Graphing Equations Chapter Test Review

Size: px
Start display at page:

Download "Graphing Equations Chapter Test Review"

Transcription

1 Graphing Equations Chapter Test Review Part 1: Calculate the slope of the following lines: (Lesson 3) Unit 2: Graphing Equations 2. Find the slope of a line that has a 3. Find the slope of the line that y-intercept of -4 and contains the point (3, -2) contains the following points: (-5, 4) (2, -4)

2 Part 2: Graphing Slope and Slope Intercept Form (Lessons 4 and 5) 4. Write the equation for the line represented on the graph: Unit 2: Graphing Equations 5. Graph the following equations on the grid: a. y = -3x+ 2 b. y = 1/3 x 8

3 Part 3: Finding Slope Given Two Points and Rate of Change (Lessons 6 & 7) 6. Find the slope of the line that contains the following points: (-6, 9)(-4, -4) Unit 2: Graphing Equations 7. A line has a y-intercept of 8 and passes through the point (-2, -9). Without graphing the line, determine the slope of the line. 8. In Jessica s first year in her career, she made $ In her sixth year, she makes $ What is Jessica s average rate of change over her six years in her career. 9. Jesse is investing money in the stock market. His initial investment when he opened the account was $50. By the end of January he had gained $250. By the end of February he had lost $150. At the end of March he remained steady with no gains or losses. By the end of April he gained $440. a. Create a graph to show the total amounts in Jesse s account each month.

4 b. What was Jesse s total amount at the end of April? c. What was the rate of change between his initial deposit and his amount at the end of April? d. What was the rate of change between February and march? Explain how you determined your answer. Part 4: Graphing Standard Form Equations (Lessons 8 & 9) 10. Identify the x and y intercepts for the following equation: 4x 3y = Write an equation that is equivalent to each of the following equations: a. 6x + 2y = x 2y = Graph the following equations: a. 2x + 4y = -16 b. -6x 4y = -24

5 13. Mel is ordering t-shirts for the lacrosse team. Short sleeve t-shirts cost $10 and long sleeve t- shirts cost $17. The total bill came to $ The equation that represents x short sleeve t-shirts and y long sleeve t-shirts is: 10x+17y = 293 Graph the equation on the grid. Let x = the number of short sleeve t-shirts y = the number of long sleeve t-shirts If 14 people ordered short sleeve t-shirts, how many long sleeve t-shirts were ordered? Justify your answer mathematically. Part 5: Graphing Absolute Value Equations 1. y= x+2 2. y= - x+2-1 Identify two solutions.

6 Graphing Equations Chapter Test Review Answer Key Part 1: Calculate the slope of the following lines: (Lesson 3) Unit 2: Graphing Equations Slope = rise Slope = 10 = 5 Run 4 2 The slope is 5/2. Slope = rise Slope = -6 = - 3 Run 2 The slope is Find the slope of a line that has a 3. Find the slope of the line that y-intercept of -4 and contains the point (3, -2) contains the following points: (-5, 4) (2, -4) Slope = rise Slope = 2 Run 3 The slope of this line is 2/3. Slope = rise Slope = 8 Run -7 The slope of this line is -8/7.

7 Part 2: Graphing Slope and Slope Intercept Form (Lessons 4 and 5) 4. Write the equation for the line represented on the graph: Unit 2: Graphing Equations y-int To write the equation in slope intercept form, we need to know the slope and y-intercept. Y = mx +b Slope (m) = -1 Y-int (b) = -2 Y = -x Graph the following equations on the grid: To write the equation in slope intercept form, we need to know the slope and y-intercept. Y = mx +b Slope (m) = 1/2 Y-int (b) = 4 Y = 1/2x + 4 a. y = -3x+ 2 b. y = 1/3 x 8 We can start by plotting the y-intercept which is y = 2. From that point, graph the slope. Slope is a rise of -3 and run of 1. We can start by plotting the y-intercept which is y = -8. From that point, graph the slope. Slope is a rise of 1 and run of 3.

8 Part 3: Finding Slope Given Two Points and Rate of Change (Lessons 6 & 7) 6. Find the slope of the line that contains the following points: (-6, 9)(-4, -4) Use the slope formula to calculate the slope when given two points. y 2 y = -13 or -6.5 x 2 - x 1-4 (-6) 2 The slope of the line is: -13/2 or -6.5 Unit 2: Graphing Equations 7. A line has a y-intercept of 8 and passes through the point (-2, -9). Without graphing the line, determine the slope of the line. In order to determine the slope of the line, we must have two points. We know one point is (-2,-9) and we know the y-intercept is 8. The y-intercept can also be written as (0,8) because the y- intercept is the point on the y-axis, so we know the x-coordinate is 0. Now we have two points. (0,8) (-2,-9) Now we can use the slope formula to find the slope. y 2 y 1 = -9-8 = -17 or 8.5 x 2 - x The slope of the line is 17/2 or In Jessica s first year in her career, she made $ In her sixth year, she makes $ What is Jessica s average rate of change over her six years in her career. If we write two ordered pairs for this problem, then we can determine the rate of change, which is also the slope. Therefore, we can use the slope formula. Let x = the number of years & y = her salary First year - $39000 can be written as: (1, 39000) Sixth year - $52500 can be written as: (6, 52500) Now we can use the slope formula to determine the rate of change. y 2 y 1 = = = 2700 x 2 - x Jessica s rate of change is $2700 per year.

