Using Excel to Build Understanding in a Pathways Course. Kathleen Almy & Heather Foes Rock Valley College Rockford, Illinois

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

Download "Using Excel to Build Understanding in a Pathways Course. Kathleen Almy & Heather Foes Rock Valley College Rockford, Illinois"

Transcription

1 Using Excel to Build Understanding in a Pathways Course Kathleen Almy & Heather Foes Rock Valley College Rockford, Illinois

2 Keurig vs. Starbucks Suppose you buy a venti latte every day at Starbucks. Is it worth it to buy a Keurig and make your own coffee at home? Estimate how many days you would need to make your own coffee at home to recover the cost of the Keurig, assuming you use one K-cup per day. How much will you spend on coffee for that number of days?

3 Keurig vs. Starbucks: Algebraic approach Assumptions: Each latte is $3.57 plus 8% sales tax. The Keurig you are interested in costs $99 and the coffee K-cups are about $16.49 for a 24-pack. Cost at Starbucks = 3.57(1.08)n Cost with Keurig = 99 + (16.49/24)n n = number of days 3.57(1.08)n = n n 32 days

4 Keurig vs. Starbucks: Numeric Approach Suppose you buy a venti latte every day at Starbucks for $3.57 plus 8% sales tax. Is it worth it to buy a Keurig and make your own coffee at home? Suppose the Keurig you are interested in costs $99 and the coffee K-cups are about $16.49 for a 24-pack. Cost at Starbucks: 3.57(1.08)= $3.86/day Cost with Keurig: Start at $99 and add $0.69/day Compare costs with graphs and tables in Excel.

5 Cost Keurig vs. Starbucks Keurig vs. Starbucks $ $ $ $80.00 Keurig $60.00 Starbucks $40.00 $20.00 $ Days

6 Keurig vs. Starbucks Takeaways: Students can approach, and solve, this problem without algebra. Students can be led from the numeric solution to an algebraic approach. Using Excel shows the full story, not just the break-even point.

7 Why use a spreadsheet? Numeric approaches take advantage of how students naturally solve problems. Using algebra requires a level of generalization and abstraction many students are still developing at this level. Numeric and graphic approaches can be more accessible and illuminating. They are not necessarily simpler or inferior. Using a spreadsheet minimizes the number crunching and allows students to focus on making sense of the numbers.

8 Is a Hybrid Car Worth It? You re considering buying a 2015 Toyota Prius which starts around $25,000 and gets 50 mpg. A similarly equipped Honda Accord will run closer to $22,000 but will get 31 mpg. Can the Prius make up the price difference with its lower fuel costs? How long would it take? $ save = $ gas Distance 1 GM now 1 GM improved

9 Hybrid Car: Algebraic Approach Assumptions: Current gas price is $2.25/gallon $ save = $ gas Distance 1 GM now 1 GM improved 1 $3,000 = $2.25 Distance ,000 = Distance Distance 108,772 miles If you drive 1,500 miles per month, this would take over 6 years.

10 Hybrid Car: Numeric Approach You re considering buying a 2015 Toyota Prius which starts around $25,000 and gets 50 mpg. A similarly equipped Honda Accord will run closer to $22,000 but will get 31 mpg. Can the Prius make up the price difference with its lower fuel costs? How long would it take? Assumptions: Current gas price is $2.25/gallon Prius: Start at $25,000 and add cost of gas times number of miles divided by mileage $25,000 + $2.25 miles 50 mpg Accord: Start at $22,000 and add cost of gas times number of miles divided by mileage $22,000 + $2.25 miles 31 mpg

11 Hybrid Car

12 Hybrid Car Takeaways: Students have some real-world experience and intuition they can bring to this problem if you let them. You can bridge from the numeric approach to the algebraic approach. The numeric approach can be used to generate the formula and discuss the factored form as well.

13 Hybrid Car: A related problem You are considering buying a new hybrid vehicle but are concerned that the benefits might not outweigh the cost. How efficient would the hybrid need to be in order to make up a $5,000 price difference if the standard vehicle gets 25 mpg? Assume gas costs $2.25/gallon. $5,000 = $2.25 Distance GM improved Can beginning algebra students solve this algebraically? Can beginning algebra students solve this numerically with a spreadsheet?

14 Years Hybrid Car $5,000 = $2.25 Distance GM improved Years needed to reach $ ,000 miles/year 7,500 miles/year 10,000 miles/year New MPG

15 Sierpinski Triangles Assume the first triangle has an area of 1 square unit. What happens to the area of the green portion as the number of green triangles increase?

16 Sierpinski Triangles: Algebraic approach Find the area of the first four triangles. Generalize the area of the nth triangle. 1 square unit 3 square units 4 9 square units square units 64 In general: 3 4 n 1 square units

17 Sierpinski Triangles: Numeric approach Find the area of the first four triangles. Use Excel to compute successive areas. Observe the pattern as more green triangles are created. 1 square unit 3 square units 4 9 square units square units 64

18 Sierpinski Triangles

19 Sierpinski Triangles Assume the first triangle has a perimeter of 3 units. What happens to the total perimeters of the green portions as the number of green triangles increases?

