Review Systems of Equations Standard: A.CED.3; A.REI.6
|
|
- Victor Powers
- 5 years ago
- Views:
Transcription
1 Name: Review Systems of Equations Standard: A.CED.3; A.REI.6 Hour: Fundamentals 1. The solution of a system is a. Line Coordinate Point Plane 2. For a point to be a solution to a system, it must make equation(s) true. One Both Neither 3. Graphically and visually, the solution to a system is the of the two lines. Y-Intercepts X-Intercepts Slope Intersection 4. Parallel lines have solution(s). One Two No Infinitely Many 5. Infinitely many solutions means that the two lines are. Parallel Intersecting the same 6. There are 3 ways to solve a system:,, and. S Examples Circle the error in each problem. Explain why it is incorrect and what should have been done. You do not need to solve all the way. 7. Elimination x + 2y = 18 3x 5y = Substitution 3y = 3x 5 2x = y + 8 3y = 48 y = 16 3x + 2( 16) = 18 3x 32 = 18 3x = 50 x = 50 3 ( 50 3, 16) y = 3(y + 8) 5 y = 3y y = 3y y = 19 y = x = x = 3 2 x = 3 4 ( 3 4, 19 2 ) 9. Graphing y = 1 x 6 2 2y 3x = 6 ( 2, 6)
2 Practice Solve each system using the method indicated. If no method is indicated, you may choose any method empty coordinate planes are provided at the end. Check your answers by plugging your solution point back in. When possible, verify your answers using the intersection feature of the graphing calculator (Graph functions, 2 ND, Trace [Calc], Intersect, Enter 3 times) 10. Substitution x = 3y + 1 2x 3y = Elimination 5x + y = 10 x + y = Graphing y = 2x 8 y = 2 3 x
3 13. y = 3 x y = 3x x + 4y = 24 y = 3 4 x x 3y = 6 2x + y = 12
4 Word Problems Write and solve a system for each situation. 16. Jack and Jill went up the hill to fetch some pails of water. Jack s pail holds twice what Jill s pail holds. Together, they can carry 9 gallons of water. How much water do Jack and Jill s pails each hold? 17. Benny is going to the bakery to pick up 37 desserts, cookies and cupcakes, which he ordered for $63. How many cupcakes and cookies did Benny purchase if cookies cost $1.50 and cupcakes cost $2? 18. On Tuesday Johnny and Susie bought a hot chocolate and two apple turnovers for $4.75. The following week, they bought 2 hot chocolates and an apple turnover for $5. How much does an apple turnover and hot chocolate each cost? Solutions Determine if the given point is a solution to the system. 19. (2, 4) y = 2x 2x = 3y (13, 10) 2x + y = 16 3y = 9 3x Extra Coordinate Planes
5 Name: Review Inequalities Standard: A.CED.3; A.REI.1; A.REI.3; A.REI.12 Hour: Fundamentals 1. > 2. < Flip the inequality sign when you or by a. 6. These signs have an open dot, or dashed line: & 7. These signs have a closed dot, or solid line: & 8. Plug in a to determine where to shade. I Examples Identify the error in each problem. Explain why it is incorrect and what should have been done. You do not need to solve the entire problem. 9. 5x 2x 12 3x 12 x y + 8 > 20y 16 8 > 8y > 8y 3 > y 11. y 4 3 x x + 3y < 24 3 Practice Solve and graph each inequality on the number line or coordinate plane provided x + 9 > 4 3 x x (4 + x) 7x + 10
6 < x < x y 3x x 6y < y < y > 3 2 x + 1 y 2x + 5 Write an inequality for each graph
7 Word Problems Write and/or solve and graph an inequality or system of inequalities for each situation. 23. You can be no more than 48 tall to play in the play place. 24. The temperature of meat must be at least 165 degrees for safe consumption. Inequality: Inequality: 25. The budget for the party you are having is $60 and you need to provide pizza and breadsticks. Pizzas are $5.00 each and breadsticks are $2.50 each. (When graphing consider, which values are possible? Positive? Zero? Negative?) 26. Valentine s Day is coming up and you want to get a gift for each of your 9 friends. Chocolates are 75 cents each and cards are $1.25 each. But you only have $10 left from Christmas. (System of Inequalities) 27. Circle all points that are a solution to the system of inequalities. y 2 x 8 3 4x y < 18 ( 5, 7) (1, 9) (0, 0) (5, 2)
