Algebra 1 Keystone Practice Exam 2019 Module 1 Solutions
Algebra 1 Keystone Practice Exam 2019 Module 1 Solutions

1-1 Variables and Epressions 1. SOLAR SYSTEM It takes Earth about 365 days to orbit the sun. It takes Uranus about 85 times as long. Write a numerical epression to describe the number of days it takes Uranus to orbit the sun. BLOCKS For Eercises 5 7, use the following information. A toy manufacturer produces a set of blocks that can be used by children to build play structures. The product packaging team is analyzing different arrangements for packaging their blocks. One idea they have is to arrange the blocks in the shape of a cube, with b blocks along one edge. 2. TECHNOLOGY There are 1024 bytes in a kilobyte. Write an epression that describes the number of bytes in a computer chip with n kilobytes. b b b 3. THEATER Howard Hughes, Professor Emeritus of Teas Wesleyan College, reportedly attended a record 6136 theatrical shows. Write an epression to represent the average number of theater shows attended if he accumulated the record over y years. Use the epression to find the average number of shows Mr. Hughes attended per year if he went to the theater for 31 years. 4. TIDES The difference between high and low tides along the Maine coast in November is 19 feet on Monday and feet on Tuesday. Write an epression to show the average rise and fall of the tide for Monday and Tuesday. 5. Write an epression representing the total number of blocks packaged in a cube measuring b blocks on one edge. 6. The packaging team decides to take one layer of blocks off the top of this package. Write an epression representing the number of blocks in the top layer of the package. 7. The team finally decides that their favorite package arrangement is to take 2 layers of blocks off the top of a cube measuring b blocks along one edge. Write an epression representing the number of blocks left behind after the top two layers are removed. Chapter 1 10 Glencoe Algebra 1

1-2 Order of Operations 1. SCHOOLS Jefferson High School has 100 less than 5 times as many students as Taft High School. Write and evaluate an epression to find the number of students at Jefferson High School if Taft High School has 300 students. 5. BIOLOGY Lavania is studying the growth of a population of fruit flies in her laboratory. She notices that the number of fruit flies in her eperiment is five times as large after any si-day period. She observes 20 fruit flies on October 1. Write and evaluate an epression to predict the population of fruit flies Lavania will observe on October 31. 2. GEOGRAPHY Guadalupe Peak in Teas has an altitude that is 671 feet more than double the altitude of Mount Sunflower in Kansas. Write and evaluate an epression for the altitude of Guadalupe Peak if Mount Sunflower has an altitude of 4039 feet. 3. TRANSPORTATION The Plaid Tai Cab Company charges \$1.75 per passenger plus \$3.45 per mile for trips less than 10 miles. Write and evaluate an epression to find the cost for Ma to take a Plaid tai 8 miles to the airport. 4. GEOMETRY The area of a circle is related to the radius of the circle such that the product of the square of the radius and a number gives the area. Write and evaluate an epression for the area of a circular pizza below. Approimate as 3.14. CONSUMER SPENDING For Eercises 6 8, use the following information. During a long weekend, Devon paid a total of dollars for a rental car so he could visit his family. He rented the car for 4 days at a rate of \$36 per day. There was an additional charge of \$0.20 per mile after the first 200 miles driven. 6. Write an algebraic epression to represent the amount Devon paid for additional mileage only. 7. Write an algebraic epression to represent the number of miles over 200 miles that Devon drove the rented car. 8. How many miles did Devon drive overall if he paid a total of \$174 for the car rental? Lesson 1-2 7 in. Chapter 1 17 Glencoe Algebra 1