20 Sierpinski Triangles: Algebraic approach Find the perimeters of the green portions of the first four triangles. Generalize the perimeter of the green portion of the nth triangle. 3 units 9 units 2 27 units 4 81 units 8 In general: n 3 n 1 units 2

21 Sierpinski Triangles: Numeric approach Find the perimeters of the green portions of the first four triangles. Use Excel to compute successive perimeters. Observe the pattern as more green triangles are created. 3 units 9 units 2 27 units 4 81 units 8

22 Sierpinski Triangles

23 Sierpinski Triangles Takeaways: The problem of analyzing the patterns of the areas and perimeters is more accessible with a spreadsheet than with algebra. Students can gain insight into geometric sequences with the numeric approach. This knowledge helps later with exponential functions.

24 Projecting Ebola in September 2014 From the NPR article: A Frightening Curve: How Fast Is The Ebola Outbreak Growing? "It's spreading and growing exponentially," President Obama said Tuesday. Right now we've had more than 5,000 cases of Ebola, and at least 2,600 people have died. Five thousand cases of Ebola is bad; 10,000 to 25,000 is unbelievable. And with this outbreak, cases are doubling every three to four weeks. So if help doesn't arrive in time and the growth rate stays the same then 15,000 Ebola cases in mid-october could turn into 30,000 cases by mid-november, and 60,000 cases by mid- December.

25 Projecting Ebola

26 Projecting Ebola: Algebraic approach When will the number of cases reach 60,000? Is the December estimate accurate? Start by making some assumptions: Starting value on Sept 7 is 4,366 cases. Number of cases doubles every 3.5 weeks. Number of cases = 4,366 2 t 60,000 = 4,366 2 t where t = # of 3.5-week periods Since developmental students do not yet know logarithms, use Excel to project the number of cases using the given function.

27 Projecting Ebola: Numeric Approach t = 3.78 time periods of 3.5 weeks each or approximately 13 weeks The December estimate is accurate.

28 Projecting Ebola Takeaway: Using Excel gives developmental students a way to solve the problem and improve their understanding of exponential modeling.

29 Projecting Ebola NOTES: The CDC predicted 1.4 million cases by January 20, According to the World Health Organization, the number of cases in January was actually 21,000. The CDC used very intricate models incorporating many variables. They projected the worst-case scenario, which increased awareness and resources. From The Economist: For a start, the models relied on old and partial figures. These were plugged into equations whose key variable was the rate at which each case gave rise to others. But this reproduction number changed as outside help arrived and those at risk went out less, avoided physical contact and took precautions around the sick and dead. So difficult are such factors to predict that epidemiologists modelling a disease often assume that they do not change. By presenting such grim projections, the experts arguably made it less likely that they would come to pass. One of their purposes, says Neil Ferguson, a member of the WHO s Ebola response team, was to wake up the world and say that this could be really bad if we don t do anything. They succeeded, and resources poured in. at all.

30 Using Excel in traditional algebra exercises Excel can illuminate the solution to a linear equation. Solve the equation 2x 8 = 5x 17.

31 Using Excel in traditional algebra exercises Excel can help students understand identities. Solve the equation 2x 8 = 2(x 4).

32 Using Excel in traditional algebra exercises Excel can help students use the slope to find more points on a line, including the y-intercept. Problem: Find the equation of line passing through the points (3, 6) and (8, 31). Find the slope and use it to fill up and down. m = 25 5 = 5 1 Identify the y-intercept. Write the equation: y = 5x x y

33 Using Excel in traditional algebra exercises Takeaway: Using Excel can help students develop a deeper understanding of algebraic exercises. It encourages students to move beyond mindless manipulations and instead make sense of the concepts involved.

34 Questions

35 For More Information

3.3 Applications of Linear Functions

3.3 Applications of Linear Functions 3.3 Applications of Linear Functions A function f is a linear function if The graph of a linear function is a line with slope m and y-intercept b. The rate of change of a linear function is the slope m.

More information

Microeconomics Sept. 16, 2010 NOTES ON CALCULUS AND UTILITY FUNCTIONS

Microeconomics Sept. 16, 2010 NOTES ON CALCULUS AND UTILITY FUNCTIONS DUSP 11.203 Frank Levy Microeconomics Sept. 16, 2010 NOTES ON CALCULUS AND UTILITY FUNCTIONS These notes have three purposes: 1) To explain why some simple calculus formulae are useful in understanding

More information

Definition 8.1 Two inequalities are equivalent if they have the same solution set. Add or Subtract the same value on both sides of the inequality.

Definition 8.1 Two inequalities are equivalent if they have the same solution set. Add or Subtract the same value on both sides of the inequality. 8 Inequalities Concepts: Equivalent Inequalities Linear and Nonlinear Inequalities Absolute Value Inequalities (Sections 4.6 and 1.1) 8.1 Equivalent Inequalities Definition 8.1 Two inequalities are equivalent

More information

Creating, Solving, and Graphing Systems of Linear Equations and Linear Inequalities

Creating, Solving, and Graphing Systems of Linear Equations and Linear Inequalities Algebra 1, Quarter 2, Unit 2.1 Creating, Solving, and Graphing Systems of Linear Equations and Linear Inequalities Overview Number of instructional days: 15 (1 day = 45 60 minutes) Content to be learned

More information

#1 Automobile Problems (answer key at end)

#1 Automobile Problems (answer key at end) #1 Automobile Problems (answer key at end) 1. A car is traveling at 60 mph and is tailgating another car at distance of only 30 ft. If the reaction time of the tailgater is 0.5 seconds (time between seeing

More information

Drive It Green. Time Frame: 3 class periods

Drive It Green. Time Frame: 3 class periods Drive It Green Lesson Overview: Millions of people around the globe are moving every day, creating a myriad of energy challenges and opportunities for new innovation. In this three-part lesson, students