8 Name: Review Functions & Families Standard: F.IF1; F.IF2; F.IF.7 Hour: A significant part of this review is accessed via Quizlet (digital flashcards and study aids). If you do not have access to Quizlet (smartphone or computer), let Ms. Heizer know. Function Families Fundamentals 1. A relation is a function if it passes the test. 2. In a table, there should be exactly y-value for every x-value, even if the x-values repeat. 3. Another way to represent y is to write. 4. In the example f(3 a), the input is. 5. To create a table in your calculator, first enter the function into Y=, then press (table). 6. functions have a common first difference. 7. Quadratic functions have a common. 8. functions have a common ratio. F Examples Identify the error in each problem. Explain why it is incorrect and what should have been done. You do not need to complete the entire problem. 9. f(x) = 3 x + 11; f(6) 2 f(6) = 3 (6) f(6) = f(6) = f(x) = 3x 1; f(x) = 14 f(14) = 3(14) 1 f(14) = 42 1 f(14) = f(x) = 2(x + 1) + 7; f(4 a) f(4 a) = 2(4 a + 1) + 7 f(4 a) = 8 a f(4 a) = 8 a + 8 f(4 a) = 16 a 12. Jimmy says that the following relation is a function because none of the y-values repeat. x f(x)
9 Practice Determine whether each of the following relations is a function or not x f(x) x f(x) {(1, 2), (2, 2), (3, 4), (4, 4)} 18. {(7, 1), (0, 7)} Evaluate. 19. f(x) = 2x 7; f( 5) 20. g(x) = 2 x + 8; g(15) h(x) = 3x 6 ; h( 3) 22. f(x) = 2x 2 + x; f(4) 23. g(x) = 4x 12; g(6a) 24. h(x) = 2x; h(5 2a)
10 25. g(x) = 7 x; g(3a + 8) 26. f(x) = 3(x 8) 9; f(6 2a) Solve for x. 27. f(x) = 2x 8; f(x) = h(x) = 3 x + 13; h(x) = g(x) = 3x; g(x) = g(x) = (x + 8) + 3; g(x) = h(x) = 2x + 8; h(x) = 3x 32. f(x) = 9 4x; f(x) = 7x = 2x 2 + x ( 1 3 )x = 1 81
11 Determine whether each table is a linear, quadratic, or exponential function or neither x y x y x y 38. x y Word Problems 39. A cross country runner runs at 9 miles per hour, whose distance is represented by M(h) = 9h. Find M(3). 40. At a frozen yogurt shop, the cost is determined by the weight (in ounces) and is represented by C(w) =.49w Find the weight of the frozen yogurt if C(w) = Over break you earned some extra money by working at your job. Explain what P(36) = 288 means.
STANDARDS OF LEARNING CONTENT REVIEW NOTES ALGEBRA I. 2 nd Nine Weeks,
STANDARDS OF LEARNING CONTENT REVIEW NOTES ALGEBRA I 2 nd Nine Weeks, 2016-2017 1 OVERVIEW Algebra I Content Review Notes are designed by the High School Mathematics Steering Committee as a resource for
More informationSTANDARDS OF LEARNING CONTENT REVIEW NOTES. ALGEBRA I Part I. 4 th Nine Weeks,
STANDARDS OF LEARNING CONTENT REVIEW NOTES ALGEBRA I Part I 4 th Nine Weeks, 2016-2017 1 OVERVIEW Algebra I Content Review Notes are designed by the High School Mathematics Steering Committee as a resource
More informationThe graph of the region that shows the number of packages of each item Kala can purchase is
2. Solve each system of inequalities by graphing. The graph of the system of inequalities is 4. CCSS REASONING The most Kala can spend on hot dogs and buns for her cookout is $35. A package of 10 hot dogs
More information9.1 Linear Inequalities in Two Variables Date: 2. Decide whether to use a solid line or dotted line:
9.1 Linear Inequalities in Two Variables Date: Key Ideas: Example Solve the inequality by graphing 3y 2x 6. steps 1. Rearrange the inequality so it s in mx ± b form. Don t forget to flip the inequality
More informationSolve the following system of equations. " 2x + 4y = 8 # $ x 3y = 1. 1 cont d. You try:
1 Solve the following system of equations. " 2x + 4y = 8 # $ x 3y = 1 Method 1: Substitution 1. Solve for x in the second equation. 1 cont d Method 3: Eliminate y 1. Multiply first equation by 3 and second
More informationSection 2.0: Getting Started
Solving Linear Equations: Graphically Tabular/Numerical Solution Algebraically Section 2.0: Getting Started Example #1 on page 128. Solve the equation 3x 9 = 3 graphically. Intersection X=4 Y=3 We are
More informationAlgebra I Notes Linear Equations and Inequalities in Two Variables Unit 04c
Big Idea: Describe the similarities and differences between equations and inequalities including solutions and graphs. Skill: graph linear equations and find possible solutions to those equations using
More informationGraphing Linear Equations
Graphing Linear Equations A.REI.10 Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane. What am I learning today? How to graph a linear
More informationMath 20 Practice Exam #2 Problems and Their Solutions!