9 9. Jesse is investing money in the stock market. His initial investment when he opened the account was $50. By the end of January he had gained $250. By the end of February he had lost $150. At the end of March he remained steady with no gains or losses. By the end of April he gained $440. a. Create a graph to show the total amounts in Jesse s account each month. b. What was Jesse s total amount at the end of April? At the end of April Jesse s total was $590. ( = 590) c. What was the rate of change between his initial deposit and his amount at the end of April? Let s write two ordered pairs for this information. Initial Deposit(month 0) - $50 is (0, 50) April (4 th month) 590 is (4, 590) Let x = the month Let y = the total amount) Now we can use our slope formula to find the rate of change. y 2 y 1 = = 540 = 135 x 2 - x The rate of change between the initial deposit and the end of April is $135. d. What was the rate of change between February and March? Explain how you determined your answer. The rate of change between February and March is 0. The problem states that at the end of March is account remained steady with no gains or losses. The ordered pairs would be: (2, 150) (3, 150)

10 Part 4: Graphing Standard Form Equations (Lessons 8 & 9) 10. Identify the x and y intercepts for the following equation: 4x 3y = 24 To identify the x intercept, we will let y = 0 To identify the y-intercept, we will let x = 0 4x 3(0) = 24 4x = 24 Substitute 0 for y Simplify 4(0) 3y = 24 Substitute 0 for x -3y = 24 Simplify 4x/4 = 24/4 Divide by 4 X = 6 The x-intercept is 6. -3y/-3 = 24/-3 Divide by -3 Y = -8 The y-intercept is Write an equation that is equivalent to each of the following equations: a. 6x + 2y = x 2y = -12 I need to write an equation in slope intercept form in order for the equation to be equivalent. Therefore, we will solve for y. I need to write an equation in slope intercept form in order for the equation to be equivalent. Therefore, we will solve for y. 6x 6x + 2y = -14 6x Subtract 6x 3x 3x 2y = x Subtract 3x 2y = -6x 14 Simplify -2y = -3x 12 Simplify 2y/2 = -6x/2-14/2 Divide by 2 Y = -3x 7 Y = -3x 7 is an equivalent equation. -2y/-2 = -3x/-2 12/-2 Divide by -2 Y = 3/2x + 6 Y = 3/2x + 6 is an equivalent equation.

11 12. Graph the following equations: a. 2x + 4y = -16 b. -6x 4y = -24 Since this equation is written in standard form, you can find the x and y intercepts. (You may also rewrite it in slope intercept form). We will find the intercepts. Since this equation is written in standard form, you can find the x and y intercepts. (You may also rewrite it in slope intercept form). We will find the intercepts. X-intercept (Let y = 0) Y-int (Let x=0) X-intercept (Let y = 0) Y-int (Let x=0) 2x +4(0) = -16 2(0) +4y = -16 2x = -16 4y = -16 2x/2 = -16/2 4y/4=-16/4 X = -8 Y = -4 **If you rewrote the equation in slope intercept form, it would be: Y = -1/2x 4-6x 4(0) = -24-6(0) 4y = -24-6x = -24-4y = -24-6x/-6 = -24/-6-4y/-4 = -24/-4 X = 4 y = 6 **If you rewrote the equation in slope intercept form, it would be: Y = -3/2 + 6

12 13. Mel is ordering t-shirts for the lacrosse team. Short sleeve t-shirts cost $10 and long sleeve t- shirts cost $17. The total bill came to $ The equation that represents x short sleeve t-shirts and y long sleeve t-shirts is: 10x+17y = 293 Graph the equation on the grid. Let x = the number of short sleeve t-shirts y = the number of long sleeve t-shirts Since this equation is written in standard form, I can find the x and y intercepts in order to graph. Since we are dealing with larger numbers, this is definitely the easiest way to graph this equation. 10x + 17y = 293 X int: (Let y = 0) Y int: (Let x = 0) 10x + 17(0) = (0) + 17y = x = y = x/10 = 293/10 17y/17 = 293/17 X = 29.3 y = 17.2 If 14 people ordered short sleeve t-shirts, how many long sleeve t-shirts were ordered? Justify your answer mathematically. According to the graph, if 14 people ordered short sleeve t-shirts, then 9 long sleeve t-shirts were ordered. Justify: 10(14) + 17(9) = = = 293

13 Part 5: Graphing Absolute Value Equations and Inequalities 1. y= x+2 2. y = - x+2-1 Identify two solutions. Two solutions are: (-5, -4) and (-4, -3) **Graphs and table of values were created using a free calculator on rentcalculators.org**

Unit 3: Writing Equations Chapter Review

Unit 3: Writing Equations Chapter Review Unit 3: Writing Equations Chapter Review Part 1: Writing Equations in Slope Intercept Form. (Lesson 1) 1. Write an equation that represents the line on the graph. 2. Write an equation that has a slope

More information

3. a) Recall that slope is calculated with formula:

3. a) Recall that slope is calculated with formula: Economics 102 Fall 2007 Homework #1 Answer Key 1. Cheri s opportunity cost of seeing the show is $115 dollars. This includes the $80 she could have earned working, plus the $30 for the ticket, plus the

More information

Review Exercise Set 13. Find the slope and the equation of the line in the following graph. If the slope is undefined, then indicate it as such.