More information

Problem of the Month: Double Down

Problem of the Month: Double Down Problem of the Month: Double Down The Problems of the Month (POM) are used in a variety of ways to promote problem solving and to foster the first standard of mathematical practice from the Common Core

More information

Pre-Algebra 2008. Academic Content Standards Grade Eight Ohio. Number, Number Sense and Operations Standard. Number and Number Systems

Pre-Algebra 2008. Academic Content Standards Grade Eight Ohio. Number, Number Sense and Operations Standard. Number and Number Systems Academic Content Standards Grade Eight Ohio Pre-Algebra 2008 STANDARDS Number, Number Sense and Operations Standard Number and Number Systems 1. Use scientific notation to express large numbers and small

More information

Advancing Electric Vehicles in New Mexico

Advancing Electric Vehicles in New Mexico Advancing Electric Vehicles in New Mexico Why should NM support electric vehicles? Economic benefits Reduced fuel costs Clean Air Plug-in Electric Vehicle Models Ford, Chevy, Toyota, Nissan, Tesla, Honda,

More information

Geometry Solve real life and mathematical problems involving angle measure, area, surface area and volume.

Geometry Solve real life and mathematical problems involving angle measure, area, surface area and volume. Performance Assessment Task Pizza Crusts Grade 7 This task challenges a student to calculate area and perimeters of squares and rectangles and find circumference and area of a circle. Students must find

More information

IV. ALGEBRAIC CONCEPTS

IV. ALGEBRAIC CONCEPTS IV. ALGEBRAIC CONCEPTS Algebra is the language of mathematics. Much of the observable world can be characterized as having patterned regularity where a change in one quantity results in changes in other

More information

Growth Models. Linear (Algebraic) Growth. Growth Models 95

Growth Models. Linear (Algebraic) Growth. Growth Models 95 Growth Models 95 Growth Models Populations of people, animals, and items are growing all around us. By understanding how things grow, we can better understand what to expect in the future. Linear (Algebraic)

More information

2. System of linear equations can be solved by graphing, substitution, or eliminating a variable.

2. System of linear equations can be solved by graphing, substitution, or eliminating a variable. 1 Subject: Algebra 1 Grade Level: 9 th Unit Plan #: 6 UNIT BACKGROUND Unit Title: Systems of Equations and Inequalities Grade Level: 9 Subject/Topic: Algebra 1 Key Words: Graphing, Substitution, Elimination

More information

Algebra Bridge Project Cell Phone Plans

Algebra Bridge Project Cell Phone Plans Algebra Bridge Project Cell Phone Plans Name Teacher Part I: Two Cell Phone Plans You are in the market for a new cell phone, and you have narrowed your search to two different cell phone companies --

More information

Lesson 4: Solving and Graphing Linear Equations

Lesson 4: Solving and Graphing Linear Equations Lesson 4: Solving and Graphing Linear Equations Selected Content Standards Benchmarks Addressed: A-2-M Modeling and developing methods for solving equations and inequalities (e.g., using charts, graphs,

More information

Chapter 10. Key Ideas Correlation, Correlation Coefficient (r),

Chapter 10. Key Ideas Correlation, Correlation Coefficient (r), Chapter 0 Key Ideas Correlation, Correlation Coefficient (r), Section 0-: Overview We have already explored the basics of describing single variable data sets. However, when two quantitative variables

More information

ALGEBRA I (Common Core) Thursday, January 28, 2016 1:15 to 4:15 p.m., only

ALGEBRA I (Common Core) Thursday, January 28, 2016 1:15 to 4:15 p.m., only ALGEBRA I (COMMON CORE) The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION ALGEBRA I (Common Core) Thursday, January 28, 2016 1:15 to 4:15 p.m., only Student Name: School Name: The

More information

Linear Approximations ACADEMIC RESOURCE CENTER

Linear Approximations ACADEMIC RESOURCE CENTER Linear Approximations ACADEMIC RESOURCE CENTER Table of Contents Linear Function Linear Function or Not Real World Uses for Linear Equations Why Do We Use Linear Equations? Estimation with Linear Approximations

More information

Algebra 1 2008. Academic Content Standards Grade Eight and Grade Nine Ohio. Grade Eight. Number, Number Sense and Operations Standard

Algebra 1 2008. Academic Content Standards Grade Eight and Grade Nine Ohio. Grade Eight. Number, Number Sense and Operations Standard Academic Content Standards Grade Eight and Grade Nine Ohio Algebra 1 2008 Grade Eight STANDARDS Number, Number Sense and Operations Standard Number and Number Systems 1. Use scientific notation to express

More information

Algebra I. In this technological age, mathematics is more important than ever. When students

Algebra I. In this technological age, mathematics is more important than ever. When students In this technological age, mathematics is more important than ever. When students leave school, they are more and more likely to use mathematics in their work and everyday lives operating computer equipment,

More information

ALGEBRA. sequence, term, nth term, consecutive, rule, relationship, generate, predict, continue increase, decrease finite, infinite

ALGEBRA. sequence, term, nth term, consecutive, rule, relationship, generate, predict, continue increase, decrease finite, infinite ALGEBRA Pupils should be taught to: Generate and describe sequences As outcomes, Year 7 pupils should, for example: Use, read and write, spelling correctly: sequence, term, nth term, consecutive, rule,

More information

HOW MUCH WILL I SPEND ON GAS?

