Algebra Meeting (Multiple topics from pre-algebra and Algebra I)
|
|
- Jennifer Long
- 5 years ago
- Views:
Transcription
1 Algebra Meeting (Multiple topics from pre-algebra and Algebra I) Topic This meeting s problems cover a variety of topics from pre-algebra and Algebra I. The topics include simplifying expressions, solving equations and inequalities, linear relationships and graphing. Materials Needed Copies of the Algebra problem set (Problems and answers can be viewed below. Complete solutions and a more student-friendly version of the problems with pictures and larger font are available for download from on the MCP Members Only page of the Club Program section.) Meeting Plan The problems in this problem set increase in difficulty as students progress. Given the wide range of topics that are covered, it is suggested that students work on the problems in pairs or small groups. Students who are taking or have completed algebra should be paired with students who have not. 1. Maya initially thought that 8 was a solution to 2x + 20 = 4x 4, but when she checked her work, she realized that her answer was incorrect. After substituting 8 for x, how much greater is the expression on the left side of the equals sign than the expression on the right side? School Handbook Warm-Up Three bags each contain the same number of marbles. (The weight of an empty bag would not affect the weight on the scale.) If three bags of marbles plus two more marbles balance 14 marbles, as shown, how many marbles are in each bag? School Handbook Warm-Up The function f (x) is defined by f (x) = x 2 x. What is the value of f (4)? 2007 School Competition Countdown Round #4 4. What is the value of x such that (x, 0) is a solution of the equation y = 3x 4? Express your answer as a common fraction School Handbook Workout What integer is tripled when nine is added to three-fourths of it? 2006 School Competition Target Round #7 6. A fitness center charges a membership fee plus a fixed amount per day for each day the center is used. If Claire paid $68 for 22 days of use and Adrian paid $71 for 24 days of use, how may dollars is the membership fee? 2006 School Competition Countdown Round #28 7. What number should be added to both the numerator and the dominator of 1/5 to get a fraction equivalent to 4/5? School Handbook Warm-Up If y = 2x + 1, which of the following equations is true? (A) x = 2y + 1 (B) x = (1/2)y + 1 (C) x = (1/2)y (1/2) (D) x = (1/2)y + (1/2) School Handbook Warm-Up This graph shows the linear relationship between the time in seconds, x, for Caroline s walk and the distance in meters, y, Caroline is from her starting point. The graph passes through the point (20, 30). According to the graph, how many meters will Caroline walk in exactly one hour? School Handbook Warm-Up Several points are plotted on a graph. For each point, the x-coordinate is the length of a side of a square while the y-coordinate is the perimeter of that same square. One such point is (2, 8) since a square with side length 2 units has a perimeter of 8 units. What is the slope of the line connecting the points? Express your answer in simplest form School Handbook Warm-Up MATHCOUNTS Club Resource Guide 45
2 11. According to the linear function represented in this table, what is the value of x when y = 8? School Handbook Warm-Up 7-10 x y How far apart are the y-intercepts of the line with the equation y = 2x + 3 and the line that goes through the point (4, 2) and has a slope of 1? School Handbook Warm-Up What is the least positive integer value of x for which the inequality 3x > 2x + 1 is true? School Handbook Warm-Up If x y = 6 and x + y = 12, what is the value of y? 2006 School Competition Countdown Round #6 15. For what value of x will (3 + x) (5 + x) = (1 + x) (2 + x) be true? 2007 School Competition Target Round #4 16. Milton spilled some ink on his homework paper. He can t read the coefficient of x, but he knows that the equation has two distinct negative, integer solutions. What is the sum of all of the distinct possible integers x that could be under the ink stain? School Handbook Warm-Up x + 36 = In the equation x 7 3 = 2, what is the product of all possible values of x? School Handbook Warm-Up 6-8 Answers: 8; 4 marbles; 12; 4/3; 4; $35; 15; C; 5400 meters; 4; 21; 3 units; 2; 3; 1; 85; 48 Possible Next Steps Problem #10 has students examine the relationship between the side length of a square and its perimeter. Based on their solution to this problem, can students predict what the slope of the line would be if they were to graph the relationship between the side length of an equilateral triangle and its perimeter? Similarly, students can graph the relationship between the side length of a square and its corresponding area to see that these relationships are not always linear MATHCOUNTS Club Resource Guide