Review Exercise Set 13. Find the slope and the equation of the line in the following graph. If the slope is undefined, then indicate it as such. Review Exercise Set 13 Exercise 1: Find the slope and the equation of the line in the following graph. If the slope is undefined, then indicate it as such. Exercise 2: Write a linear function that can

More information

Mathematics Success Grade 8

Mathematics Success Grade 8 Mathematics Success Grade 8 T379 [OBJECTIVE] The student will derive the equation of a line and use this form to identify the slope and y-intercept of an equation. [PREREQUISITE SKILLS] Slope [MATERIALS]

More information

Algebra Success. LESSON 14: Discovering y = mx + b

Algebra Success. LESSON 14: Discovering y = mx + b T282 Algebra Success [OBJECTIVE] The student will determine the slope and y-intercept of a line by examining the equation for the line written in slope-intercept form. [MATERIALS] Student pages S7 S Transparencies

More information

Section 4.3 Objectives

Section 4.3 Objectives CHAPTER ~ Linear Equations in Two Variables Section Equation of a Line Section Objectives Write the equation of a line given its graph Write the equation of a line given its slope and y-intercept Write

More information

Finding the Equation from a Slope and y-intercept

Finding the Equation from a Slope and y-intercept Lesson 4.4 Objectives Write linear equations given a slope and y-intercept, a slope and a point, or a graph. Writing Linear Equations Michael turns on the high-temperature oven each morning when he comes

More information

CH 39 CREATING THE EQUATION OF A LINE

CH 39 CREATING THE EQUATION OF A LINE 9 CH 9 CREATING THE EQUATION OF A LINE Introduction S ome chapters back we played around with straight lines. We graphed a few, and we learned how to find their intercepts and slopes. Now we re ready to

More information

Section 7C Finding the Equation of a Line

Section 7C Finding the Equation of a Line Section 7C Finding the Equation of a Line When we discover a linear relationship between two variables, we often try to discover a formula that relates the two variables and allows us to use one variable

More information

Topic #1: Evaluating and Simplifying Algebraic Expressions

Topic #1: Evaluating and Simplifying Algebraic Expressions John Jay College of Criminal Justice The City University of New York Department of Mathematics and Computer Science MAT 105 - College Algebra Departmental Final Examination Review Topic #1: Evaluating

More information

Lesson 8: Systems of Inequalities Word Problems

Lesson 8: Systems of Inequalities Word Problems Lesson 8: Systems of Inequalities Word Problems Example 1 The girls swim team is hosting a fund raiser. They would like to raise at least $500. They are selling candles for $5 and flower arrangements for

More information

1. You are given two pairs of coordinates that have a linear relationship. The two pairs of coordinates are (x, y) = (30, 70) and (20, 50).

1. You are given two pairs of coordinates that have a linear relationship. The two pairs of coordinates are (x, y) = (30, 70) and (20, 50). Economics 102 Fall 2017 Answers to Homework #1 Due 9/26/2017 Directions: The homework will be collected in a box before the lecture. Please place your name, TA name and section number on top of the homework

More information

Section 1.4: Slope-Intercept Form

Section 1.4: Slope-Intercept Form Section 1.4: Slope-Intercept Form Objective: Give the equation of a line with a known slope and y-intercept. When graphing a line we found one method we could use is to make a table of values. However,

More information

Slope-Intercept Form Practice True False Questions Indicate True or False for the following Statements.

Slope-Intercept Form Practice True False Questions Indicate True or False for the following Statements. www.ck2.org Slope-Intercept Form Practice True False Questions Indicate True or False for the following Statements.. The slope-intercept form of the linear equation makes it easier to graph because the

More information

Math Released Item Grade 8. Slope Intercept Form VH049778

Math Released Item Grade 8. Slope Intercept Form VH049778 Math Released Item 2018 Grade 8 Slope Intercept Form VH049778 Anchor Set A1 A8 With Annotations Prompt Score Description VH049778 Rubric 3 Student response includes the following 3 elements. Computation

More information

Review for Test 3: Linear Functions

Review for Test 3: Linear Functions Name: Date: Period: Review for Test 3: Linear Functions Slope Formula: y 2 y 1 x 2 x 1 1. Graph the line that passes through the given points. Then identify the slope, whichever intercept is asked for,

More information

Question 3: How do you find the relative extrema of a function?

Question 3: How do you find the relative extrema of a function? Question 3: How do you find the relative extrema of a function? The strategy for tracking the sign of the derivative is useful for more than determining where a function is increasing or decreasing. It

More information

A. B. C. D. Graphing Quadratics Practice Quiz. Question 1. Select the graph of the quadratic function. f (x ) = 2x 2. 2/26/2018 Print Assignment

A. B. C. D. Graphing Quadratics Practice Quiz. Question 1. Select the graph of the quadratic function. f (x ) = 2x 2. 2/26/2018 Print Assignment Question 1. Select the graph of the quadratic function. f (x ) = 2x 2 C. D. https://my.hrw.com/wwtb2/viewer/printall_vs23.html?umk5tfdnj31tcldd29v4nnzkclztk3w8q6wgvr2629ca0a5fsymn1tfv8j1vs4qotwclvofjr8uon4cldd29v4

More information

Extra Practice Chapter 6

Extra Practice Chapter 6 Extra Practice Chapter 6 Topics Include: Equation of a Line y = mx + b & Ax + By + C = 0 Graphing from Equations Parallel & Perpendicular Find an Equation given Solving Systems of Equations 6. - Practice:

More information

Mathematics Success Level H

Mathematics Success Level H Mathematics Success Level H T473 [OBJECTIVE] The student will graph a line given the slope and y-intercept. [MATERIALS] Student pages S160 S169 Transparencies T484, T486, T488, T490, T492, T494, T496 Wall-size

More information

35 38 point slope day 2.notebook February 26, a) Write an equation in point slope form of the line.