1-3 Open Sentences 1. TIME There are 6 time zones in the United States. The eastern part of the U.S., including New York City, is in the Eastern Time Zone. The central part of the U.S., including Dallas, is in the Central Time Zone, which is one hour behind Eastern Time. San Diego is in the Pacific Time Zone, which is 3 hours behind Eastern Time. Write and solve an equation to determine what time it is in California if it is noon in New York. 4. POOLS There are approimately 202 gallons per cubic yard of water. Write and solve an equation for the number of gallons of water that fill a pool with a volume of 1161 cubic feet. (Hint: There are 27 cubic feet per cubic yard.) 2. FOOD Part of the Nutrition Facts label from a bo of macaroni and cheese is shown below. Nutrition Facts Serving Size 1 cup (228g) Servings Per Container 2 Amount Per Serving Calories 250 Calories from Fat 110 % Daily Value * 18 % 15 % VEHICLES For Eercises 5 and 6, use the following information. Recently developed hybrid cars contain both an electric and a gasoline engine. Hybrid car batteries store etra energy, such as the energy produced by braking. Since the car can use this stored energy to power the car, the hybrid uses less gasoline per mile than cars powered only by gasoline. Suppose a new hybrid car is rated to drive 45 miles per gallon of gasoline. Total Fat 12g Saturated Fat 3g Trans Fat 3g Cholesterol 30mg 10 % Write and solve an inequality to determine how many servings of this item that Alisa can have for lunch if she is restricted no more than 45 grams of cholesterol. 3. CRAFTS You need at least 30 yards of yarn to crochet a small scarf. Cheryl bought a 100-yard ball of yarn and has already used 10 yards. Write and solve an inequality to find how many scarves she can crochet. 5. It costs \$40 to fill the gasoline tank with gas that costs \$2.50 per gallon. Write and solve an equation to find the distance the hybrid car can go using one tank of gas. 6. Write and solve an equation to find the cost of gasoline per mile for this hybrid car. Round to the nearest cent. Lesson 1-3 Chapter 1 25 Glencoe Algebra 1

1-4 Identity and Equality Properties 1. EXERCISE Annika goes on a walk every day in order to get the eercise her doctor recommends. If she walks at a rate of 3 miles per hour for 1 3 of an hour, then she will have walked 3 1 3 miles. Evaluate the epression and name the property used. 4. PARTY PLANNING Chase is planning a dinner party for 18 guests. He needs to have the same number of place settings as guests, and the same number of water glasses as place settings. What property must be used to determine the number of water glasses he needs for the party? Eplain. 2. MAIL The chart below shows the cost of mailing letters of various weight through the United States Postal Service. USPS First Class Mail: Standard Letter Rates Weight (ounces) Cost 0.25 \$0.39 TOLL ROADS For Eercises 5 and 6, use the following information. Some toll highways assess tolls based on where a car entered and eited. The table below shows the highway tolls for a car entering and eiting at a variety of eits. Assume that the toll for the reverse direction is the same. 0.5 \$0.39 Entered Eited Toll 0.75 \$0.39 Eit 5 Eit 8 \$0.50 1 \$0.39 Eit 8 Eit 10 \$0.25 1.25 \$0.60 1.5 \$0.60 1.75 \$0.60 Source: www.usps.gov Write an equation that represents the difference between the cost of mailing a 0.5 ounce and a 1.0 ounce letter. Name the property illustrated. 3. CAPACITY Use the substitution and transitive properties to find how many 1-cup servings there are in 1 gallon of sports drink. Eit 10 Eit 15 \$1.00 Eit 15 Eit 18 \$0.50 Eit 18 Eit 22 \$0.75 5. Running an errand, Julio travels from Eit 8 to Eit 5. What property would you use to determine the toll? 6. Gordon travels from home to work and back each day. He lives at Eit 15 on the toll road and works at Eit 22. Write and evaluate an epression to find his daily toll cost. What property or properties did you use? Lesson 1-4 Chapter 1 33 Glencoe Algebra 1