3 Algebra Student Sheet 1. Maya initially thought that 8 was a solution to 2x + 20 = 4x 4, but when she checked her work, she realized that her answer was incorrect. After substituting 8 for x, how much greater is the expression on the left side of the equals sign than the expression on the right side? 2. marbles Three bags each contain the same number of marbles. (The weight of an empty bag would not affect the weight on the scale.) If three bags of marbles plus two more marbles balance 14 marbles, as shown, how many marbles are in each bag? 3. The function f (x) is defined by f (x) = x 2 x. What is the value of f (4)? 4. What is the value of x such that (x, 0) is a solution of the equation y = 3x 4? Express your answer as a common fraction. 5. What integer is tripled when nine is added to three-fourths of it? 6. $ A fitness center charges a membership fee plus a fixed amount per day for each day the center is used. If Claire paid $68 for 22 days of use and Adrian paid $71 for 24 days of use, how many dollars is the membership fee? 7. What number should be added to both the numerator and the dominator of 1/5 to get a fraction equivalent to 4/5? 8. If y = 2x + 1, which of the following equations is true? (A) x = 2y + 1 (B) x = (1/2)y + 1 (C) x = (1/2)y (1/2) (D) x = (1/2)y + (1/2) Copyright MATHCOUNTS, Inc MATHCOUNTS Club Resource Guide Problem Set
4 9. meters This graph shows the linear relationship between the time in seconds, x, for Caroline s walk and the distance in meters, y, Caroline is from her starting point. The graph passes through the point (20, 30). According to the graph, how many meters will Caroline walk in exactly one hour? 10. Several points are plotted on a graph. For each point, the x- coordinate is the length of a side of a square while the y-coordinate is the perimeter of that same square. One such point is (2, 8) since a square with side length 2 units has a perimeter of 8 units. What is the slope of the line connecting the points? Express your answer in simplest form. 11. According to the linear function represented in this table, what is the value of x when y = 8? x y units How far apart are the y-intercepts of the line with the equation y = 2x + 3 and the line that goes through the point (4, 2) and has a slope of 1? 13. What is the least positive integer value of x for which the inequality 3x > 2x + 1 is true? 14. If x y = 6 and x + y = 12, what is the value of y? 15. For what value of x will (3 + x) (5 + x) = (1 + x) (2 + x) be true? 16. Milton spilled some ink on his homework paper. x 2 + x + 36 = 0 He can t read the coefficient of x, but he knows that the equation has two distinct negative, integer solutions. What is the sum of all of the distinct possible integers that could be under the ink stain? 17. In the equation x 7 3 = 2, what is the product of all possible values of x? Copyright MATHCOUNTS, Inc MATHCOUNTS Club Resource Guide Problem Set
5 Algebra Meeting Solutions ( MCP Club Resource Guide) Problem 1. When Maya substitutes her 8 in for x, she finds that the left side of the equation has a value of 2(8) + 20 = 36 and the right side of the equation has a value of 4(8) 4 = 28. The expression on the left of her original equation is then = 8 greater than the expression on the right side. Problem 2. Since the 2 loose marbles on the left balance with 2 marbles on the right, we know that the contents of the three plastic bags must balance with the other 12 marbles on the right. If three equal bags have a total of 12 marbles, then each bag must have 12 3 = 4 marbles. Problem 3. When 4 is plugged in for x, we see f(4) = Simplifying the expression on the right gives us 16 4 = 12. Problem 4. If (x, 0) is a solution of the equation y = 3x 4, then we can solve the equation 0 = 3x 4 to find the value of x. Adding 4 to both sides of the equation, we get 4 = 3x. Dividing both sides by 3, we get 4/3 = x, or x = 4/3. Since the point (x, 0) is on the x-axis, we also could use a graphing calculator to see where the graph of y = 3x + 4 intersects the x-axis or where the lines y = 3x + 4 and y = 0 intersect. Problem 5. Translating the English to algebra and letting our unknown integer be x, we have 3x = (3/4)x + 9. Multiplying both sides of the equation by 4 gives us 12x = 3x Subtracting 3x from both sides (9x = 36) and then dividing by 9 results in x = 4. Problem 6. Adrian s total fee was $71 $68 = $3 more than Claire s and was for 2 additional days. This tells us each day s fee is $3 2 = $1.50. For Claire s 22 days, she would have paid 22 $1.50 = $33 for her daily fees and $68 $33 = $35 for the membership fee. Problem 7. Translating from English to algebra and letting our unknown number be x, we have (1 + x)/(5 + x) = 4/5. When cross products are set equal, this simplifies to 5(1 + x) = 4(5 + x) or 5 + 5x = x. Subtracting 4x and 5 from both sides gives us x = 15. Problem 8. The equation y = 2x + 1 is to be solved for x in terms of y. Subtracting 1 from both sides of the equation, we get y 1 = 2x. Now we can divide both sides of the equation by 2, which gives (y 1)/2 = x. Distributing this division by 2, we can rewrite this as x = (1/2)y 1/2, which is choice C. Problem 9. The graph shows a linear relationship, which tells us we can use proportional reasoning for this problem. We want to know how far Caroline can walk in one hour. The glitch is that we are given information in seconds and looking for information in hours. If Caroline walks 30 meters in 20 seconds she will walk 30 meters 3 = 90 meters in 20 seconds 3 = 60 seconds or 1 minute. One hour is 60 minutes, so Caroline will walk 90 meters 60 = 5400 meters in 1 minute 60 = 60 minutes or 1 hour. If we want to use the graph, we could use the fact that 1 hour is 3600 seconds and y = 1.5(3600) = 5400 meters. Problem 10. The perimeter of a square is always four times its side length, so the equation of the line is y = 4x. If we add one unit to the side length of a square, then the perimeter will increase by four units. The slope of the line is 4. We also could choose two points on the line and apply the slope formula. We know (2, 8) is on the line, and because a square with a side Copyright MATHCOUNTS, Inc MATHCOUNTS Club Resource Guide Solution Set