HOW MUCH WILL I SPEND ON GAS? HOW MUCH WILL I SPEND ON GAS? Outcome (lesson objective) The students will use the current and future price of gasoline to construct T-charts, write algebraic equations, and plot the equations on a graph.

More information

High School Algebra Reasoning with Equations and Inequalities Solve systems of equations.

High School Algebra Reasoning with Equations and Inequalities Solve systems of equations. Performance Assessment Task Graphs (2006) Grade 9 This task challenges a student to use knowledge of graphs and their significant features to identify the linear equations for various lines. A student

More information

Homework 1 1. Calculus. Homework 1 Due Date: September 26 (Wednesday) 60 1.75x 220 270 160 x 280. R = 115.95x. C = 95x + 750.

Homework 1 1. Calculus. Homework 1 Due Date: September 26 (Wednesday) 60 1.75x 220 270 160 x 280. R = 115.95x. C = 95x + 750. Homework 1 1 Calculus Homework 1 Due Date: September 26 (Wednesday) 1. A doughnut shop sells a dozen doughnuts for $4.50. Beyond the fixed cost of $220 per day, it costs $2.75 for enough materials and

More information

Models of a Vending Machine Business

Models of a Vending Machine Business Math Models: Sample lesson Tom Hughes, 1999 Models of a Vending Machine Business Lesson Overview Students take on different roles in simulating starting a vending machine business in their school that

More information

Part 1 will be selected response. Each selected response item will have 3 or 4 choices.

Part 1 will be selected response. Each selected response item will have 3 or 4 choices. Items on this review are grouped by Unit and Topic. A calculator is permitted on the Algebra 1 A Semester Exam The Algebra 1 A Semester Exam will consist of two parts. Part 1 will be selected response.

More information

Acquisition Lesson Plan for the Concept, Topic or Skill---Not for the Day

Acquisition Lesson Plan for the Concept, Topic or Skill---Not for the Day Acquisition Lesson Plan Concept: Linear Systems Author Name(s): High-School Delaware Math Cadre Committee Grade: Ninth Grade Time Frame: Two 45 minute periods Pre-requisite(s): Write algebraic expressions

More information

Big Ideas in Mathematics

Big Ideas in Mathematics Big Ideas in Mathematics which are important to all mathematics learning. (Adapted from the NCTM Curriculum Focal Points, 2006) The Mathematics Big Ideas are organized using the PA Mathematics Standards

More information

c 2008 Je rey A. Miron We have described the constraints that a consumer faces, i.e., discussed the budget constraint.

c 2008 Je rey A. Miron We have described the constraints that a consumer faces, i.e., discussed the budget constraint. Lecture 2b: Utility c 2008 Je rey A. Miron Outline: 1. Introduction 2. Utility: A De nition 3. Monotonic Transformations 4. Cardinal Utility 5. Constructing a Utility Function 6. Examples of Utility Functions

More information

Temperature Scales. The metric system that we are now using includes a unit that is specific for the representation of measured temperatures.

Temperature Scales. The metric system that we are now using includes a unit that is specific for the representation of measured temperatures. Temperature Scales INTRODUCTION The metric system that we are now using includes a unit that is specific for the representation of measured temperatures. The unit of temperature in the metric system is

More information

8.7 Exponential Growth and Decay

8.7 Exponential Growth and Decay Section 8.7 Exponential Growth and Decay 847 8.7 Exponential Growth and Decay Exponential Growth Models Recalling the investigations in Section 8.3, we started by developing a formula for discrete compound

More information

MBA Teaching Note 08-02 Net Present Value Analysis of the Purchase of a Hybrid Automobile 1

MBA Teaching Note 08-02 Net Present Value Analysis of the Purchase of a Hybrid Automobile 1 MBA Teaching Note 08-02 Net Present Value Analysis of the Purchase of a Hybrid Automobile 1 In this day and age of high energy prices and a desire to be more environmentally friendly, the automobile industry

More information

Week 1: Functions and Equations

Week 1: Functions and Equations Week 1: Functions and Equations Goals: Review functions Introduce modeling using linear and quadratic functions Solving equations and systems Suggested Textbook Readings: Chapter 2: 2.1-2.2, and Chapter

More information

Let s explore the content and skills assessed by Heart of Algebra questions.

Let s explore the content and skills assessed by Heart of Algebra questions. Chapter 9 Heart of Algebra Heart of Algebra focuses on the mastery of linear equations, systems of linear equations, and linear functions. The ability to analyze and create linear equations, inequalities,

More information

Task: Representing the National Debt 7 th grade

Task: Representing the National Debt 7 th grade Tennessee Department of Education Task: Representing the National Debt 7 th grade Rachel s economics class has been studying the national debt. The day her class discussed it, the national debt was $16,743,576,637,802.93.

More information

with functions, expressions and equations which follow in units 3 and 4.

with functions, expressions and equations which follow in units 3 and 4. Grade 8 Overview View unit yearlong overview here The unit design was created in line with the areas of focus for grade 8 Mathematics as identified by the Common Core State Standards and the PARCC Model

More information

Correlation key concepts:

Correlation key concepts: CORRELATION Correlation key concepts: Types of correlation Methods of studying correlation a) Scatter diagram b) Karl pearson s coefficient of correlation c) Spearman s Rank correlation coefficient d)

More information

What does the number m in y = mx + b measure? To find out, suppose (x 1, y 1 ) and (x 2, y 2 ) are two points on the graph of y = mx + b.

