equations and Inequalities Figure 1 CHAPTER OUTLINE.1 The Rectangular Coordinate Systems and Graphs. Linear Equations in One Variable.3 Models and Applications. Comple Numbers.5 Quadratic Equations.6 Other
More informationLESSON 9.1 ROOTS AND RADICALS
LESSON 9.1 ROOTS AND RADICALS LESSON 9.1 ROOTS AND RADICALS 67 OVERVIEW Here s what you ll learn in this lesson: Square Roots and Cube Roots a. Definition of square root and cube root b. Radicand, radical
More informationMATH SKILL HANDBOOK. a (b ) II. Measurements and Significant Figures. 0 mm
I. Symbols Δ change in quantity is defined as ± plus or minus a quantity a b ab is proportional to a (b ) = is equal to a b is approimately equal to a/b a_ b is less than or equal to a multiplied by b
More information5. Find the slope intercept equation of the line parallel to y = 3x + 1 through the point (4, 5).
Rewrite using rational eponents. 2 1. 2. 5 5. 8 4 4. 4 5. Find the slope intercept equation of the line parallel to y = + 1 through the point (4, 5). 6. Use the limit definition to find the derivative
More informationAP CALCULUS SUMMER REVIEW WORK
AP CALCULUS SUMMER REVIEW WORK The following problems are all ALGEBRA concepts you must know cold in order to be able to handle Calculus. Most of them are from Algebra, some are from Pre-Calc. This packet
More informationLevel Unit Chapter Lesson ChapterTitle LessonTitle Introduction Introduction How to take the placement tests How to take the
Level Unit Chapter Lesson ChapterTitle LessonTitle 0 0 1 1 Introduction Introduction 0 0 2 1 How to take the placement tests How to take the placement tests 0 0 3 0 Placement Test I 0 0 4 0 Placement Test
More informationAlgebra II Notes Polynomial Functions Unit Introduction to Polynomials. Math Background
Introduction to Polynomials Math Background Previously, you Identified the components in an algebraic epression Factored quadratic epressions using special patterns, grouping method and the ac method Worked
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 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 information5.5 Special Rights. A Solidify Understanding Task
SECONDARY MATH III // MODULE 5 MODELING WITH GEOMETRY 5.5 In previous courses you have studied the Pythagorean theorem and right triangle trigonometry. Both of these mathematical tools are useful when
More informationFOR ALL STUDENTS TAKING ALGEBRA I SUMMER REVIEW PACKET
FOR ALL STUDENTS TAKING ALGEBRA I - SUMMER REVIEW PACKET Dear Student and Parent/Guardian, The math department at Central Dauphin School District wants ou to be successful in Algebra I. We also want ou
More informationChapter 7: Exponents
Chapter : Exponents Algebra Chapter Notes Name: Notes #: Sections.. Section.: Review Simplify; leave all answers in positive exponents:.) m -.) y -.) m 0.) -.) -.) - -.) (m ) 0.) 0 x y Evaluate if a =
More informationMA094 Part 2 - Beginning Algebra Summary
MA094 Part - Beginning Algebra Summary Page of 8/8/0 Big Picture Algebra is Solving Equations with Variables* Variable Variables Linear Equations x 0 MA090 Solution: Point 0 Linear Inequalities x < 0 page
More informationRemember, you may not use a calculator when you take the assessment test.
Elementary Algebra problems you can use for practice. Remember, you may not use a calculator when you take the assessment test. Use these problems to help you get up to speed. Perform the indicated operation.
More informationPre-Algebra Curriculum Map Unit 1: The Number System M08.A-N Essential Questions Standards Content Skills Vocabulary
Unit 1: The Number System M08.A-N Essential Questions Standards Content Skills Vocabulary Why is it helpful to write numbers in different ways? M08.A-N.1.1.1 Determine whether a number is rational or irrational.
More informationPart 2 - Beginning Algebra Summary
Part - Beginning Algebra Summary Page 1 of 4 1/1/01 1. Numbers... 1.1. Number Lines... 1.. Interval Notation.... Inequalities... 4.1. Linear with 1 Variable... 4. Linear Equations... 5.1. The Cartesian
More informationAccessible Topic - Topics accessible to visually impaired students using a screen reader.