6 length of 1 unit has a perimeter of 4 units, the point (1, 4) is on the line. Using the slope formula, we get (8 4)/(2 1) = 4/1 = 4. Problem 11. The x-values increase by 5 while the y-values decrease by 3. If we write the next three ordered pairs in the table, we get (11, 14), then (16, 11), then (21, 8). We have stumbled onto the desired y-value of 8, and the corresponding x-value is 21. Problem 12. The y-intercept of the line with the equation y = 2x + 3 is said to be 3, which means more specifically the point (0, 3). The slope of the other line is 1, which means that as we move 1 unit to the right the line drops down 1 unit. If we start at the point (4, 2) and move to the left 1 units, the line goes up 1 unit. If we go four units left, the line goes four units up to the point (0, 6), which means that the y-intercept of this line is 6. These two y-intercepts are 6 3 = 3 units apart. Problem 13. We start with the inequality 3x > 2x + 1. If we subtract 2x from both sides of the inequality, we have x > 1. The least integer that is greater than 1 is 2. Problem 14. If we add the expressions on the left sides of the two equations together, they will equal the sum of the expressions on the right sides of the two equations. This gets us to 2x = 18. Now we see x = 9. Substituting into the first equation, we have 9 y = 6, so y = 3. Problem 15. The first step is to set the cross products of the equation equal to each other. This gives us (3 + x)(2 + x) = (1 + x)(5 + x) and simplifies to x 2 + 5x + 6 = x 2 + 6x + 5. Subtracting x 2 from both sides gives us 5x + 6 = 6x + 5. Now we subtract 5x and 5 from each side to see x = 1. Problem 16. The fact that the equation has two distinct negative, integer solutions means that it can be factored into the product of two binomials of the form (x + a)(x + b), with integers a and b. This in turn means that the coefficient under the ink stain must be a sum of two integers whose product is equal to the 36 that we can see. The possibilities are = 37, = 20, = 15 and = 13. The possibility of = 12 would not give us two distinct solutions. The sum of these distinct possibilities is = 85. Problem 17. Adding 3 to both sides of the equation, we get the simpler x 7 = 1. The value of x 7 could be either 1 or 1, so x = 8 or 6. The product of these two values is 48. Copyright MATHCOUNTS, Inc MATHCOUNTS Club Resource Guide Solution Set
Math 46 Final Exam Review Packet
Math 46 Final Exam Review Packet Question 1. Perform the indicated operation. Simplify if possible. 7 x x 2 2x + 3 2 x Question 2. The sum of a number and its square is 72. Find the number. Question 3.
More informationIn order to prepare for the final exam, you need to understand and be able to work problems involving the following topics:
MATH 080: Review for the Final Exam In order to prepare for the final exam, you need to understand and be able to work problems involving the following topics: I. Simplifying Expressions: Do you know how
More informationUnit 1 Foundations of Algebra
1 Unit 1 Foundations of Algebra Real Number System 2 A. Real Number System 1. Counting Numbers (Natural Numbers) {1,2,3,4, } 2. Whole Numbers { 0,1,2,3,4, } 3. Integers - Negative and Positive Whole Numbers
More informationALGEBRA 1 FINAL EXAM 2006
Overall instructions: Your Name Teacher ALGEBRA FINAL EXAM 2006 There is a mix of easier and harder problems. Don t give up if you see some questions that you don t know how to answer. Try moving on to
More informationUsing Linear Equations to Solve Problems
Chapter 5: Writing Linear Equations Sections 1-4 Name Algebra Notes Using Linear Equations to Solve Problems Slope-Intercept Point Slope Standard Form y = mx + b y- y 1 = m ( x = x 1 ) Ax + By = C So,
More information= = =
. D - To evaluate the expression, we can regroup the numbers and the powers of ten, multiply, and adjust the decimal and exponent to put the answer in correct scientific notation format: 5 0 0 7 = 5 0
More informationShow all work on separate grid and lined paper. Number each question clearly.
Algebra summer homework 2015 In addition to the practice problems below, students are to work in IXL.com in the 8 th grade content. Students must know all of the perfect squares from 1 to 625 for automatic
More informationPatterns and Relations Unit Review
Patterns and Relations Unit Review 1. In the equation, determine the value of R when w = 13.. The pattern in this table continues. Write an equation that relates the number of squares to the figure number.