What does the number m in y = mx + b measure? To find out, suppose (x 1, y 1 ) and (x 2, y 2 ) are two points on the graph of y = mx + b. PRIMARY CONTENT MODULE Algebra - Linear Equations & Inequalities T-37/H-37 What does the number m in y = mx + b measure? To find out, suppose (x 1, y 1 ) and (x 2, y 2 ) are two points on the graph of

More information

Grade 5 Math Content 1

Grade 5 Math Content 1 Grade 5 Math Content 1 Number and Operations: Whole Numbers Multiplication and Division In Grade 5, students consolidate their understanding of the computational strategies they use for multiplication.

More information

Pennsylvania System of School Assessment

Pennsylvania System of School Assessment Pennsylvania System of School Assessment The Assessment Anchors, as defined by the Eligible Content, are organized into cohesive blueprints, each structured with a common labeling system that can be read

More information

Elasticity. I. What is Elasticity?

Elasticity. I. What is Elasticity? Elasticity I. What is Elasticity? The purpose of this section is to develop some general rules about elasticity, which may them be applied to the four different specific types of elasticity discussed in

More information

1 Functions, Graphs and Limits

1 Functions, Graphs and Limits 1 Functions, Graphs and Limits 1.1 The Cartesian Plane In this course we will be dealing a lot with the Cartesian plane (also called the xy-plane), so this section should serve as a review of it and its

More information

Chapter 27: Taxation. 27.1: Introduction. 27.2: The Two Prices with a Tax. 27.2: The Pre-Tax Position

Chapter 27: Taxation. 27.1: Introduction. 27.2: The Two Prices with a Tax. 27.2: The Pre-Tax Position Chapter 27: Taxation 27.1: Introduction We consider the effect of taxation on some good on the market for that good. We ask the questions: who pays the tax? what effect does it have on the equilibrium

More information

Elasticity. Demand is inelastic if it does not respond much to price changes, and elastic if demand changes a lot when the price changes.

Elasticity. Demand is inelastic if it does not respond much to price changes, and elastic if demand changes a lot when the price changes. Elasticity The price elasticity of demand measures the sensitivity of the quantity demanded to changes in the price. Demand is inelastic if it does not respond much to price changes, and elastic if demand

More information

Nonlinear Systems and the Conic Sections

Nonlinear Systems and the Conic Sections C H A P T E R 11 Nonlinear Systems and the Conic Sections x y 0 40 Width of boom carpet Most intense sonic boom is between these lines t a cruising speed of 1,40 miles per hour, the Concorde can fly from

More information

You and your friends head out to a favorite restaurant

You and your friends head out to a favorite restaurant 19 Cost-Volume-Profit Analysis Learning Objectives 1 Identify how changes in volume affect costs 2 Use CVP analysis to compute breakeven points 3 Use CVP analysis for profit planning, and graph the CVP

More information

Characteristics of the Four Main Geometrical Figures

Characteristics of the Four Main Geometrical Figures Math 40 9.7 & 9.8: The Big Four Square, Rectangle, Triangle, Circle Pre Algebra We will be focusing our attention on the formulas for the area and perimeter of a square, rectangle, triangle, and a circle.

More information

This unit will lay the groundwork for later units where the students will extend this knowledge to quadratic and exponential functions.

This unit will lay the groundwork for later units where the students will extend this knowledge to quadratic and exponential functions. Algebra I Overview View unit yearlong overview here Many of the concepts presented in Algebra I are progressions of concepts that were introduced in grades 6 through 8. The content presented in this course

More information

01 In any business, or, indeed, in life in general, hindsight is a beautiful thing. If only we could look into a

01 In any business, or, indeed, in life in general, hindsight is a beautiful thing. If only we could look into a 01 technical cost-volumeprofit relevant to acca qualification paper F5 In any business, or, indeed, in life in general, hindsight is a beautiful thing. If only we could look into a crystal ball and find

More information

Mathematics 31 Pre-calculus and Limits

Mathematics 31 Pre-calculus and Limits Mathematics 31 Pre-calculus and Limits Overview After completing this section, students will be epected to have acquired reliability and fluency in the algebraic skills of factoring, operations with radicals

More information

Prentice Hall Algebra 2 2011 Correlated to: Colorado P-12 Academic Standards for High School Mathematics, Adopted 12/2009

Prentice Hall Algebra 2 2011 Correlated to: Colorado P-12 Academic Standards for High School Mathematics, Adopted 12/2009 Content Area: Mathematics Grade Level Expectations: High School Standard: Number Sense, Properties, and Operations Understand the structure and properties of our number system. At their most basic level

More information

Managerial Economics Prof. Trupti Mishra S.J.M. School of Management Indian Institute of Technology, Bombay. Lecture - 13 Consumer Behaviour (Contd )

Managerial Economics Prof. Trupti Mishra S.J.M. School of Management Indian Institute of Technology, Bombay. Lecture - 13 Consumer Behaviour (Contd ) (Refer Slide Time: 00:28) Managerial Economics Prof. Trupti Mishra S.J.M. School of Management Indian Institute of Technology, Bombay Lecture - 13 Consumer Behaviour (Contd ) We will continue our discussion

More information

When are Alternative Fuel Vehicles a Cost-Effective Option for Local Governments? Christopher R Sherman

When are Alternative Fuel Vehicles a Cost-Effective Option for Local Governments? Christopher R Sherman by Christopher R Sherman A paper submitted to the faculty of the University of North Carolina at Chapel Hill in partial fulfillment of the requirements for the degree of Master of Public Administration