Math 20 Practice Exam #2 Problems and Their Solutions! #1) Solve the linear system by graphing: Isolate for in both equations. Graph the two lines using the slope-intercept method. The two lines intersect
More informationI(g) = income from selling gearboxes C(g) = cost of purchasing gearboxes The BREAK-EVEN PT is where COST = INCOME or C(g) = I(g).
Page 367 I(g) = income from selling gearboxes C(g) = cost of purchasing gearboxes The BREAK-EVEN PT is where COST = INCOME or C(g) = I(g). PROFIT is when INCOME > COST or I(g) > C(g). I(g) = 8.5g g = the
More information2-1 Power and Radical Functions
Graph and analyze each function. Describe the domain, range, intercepts, end behavior, continuity, and where the function is increasing or decreasing. 35. Evaluate the function for several x-values in
More informationEssential Questions. Key Terms. Algebra. Arithmetic Sequence
Linear Equations and Inequalities Introduction Average Rate of Change Coefficient Constant Rate of Change Continuous Discrete Domain End Behaviors Equation Explicit Formula Expression Factor Inequality
More information3-2 Solving Systems of Inequalities by Graphing. Solve each system of inequalities by graphing.
8 Solve each system of inequalities by graphing Graph the system of inequalities in a coordinate plane 9 Graph the system of inequalities in a coordinate plane 10 Graph the system of inequalities in a
More information2.2 Graphs Of Functions. Copyright Cengage Learning. All rights reserved.
2.2 Graphs Of Functions Copyright Cengage Learning. All rights reserved. Objectives Graphing Functions by Plotting Points Graphing Functions with a Graphing Calculator Graphing Piecewise Defined Functions
More informationSection 18-1: Graphical Representation of Linear Equations and Functions
Section 18-1: Graphical Representation of Linear Equations and Functions Prepare a table of solutions and locate the solutions on a coordinate system: f(x) = 2x 5 Learning Outcome 2 Write x + 3 = 5 as
More information6.7. Graph Linear Inequalities in Two Variables. Warm Up Lesson Presentation Lesson Quiz
6.7 Graph Linear Inequalities in Two Variables Warm Up Lesson Presentation Lesson Quiz 6.7 Warm-Up Tell whether the ordered pair is a solution of the equation. 1. x + 2y = 4; (2, 1) no 2. 4x + 3y = 22;
More informationChapter 3 Linear Programming: A Geometric Approach
Chapter 3 Linear Programming: A Geometric Approach Section 3.1 Graphing Systems of Linear Inequalities in Two Variables y 4x + 3y = 12 4 3 4 x 3 y 12 x y 0 x y = 0 2 1 P(, ) 12 12 7 7 1 1 2 3 x We ve seen
More information6-1: Solving Systems by Graphing
6-1: Solving Sstems b Graphing Objective: To solve sstems of linear equations b graphing Warm Up: Graph each equation using - and -intercepts. 1. 1. 4 8. 6 9 18 4. 5 10 5 sstem of linear equations: two
More informationBecause the inequality involves, graph the boundary using a solid line. Choose (0, 0) as a test point.
Graph each inequality. 12. y < x 3 y < x 3 Because the inequality involves
More informationFunctions. Copyright Cengage Learning. All rights reserved.
Functions Copyright Cengage Learning. All rights reserved. 2.2 Graphs Of Functions Copyright Cengage Learning. All rights reserved. Objectives Graphing Functions by Plotting Points Graphing Functions with
More informationUNIT 4 NOTES. 4-1 and 4-2 Coordinate Plane
UNIT 4 NOTES 4-1 and 4-2 Coordinate Plane y Ordered pairs on a graph have several names. (X coordinate, Y coordinate) (Domain, Range) (Input,Output) Plot these points and label them: a. (3,-4) b. (-5,2)
More informationMath 7 Notes - Unit 4 Pattern & Functions
Math 7 Notes - Unit 4 Pattern & Functions Syllabus Objective: (.) The student will create tables, charts, and graphs to etend a pattern in order to describe a linear rule, including integer values. Syllabus
More informationUnit Essential Questions: Does it matter which form of a linear equation that you use?