1-5 The Distributive Property 1. OPERA Mr. Delong s drama class is planning a field trip to see Mozart s famous opera Don Giovanni. Tickets cost \$39 each, and there are 23 students and 2 teachers going on the field trip. Write and evaluate an epression to find the group s total ticket cost. 2. LIBRARY In Cook County Library s children s section there are 7 shelves and 4 tables. Each shelf and table displays 12 books. Write and evaluate an epression to find how many books are in the children s section. 5. MENTAL MATH During a math facts speed contest, Jamal calculated the following epression faster than anyone else in his class. 197 4 When classmates asked him how he was able to answer so quickly, he told them he used the Distributive Property to think of the problem differently. Write and evaluate an epression using the Distributive Property that would help Jamal perform the calculation quickly. 3. COSTUMES Isabella s ballet class is performing a spring recital for which they need butterfly costumes. Each butterfly costume is made from 3 3 5 yards of fabric. Use the Distributive Property to find the number of yards of fabric needed for 5 costumes. (Hint: a mied number can be written as the sum of an integer and a fraction.) 4. FENCES Demonstrate the Distributive Property by writing two equivalent epressions to represent the perimeter of the fenced dog pen below. m Dog Pen n INVESTMENTS For Eercises 6 and 7, use the following information. Letisha and Noel each opened a checking account, a savings account, and a college fund. The chart below shows the amounts that they deposited into each account. Checking Savings College Letisha \$125 \$75 \$50 Noel \$250 \$50 \$50 6. If Noel used only \$50 bills when he deposited the money to open his accounts, how many \$50 bills did he deposit? 7. If all accounts earn 1.5% interest per year and no further deposits are made, how much interest will Letisha have earned one year after her accounts were opened? Chapter 1 40 Glencoe Algebra 1

1-6 Commutative and Associative Properties 1. SCHOOL SUPPLIES At a local school supply store, a highlighter costs \$1.25, a ballpoint pen costs \$0.80, and a spiral notebook costs \$2.75. Use mental math and the Associative Property of Addition to find the total cost if one of each item is purchased. 4. ANATOMY The human body has 60 bones in the arms and hands, 84 bones in the upper body and head, and 62 bones in the legs and feet. Use the Associative Property to write and evaluate an epression that represents the total number of bones in the human body. Lesson 1-6 2. BUS STOPS Mr. McGowan drives a city bus. Occasionally he keeps track of the number of riders for market research. The chart below shows a morning route. First stop Second stop Third stop Fourth stop Bus Route 12 people got on How many people are on the bus after the fourth stop? 3. MENTAL MATH The triangular banner has a base of 9 centimeters and a height of 6 centimeters. Using the formula for area of a triangle, the banner s area can be epressed as 1 2 9 6. Gabrielle finds it easier to write and evaluate 1 2 6 9 to find the area. Is Gabrielle s epression equivalent to the area formula? Eplain. h 4 people off; 15 on 16 people off; 7 on 11 people off; 14 on b SPORTS For Eercises 5 7, use the following information. Kim, Doug, and Conner all run on the cross country team. In the last race Doug finished first, Kim finished 3 minutes after Doug, and Conner finished with a time that was twice Doug s time. 5. What is the sum of their times? 6. What property or properties did you use? 7. Evaluate the epression if Doug ran the race in 27 minutes. Chapter 1 47 Glencoe Algebra 1

1-7 Logical Reasoning and Countereamples 1. KINDERGARTEN Identify the hypothesis and conclusion and write the statement in if-then form. Helene will go to school when she is five years old. 4. AUTOMOBILES Is the following conclusion valid? If not, find a countereample. If the weather is sunny, it is a good day to wear a T-shirt. 2. GEOMETRY Write a valid conclusion that follows from the statement below for the given condition. If a valid conclusion does not follow, write no valid conclusion and eplain why. If the radius of a circle is multiplied by 10, its area is multiplied by 100. Circle A has a radius of 5 centimeters and an area equal to 78.5 square centimeters, while circle B has a radius of 50 centimeters. QUADRILATERALS For Eercises 5 7, use the following information. The Venn diagram shows the relationships of various quadrilaterals. Parallelograms Rectangles Squares Rhombuses Quadrilaterals Trapezoids 3. PRIME NUMBERS For centuries, mathematicians have tried to develop a formula to generate prime numbers. Legendre and Euler each came up with a number of polynomial formulas that generate primes. Consider the following conditional statement and find a countereample to show that it is not always true. If n is a whole number, 2n 2 11 is a prime number. State whether each statement is valid. If it is not valid, write a new statement that is valid. 5. If a square is a rhombus and a square is a rectangle, then a rhombus is a rectangle. 6. If a quadrilateral is not a parallelogram, it is a trapezoid. 7. If a quadrilateral is not a square, it is not a rhombus. Chapter 1 54 Glencoe Algebra 1