More informationCOMMON CORE MATHEMATICS CURRICULUM
COMMON CORE MATHEMATICS CURRICULUM Lesson 1 8 4 Lesson 1: Writing Equations Using Symbols Write each of the following statements using symbolic language. 1. When you square five times a number you get
More informationUnit #3 Linear Algebra Review
Name: Unit # Linear Algebra Review Date: 1. The expression x + 5y 7x+ 4y is equivalent to which of the following? (1) 4x 9y () 4x y () 9y 4x (4) 10x + 9y. Written without parentheses, the expression 5
More informationNAME DATE PER. FALL FINAL EXAM REVIEW ALGEBRA 1 Solve = 6 3v = -3(c + 5)
FINAL EXAM REVIEW, p. 1 NAME DATE PER. FALL FINAL EXAM REVIEW ALGEBRA 1 Solve. 1. = 6 v. 1 = -(c + 5). 5 (x ) = 6. 7x + = 5x + 8 5. r 1 1 6. x 1 x 5 Write an equation, and then solve. 7. Ben joined The
More informationFranklin Math Bowl 2010 Group Problem Solving Test Grade 6
Group Problem Solving Test Grade 6 1. Carrie lives 10 miles from work. She leaves in the morning before traffic is heavy and averages 30 miles per hour. When she goes home at the end of the day, traffic
More informationVOTE FOR YOUR FAVORITE SODA BRAND!!
VOTE FOR YOUR FAVORITE SODA BRAND!! NUMBER OF VOTES 1000 995 990 985 980 975 970 965 960 955 950 PEPSI COCA-COLA STORE BRAND FAVORITE SODA NUMBER OF VOTES 1000 900 800 700 600 500 400 300 200 100 0 PEPSI
More informationUnit 5. Linear equations and inequalities OUTLINE. Topic 13: Solving linear equations. Topic 14: Problem solving with slope triangles
Unit 5 Linear equations and inequalities In this unit, you will build your understanding of the connection between linear functions and linear equations and inequalities that can be used to represent and
More informationAlgebra I+ Pacing Guide. Days Units Notes Chapter 1 ( , )
Algebra I+ Pacing Guide Days Units Notes Chapter 1 (1.1-1.4, 1.6-1.7) Expressions, Equations and Functions Differentiate between and write expressions, equations and inequalities as well as applying order
More informationUnit 5. Linear equations and inequalities OUTLINE. Topic 13: Solving linear equations. Topic 14: Problem solving with slope triangles
Unit 5 Linear equations and inequalities In this unit, you will build your understanding of the connection between linear functions and linear equations and inequalities that can be used to represent and
More informationPre-Algebra Mastery Test #8 Review
Class: Date: Pre-Algebra Mastery Test #8 Review Find the value of x for the figure. 1 Perimeter = 26 Solve the equation. Check your solution. 2 1 y + 45 = 51 The smaller box is 2 feet tall and casts a
More informationMATHCOUNTS State Competition Countdown Round Problems This section contains problems to be used in the Countdown Round.
MATHCOUNTS 2011 State Competition Countdown Round Problems 1 80 This section contains problems to be used in the Countdown Round. National Sponsors Raytheon Company * National Defense Education Program
More information7 = 8 (Type a simplified fraction.)
Student: Date: Assignment: Exponential and Radical Equations 1. Perform the indicated computation. Write the answer in scientific notation. 3. 10 6 10. 3. 4. 3. 10 6 10 = (Use the multiplication symbol
More informationUnit 3 Linear Algebra & Unit 4 Systems of Linear Equations REVIEW. + is equal to 2.
Unit 3 Linear Algebra & Unit 4 Systems of Linear Equations REVIEW 1. The expression 3x + 5y 7x+ 4y is equivalent to which of the following? 1. (1) 4x 9y () 9y 4 x (3) 4x y (4) 10x + 9y. Written without
More informationA2.MidtermRev2015. Algebra 2 Midterm Exam Review Part 1: Multiple Choice (75pts)
Name: UNIT 1 Algebra 2 Midterm Exam Review Part 1: Multiple Choice (75pts) Patterns & Expressions 1. Which of the following is the seventh term in the pattern below? 2. Which of the following is the eighth
More informationPractice Test 1 BLACKLINE MASTERS
Practice Test 1 BLACKLINE MASTERS Name Date Chapter 1: The Number System Answer the questions that follow. 1. Which of the numbers below is not irrational? A. 5 C. 2 9 B. D. 1.34344344434444 2. Which of
More informationAlgebra I Exam Review
Name Algebra I Exam Review Assigned on Assignment 1/17 Final Exam Practice Units 1 and Problems 1-4 1/18 Final Exam Practice Units and 4 Problems 5-5 1/19 Practice Final Exam Multiple Choice 1-16 1/ Practice
More informationAlgebra I - Study Guide for Final
Name: Date: Period: Algebra I - Study Guide for Final Multiple Choice Identify the choice that best completes the statement or answers the question. To truly study for this final, EXPLAIN why the answer
More informationIMPORTANT DEFINITIONS. One fourth is white. Two fourths are white. One half is black. Three fourths are white. Four fourths are white
Chapter Fractions IMPORTANT DEFINITIONS. Fractions A fraction is a number representing a part of a whole. The whole may be a single object is a group of objects. A fraction is part of an entire object.