Unit Essential Questions: Does it matter which form of a linear equation that you use? How do you use transformations to help graph absolute value functions? How can you model data with linear equations?
More informationUNIT 3 EXPRESSIONS AND EQUATIONS Lesson 3: Creating Quadratic Equations in Two or More Variables
Guided Practice Example 1 Find the y-intercept and vertex of the function f(x) = 2x 2 + x + 3. Determine whether the vertex is a minimum or maximum point on the graph. 1. Determine the y-intercept. The
More informationMath 7 Notes - Unit 4 Pattern & Functions
Math 7 Notes - Unit 4 Pattern & Functions Syllabus Objective: (3.2) The student will create tables, charts, and graphs to extend a pattern in order to describe a linear rule, including integer values.
More informationAlgebra II Notes Unit Two: Linear Equations and Functions
Syllabus Objectives:.1 The student will differentiate between a relation and a function.. The student will identify the domain and range of a relation or function.. The student will derive a function rule
More informationMathematics for Business and Economics - I. Chapter7 Linear Inequality Systems and Linear Programming (Lecture11)
Mathematics for Business and Economics - I Chapter7 Linear Inequality Systems and Linear Programming (Lecture11) A linear inequality in two variables is an inequality that can be written in the form Ax
More informationUnit 12 Special Functions
Algebra Notes Special Functions Unit 1 Unit 1 Special Functions PREREQUISITE SKILLS: students should be able to describe a relation and a function students should be able to identify the domain and range
More information10-2 Circles. Warm Up Lesson Presentation Lesson Quiz. Holt Algebra2 2
10-2 Circles Warm Up Lesson Presentation Lesson Quiz Holt Algebra2 2 Warm Up Find the slope of the line that connects each pair of points. 1. (5, 7) and ( 1, 6) 1 6 2. (3, 4) and ( 4, 3) 1 Warm Up Find
More informationGraphing Method. Graph of x + y < > y 10. x
Graphing Method Eample: Graph the inequalities on the same plane: + < 6 and 2 - > 4. Before we graph them simultaneousl, let s look at them separatel. 10-10 10 Graph of + < 6. ---> -10 Graphing Method
More informationAlgebra I EOC Packet #
1. Which inequality best describes the graph shown below? A y > x + 5 B y < x + 5 C y < x + 5 D y > x + 5 2. The table shows a set of values for x and y. x -3-2 1 3 6 y 7 5-1 -5-11 Which equation best
More informationMath 1313 Prerequisites/Test 1 Review
Math 1313 Prerequisites/Test 1 Review Test 1 (Prerequisite Test) is the only exam that can be done from ANYWHERE online. Two attempts. See Online Assignments in your CASA account. Note the deadline too.
More informationRationale. Is it feasible?
Learning Targets: Represent constraints by equations or inequalities. Use a graph to determine solutions of a system of inequalities. SUGGESTED LEARNING STRATEGIES: Think-Pair-Share, Interactive Word Wall,
More informationCLASSROOM INVESTIGATION:
MHS CLASSROOM INVESTIGATION: LINEAR PROGRAMMING LEARNING GOALS By completing this lesson you will: Practice establishing systems of inequalities Review graphing half-planes Investigate using a polygon
More informationFunction Transformations and Symmetry
CHAPTER Function Transformations and Symmetry The first well-documented postal system was in ancient Rome, where mail was carried by horsedrawn carriages and ox-drawn wagons. The US Postal Service delivers
More informationVertical Line Test a relationship is a function, if NO vertical line intersects the graph more than once
Algebra 2 Chapter 2 Domain input values, X (x, y) Range output values, Y (x, y) Function For each input, there is exactly one output Example: Vertical Line Test a relationship is a function, if NO vertical
More informationChapter P: Preparation for Calculus
1. Which of the following is the correct graph of y = x x 3? E) Copyright Houghton Mifflin Company. All rights reserved. 1 . Which of the following is the correct graph of y = 3x x? E) Copyright Houghton
More informationSection 2.2 Graphs of Linear Functions
Section. Graphs of Linear Functions Section. Graphs of Linear Functions When we are working with a new function, it is useful to know as much as we can about the function: its graph, where the function
More informationReview for Mastery Using Graphs and Tables to Solve Linear Systems
3-1 Using Graphs and Tables to Solve Linear Systems A linear system of equations is a set of two or more linear equations. To solve a linear system, find all the ordered pairs (x, y) that make both equations
More informationFOA/Algebra 1. Unit 2B Review - Linear Functions
FOA/Algebra Unit B Review Name: Date: Block: Unit B Review - Linear Functions What you need to know & be able to do. Determine if a relation is a Things to remember Every input only has one output (each
More informationIntro. To Graphing Linear Equations
Intro. To Graphing Linear Equations The Coordinate Plane A. The coordinate plane has 4 quadrants. B. Each point in the coordinate plain has an x-coordinate (the abscissa) and a y-coordinate (the ordinate).