1-8 Number Systems 1. MATH CLASS In Mrs. Carson s math class, students draw numbers to determine the order in which each will solve a problem on the board. If the order is least to greatest value, list the students in order of their turn. Amanda Boyd Celeste 97 2.56 2 3 8 Dominic Eve 2. 56 7 49 4. LIGHTING The brightness of a light bulb depends on the observer s distance from the bulb. For a 200-watt bulb, the distance D (in inches) from the bulb is given by the equation D 3 18 B, where B is the brightness (in lumens per square inch). Using a light meter, a product engineer finds the brightness of a 200-watt bulb is 0.244 lumens per square inch. How far is the light meter from the bulb? 2. SPORTS Matthew won the 100-yard dash in a photo-finish race with a time of 15.83 seconds. Brady s time was 15.84 seconds, and he came in third place. Use a number line to graph Matthew s time, Brady s time, and the possible time of the person who finished in second place. GEOMETRY For Eercises 5 and 6, use the following information. The Pythagorean Theorem is used to find the length of an unknown side of a right triangle when two side lengths are known. Pythagorean Theorem a 2 b 2 c 2 Lesson 1-8 15.80 15.81 15.82 15.83 15.84 15.85 b c 3. WEATHER The table shows how the average temperature for each month varied from the normal mean temperature each month for Barrow, Alaska. Graph these values on a number. Month Change in Month Change in Temp. ( F) Temp. ( F) Jan. 3 Jul. 5 Feb. 2 Aug. 1 Mar. 2 Sep. 8 Apr. 13 Oct. 16 May 21 Nov. 16 Jun. 15 Dec. 10 Source: World Almanac 2005, pg 185 The length of side c can be found by using the following rearrangement of the Pythagorean Theorem: c a 2 b 2. 5. Should c a 2 b 2 have a symbol in front of the c? a 6. Find the length of the hypotenuse c if a 6 centimeters and b 8 centimeters. Chapter 1 61 Glencoe Algebra 1

1-9 Functions and Graphs 1. BAKING Identify the graph that shows the relationship between the number of cookies and the equivalent number of dozens. Number of cookies y Graph A Number of dozens Number of cookies y Graph B Number of dozens Number of cookies y Graph C Number of dozens 4. AGING A person born in the early 1800s had a life epectancy of about 37 years. With improvements in medical care and pharmaceuticals, life epectancy has increased significantly. In 1900, it rose to 48 years and in 2006 to almost 78 years. Draw a reasonable graph showing the change in life epectancy. 2. NATURE It takes about 40 gallons of sap from maple trees to make 1 gallon of syrup. Let the number of gallons of sap be the independent variable. Draw a reasonable graph showing the number of gallons of syrup produced from a given amount of sap. Maple Syrup y 6 5 4 3 2 1 0 40 80 120 160 200 240 3. SALES TAX The graph below shows the amount of ta paid on items of a certain cost. Name the independent and dependent variables. amount of ta (\$) 2.00 1.50 1.00 0.50 y Sales Ta WEATHER For Eercises 5 7, use the following information. One way to estimate the distance of a thunderstorm is to count the number of seconds that pass from the sight of a flash of lightning until thunder is heard. Divide this number by 5 to get the approimate distance (in miles) of the storm. 5. Identify the independent and dependent variables. 6. Suppose you can generally hear thunder up to 10 miles away. Identify an appropriate domain and range for this situation. Lesson 1-9 0 5 10 15 20 25 cost of item (\$) 7. Is the function discrete or continuous? Chapter 1 69 Glencoe Algebra 1

2-1 Writing Equations 1. HOUSES The area of the Hartstein s kitchen is 182 square feet. This is 20% of the area of the first floor of their house. Let F represent the area of the first floor. Write an equation to represent the situation. 4. WIRELESS PHONE Spinfrog wireless phone company bills on a monthly basis. Each bill includes a \$29.95 service fee for 1000 minutes plus a \$2.95 federal communication ta. Additionally, there is a charge of \$0.05 for each minute used over 1000. Let m represent the number of minutes over 1000 used during the month. Write an equation to describe the cost c of the wireless phone service per month. 2. FAMILY Katie is twice as old as her sister Mara. The sum of their ages is 24. Write a one-variable equation to represent the situation. TEMPERATURE For Eercises 5 and 6, use the table showing degrees Fahrenheit and degrees Celsius temperatures. 3. GEOMETRY The formula F V E 2 shows the relationship between the number of faces F, edges E, and vertices V of a polyhedron, such as a pyramid. Write the formula in words. Verte Face Edge Celsius Fahrenheit 20 4 10 14 0 32 10 50 20 68 30 86 5. Write a formula for converting Celsius temperatures to Fahrenheit temperatures. 6. Find the Fahrenheit equivalents for 25ºC and 35ºC. Chapter 2 10 Glencoe Algebra 1