35 38 point slope day 2.notebook February 26, a) Write an equation in point slope form of the line. LT 6: I can write and graph equations in point slope form. p.35 What is point slope form? What is slope intercept form? Let's Practice: There is a line that passes through the point (4, 3) and has a slope

More information

3.3 rates and slope intercept form ink.notebook. October 23, page 103. page 104. page Rates and Slope Intercept Form

3.3 rates and slope intercept form ink.notebook. October 23, page 103. page 104. page Rates and Slope Intercept Form 3.3 rates and slope intercept form ink.notebook page 103 page 104 page 102 3.3 Rates and Slope Intercept Form Lesson Objectives 3.3 Rates and Slope-Intercept Form Press the tabs to view details. Standards

More information

1.1. Simple Interest. INVESTIGATE the Math

1.1. Simple Interest. INVESTIGATE the Math 1.1 Simple Interest YOU WILL NEED calculator graph paper straightedge EXPLORE An amount of money was invested. Interpret the graph below to determine a) how much money was invested, b) the value of the

More information

6.4 Solving Linear Inequalities by Using Addition and Subtraction

6.4 Solving Linear Inequalities by Using Addition and Subtraction 6.4 Solving Linear Inequalities by Using Addition and Subtraction Solving EQUATION vs. INEQUALITY EQUATION INEQUALITY To solve an inequality, we USE THE SAME STRATEGY AS FOR SOLVING AN EQUATION: ISOLATE

More information

Math Studio College Algebra

Math Studio College Algebra - Studio College Algebra Kansas State University August 31, 2016 Format of a Linear Function Terminology: What are intercepts on the graph of a function? Format of a Linear Function Terminology: What are

More information

Name Date. Key Math Concepts

Name Date. Key Math Concepts 2-1 Interpret Scatterplots Key Math Concepts Bivariate data is pairs of numbers, (x,y), that represent variables. Positive correlation: the value of one variable increases as the other increases. Negative

More information

1) Please EXPLAIN below your error in problem #1. What will you do to correct this error in the future?

1) Please EXPLAIN below your error in problem #1. What will you do to correct this error in the future? Individualized Quiz Remedial Help Name: ALL QUESTIONS REQUIRING YOU TO WRITE IN ENGLISH MUST BE ANSWERED IN COMPLETE SENTENCES. If you answered question #1 incorrectly please answer the following. 1) Please

More information

Math Performance Task Teacher Instructions

Math Performance Task Teacher Instructions Math Performance Task Teacher Instructions Stock Market Research Instructions for the Teacher The Stock Market Research performance task centers around the concepts of linear and exponential functions.

More information

Lesson 2.6 Creating and Graphing Linear Equations in Two Variables

Lesson 2.6 Creating and Graphing Linear Equations in Two Variables Lesson 2.6 Creating and Graphing Linear Equations in Two Variables Concept: Graphing Linear Equations EQ: How do I create and graph a linear equation in two variables from a word problem? (Standard CED.2)

More information

EOC Review Days 2 & 3: Linear Basics, Slope, and Intercepts

EOC Review Days 2 & 3: Linear Basics, Slope, and Intercepts Name: Date: Period: Algebra 1 Bowling, Cawthon, Fletcher, Skiles EOC Review Days 2 & 3: Linear Basics, Slope, and Intercepts 1. Find the x-intercept and the y-intercept for the function represented in

More information

WEEK 1 REVIEW Lines and Linear Models. A VERTICAL line has NO SLOPE. All other lines have change in y rise y2-

WEEK 1 REVIEW Lines and Linear Models. A VERTICAL line has NO SLOPE. All other lines have change in y rise y2- WEEK 1 REVIEW Lines and Linear Models SLOPE A VERTICAL line has NO SLOPE. All other lines have change in y rise y- y1 slope = m = = = change in x run x - x 1 Find the slope of the line passing through

More information

Chapter 6: Quadratic Functions & Their Algebra

Chapter 6: Quadratic Functions & Their Algebra Chapter 6: Quadratic Functions & Their Algebra Topics: 1. Quadratic Function Review. Factoring: With Greatest Common Factor & Difference of Two Squares 3. Factoring: Trinomials 4. Complete Factoring 5.

More information

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Algebra - Final Exam Review Part Name SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Use intercepts and a checkpoint to graph the linear function. )

More information

4.5 Comparing Exponential Functions

4.5 Comparing Exponential Functions 4.5 Comparing Exponential Functions So far we have talked in detail about both linear and exponential functions. In this section we ll compare exponential functions to other exponential functions and also

More information

Final Project. College Algebra. Upon successful completion of this course, the student will be able to:

Final Project. College Algebra. Upon successful completion of this course, the student will be able to: COURSE OBJECTIVES Upon successful completion of this course, the student will be able to: 1. Perform operations on algebraic expressions 2. Perform operations on functions expressed in standard function

More information

Algebra Review (New Version) Homework Problems

Algebra Review (New Version) Homework Problems MATH 119 Algebra Review (New Version) Homework Problems The following set is only to review the Algebra needed for this class. It should be familiar to you from previous class such as M110, M111 or others.

More information

Prentice Hall Connected Mathematics 2, 7th Grade Units 2009 Correlated to: Minnesota K-12 Academic Standards in Mathematics, 9/2008 (Grade 7)

Prentice Hall Connected Mathematics 2, 7th Grade Units 2009 Correlated to: Minnesota K-12 Academic Standards in Mathematics, 9/2008 (Grade 7) 7.1.1.1 Know that every rational number can be written as the ratio of two integers or as a terminating or repeating decimal. Recognize that π is not rational, but that it can be approximated by rational

More information

b) According to the statistics above the graph, the slope is What are the units and meaning of this value?

b) According to the statistics above the graph, the slope is What are the units and meaning of this value? ! Name: Date: Hr: LINEAR MODELS Writing Motion Equations 1) Answer the following questions using the position vs. time graph of a runner in a race shown below. Be sure to show all work (formula, substitution,

More information

Practice 5-5. The y-intercept of a Line. Name Class Date. 2. Graph the equation y = x + 7. What is the y-intercept of the graph of the equation?