More informationKEYSTONE ALGEBRA I REVIEW
1. Which graph represents a linear function 4. The faces of a cube are numbered from 1 to 6. If the cube is tossed once, what is the probability that a prime number or a number divisible by 2 is obtained
More informationCORE. Chapter 3: Interacting Linear Functions, Linear Systems. Algebra Assessments
CORE Algebra Assessments Chapter 3: Interacting Linear Functions, Linear Systems 97 98 Bears Band Booster Club The Bears Band Booster Club has decided to sell calendars to the band members and their parents.
More informationKansas City Area Teachers of Mathematics 2018 KCATM Math Competition ALGEBRA GRADE 8
Kansas City Area Teachers of Mathematics 2018 KCATM Math Competition ALGEBRA GRADE 8 INSTRUCTIONS Do not open this booklet until instructed to do so. Time limit: 20 minutes You may use calculators. Mark
More informationA Partial List of Topics: Math Spring 2009
A Partial List of Topics: Math 112 - Spring 2009 This is a partial compilation of a majority of the topics covered this semester and may not include everything which might appear on the exam. The purpose
More informationLHS Algebra Pre-Test
Your Name Teacher Block Grade (please circle): 9 10 11 12 Course level (please circle): Honors Level 1 Instructions LHS Algebra Pre-Test The purpose of this test is to see whether you know Algebra 1 well
More informationAlgebra II Polynomials: Operations and Functions
Slide 1 / 276 Slide 2 / 276 Algebra II Polynomials: Operations and Functions 2014-10-22 www.njctl.org Slide 3 / 276 Table of Contents click on the topic to go to that section Properties of Exponents Review
More informationSolving Equations Quick Reference
Solving Equations Quick Reference Integer Rules Addition: If the signs are the same, add the numbers and keep the sign. If the signs are different, subtract the numbers and keep the sign of the number
More informationAlgebra Supplement Homework Packet #1
Algebra Supplement Homework Packet #1 Day 1: Fill in each blank with one of the words or phrases listed below. Distributive Real Reciprocals Absolute value Opposite Associative Inequality Commutative Whole
More informationAlgebra 1 Spencer Unit 4 Notes: Inequalities and Graphing Linear Equations. Unit Calendar
Algebra 1 Spencer Unit 4 Notes: Inequalities and Graphing Linear Equations Unit Calendar Date Topic Homework Nov 5 (A ) 6.1 Solving Linear Inequalities +/- 6.2 Solving Linear Inequalities x/ 6.3 Solving
More informationEureka Math. Grade, Module 4. Student File_B Contains Sprint and Fluency, Exit Ticket, and Assessment Materials
A Story of Eureka Math Grade, Module 4 Student File_B Contains Sprint and Fluency,, and Assessment Materials Published by the non-profit Great Minds. Copyright 2015 Great Minds. No part of this work may
More informationLHS June 2012 Algebra 1 Final Exam
Teacher: (circle one) Mrs. Gordon Mr. Normile E-block Mr. Normile F-block LHS June 2012 Algebra 1 Final Exam Multiple Choice + Short Answer = /65 Part I Multiple Choice 33 questions 33 points This is a
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 informationOn Your Own. Applications. Unit 1. 1 p = 7.5n - 55, where n represents the number of car washes and p represents the profit in dollars.
Applications 1 p = 7.5n - 55, where n represents the number of car washes and p represents the profit in dollars. 2 t = 0.5 + 2a, where a represents the area of the grass and t represents the time in hours
More informationPennsylvania Algebra I Assessment Anchors and Eligible Content
A Correlation of Algebra 1, 2018 To the Assessment Anchors and Eligible Content Copyright 2017 Pearson Education, Inc. or its affiliate(s). All rights reserved to the MODULE 1 Operations and Linear Equations
More information6.6 General Form of the Equation for a Linear Relation
6.6 General Form of the Equation for a Linear Relation FOCUS Relate the graph of a line to its equation in general form. We can write an equation in different forms. y 0 6 5 y 10 = 0 An equation for this
More informationMath: Question 1. Which of the following values satisfies the equation above? A. B. C. D.