2-2 Solving Equations by Using Addition and Subtraction 1. SUPREME COURT Chief Justice William Rehnquist served on the Supreme Court for 33 years until his death in 2005. Write and solve an equation to determine the year he was confirmed as a justice on the Supreme Court. 4. SEA LEVEL Many parts of the city of Bangkok, Thailand, sit below sea level and the city continues to sink every year. The water is held back by a system of dikes so that the city will remain dry. The base of a building in the center of Bangkok sits at an altitude of 6 feet, meaning that it is 6 feet below sea level. The top of the building is 45 feet above sea level. Write and solve an equation to find the height of the building. 45 ft above sea 2. SALARY In 2004, the annual salary of the Governor of New Jersey was \$157,000. During the same year, the annual salary of the Governor of Tennessee was \$72,000 less. Write and solve an equation it to find the annual salary of the Governor of Tennessee in 2004. dike Sea level 6 ft Lesson 2-2 3. WEATHER On a cold January day, Mavis noticed that the temperature dropped 21 degrees over the course of the day to 9ºC. Write and solve an equation to determine what the temperature was at the beginning of the day. SAVINGS For Eercises 5 and 6, use the following information. Ophace is saving \$144 to buy three concert tickets. He has already saved \$65. 5. Write and solve an equation to find the amount of money a he still needs to save. 6. Of the three tickets he plans to buy, two are for adults and one is for a child. The adult tickets together cost \$120. Write and solve an equation to find the cost of the child ticket. Chapter 2 17 Glencoe Algebra 1

2-3 Solving Equations by Using Multiplication and Division 1. HEART RATE According to the American Heart Association, the target heart rate during eercise for a healthy 20-year-old person is 150 beats per minute. The target heart rate during eercise for a 70-year-old person is one half of that rate. Write and solve an equation to find the target eercise heart rate for a 70-year-old. 4. FARMING Mr. Hill s farm is 126 acres. Mr. Hill s farm is 1 4 the size of Mr. Miller s farm. How many acres is Mr. Miller s farm? NAUTICAL For Eercises 5 and 6, use the following information. On the sea, distances are measured in nautical miles rather than miles. 2. TREES A redwood tree can grow to be about si times as tall as a pine tree. Suppose a common pine tree measures about 56 feet tall. Write and solve an equation it to find the approimate height of a redwood tree. 3. SHOPPING Raul bought fudge at the candy shop. After he gave his sister 1 2 of the fudge he bought, he still had 3 4 of a pound. How much fudge did Raul originally buy? 1 nautical mile 6080 feet 1 knot 1 nau tical mile hour 5. If a boat travels 16 knots in 1 hour, how far will it have traveled in feet? Write and solve an equation. 6. About how fast was the boat traveling in miles per hour? Round your answer to the nearest hundredth. Chapter 2 24 Glencoe Algebra 1

2-4 Solving Multi-Step Equations 1. TEMPERATURE The formula for converting a Fahrenheit temperature to F 32 a Celsius temperature is C 1.8. Find the equivalent Celsius temperature for 68ºF. 4. NUMBER THEORY Write and solve an equation to find three consecutive odd integers whose sum is 3. GEOMETRY For Eercises 5 7, use the following information. 2. HUMAN HEIGHT It is a commonly used guideline that for the average American child, their maimum adult height will be about twice their height at age 2. Suppose that Micah s adult height fits the following equation a 2c 1, where a represents his adult height and c represents his height at age 2. At age 2 Micah was 35 inches tall. What is Micah s adult height? Write and solve an equation. A rectangular swimming pool is surrounded by a concrete sidewalk that is 3 feet wide. The dimensions of the rectangle created by the sidewalk are 21 feet by 31 feet. 3 ft pool 21 ft 3. CHEMISTRY The half-life of a radioactive substance is the time required for half of a sample to undergo radioactive decay, or for the quantity to fall to half its original amount. Carbon- 14 has a half-life of 5730 years. Suppose given samples of Carbon-14 weigh 5 8 of a pound and 7 8 of a pound. What was the total weight of the samples 11,460 years ago? 31 ft 5. Find the length and width of the pool. 6. Find the area of the pool. 7. Write and solve an equation to find the area of the sidewalk in square feet. Lesson 2-4 Chapter 2 31 Glencoe Algebra 1