Practice 5-5. The y-intercept of a Line. Name Class Date. 2. Graph the equation y = x + 7. What is the y-intercept of the graph of the equation? Name Class Date Practice 5-5 The y-intercept of a Line 5-5 The y-intercept of a Line 1. What is the y-intercept of the graph? 2. Graph the equation y = x + 7. What is the y-intercept of the graph of the

More information

Exponential Modeling. Growth and Decay

Exponential Modeling. Growth and Decay Exponential Modeling Growth and Decay Identify each as growth or Decay What you should Know y Exponential functions 0

More information

notebook October 08, What are the x and y intercepts? (write your answers as coordinates).

notebook October 08, What are the x and y intercepts? (write your answers as coordinates). 3.4 Opening Activity: Draw a graph of the equation y = 5x + 20 What are the x and y intercepts? (write your answers as coordinates). How are you able to use the equation but NOT the graph to find the x

More information

CCAC ELEMENTARY ALGEBRA

CCAC ELEMENTARY ALGEBRA CCAC ELEMENTARY ALGEBRA Sample Questions TOPICS TO STUDY: Evaluate expressions Add, subtract, multiply, and divide polynomials Add, subtract, multiply, and divide rational expressions Factor two and three

More information

2-4 Completing the Square

2-4 Completing the Square 2-4 Completing the Square Warm Up Lesson Presentation Lesson Quiz Algebra 2 Warm Up Write each expression as a trinomial. 1. (x 5) 2 x 2 10x + 25 2. (3x + 5) 2 9x 2 + 30x + 25 Factor each expression. 3.

More information

Algebra 1 Unit 3: Writing Equations

Algebra 1 Unit 3: Writing Equations Lesson 8: Making Predictions and Creating Scatter Plots The table below represents the cost of a car over the recent years. Year Cost of a Car (in US dollars) 2000 22,500 2002 26,000 2004 32,000 2006 37,500

More information

par ( 12). His closest competitor, Ernie Els, finished 3 strokes over par (+3). What was the margin of victory?

par ( 12). His closest competitor, Ernie Els, finished 3 strokes over par (+3). What was the margin of victory? Exam Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) Tiger Woods won the 000 U.S. Open golf tournament with a score of 1 strokes under par

More information

Name: Date: Period: Activity 4.3.1: What is Slope?

Name: Date: Period: Activity 4.3.1: What is Slope? Name: Date: Period: Activity 4.3.: What is Slope? What is slope? If you have ever walked up or down a hill, then you have already experienced a real life example of slope. Keeping this fact in mind, by

More information

Mathematics (Project Maths Phase 2)

Mathematics (Project Maths Phase 2) L.17 NAME SCHOOL TEACHER Pre-Leaving Certificate Examination, 2013 Mathematics (Project Maths Phase 2) Paper 1 Higher Level Time: 2 hours, 30 minutes 300 marks For examiner Question 1 Centre stamp 2 3

More information

car, in years 0 (new car)

car, in years 0 (new car) Chapter 2.4: Applications of Linear Equations In this section, we discuss applications of linear equations how we can use linear equations to model situations in our lives. We already saw some examples

More information

Read the following situation to determine whether the inequality correctly models the company s information.

Read the following situation to determine whether the inequality correctly models the company s information. Algebra 1 EOC Review #7 m w2q0y1c7h \KquntBaE qsoohfhthwwabrhei vlxlvcc.e a naslzlu BrniVgwhgtosV er_e\sxeerivdeado. Additional Practice 1) Selected-Response Name Date Period Sandra sells necklaces at

More information

Cost (in dollars) 0 (free) Number of magazines purchased

Cost (in dollars) 0 (free) Number of magazines purchased Math 1 Midterm Review Name *****Don t forget to study the other methods for solving systems of equations (substitution and elimination) as well as systems of linear inequalities and line of best fit! Also,

More information

2) Endpoints of a diameter (-1, 6), (9, -2) A) (x - 2)2 + (y - 4)2 = 41 B) (x - 4)2 + (y - 2)2 = 41 C) (x - 4)2 + y2 = 16 D) x2 + (y - 2)2 = 25

2) Endpoints of a diameter (-1, 6), (9, -2) A) (x - 2)2 + (y - 4)2 = 41 B) (x - 4)2 + (y - 2)2 = 41 C) (x - 4)2 + y2 = 16 D) x2 + (y - 2)2 = 25 Math 101 Final Exam Review Revised FA17 (through section 5.6) The following problems are provided for additional practice in preparation for the Final Exam. You should not, however, rely solely upon these

More information

Final Exam Review - MAT 0028

Final Exam Review - MAT 0028 Final Exam Review - MAT 0028 All questions on the final exam are multiple choice. You will be graded on your letter choices only - no partial credit will be awarded. To maximize the benefit of this review,

More information

Lesson 4.5 Real-World Problems: Linear Equations

Lesson 4.5 Real-World Problems: Linear Equations Lesson 4.5 Real-World Problems: Linear Equations Explain the meaning of the slope and y-intercept in real-world problems. Example A telecommunication company charges their customers a fee for phone calls.