Math: Question 1 Which of the following values satisfies the equation above? Choice C is correct. Subtracting 4x from both sides of the equation gives 2x + 9 = 11. Then, subtracting 9 from both sides of
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 informationChapter 6 Complex Numbers
Chapter 6 Complex Numbers Lesson 1: Imaginary Numbers Lesson 2: Complex Numbers Lesson 3: Quadratic Formula Lesson 4: Discriminant This assignment is a teacher-modified version of Algebra 2 Common Core
More information2014 Chapter Competition Sprint Round Problems 1 30
014 Chapter Competition Sprint Round Problems 1 0 HONOR PLEDGE I pledge uphold the highest principles of honesty and integrity as a Mathlete. I will neither give nor accept unauthorized assistance of any
More informationGrade 8 Mathematics MCA Item Sampler Teacher Guide
Grade 8 Mathematics MCA Item Sampler Teacher Guide Overview of Item Samplers Item samplers are one type of student resource provided to help students and educators prepare for test administration. While
More informationFlorida Math Curriculum (433 topics)
Florida Math 0028 This course covers the topics shown below. Students navigate learning paths based on their level of readiness. Institutional users may customize the scope and sequence to meet curricular
More informationSOLVING LINEAR INEQUALITIES
Topic 15: Solving linear inequalities 65 SOLVING LINEAR INEQUALITIES Lesson 15.1 Inequalities on the number line 15.1 OPENER Consider the inequality x > 7. 1. List five numbers that make the inequality
More informationSAMPLE. The SSAT Course Book MIDDLE & UPPER LEVEL QUANTITATIVE. Focusing on the Individual Student
The SSAT Course Book MIDDLE & UPPER LEVEL QUANTITATIVE Focusing on the Individual Student Copyright Statement The SSAT Course Book, along with all Summit Educational Group Course Materials, is protected
More informationEureka Math. Grade 8, Module 4. Student File_B. Contains Exit Ticket, and Assessment Materials
A Story of Ratios Eureka Math Grade 8, Module 4 Student File_B Contains, and Assessment Materials Published by the non-profit Great Minds. Copyright 2015 Great Minds. No part of this work may be reproduced,
More informationSummer 2017 Math Packet
Summer 017 Math Packet for Rising Geometry Students This packet is designed to help you review your Algebra Skills and help you prepare for your Geometry class. Your Geometry teacher will expect you to
More informationAdvanced Honors and Honors Integrated Math 1 Summer Packet
Advanced Honors and Honors Integrated Math 1 Summer Packet This packet is designed to help you review skills from 8 th grade as well as preview additional skills not learned in 8 th grade that you will
More informationALGEBRA I SEMESTER EXAMS PRACTICE MATERIALS SEMESTER Use the diagram below. 9.3 cm. A = (9.3 cm) (6.2 cm) = cm 2. 6.
1. Use the diagram below. 9.3 cm A = (9.3 cm) (6.2 cm) = 57.66 cm 2 6.2 cm A rectangle s sides are measured to be 6.2 cm and 9.3 cm. What is the rectangle s area rounded to the correct number of significant
More information2. If the discriminant of a quadratic equation is zero, then there (A) are 2 imaginary roots (B) is 1 rational root
Academic Algebra II 1 st Semester Exam Mr. Pleacher Name I. Multiple Choice 1. Which is the solution of x 1 3x + 7? (A) x -4 (B) x 4 (C) x -4 (D) x 4. If the discriminant of a quadratic equation is zero,
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 informationGAP CLOSING. Algebraic Expressions. Intermediate / Senior Facilitator s Guide
GAP CLOSING Algebraic Expressions Intermediate / Senior Facilitator s Guide Topic 6 Algebraic Expressions Diagnostic...5 Administer the diagnostic...5 Using diagnostic results to personalize interventions...5
More informationBig Bend Community College. Beginning Algebra MPC 095. Lab Notebook
Big Bend Community College Beginning Algebra MPC 095 Lab Notebook Beginning Algebra Lab Notebook by Tyler Wallace is licensed under a Creative Commons Attribution 3.0 Unported License. Permissions beyond
More informationAlgebra 2 Summer Work Packet Review and Study Guide
Algebra Summer Work Packet Review and Study Guide This study guide is designed to accompany the Algebra Summer Work Packet. Its purpose is to offer a review of the nine specific concepts covered in the
More informationKEYSTONE ALGEBRA I REVIEW
1. Which graph represents a linear function 4. The faces of a cube are numbered from 1 to 6. If the cube is tossed once, what is the probability that a prime number or a number divisible by 2 is obtained
More informationA. 16 B. 16 C. 4 D What is the solution set of 4x + 8 > 16?
Algebra II Honors Summer Math Packet 2017 Name: Date: 1. Solve for x: x + 6 = 5x + 12 2. What is the value of p in the equation 8p + 2 = p 10? F. 1 G. 1 H. J.. Solve for x: 15x (x + ) = 6 11. Solve for
More informationGUIDED NOTES. College. Algebra. + Integrated. Review
GUIDED NOTES College Algebra + Integrated Review Editor: Kara Roche Content Contributors: Daniel Breuer, Jennifer Comer Lead Designer: Tee Jay Zajac Designers: B. Syam Prasad, Patrick Thompson, James Smalls
More information2) If an athletic conference has 12 teams and each of the teams plays each of the other teams, how many games will there be?