Course Name: Winter 2018 Math 95 - Course Code: ALEKS Course: Developmental Math Instructor: Course Dates: Begin: 01/07/2018 End: 03/23/2018 Course Content: 390 Topics (172 goal + 218 prerequisite) / 334
More informationThe letter m is used to denote the slope and we say that m = rise run = change in y change in x = 5 7. change in y change in x = 4 6 =
Section 4 3: Slope Introduction We use the term Slope to describe how steep a line is as ou move between an two points on the line. The slope or steepness is a ratio of the vertical change in (rise) compared
More informationAlgebra 1. Math Review Packet. Equations, Inequalities, Linear Functions, Linear Systems, Exponents, Polynomials, Factoring, Quadratics, Radicals
Algebra 1 Math Review Packet Equations, Inequalities, Linear Functions, Linear Systems, Exponents, Polynomials, Factoring, Quadratics, Radicals 2017 Math in the Middle 1. Clear parentheses using the distributive
More informationFor problems 1 4, evaluate each expression, if possible. Write answers as integers or simplified fractions
/ MATH 05 TEST REVIEW SHEET TO THE STUDENT: This Review Sheet gives you an outline of the topics covered on Test as well as practice problems. Answers are at the end of the Review Sheet. I. EXPRESSIONS
More informationPreCalculus. American Heritage Upper School Summer Math Packet
! PreCalculus American Heritage Upper School Summer Math Packet All Upper School American Heritage math students are required to complete a summer math packet. This packet is intended for all students
More informationAlgebra Review. 1. Evaluate the expression when a = -3 and b = A) 17 B) 1 C) Simplify: A) 17 B) 29 C) 16 D)
Algebra Review a b. Evaluate the epression when a = - and b = -. A) B) C). Simplify: 6 A) B) 9 C) 6 0. Simplify: A) 0 B) 8 C) 6. Evaluate: 6z y if =, y = 8, and z =. A) B) C) CPT Review //0 . Simplify:
More informationAlgebra I Unit Report Summary
Algebra I Unit Report Summary No. Objective Code NCTM Standards Objective Title Real Numbers and Variables Unit - ( Ascend Default unit) 1. A01_01_01 H-A-B.1 Word Phrases As Algebraic Expressions 2. A01_01_02
More information1 a) Remember, the negative in the front and the negative in the exponent have nothing to do w/ 1 each other. Answer: 3/ 2 3/ 4. 8x y.
AP Calculus Summer Packer Key a) Remember, the negative in the front and the negative in the eponent have nothing to do w/ each other. Answer: b) Answer: c) Answer: ( ) 4 5 = 5 or 0 /. 9 8 d) The 6,, and
More informationA. Incorrect. Solve for a variable on the bottom by first moving it to the top. D. Incorrect. This answer has too many significant figures.
MCAT Physics - Problem Drill 03: Math for Physics Question No. 1 of 10 1. Solve the following equation for time, with the correct number of significant figures: Question #01 m 15.0 m 2.5 = s time (A) 0.17
More informationALGEBRA SUMMER MATH PACKET
Algebra Summer Packet 0 NAME DATE ALGEBRA SUMMER MATH PACKET Write an algebraic epression to represent the following verbal epressions. ) Double the sum of a number and. Solve each equation. ) + y = )
More informationRising 8th Grade Math. Algebra 1 Summer Review Packet
Rising 8th Grade Math Algebra 1 Summer Review Packet 1. Clear parentheses using the distributive property. 2. Combine like terms within each side of the equal sign. Solving Multi-Step Equations 3. Add/subtract
More informationThe slope, m, compares the change in y-values to the change in x-values. Use the points (2, 4) and (6, 6) to determine the slope.
LESSON Relating Slope and -intercept to Linear Equations UNDERSTAND The slope of a line is the ratio of the line s vertical change, called the rise, to its horizontal change, called the run. You can find
More informationAppendix A. Common Mathematical Operations in Chemistry
Appendix A Common Mathematical Operations in Chemistry In addition to basic arithmetic and algebra, four mathematical operations are used frequently in general chemistry: manipulating logarithms, using
More informationMathematics GRADE 8 Teacher Packet
COMMON CORE Standards Plus Mathematics GRADE 8 Teacher Packet Copyright 01 Learning Plus Associates All Rights Reserved; International Copyright Secured. Permission is hereby granted to teachers to reprint
More informationRadicals: To simplify means that 1) no radicand has a perfect square factor and 2) there is no radical in the denominator (rationalize).
Summer Review Packet for Students Entering Prealculus Radicals: To simplify means that 1) no radicand has a perfect square factor and ) there is no radical in the denominator (rationalize). Recall the
More 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 informationName Class Date. You can use the properties of equality to solve equations. Subtraction is the inverse of addition.
2-1 Reteaching Solving One-Step Equations You can use the properties of equality to solve equations. Subtraction is the inverse of addition. What is the solution of + 5 =? In the equation, + 5 =, 5 is
More informationMath 8 Curriculum Map and I Can Statements Diane Hamilton
Math 8 Curriculum Map and I Can Statements 203 204 Diane Hamilton Unit : Numbers Review A Whole Numbers Place Value 2 Identify the place value of a whole number 2 Decimals Place Value 2 Identify the place
More information