More information

Algebra I EOC 10-Day STAAR Review. Hedgehog Learning

Algebra I EOC 10-Day STAAR Review. Hedgehog Learning Algebra I EOC 10-Day STAAR Review Hedgehog Learning Day 1 Day 2 STAAR Reporting Category Number and Algebraic Methods Readiness Standards 60% - 65% of STAAR A.10(E) - factor, if possible, trinomials with

More information

f x f x f x f x x 5 3 y-intercept: y-intercept: y-intercept: y-intercept: y-intercept of a linear function written in function notation

f x f x f x f x x 5 3 y-intercept: y-intercept: y-intercept: y-intercept: y-intercept of a linear function written in function notation Questions/ Main Ideas: Algebra Notes TOPIC: Function Translations and y-intercepts Name: Period: Date: What is the y-intercept of a graph? The four s given below are written in notation. For each one,

More information

Algebra 1 Predicting Patterns & Examining Experiments

Algebra 1 Predicting Patterns & Examining Experiments We will explicitly define slope-intercept form. We have already examined slope, y- intercepts, and graphing from tables, now we are putting all of that together. This lesson focuses more upon the notation

More information

Name Date

Name Date NEW DORP HIGH SCHOOL Deirdre A. DeAngelis, Principal MATHEMATICS DEPARTMENT Li Pan, Assistant Principal Name Date Summer Math Assignment for a Student whose Official Class starts with 7, 8, and 9 Directions:

More information

HIGH-LOW METHOD. Key Terms and Concepts to Know

HIGH-LOW METHOD. Key Terms and Concepts to Know HIGH-LOW METHOD Key Terms and Concepts to Know Variable, Fixed and Mixed Costs Many costs are clearly variable, such as direct labor and direct materials, or clearly fixed, such as rent and salaries. Other

More information

Representing Linear Functions. Constant Rate of Change and Direct Variation. Writing Linear Equations

Representing Linear Functions. Constant Rate of Change and Direct Variation. Writing Linear Equations Lesson 7-1 Lesson 7-2 Lesson 7-3 Lesson 7-4 Lesson 7-5 Lesson 7-6 Lesson 7-7 Lesson 7-8 Functions Representing Linear Functions Rate of Change Constant Rate of Change and Direct Variation Slope Slope-Intercept

More information

MA 162: Finite Mathematics - Chapter 1

MA 162: Finite Mathematics - Chapter 1 MA 162: Finite Mathematics - Chapter 1 Fall 2014 Ray Kremer University of Kentucky Linear Equations Linear equations are usually represented in one of three ways: 1 Slope-intercept form: y = mx + b 2 Point-Slope

More information

WEEK 2 REVIEW. Straight Lines (1.2) Linear Models (1.3) Intersection Points (1.4) Least Squares (1.5)

WEEK 2 REVIEW. Straight Lines (1.2) Linear Models (1.3) Intersection Points (1.4) Least Squares (1.5) WEEK 2 REVIEW Straight Lines (1.2) Linear Models (1.3) Intersection Points (1.4) Least Squares (1.5) 1 STRAIGHT LINES SLOPE A VERTICAL line has NO SLOPE. All other lines have a slope given by m = rise

More information

Lesson 4: Real World Problems Using Inequalities

Lesson 4: Real World Problems Using Inequalities Lesson 4: Real World Problems Using Inequalities Key Words in Real World Problems that Involve Inequalities Example 1 Keith must rent a truck for the day to clean up the house and yard. Home Store Plus

More information

Mix Review» Form A (Master Copy)» Teacher Version. Directions: Please choose the best answer choice for each of the following questions.

Mix Review» Form A (Master Copy)» Teacher Version. Directions: Please choose the best answer choice for each of the following questions. Directions: Please choose the best answer choice for each of the following questions. 1. What is the value of 3. Nature's Nursery had maple trees on sale for 15% off the original price of $30.00. When

More information

SA2 Unit 4 Investigating Exponentials in Context Classwork A. Double Your Money. 2. Let x be the number of assignments completed. Complete the table.

SA2 Unit 4 Investigating Exponentials in Context Classwork A. Double Your Money. 2. Let x be the number of assignments completed. Complete the table. Double Your Money Your math teacher believes that doing assignments consistently will improve your understanding and success in mathematics. At the beginning of the year, your parents tried to encourage

More information

Mrs Mat. Name: 2. Which is the following equation rewritten in slopeintercept. A) y = x + 1. B) y = 4x + 1. C) y = -4x + 1.

Mrs Mat. Name: 2. Which is the following equation rewritten in slopeintercept. A) y = x + 1. B) y = 4x + 1. C) y = -4x + 1. Slope, Intercepts, and Graphing Equations Exam Expressions and Equations 8.EE - Understand the connections between proportional relationships, lines, and linear equations. No Calculator! Make sure all

More information

Coimisiún na Scrúduithe Stáit State Examinations Commission. Leaving Certificate Examination Mathematics

Coimisiún na Scrúduithe Stáit State Examinations Commission. Leaving Certificate Examination Mathematics 2016. M27 Coimisiún na Scrúduithe Stáit State Examinations Commission Leaving Certificate Examination 2016 Paper 1 Ordinary Level Friday 10 June Afternoon 2:00 4:30 300 marks Running total Examination

More information

List the quadrant(s) in which the given point is located. 1) (-10, 0) A) On an axis B) II C) IV D) III

List the quadrant(s) in which the given point is located. 1) (-10, 0) A) On an axis B) II C) IV D) III MTH 55 Chapter 2 HW List the quadrant(s) in which the given point is located. 1) (-10, 0) 1) A) On an axis B) II C) IV D) III 2) The first coordinate is positive. 2) A) I, IV B) I, II C) III, IV D) II,

More information

Find each percent of change. Round answers to the nearest tenth of a percent, if necessary. A. 65 is decreased to 38.