Pre-Algebra Review Worksheet Final Exam Mr. Cierech Name: Date: Chapter 1: Number Patterns 1) Find the next three numbers in the sequence: a) 4, 9, 14, 19, 4... b) 16, 8, 4,, 1, ) If an athletic conference
More informationIntermediate Algebra
Intermediate Algebra The purpose of this course is to strengthen students foundational conceptual and procedural skills in order to prepare students for college-and-career readiness. The course textbook,
More informationPark Forest Math Team. Meet #5. Algebra. Self-study Packet
Park Forest Math Team Meet #5 Self-study Packet Problem Categories for this Meet: 1. Mystery: Problem solving 2. Geometry: Angle measures in plane figures including supplements and complements 3. Number
More informationElementary Algebra Sample Final Exam Spring 2017
Elementary Algebra NAME: Sample Final Exam Spring 2017 You will have 2 hours to complete this exam. You may use a calculator but must show all algebraic work in the space provided to receive full credit.
More informationSCIE 4101 Fall Math Review Packet #2 Notes Patterns and Algebra I Topics
SCIE 4101 Fall 014 Math Review Packet # Notes Patterns and Algebra I Topics I consider Algebra and algebraic thought to be the heart of mathematics everything else before that is arithmetic. The first
More informationSaturday, September 7, 2013 TEST BOOKLET. Test Version A. Your test version (A, B, C, or D) is above on this page.
AdvAntAge testing FoundAtion MAth The Fifth Prize Annual For girls Math Prize for Girls Saturday, September 7, 2013 TEST BOOKLET Test Version A DIRECTIONS 1. Do not open this test until your proctor instructs
More informationMathematics Diagnostic Examination Guidance
Mathematics Diagnostic Examination Guidance Examination Overview The mathematics examination will be 45 minutes long and will be worth 50 points. There will be three sections on the examination: Section
More informationPrep for the CSU ELM
Prep for the CSU ELM This course covers the topics shown below. Students navigate learning paths based on their level of readiness. Institutional users may customize the scope and sequence to meet curricular
More informationMinnesota State Colleges and Universities Intermediate Algebra Sample Questions
Minnesota State Colleges and Universities Intermediate Algebra Sample Questions 013 The College Board. College Board, ACCUPLACER, WritePlacer and the acorn logo are registered trademarks of the College
More informationAnswers to the problems will be posted on the school website, go to Academics tab, then select Mathematics and select Summer Packets.
Name Geometry SUMMER PACKET This packet contains Algebra I topics that you have learned before and should be familiar with coming into Geometry. We will use these concepts on a regular basis throughout
More informationLinear Functions, Equations, and Inequalities
CHAPTER Linear Functions, Equations, and Inequalities Inventory is the list of items that businesses stock in stores and warehouses to supply customers. Businesses in the United States keep about.5 trillion
More informationTEST BANK. How TO USE THIS TEST BANK
TEST BANK How TO USE THIS TEST BANK In this section you will find one chap-ter test for each of the 14 chapters in Algebra: Themes, Tools, Concepts. For Chapters 3, 5, 6, 7, 9, 10, and 13, you will also
More informationStudent Performance Analysis. Algebra I Standards of Learning
Student Performance Analysis Algebra I Standards of Learning Practice for SOL A.1 Select each phrase that verbally translates this algebraic expression: One fourth times the cube root of x less five. One
More informationMoving Straight Ahead - Unit Test Review Sheet
Name: Class: Date: ID: A Moving Straight Ahead - Unit Test Review Sheet Short Answer 1. Use the graph at the right. a. Find the slope of the line. b. Find the equation of the line. 2. Does the table below
More informationCheck boxes of Edited Copy of Sp Topics (was 145 for pilot) Beginning Algebra, 3rd Ed. [open all close all] Course Readiness and
Check boxes of Edited Copy of 10021 Sp 11 152 Topics (was 145 for pilot) Beginning Algebra, 3rd Ed. [open all close all] Course Readiness and Additional Topics Appendix Course Readiness Multiplication
More 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 - - 2-2 + 3 2 - A) + - 2 B) - + 4-2 C) + 4-2 D) - + - 2 Solve the problem. 2) The sum of a number and its
More informationCourse Name: MAT 135 Spring 2017 Master Course Code: N/A. ALEKS Course: Intermediate Algebra Instructor: Master Templates
Course Name: MAT 135 Spring 2017 Master Course Code: N/A ALEKS Course: Intermediate Algebra Instructor: Master Templates Course Dates: Begin: 01/15/2017 End: 05/31/2017 Course Content: 279 Topics (207
More informationGrade 8 Math Curriculum Map Erin Murphy
Topic 1 Variables and Expressions 2 Weeks Summative Topic Test: Students will be able to (SWBAT) use symbols o represent quantities that are unknown or that vary; demonstrate mathematical phrases and real-world
More informationMAT 135 In-Class Assignments Answer Key
MAT 135 In-Class Assignments Answer Key Answers are listed under the heading of each section. Where a section was continued on multiple pages, the answers are all listed under the section heading. If there
More information2-4. Warm Up Lesson Presentation Lesson Quiz
Warm Up Lesson Presentation Lesson Quiz Holt Algebra McDougal 1 Algebra 1 Warm Up Solve each equation. 1. 2x 5 = 17 6 2. 14 Solve each inequality and graph the solutions. 3. 5 < t + 9 t > 4 4. a 8 Objective
More informationChetek-Weyerhaeuser High School
Chetek-Weyerhaeuser High School Unit 1 Variables and Expressions Math RtI Units and s Math RtI A s 1. I can use mathematical properties to evaluate expressions. I can use mathematical properties to evaluate
More informationSummary for a n = b b number of real roots when n is even number of real roots when n is odd
Day 15 7.1 Roots and Radical Expressions Warm Up Write each number as a square of a number. For example: 25 = 5 2. 1. 64 2. 0.09 3. Write each expression as a square of an expression. For example: 4. x
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 informationALGEBRA 1 CST Questions (2009)
1 Is the equation 3(x ) = 18 equivalent to 6x 1 = 18? Yes, the equations are equivalent by the ssociative Property of Multiplication. Yes, the equations are equivalent by the ommutative Property of Multiplication.