More informationSec 4.1 Coordinates and Scatter Plots. Coordinate Plane: Formed by two real number lines that intersect at a right angle.
Algebra I Chapter 4 Notes Name Sec 4.1 Coordinates and Scatter Plots Coordinate Plane: Formed by two real number lines that intersect at a right angle. X-axis: The horizontal axis Y-axis: The vertical
More informationUnit 0: Extending Algebra 1 Concepts
1 What is a Function? Unit 0: Extending Algebra 1 Concepts Definition: ---Function Notation--- Example: f(x) = x 2 1 Mapping Diagram Use the Vertical Line Test Interval Notation A convenient and compact
More informationMath 370 Exam 1 Review Name. Use the vertical line test to determine whether or not the graph is a graph in which y is a function of x.
Math 370 Exam 1 Review Name Determine whether the relation is a function. 1) {(-6, 6), (-6, -6), (1, 3), (3, -8), (8, -6)} Not a function The x-value -6 corresponds to two different y-values, so this relation
More informationName: Unit 3 Beaumont Middle School 8th Grade, Introduction to Algebra
Unit 3 Beaumont Middle School 8th Grade, 2016-2017 Introduction to Algebra Name: I can identify a function, the domain and range. I can identify a linear relationship from a situation, table, graph and
More informationName: Date: Study Guide: Systems of Equations and Inequalities
Name: Date: Study Guide: Systems of Equations and Inequalities Systems of Equations Linear systems consist of two or more linear equations in the same variables. A solution to the linear system of equations
More informationMath A Regents Exam 0102 Page 1
Math A Regents Exam 0102 Page 1 1. 010201a, P.I. A.A.19 Expressed in factored form, the binomial 2 2 4a 9b is equivalent to [A] (2a - 9b)(2a + b) [B] (2a + 3b)(2a - 3b) [C] (2a - 3b)(2a - 3b) [D] (4a -
More informationGraphing Linear Functions - Review 1. = 6 2. = = = Sketch the graph of each line
FOM 11 Graphing Linear Functions - Review Sketch the graph of each line 1. =. = +1 3. 3 =1. +7= 5. a) Graph the linear function that goes through (, 3) and is perpendicular to = 11 b) What is the equation
More informationMath Analysis Chapter 1 Notes: Functions and Graphs
Math Analysis Chapter 1 Notes: Functions and Graphs Day 6: Section 1-1 Graphs Points and Ordered Pairs The Rectangular Coordinate System (aka: The Cartesian coordinate system) Practice: Label each on the
More informationSlide 1 / 220. Linear Relations and Functions
Slide 1 / 220 Linear Relations and Functions Slide 2 / 220 Table of Contents Domain and Range Discrete v Continuous Relations and Functions Function Notation Linear Equations Graphing a Linear Equation
More informationAlgebra I Notes Linear Functions & Inequalities Part I Unit 5 UNIT 5 LINEAR FUNCTIONS AND LINEAR INEQUALITIES IN TWO VARIABLES
UNIT LINEAR FUNCTIONS AND LINEAR INEQUALITIES IN TWO VARIABLES PREREQUISITE SKILLS: students must know how to graph points on the coordinate plane students must understand ratios, rates and unit rate VOCABULARY:
More informationWEEK 4 REVIEW. Graphing Systems of Linear Inequalities (3.1)
WEEK 4 REVIEW Graphing Systems of Linear Inequalities (3.1) Linear Programming Problems (3.2) Checklist for Exam 1 Review Sample Exam 1 Graphing Linear Inequalities Graph the following system of inequalities.