Find each percent of change. Round answers to the nearest tenth of a percent, if necessary. A. 65 is decreased to 38. LESSON 6-6 Percent of Change Lesson Objectives Solve problems involving percent of change Vocabulary percent of change (p. 352) percent of increase (p. 352) percent of decrease (p. 352) Additional Examples

More information

6-6 Simple and Compound Interest

6-6 Simple and Compound Interest Find the simple interest. Round to the nearest cent, if necessary. 1. $1350 at 6% for 7 years The simple interest is $567. 2. $240 at 8% for 9 months 9 months is equivalent to of a year. The simple interest

More information

Unit 7 Exponential Functions. Name: Period:

Unit 7 Exponential Functions. Name: Period: Unit 7 Exponential Functions Name: Period: 1 AIM: YWBAT evaluate and graph exponential functions. Do Now: Your soccer team wants to practice a drill for a certain amount of time each day. Which plan will

More information

Chapter 4 Factoring and Quadratic Equations

Chapter 4 Factoring and Quadratic Equations Chapter 4 Factoring and Quadratic Equations Lesson 1: Factoring by GCF, DOTS, and Case I Lesson : Factoring by Grouping & Case II Lesson 3: Factoring by Sum and Difference of Perfect Cubes Lesson 4: Solving

More information

MULTIPLE-CHOICE QUESTIONS

MULTIPLE-CHOICE QUESTIONS MULTIPLE-CHOICE QUESTIONS A1.1.1.1.1 1. An expression is shown below. 629542 2 Ï } 51x Which value of x makes the expression equivalent to 10 Ï } 51? A. 5 B. 25 * C. 50 D. 100 A student could determine

More information

r 1. Discuss the meaning of compounding using the formula A= A0 1+

r 1. Discuss the meaning of compounding using the formula A= A0 1+ Money and the Exponential Function Goals: x 1. Write and graph exponential functions of the form f ( x) = a b (3.15) 2. Use exponential equations to solve problems. Solve by graphing, substitution. (3.17)

More information

EXAMPLE 2 COMMON CORE

EXAMPLE 2 COMMON CORE REFLECT. Why can it be helpful to solve a linear equation for y? Graphing a Linear Function Using the Slope and y-intercept You can graph the linear function f() = m + b using only the slope m and y-intercept

More information

Economics 101 Fall 2018 Answers to Homework #1 Due Thursday, September 27, Directions:

Economics 101 Fall 2018 Answers to Homework #1 Due Thursday, September 27, Directions: Economics 101 Fall 2018 Answers to Homework #1 Due Thursday, September 27, 2018 Directions: The homework will be collected in a box labeled with your TA s name before the lecture. Please place your name,

More information

Student Activity: Show Me the Money!

Student Activity: Show Me the Money! 1.2 The Y-Intercept: Student Activity Student Activity: Show Me the Money! Overview: Objective: Terms: Materials: Procedures: Students connect recursive operations with graphs. Algebra I TEKS b.3.b Given

More information

dollars per person; the cost is $45 for each person. dollars per person; the cost is $1 for 225 people.

dollars per person; the cost is $45 for each person. dollars per person; the cost is $1 for 225 people. Name: ate: 1 The table shows the cost of a vacation package for a given number of people. The rate of change is constant in the table. Find the rate of change. Explain what the rate of change means for

More information

LINES AND SLOPES. Required concepts for the courses : Micro economic analysis, Managerial economy.

LINES AND SLOPES. Required concepts for the courses : Micro economic analysis, Managerial economy. LINES AND SLOPES Summary 1. Elements of a line equation... 1 2. How to obtain a straight line equation... 2 3. Microeconomic applications... 3 3.1. Demand curve... 3 3.2. Elasticity problems... 7 4. Exercises...

More information

Math 116: Business Calculus

Math 116: Business Calculus Math 116: Business Calculus Instructor: Colin Clark Spring 2017 Exam 1 - Thursday February 9. 1.1 Slopes and Equations of Lines. 1.2 Linear Functions and Applications. 2.1 Properties of Functions. 2.2

More information

2.01 Products of Polynomials

2.01 Products of Polynomials 2.01 Products of Polynomials Recall from previous lessons that when algebraic expressions are added (or subtracted) they are called terms, while expressions that are multiplied are called factors. An algebraic

More information

Algebra with Calculus for Business: Review (Summer of 07)

Algebra with Calculus for Business: Review (Summer of 07) Algebra with Calculus for Business: Review (Summer of 07) 1. Simplify (5 1 m 2 ) 3 (5m 2 ) 4. 2. Simplify (cd) 3 2 (c 3 ) 1 4 (d 1 4 ) 3. 3. Simplify (x 1 2 + y 1 2 )(x 1 2 y 1 2 ) 4. Solve the equation

More information

Algebra 1 Semester 1 Final Exam Review (Chapters 2, 3, 4, & 5)

Algebra 1 Semester 1 Final Exam Review (Chapters 2, 3, 4, & 5) Name: Date Block: Algebra 1 Semester 1 Final Exam Review (Chapters 2, 3, 4, & 5) Chapter 2: Solving Equations 1. Solve each equation. Show your work! 5 1 3n y a) f + 9.8 = 8 b) h + = c) 2p = 54 d) - 15

More information

EXPONENTIAL FUNCTIONS

EXPONENTIAL FUNCTIONS EXPONENTIAL FUNCTIONS 7.. 7..6 In these sections, students generalize what they have learned about geometric sequences to investigate exponential functions. Students study exponential functions of the

More information

Firrhill High School. Mathematics Department. Level 5

Firrhill High School. Mathematics Department. Level 5 Firrhill High School Mathematics Department Level 5 Home Exercise 1 - Basic Calculations Int 2 Unit 1 1. Round these numbers to 2 significant figures a) 409000 (b) 837500000 (c) 562 d) 0.00000009 (e)