More informationFinal Review. Intermediate Algebra / MAT135 S2014
Final Review Intermediate Algebra / MAT135 S2014 1. Solve for. 2. Solve for. 3. Solve for. 4. Jenny, Abdul, and Frank sent a total of text messages during the weekend. Abdul sent more messages than Jenny.
More information7.12 The student will represent relationships with tables, graphs, rules, and words.
7.12 The student will represent relationships with tables, graphs, rules, and words. HINTS & NOTES Relation- is a set of ordered pairs. Remember to always start from the origin. Origin is (0,0) Move horizontally
More information6-A2 Problem Solving Using Inequalities Alg 1H
6-A Problem Solving Using Inequalities Alg H Solve by using a variable to write an inequality based on the given information. All work must be shown neatly on notebook paper.. The sum of two consecutive
More information3. Find the area of each rectangle shown below. 4. Simplify the expressions below. 5. If the expression 3a 2 9. is equal to 3, what is the value of d?
Permitted resources: 2018 2019 Algebra 1 Midterm Review FSA Approved calculator Algebra 1 FSA Reference Sheet 1. The expression 13x + 5 represents the number of marbles you have after purchasing 13 bags
More informationMathematics Department. Summer Course Work. Algebra I
Bergenfield High School Bergenfield, New Jersey Mathematics Department Summer Course Work in preparation for Algebra I Completion of this summer work is required on the first day of the 2016-2017 school
More informationDefine the word inequality
Warm Up: Define the word inequality Agenda: Objective- Students can solve linear inequalities in one variable, including equations with coefficients represented by letters. Define Inequalities One & Two
More informationBeginning Algebra. 1. Review of Pre-Algebra 1.1 Review of Integers 1.2 Review of Fractions
1. Review of Pre-Algebra 1.1 Review of Integers 1.2 Review of Fractions Beginning Algebra 1.3 Review of Decimal Numbers and Square Roots 1.4 Review of Percents 1.5 Real Number System 1.6 Translations:
More information5.1 Modelling Polynomials
5.1 Modelling Polynomials FOCUS Model, write, and classify polynomials. In arithmetic, we use Base Ten Blocks to model whole numbers. How would you model the number 234? In algebra, we use algebra tiles
More informationContents. Introduction... 5
Contents Introduction... 5 The Language of Algebra Order of Operations... Expressions... Equations... Writing Expressions and Equations... Properties of The Four Operations... Distributive Property...
More informationWhat students need to know for PRE-CALCULUS Students expecting to take Pre-Calculus should demonstrate the ability to:
What students need to know for PRE-CALCULUS 2014-2015 Students expecting to take Pre-Calculus should demonstrate the ability to: General: keep an organized notebook take good notes complete homework every
More informationMath 1 Variable Manipulation Part 4 Student
Math 1 Variable Manipulation Part 4 Student 1 SOLVING AN EQUATION THAT INCLUDES ABSOLUTE VALUE SIGNS To solve an equation that includes absolute value signs, think about the two different cases-one where
More informationWhy It s Important. What You ll Learn
How could you solve this problem? Denali and Mahala weed the borders on the north and south sides of their rectangular yard. Denali starts first and has weeded m on the south side when Mahala says he should
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 informationAlgebra 1 End-of-Course Assessment Practice Test with Solutions
Algebra 1 End-of-Course Assessment Practice Test with Solutions For Multiple Choice Items, circle the correct response. For Fill-in Response Items, write your answer in the box provided, placing one digit
More informationExpressions, Equations and Inequalities Guided Notes
Expressions, Equations and Inequalities Guided Notes Standards: Alg1.M.A.SSE.A.01a - The Highly Proficient student can explain the context of different parts of a formula presented as a complicated expression.
More informationImportant Math 125 Definitions/Formulas/Properties
Exponent Rules (Chapter 3) Important Math 125 Definitions/Formulas/Properties Let m & n be integers and a & b real numbers. Product Property Quotient Property Power to a Power Product to a Power Quotient
More information