More information

Average rate of change

Average rate of change Average rate of change 1 1 Average rate of change A fundamental philosophical truth is that everything changes. 1 Average rate of change A fundamental philosophical truth is that everything changes. In

More information

Finding Rates and the Geometric Mean

Finding Rates and the Geometric Mean Finding Rates and the Geometric Mean So far, most of the situations we ve covered have assumed a known interest rate. If you save a certain amount of money and it earns a fixed interest rate for a period

More information

Exponents and Radicals

Exponents and Radicals Exponents and Radicals (a + b) 10 Exponents are a very important part of algebra. An exponent is just a convenient way of writing repeated multiplications of the same number. Radicals involve the use of

More information

Q: What types of businesses/industries can benefit from the SBA loan programs? A: Most small owner-operated business can benefit from SBA loans

Q: What types of businesses/industries can benefit from the SBA loan programs? A: Most small owner-operated business can benefit from SBA loans Interview with Alan Thomes, President, SBA Loan Division State Bank and Trust Company For many new start-ups and small businesses, an SBA loan may be an appropriate form of financing. In this interview

More information

Overview. Essential Questions. Precalculus, Quarter 4, Unit 4.5 Build Arithmetic and Geometric Sequences and Series

Overview. Essential Questions. Precalculus, Quarter 4, Unit 4.5 Build Arithmetic and Geometric Sequences and Series Sequences and Series Overview Number of instruction days: 4 6 (1 day = 53 minutes) Content to Be Learned Write arithmetic and geometric sequences both recursively and with an explicit formula, use them

More information

Overview for Families

Overview for Families unit: Ratios and Rates Mathematical strand: Number The following pages will help you to understand the mathematics that your child is currently studying as well as the type of problems (s)he will solve

More information

Teacher: Maple So School: Herron High School. Comparing the Usage Cost of Electric Vehicles Versus Internal Combustion Vehicles

Teacher: Maple So School: Herron High School. Comparing the Usage Cost of Electric Vehicles Versus Internal Combustion Vehicles Teacher: Maple So School: Herron High School Name of Lesson: Comparing the Usage Cost of Electric Vehicles Versus Internal Combustion Vehicles Subject/ Course: Mathematics, Algebra I Grade Level: 9 th

More information

For additional information, see the Math Notes boxes in Lesson B.1.3 and B.2.3.

For additional information, see the Math Notes boxes in Lesson B.1.3 and B.2.3. EXPONENTIAL FUNCTIONS B.1.1 B.1.6 In these sections, students generalize what they have learned about geometric sequences to investigate exponential functions. Students study exponential functions of the

More information

Common sense, and the model that we have used, suggest that an increase in p means a decrease in demand, but this is not the only possibility.

Common sense, and the model that we have used, suggest that an increase in p means a decrease in demand, but this is not the only possibility. Lecture 6: Income and Substitution E ects c 2009 Je rey A. Miron Outline 1. Introduction 2. The Substitution E ect 3. The Income E ect 4. The Sign of the Substitution E ect 5. The Total Change in Demand

More information

Management Accounting 243 Pricing Decision Analysis

Management Accounting 243 Pricing Decision Analysis Management Accounting 243 Pricing Decision Analysis The setting of a price for a product is one of the most important decisions and certainly one of the more complex. A change in price not only directly

More information

The fundamental question in economics is 2. Consumer Preferences

The fundamental question in economics is 2. Consumer Preferences A Theory of Consumer Behavior Preliminaries 1. Introduction The fundamental question in economics is 2. Consumer Preferences Given limited resources, how are goods and service allocated? 1 3. Indifference

More information

The Cost of Production

The Cost of Production The Cost of Production 1. Opportunity Costs 2. Economic Costs versus Accounting Costs 3. All Sorts of Different Kinds of Costs 4. Cost in the Short Run 5. Cost in the Long Run 6. Cost Minimization 7. The

More information

Relationships Between Two Variables: Scatterplots and Correlation

Relationships Between Two Variables: Scatterplots and Correlation Relationships Between Two Variables: Scatterplots and Correlation Example: Consider the population of cars manufactured in the U.S. What is the relationship (1) between engine size and horsepower? (2)

More information

DELAWARE MATHEMATICS CONTENT STANDARDS GRADES 9-10. PAGE(S) WHERE TAUGHT (If submission is not a book, cite appropriate location(s))

DELAWARE MATHEMATICS CONTENT STANDARDS GRADES 9-10. PAGE(S) WHERE TAUGHT (If submission is not a book, cite appropriate location(s)) Prentice Hall University of Chicago School Mathematics Project: Advanced Algebra 2002 Delaware Mathematics Content Standards (Grades 9-10) STANDARD #1 Students will develop their ability to SOLVE PROBLEMS

More information

1 of 7 9/5/2009 6:12 PM

1 of 7 9/5/2009 6:12 PM 1 of 7 9/5/2009 6:12 PM Chapter 2 Homework Due: 9:00am on Tuesday, September 8, 2009 Note: To understand how points are awarded, read your instructor's Grading Policy. [Return to Standard Assignment View]

More information

1. Which of the 12 parent functions we know from chapter 1 are power functions? List their equations and names.

1. Which of the 12 parent functions we know from chapter 1 are power functions? List their equations and names. Pre Calculus Worksheet. 1. Which of the 1 parent functions we know from chapter 1 are power functions? List their equations and names.. Analyze each power function using the terminology from lesson 1-.