More information

Applications of Exponential Functions Group Activity 7 Business Project Week #10

Applications of Exponential Functions Group Activity 7 Business Project Week #10 Applications of Exponential Functions Group Activity 7 Business Project Week #10 In the last activity we looked at exponential functions. This week we will look at exponential functions as related to interest

More information

1. Factors: Write the pairs of factors for each of the following numbers:

1. Factors: Write the pairs of factors for each of the following numbers: Attached is a packet containing items necessary for you to have mastered to do well in Algebra I Resource Room. Practicing math skills is especially important over the long summer break, so this summer

More information

Section 1.1 Notes. May 29, 2018

Section 1.1 Notes. May 29, 2018 Section 1.1 Notes May 29, 2018 Mathematical Models Goal: Recall the following facts about lines: 1) Equation: 2) Slope: 3) x-intercept: 4) y-intercept: Definition 1. Let D and R be two collections of objects.

More information

MLC at Boise State Polynomials Activity 3 Week #5

MLC at Boise State Polynomials Activity 3 Week #5 Polynomials Activity 3 Week #5 This activity will be discuss maximums, minimums and zeros of a quadratic function and its application to business, specifically maximizing profit, minimizing cost and break-even

More information

How can we factor polynomials?

How can we factor polynomials? How can we factor polynomials? Factoring refers to writing something as a product. Factoring completely means that all of the factors are relatively prime (they have a GCF of 1). Methods of factoring:

More information

Chap3a Introduction to Exponential Functions. Y = 2x + 4 Linear Increasing Slope = 2 y-intercept = (0,4) f(x) = 3(2) x

Chap3a Introduction to Exponential Functions. Y = 2x + 4 Linear Increasing Slope = 2 y-intercept = (0,4) f(x) = 3(2) x Name Date HW Packet Lesson 3 Introduction to Exponential Functions HW Problem 1 In this problem, we look at the characteristics of Linear and Exponential Functions. Complete the table below. Function If

More information

Equations. Krista Hauri I2T2 Project

Equations. Krista Hauri I2T2 Project Applied Linear Equations Krista Hauri I2T2 Project Grade Level: 9 th Intergraded Algebra 1 Time Span : 5 (40 minute) days Tools: Calculator Base Ranger (CBR) at least 4 TI-84 Graphing Calculator for each

More information

5.6 Special Products of Polynomials

5.6 Special Products of Polynomials 5.6 Special Products of Polynomials Learning Objectives Find the square of a binomial Find the product of binomials using sum and difference formula Solve problems using special products of polynomials

More information

13.2. KenKen has been a popular mathematics puzzle game around the world since at. They re Multiplying Like Polynomials! Multiplying Polynomials

13.2. KenKen has been a popular mathematics puzzle game around the world since at. They re Multiplying Like Polynomials! Multiplying Polynomials They re Multiplying Like Polynomials! Multiplying Polynomials.2 Learning Goals In this lesson, you will: Model the multiplication of a binomial by a binomial using algebra tiles. Use multiplication tables

More information

4.1 Write Linear Equations by Using a Tables of Values

4.1 Write Linear Equations by Using a Tables of Values 4.1 Write Linear Equations by Using a Tables of Values Review: Write y = mx + b by finding the slope and y-intercept m = b = y = x + Every time x changes units, y changes units m = b = y = x + Every time

More information

Economics 101 Fall 2016 Answers to Homework #1 Due Thursday, September 29, 2016

Economics 101 Fall 2016 Answers to Homework #1 Due Thursday, September 29, 2016 Economics 101 Fall 2016 Answers to Homework #1 Due Thursday, September 29, 2016 Directions: The homework will be collected in a box before the lecture. Please place your name, TA name and section number

More information

Linear Modeling Business 5 Supply and Demand

Linear Modeling Business 5 Supply and Demand Linear Modeling Business 5 Supply and Demand Supply and demand is a fundamental concept in business. Demand looks at the Quantity (Q) of a product that will be sold with respect to the Price (P) the product

More information

A warm up to review identifying proportional and non-proportional relationships from tables and graphs would give students entry to the activity.

A warm up to review identifying proportional and non-proportional relationships from tables and graphs would give students entry to the activity. 1 Interpreting Slopes and Y-Intercepts of Proportional and Non-Proportional Relationships Task 1: Investigating Proportional and Non-Proportional Relationships Framework Cluster Standard(s) Materials/Links

More information

Math1090 Midterm 2 Review Sections , Solve the system of linear equations using Gauss-Jordan elimination.

Math1090 Midterm 2 Review Sections , Solve the system of linear equations using Gauss-Jordan elimination. Math1090 Midterm 2 Review Sections 2.1-2.5, 3.1-3.3 1. Solve the system of linear equations using Gauss-Jordan elimination. 5x+20y 15z = 155 (a) 2x 7y+13z=85 3x+14y +6z= 43 x+z= 2 (b) x= 6 y+z=11 x y+

More information

Go for the Curve! Comparing Linear and Exponential Functions. Lesson 5.1 Assignment

Go for the Curve! Comparing Linear and Exponential Functions. Lesson 5.1 Assignment Lesson.1 Assignment Name Date Go for the Curve! Comparing Linear and Exponential Functions 1. Chanise just received a $200 bonus check from her employer. She is going to put it into an account that will

More information

Chapter 6 Diagnostic Test

Chapter 6 Diagnostic Test Chapter 6 Diagnostic Test STUDENT BOOK PAGES 310 364 1. Consider the quadratic relation y = x 2 6x + 3. a) Use partial factoring to locate two points with the same y-coordinate on the graph. b) Determine

More information