2-5 Solving Equations with the Variable on Each Side 1. OLYMPICS In the 2004 Summer Olympic Games in Athens, Greece, the United States athletes won 2 more than 3 times the number of gold metals won by the French athletes. The United States won 24 more gold metals than the French. Solve the equation 24 F 3F 2 to find the number of gold metals won by the French athletes. 4. NATURE The table shows the current heights and average growth rates of two different species of trees. How long will it take for the two trees to be the same height? Tree Species Current Height Annual growth A 38 inches 4 inches B 45.5 inches 2.5 inches 2. AGE Diego s mother is twice as old as he is. She is also as old as the sum of the ages of Diego and both of his younger twin brothers. The twins are 11 years old. Solve the equation 2d d 11 11 to find the age of Diego. NUMBER THEORY For Eercises 5 and 6, use the following information. Mrs. Simms told her class to find two consecutive even integers such that twice the lesser of two integers is 4 less than two times the greater integer. 3. GEOMETRY Supplementary angles are angles whose measures have a sum of 180º. Complementary angles are angles whose measures have a sum of 90º. Find the measure of an angle whose supplement is 10º more than twice its complement. Let 90 equal the degree measure of its complement and 180 equal the degree measure of its supplement. Write and solve an equation. 5. Write and solve an equation to find the integers. 6. Does the equation have one solution, no solutions, or is it an identity? Eplain. Chapter 2 38 Glencoe Algebra 1

2-6 Ratios and Proportions 1. WATER A dripping faucet wastes 3 cups of water every 24 hours. How much water is wasted in a week? MAPS For Eercises 5 7 use the map below. 0 5 mi Teas China Spring Ross 35 2. GASOLINE In mid-2005 the average price of 5 gallons of regular unleaded gasoline in the United States was \$12.95. What was the price for 16 gallons of gas? 84 6 Waco Bellmead 484 Robinson Neale Hewitt 3. SHOPPING Stevenson s Market is selling 3 packs of toothpicks for \$0.87. How much will 10 packs of toothpicks cost at this price? Round your answer to the nearest cent. 4. BUILDINGS The Sears Tower in Chicago is 1450 feet tall. The John Hancock Center in Chicago is 1127 feet tall. Suppose you are asked to build a smallscale replica of each. If you make the Sears Tower 3 meters tall, what would be the approimate height of the John Hancock replica? Round your answer to the nearest hundredth. 5. Use a metric ruler to measure the distances between Robinson and Neale on the map. 6. Using the scale of the map, find the approimate actual distance by air (not by roads), between Robinson and Neale. 7. Approimately how many square miles are shown on this map? Chapter 2 46 Glencoe Algebra 1

2-7 Percent of Change 1. SPORTS A regulation girls fast pitch softball diamond has bases that are 60 feet apart. A regulation professional baseball diamond has bases that are 50% farther apart. Label the distance between the bases on the regulation baseball diamond diagram. MUSIC For Eercises 5 7, use the table below that shows the total number of CDs, cassettes, and DVD music videos sold from 2002 to 2004. Sales of Recorded Music and Music Videos (millions of units) Format 2002 2003 2004 CD 803.3 745.9 766.9 Cassette 31.1 17.2 5.2 DVD video 10.7 17.5 29.01 Source: Recording Industry Association of America 5. Find the percent of change in the number of units sold between 2002 and 2003 and between 2003 and 2004 for each format. Round to the nearest tenth. Lesson 2-7 2. SALES TAX Olivia purchases a DVD movie priced at \$21.99. The sales ta is 6.5%. What is the total price of the movie, including ta? 3. EDUCATION The ACT is a college entrance eam taken by high school students. The maimum score that can be earned is 36. The average score in the United States was 20.9 during the 2005 school year. The average score for Vermont students was 8.1% higher than the national average. What was the average ACT score for Vermont students? Round your answer to the nearest tenth. 4. CARS Mr. Thompson plans to purchase a used car priced at \$8400. He will receive a 15% employee discount and then will have to pay a 5.5% sales ta. What will be the final price of the car? 6. Tell whether each percent of change in Eercise 5 is a percent of increase or a percent of decrease. 7. Did these trends change from 2003 to 2004? Eplain. Chapter 2 53 Glencoe Algebra 1