More informationReteaching Transforming Linear Functions
Name Date Class Transforming Linear Functions INV 6 You have graphed linear functions on the coordinate plane. Now you will investigate transformations of the parent function for a linear function, f(x)
More informationChapter 7: Linear Functions and Inequalities
Chapter 7: Linear Functions and Inequalities Index: A: Absolute Value U4L9 B: Step Functions U4L9 C: The Truth About Graphs U4L10 D: Graphs of Linear Inequalities U4L11 E: More Graphs of Linear Inequalities
More informationMath Analysis Chapter 1 Notes: Functions and Graphs
Math Analysis Chapter 1 Notes: Functions and Graphs Day 6: Section 1-1 Graphs; Section 1- Basics of Functions and Their Graphs Points and Ordered Pairs The Rectangular Coordinate System (aka: The Cartesian
More informationModule 11 & 12. Solving Systems of Equations Graphing Substitution Elimination Modeling Linear Systems Solving Systems of Inequalities
Module 11 & 12 Solving Systems of Equations Graphing Substitution Elimination Modeling Linear Systems Solving Systems of Inequalities What is a System of Equations? A system of linear equations consists
More information2.6: Solving Systems of Linear Inequalities
Quick Review 2.6: Solving Systems of Linear Inequalities = - What is the difference between an equation and an inequality? Which one is shaded? Inequality - When is the line solid?, - When is the line
More informationGraphs of Exponential
Graphs of Exponential Functions By: OpenStaxCollege As we discussed in the previous section, exponential functions are used for many realworld applications such as finance, forensics, computer science,
More informationSUMMER REVIEW FOR STUDENTS COMPLETING GEOMETRY show your work. WEEK 1
Name: 1. Given: 2x 2 3x = 8 SUMMER REVIEW FOR STUDENTS COMPLETING GEOMETRY show your work. WEEK 1 a. Write in standard form. ax 2 +bx+c=0 2. Write an equation for a line parallel to y = -3x + 2 that passes
More informationMath 3A Meadows or Malls? Review
Math 3A Meadows or Malls? Review Name Linear Programming w/o Graphing (2 variables) 1. A manufacturer makes digital watches and analogue (non-digital) watches. It cost $15 to make digital watch and $20
More informationSection 3.1 Graphing Using the Rectangular Coordinate System
Objectives Section 3.1 Graphing Using the Rectangular Coordinate System n Construct a rectangular coordinate system n Plot ordered pairs and determine the coordinates of a point n Graph paired data n Read
More informationLinear Programming: A Geometric Approach
Chapter 3 Linear Programming: A Geometric Approach 3.1 Graphing Systems of Linear Inequalities in Two Variables The general form for a line is ax + by + c =0. The general form for a linear inequality is
More informationGraphing Linear Equations. 8th Grade
Slide 1 / 309 Slide 2 / 309 Graphing Linear Equations 8th Grade 2015-01-26 www.njctl.org Slide 3 / 309 Table of Contents Vocabulary Review Tables Slope & y-intercept Defining Slope on the Coordinate Plane
More informationMath: Question 10
1 of 1 9/22/2016 7:55 PM Math: Question 10 A carpenter has $60 with which to buy supplies. The carpenter needs to buy both nails and screws. Nails cost $12.99 per box, and screws cost $14.99 per box. If
More informationDid You Find a Parking Space?
Lesson.4 Skills Practice Name Date Did You Find a Parking Space? Parallel and Perpendicular Lines on the Coordinate Plane Vocabulary Complete the sentence. 1. The point-slope form of the equation of the
More informationChapter 4: Solving Linear Equations Study Guide
4.1: Plot Points in the Coordinate Plane Chapter 4: Solving Linear Equations Study Guide - Identify/graph ordered pairs Ex: Write the coordinates of - Identify the 4 quadrants point graphed and identify
More informationName the set(s) of numbers to which each number belongs 7.) ) 0 9.) -7. 4(2 f 3 g) (6 g 2
Algebra Midterm Review Packet Notes #: Review of Chapters - Convert to an algebraic expression.) the product of and less.) three times the sum of and than p a number Name:.) the quotient of and the sum
More information3.1 Generating Inverses of Functions 263
3.1 Generating Inverses of Functions FOCUSING QUESTION What is the inverse of a function? LEARNING OUTCOMES I can compare and contrast the key attributes of a function and its inverse when I have the function
More informationCommon Core Algebra 2. Chapter 1: Linear Functions
Common Core Algebra 2 Chapter 1: Linear Functions 1 1.1 Parent Functions and Transformations Essential Question: What are the characteristics of some of the basic parent functions? What You Will Learn
More informationHomework Packet Week #2
All problems with answers or work are examples. Homework Packet Week #2 Section 1.1 Determine the independent and dependent quantities in each scenario. (1-2) 1. Phillip enjoys rock climbing on the weekends.