More information

Cost-Volume-Profit. Managerial Accounting Fifth Edition Weygandt Kimmel Kieso. Page 5-2

Cost-Volume-Profit. Managerial Accounting Fifth Edition Weygandt Kimmel Kieso. Page 5-2 5-1 Cost-Volume-Profit Managerial Accounting Fifth Edition Weygandt Kimmel Kieso 5-2 study objectives 1. Distinguish between variable and fixed costs. 2. Explain the significance of the relevant range.

More information

Objectives. Day Day 1 Day 2 Day 3 Day 4 Day 5 Day 6 Day 7. Inventory 2,782 2,525 2,303 2,109 1,955 1,788 1,570

Objectives. Day Day 1 Day 2 Day 3 Day 4 Day 5 Day 6 Day 7. Inventory 2,782 2,525 2,303 2,109 1,955 1,788 1,570 Activity 4 Objectives Use the CellSheet App to predict future trends based on average daily use Use a linear regression model to predict future trends Introduction Have you ever gone to buy a new CD or

More information

Unit 1 Equations, Inequalities, Functions

Unit 1 Equations, Inequalities, Functions Unit 1 Equations, Inequalities, Functions Algebra 2, Pages 1-100 Overview: This unit models real-world situations by using one- and two-variable linear equations. This unit will further expand upon pervious

More information

Midterm Exam 1. 1. (20 points) Determine whether each of the statements below is True or False:

Midterm Exam 1. 1. (20 points) Determine whether each of the statements below is True or False: Econ 353 Money, Banking, and Financial Institutions Spring 2006 Midterm Exam 1 Name The duration of the exam is 1 hour 20 minutes. The exam consists of 11 problems and it is worth 100 points. Please write

More information

Microeconomic Theory: Basic Math Concepts

Microeconomic Theory: Basic Math Concepts Microeconomic Theory: Basic Math Concepts Matt Van Essen University of Alabama Van Essen (U of A) Basic Math Concepts 1 / 66 Basic Math Concepts In this lecture we will review some basic mathematical concepts

More information

1.4 Linear Models. Cost, Revenue, and Profit Functions. Example 1 Linear Cost Function

1.4 Linear Models. Cost, Revenue, and Profit Functions. Example 1 Linear Cost Function 16314_02_ch1_p033-112.qxd 7/17/06 4:10 PM Page 66 66 Chapter 1 Functions and Linear Models 77. If y and x are related by the linear expression y = mx + b, how will y change as x changes if m is positive?

More information

COWLEY COUNTY COMMUNITY COLLEGE REVIEW GUIDE Compass Algebra Level 2

COWLEY COUNTY COMMUNITY COLLEGE REVIEW GUIDE Compass Algebra Level 2 COWLEY COUNTY COMMUNITY COLLEGE REVIEW GUIDE Compass Algebra Level This study guide is for students trying to test into College Algebra. There are three levels of math study guides. 1. If x and y 1, what

More information

Graphing: Slope-Intercept Form

Graphing: Slope-Intercept Form Graphing: Slope-Intercept Form A cab ride has an initial fee of $5.00 plus $0.20 for every mile driven. Let s define the variables and write a function that represents this situation. We can complete the

More information

Section 1.4. Difference Equations

Section 1.4. Difference Equations Difference Equations to Differential Equations Section 1.4 Difference Equations At this point almost all of our sequences have had explicit formulas for their terms. That is, we have looked mainly at sequences

More information

Solution to Exercise 7 on Multisource Pollution

Solution to Exercise 7 on Multisource Pollution Peter J. Wilcoxen Economics 437 The Maxwell School Syracuse University Solution to Exercise 7 on Multisource Pollution 1 Finding the Efficient Amounts of Abatement There are two ways to find the efficient

More information

2013 MBA Jump Start Program

2013 MBA Jump Start Program 2013 MBA Jump Start Program Module 2: Mathematics Thomas Gilbert Mathematics Module Algebra Review Calculus Permutations and Combinations [Online Appendix: Basic Mathematical Concepts] 2 1 Equation of

More information

Objectives. Materials

Objectives. Materials Activity 4 Objectives Understand what a slope field represents in terms of Create a slope field for a given differential equation Materials TI-84 Plus / TI-83 Plus Graph paper Introduction One of the ways

More information

https://williamshartunionca.springboardonline.org/ebook/book/27e8f1b87a1c4555a1212b...

https://williamshartunionca.springboardonline.org/ebook/book/27e8f1b87a1c4555a1212b... of 19 9/2/2014 12:09 PM Answers Teacher Copy Plan Pacing: 1 class period Chunking the Lesson Example A #1 Example B Example C #2 Check Your Understanding Lesson Practice Teach Bell-Ringer Activity Students

More information

Strategy and Analysis in Using NPV. How Positive NPV Arises

Strategy and Analysis in Using NPV. How Positive NPV Arises Strategy and Analysis in Using NPV (Text reference: Chapter 8) Topics how positive NPV arises decision trees sensitivity analysis scenario analysis break-even analysis investment options AFM 271 - Strategy

More information

SEQUENCES ARITHMETIC SEQUENCES. Examples

SEQUENCES ARITHMETIC SEQUENCES. Examples SEQUENCES ARITHMETIC SEQUENCES An ordered list of numbers such as: 4, 9, 6, 25, 36 is a sequence. Each number in the sequence is a term. Usually variables with subscripts are used to label terms. For example,

More information

In addition to looking for applications that can be profitably examined algebraically,