More informationMath 3 Coordinate Geometry part 1 Unit November 3, 2016
Reviewing the basics The number line A number line is a visual representation of all real numbers. Each of the images below are examples of number lines. The top left one includes only positive whole numbers,
More informationQUADRATIC FUNCTIONS TEST REVIEW NAME: SECTION 1: FACTORING Factor each expression completely. 1. 3x p 2 16p. 3. 6x 2 13x 5 4.
QUADRATIC FUNCTIONS TEST REVIEW NAME: SECTION 1: FACTORING Factor each expression completely. 1. 3x 2 48 2. 25p 2 16p 3. 6x 2 13x 5 4. 9x 2 30x + 25 5. 4x 2 + 81 6. 6x 2 14x + 4 7. 4x 2 + 20x 24 8. 4x
More informationMini-Lecture 3.1 Graphing Equations
Copyright 0 Pearson Education, Inc. Mini-Lecture. Graphing Equations. Plot ordered pairs.. Determine whether an ordered pair of numbers is a solution to an equation in two variables.. Graph linear equations.
More informationContent Standards Two-Variable Inequalities
-8 Content Standards Two-Variable Inequalities A.CED. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate aes with labels and scales.
More information1. Solve the following equation, please show your steps for full credit: (3.1)
Ope Steiner Test 1 Practice Test Identif the choice that best completes the statement or answers the question. 1. Solve the following equation, please show our steps for full credit: (3.1) 1 1 (x + 5)
More informationIndependent Practice #2
All problems with answers or work are examples. Independent Practice #2 Section 1.1 Determine the independent and dependent quantities in each scenario. (1-2) 1. Phillip enjoys rock climbing on the weekends.
More informationAlgebra Unit 2: Linear Functions Notes. Slope Notes. 4 Types of Slope. Slope from a Formula
Undefined Slope Notes Types of Slope Zero Slope Slope can be described in several ways: Steepness of a line Rate of change rate of increase or decrease Rise Run Change (difference) in y over change (difference)
More informationOther Functions and their Inverses
CHAPTER Other Functions and their Inverses Water tanks have been used throughout human history to store water for consumption. Many municipal water tanks are placed on top of towers so that water drawn
More informationName: Checking solutions of equations with graphing calculator Inequalities Translating to and from words
Name: Midterm Review 2018-2019 Units 1, 2, 3, and 4 *Use notes, activities, quizzes, and tests to help remember how to solve problems* Unit 1: Patterns Graphing Extending the line? Connecting points? Title
More information25 Questions EOG Review #1 EOG REVIEW
Questions EOG Review # EOG REVIEW Solve each: Give the BEST Answer. Name Period 9. Represent as a percent: 8% b. 80% c..4% d..8%. A rectangle is 4 meters long. It has a diagonal that is meters. How wide
More information3.1. 3x 4y = 12 3(0) 4y = 12. 3x 4y = 12 3x 4(0) = y = x 0 = 12. 4y = 12 y = 3. 3x = 12 x = 4. The Rectangular Coordinate System
3. The Rectangular Coordinate System Interpret a line graph. Objectives Interpret a line graph. Plot ordered pairs. 3 Find ordered pairs that satisfy a given equation. 4 Graph lines. 5 Find x- and y-intercepts.
More informationModule 11 & 12. Solving Systems of Equations Graphing Substitution Elimination Modeling Linear Systems Solving Systems of Inequalities
Module 11 & 12 Solving Systems of Equations Graphing Substitution Elimination Modeling Linear Systems Solving Systems of Inequalities What is a System of Equations? A system of linear equations consists
More informationPrecalculus Notes: Unit 7 Systems of Equations and Matrices
Date: 7.1, 7. Solving Systems of Equations: Graphing, Substitution, Elimination Syllabus Objectives: 8.1 The student will solve a given system of equations or system of inequalities. Solution of a System
More informationModesto City Schools. Secondary Math I. Module 1 Extra Help & Examples. Compiled by: Rubalcava, Christina
Modesto City Schools Secondary Math I Module 1 Extra Help & Examples Compiled by: Rubalcava, Christina 1.1 Ready, Set, Go! Ready Topic: Recognizing a solution to an equation. The solution to an equation
More informationWARM UP DESCRIBE THE TRANSFORMATION FROM F(X) TO G(X)
WARM UP DESCRIBE THE TRANSFORMATION FROM F(X) TO G(X) 2 5 5 2 2 2 2 WHAT YOU WILL LEARN HOW TO GRAPH THE PARENT FUNCTIONS OF VARIOUS FUNCTIONS. HOW TO IDENTIFY THE KEY FEATURES OF FUNCTIONS. HOW TO TRANSFORM