In addition to looking for applications that can be profitably examined algebraically, The mathematics of stopping your car Eric Wood National Institute of Education, Singapore In addition to looking for applications that can be profitably examined algebraically, numerically

More information

Sums & Series. a i. i=1

Sums & Series. a i. i=1 Sums & Series Suppose a,a,... is a sequence. Sometimes we ll want to sum the first k numbers (also known as terms) that appear in a sequence. A shorter way to write a + a + a 3 + + a k is as There are

More information

DRAFT. New York State Testing Program Grade 8 Common Core Mathematics Test. Released Questions with Annotations

DRAFT. New York State Testing Program Grade 8 Common Core Mathematics Test. Released Questions with Annotations DRAFT New York State Testing Program Grade 8 Common Core Mathematics Test Released Questions with Annotations August 2014 Developed and published under contract with the New York State Education Department

More information

Algebra 1 Course Information

Algebra 1 Course Information Course Information Course Description: Students will study patterns, relations, and functions, and focus on the use of mathematical models to understand and analyze quantitative relationships. Through

More information

The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION INTEGRATED ALGEBRA. Wednesday, June 12, 2013 1:15 to 4:15 p.m.

The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION INTEGRATED ALGEBRA. Wednesday, June 12, 2013 1:15 to 4:15 p.m. INTEGRATED ALGEBRA The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION INTEGRATED ALGEBRA Wednesday, June 12, 2013 1:15 to 4:15 p.m., only Student Name: School Name: The possession

More information

MATD 0390 - Intermediate Algebra Review for Pretest

MATD 0390 - Intermediate Algebra Review for Pretest MATD 090 - Intermediate Algebra Review for Pretest. Evaluate: a) - b) - c) (-) d) 0. Evaluate: [ - ( - )]. Evaluate: - -(-7) + (-8). Evaluate: - - + [6 - ( - 9)]. Simplify: [x - (x - )] 6. Solve: -(x +

More information

due date: third day of class estimated time: 10 hours (for planning purposes only; work until you finish)

due date: third day of class estimated time: 10 hours (for planning purposes only; work until you finish) AP Statistics Summer Work 05 due date: third day of class estimated time: 0 hours (for planning purposes only; work until you finish) Dear AP Statistics Students, This assignment is designed to make sure

More information

Anchorage School District/Alaska Sr. High Math Performance Standards Algebra

Anchorage School District/Alaska Sr. High Math Performance Standards Algebra Anchorage School District/Alaska Sr. High Math Performance Standards Algebra Algebra 1 2008 STANDARDS PERFORMANCE STANDARDS A1:1 Number Sense.1 Classify numbers as Real, Irrational, Rational, Integer,

More information

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Review MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) All but one of these statements contain a mistake. Which could be true? A) There is a correlation

More information

F.IF.7b: Graph Root, Piecewise, Step, & Absolute Value Functions

F.IF.7b: Graph Root, Piecewise, Step, & Absolute Value Functions F.IF.7b: Graph Root, Piecewise, Step, & Absolute Value Functions F.IF.7b: Graph Root, Piecewise, Step, & Absolute Value Functions Analyze functions using different representations. 7. Graph functions expressed

More information

Part 1: Background - Graphing

Part 1: Background - Graphing Department of Physics and Geology Graphing Astronomy 1401 Equipment Needed Qty Computer with Data Studio Software 1 1.1 Graphing Part 1: Background - Graphing In science it is very important to find and

More information

Pearson Algebra 1 Common Core 2015

Pearson Algebra 1 Common Core 2015 A Correlation of Pearson Algebra 1 Common Core 2015 To the Common Core State Standards for Mathematics Traditional Pathways, Algebra 1 High School Copyright 2015 Pearson Education, Inc. or its affiliate(s).

More information

MATH REVIEW SHEETS BEGINNING ALGEBRA MATH 60

MATH REVIEW SHEETS BEGINNING ALGEBRA MATH 60 MATH REVIEW SHEETS BEGINNING ALGEBRA MATH 60 A Summar of Concepts Needed to be Successful in Mathematics The following sheets list the ke concepts which are taught in the specified math course. The sheets

More information

3 e) x f) 2. Precalculus Worksheet P.1. 1. Complete the following questions from your textbook: p11: #5 10. 2. Why would you never write 5 < x > 7?

3 e) x f) 2. Precalculus Worksheet P.1. 1. Complete the following questions from your textbook: p11: #5 10. 2. Why would you never write 5 < x > 7? Precalculus Worksheet P.1 1. Complete the following questions from your tetbook: p11: #5 10. Why would you never write 5 < > 7? 3. Why would you never write 3 > > 8? 4. Describe the graphs below using

More information

chapter >> First Principles Section 1: Individual Choice: The Core of Economics

chapter >> First Principles Section 1: Individual Choice: The Core of Economics chapter 1 Individual choice is the decision by an individual of what to do, which necessarily involves a decision of what not to do. >> First Principles Section 1: Individual Choice: The Core of Economics

More information

EL CAMINO COLLEGE COURSE OUTLINE OF RECORD. Grading Method: Letter Credit/No Credit Both No Grade

EL CAMINO COLLEGE COURSE OUTLINE OF RECORD. Grading Method: Letter Credit/No Credit Both No Grade EL CAMINO COLLEGE COURSE OUTLINE OF RECORD I. COURSE DESCRIPTION Course Title and Number: Mathematics 43 Descriptive Title: Extended Elementary Algebra, Part II Discipline: Mathematics Division: Mathematical

More information