More informationMath 2 Coordinate Geometry Part 1 Slope & Transformations
Math 2 Coordinate Geometry Part 1 Slope & Transformations 1 MATH 1 REVIEW: THE NUMBER LINE A number line is a visual representation of all real numbers. Each of the images below are examples of number
More informationTopic 6: Calculus Integration Volume of Revolution Paper 2
Topic 6: Calculus Integration Standard Level 6.1 Volume of Revolution Paper 1. Let f(x) = x ln(4 x ), for < x
More informationMATH 099 HOMEWORK TWO
MATH 099 HOMEWORK TWO STUDENT S NAME 1) Matthew needs to rent a car for 1 day. He will be charged a daily fee of $30.00 in addition to 5 cents for every mile he drives. Assign the variable by letting x
More information3.1 INTRODUCTION TO THE FAMILY OF QUADRATIC FUNCTIONS
3.1 INTRODUCTION TO THE FAMILY OF QUADRATIC FUNCTIONS Finding the Zeros of a Quadratic Function Examples 1 and and more Find the zeros of f(x) = x x 6. Solution by Factoring f(x) = x x 6 = (x 3)(x + )
More informationQuadratic Equations Group Acitivity 3 Business Project Week #5
MLC at Boise State 013 Quadratic Equations Group Acitivity 3 Business Project Week #5 In this activity we are going to further explore quadratic equations. We are going to analyze different parts of the
More informationLESSON 5.3 SYSTEMS OF INEQUALITIES
LESSON 5. SYSTEMS OF INEQUALITIES LESSON 5. SYSTEMS OF INEQUALITIES OVERVIEW Here s what ou ll learn in this lesson: Solving Linear Sstems a. Solving sstems of linear inequalities b graphing As a conscientious
More informationx when Algebra: Midterm Review Sheet Unit 1- Operations with Real Numbers, Properties & Expressions
Name: Date: Algebra: Midterm Review Sheet Unit - Operations with Real Numbers, Properties & Expressions. Fill in each circle of the following flow diagram with one of the letters C for Commutative Property
More informationMAT 003 Brian Killough s Instructor Notes Saint Leo University
MAT 003 Brian Killough s Instructor Notes Saint Leo University Success in online courses requires self-motivation and discipline. It is anticipated that students will read the textbook and complete sample
More informationScott Hendrickson, Joleigh Honey, Barbara Kuehl, Travis Lemon, and Janet Sutorius. Mathematics, Secondary I
Resource Title: Secondary One Mathematics Student Edition Publisher: Mathematics Vision Project ISBN: This is an e-book located at http://www.mathematicsvisionproject.org Media: Authors: internet pdf Scott
More informationCLEP Pre-Calculus. Section 1: Time 30 Minutes 50 Questions. 1. According to the tables for f(x) and g(x) below, what is the value of [f + g]( 1)?
CLEP Pre-Calculus Section : Time 0 Minutes 50 Questions For each question below, choose the best answer from the choices given. An online graphing calculator (non-cas) is allowed to be used for this section..
More informationE Linear Equations, Lesson 2, Graphing Linear Functions (r. 2018) LINEAR EQUATIONS Graphing Linear Functions Common Core Standards
E Linear Equations, Lesson 2, Graphing Linear Functions (r. 2018) LINEAR EQUATIONS Graphing Linear Functions Common Core Standards Next Generation Standards A-CED.A.2 Create equations in two or more variables
More information12/11/2018 Algebra II - Semester 1 Review
Name: Semester Review - Study Guide Score: 72 / 73 points (99%) Algebra II - Semester 1 Review Multiple Choice Identify the choice that best completes the statement or answers the question. Name the property
More informationApril 25, Lesson 8.2B
Lesson 8.2B Content Objective: I can substitute a number in for a variable and solve for the expression I can turn word problems into expressions, equations, and inequalities and solve for the variable.
More informationPlot the points (-1,9) (4,-3), estimate (put a dot) where you think the midpoint is
Algebra Review while 9 th graders are at Club Getaway 1-1 dist and mid pt cw. p. 4 (1,3,5,6,7,8, Hw p. 5 (1-10) Plot the points (-1,9) (4,-3), estimate (put a dot) where you think the midpoint is Find
More informationState the domain and range of the relation. EX: {(-1,1), (1,5), (0,3)} 1 P a g e Province Mathematics Southwest TN Community College
A relation is a set of ordered pairs of real numbers. The domain, D, of a relation is the set of all first coordinates of the ordered pairs in the relation (the xs). The range, R, of a relation is the
More information