2-8 Solving Equations and Formulas 1. INTEREST Simple interest that you may earn on money in a savings account can be calculated with the formula I prt. I is the amount of interest earned, p is the principal or initial amount invested, r is the interest rate, and t is the amount of time the money is invested for. Solve the formula for p. 4. PHYSICS The pressure eerted on an object is calculated by the formula P F/A, where P is the pressure, F is the force, and A is the surface area of the object. Water shooting from a hose has a pressure of 75 pounds per square inch (psi). Suppose the surface area covered by the direct hose spray is 0.442 square inches. Solve the equation for F and find the force of the spray. 2. DISTANCE The distance d a car can travel is found by multiplying its rate of speed r by the amount of time t that it took to travel the distance. If a car has already traveled 5 miles, the total distance d is found by the formula d rt 5. Solve the formula for r. GEOMETRY For Eercises 5 7, use the following information. The regular octagon is divided into 8 congruent triangles. Each triangle has an area of 12 square centimeters. The perimeter of the octagon is 48 centimeters. Lesson 2-8 3. GEOMETRY The volume of a rectangular prism is given by the formula V w h. Suppose a cereal company wants to package 270 cubic inches of cereal in a full bo. The width of the bo must be 9 inches and the height of the bo must be 12 inches to fit on store shelves. Solve the equation for and find the length of the bo. 5. What is the length of each side of the octagon? 6. Solve the area of a triangle formula for h. 7. What is the height of each triangle? h Chapter 2 61 Glencoe Algebra 1

3-1 Representing Relations 1. HEALTH The American Heart Association recommends that your target heart rate during eercise should be between 50% and 75% of your maimum heart rate. Use the data in the table below to graph the approimate maimum heart rates for people of given ages. Source: www.americanheart.org Heart Rate 2. NATURE Maple syrup is made by collecting sap from sugar maple trees and boiling it down to remove ecess water. The graph shows the number of gallons of tree sap required to make different quantities of maple syrup. Epress the relation as a set of ordered pairs and then write the inverse. Gallons of Sap Age (years) 20 25 30 35 40 Maimum Heart Rate (beats per minute) Maimum Heart Rate 200 190 180 170 160 0 20 25 30 35 40 Age 320 280 240 200 160 120 80 y y 200 195 190 185 180 Maple Sap to Syrup 0 1 2 4 5 3 6 7 8 9 Gallons of Syrup Source: www.vermontmaple.org 3. COOKING A chocolate chip cookie recipe calls for 2 1 4 cups of flour for each batch of 30 cookies. Draw a mapping to show the relation between cups of flour, c, and number of cookies, n, for 1, 2, 3, and 4 batches. DATA COLLECTION For Eercises 4 6, use the following information. Margaret collected data to determine the number of books her schoolmates were bringing home each evening. She recorded her data as a set of ordered pairs. She let be the number of tetbooks brought home after school, and y be the number of students with tetbooks. The relation is shown in the mapping. 0 1 2 3 4 5 4. Epress the relation as a set of ordered pairs. 5. What is the domain of the relation? 6. What is the range of the relation? y 8 11 12 23 28 873946 Alg1 CH03 EP7 Chapter 3 10 Glencoe Algebra 1

3-2 Representing Functions Alg1 CH03 EP7 873946 1. TRANSPORTATION The cost of riding in a cab is \$3.00 plus \$0.75 per mile. The equation that represents this relation is y 0.75 3, where is the number of miles traveled and y is the cost of the trip. Look at the graph of the equation and determine whether the relation is a function. Cost (\$) 16 14 12 10 8 6 4 2 y 0 1 2 3 4 5 6 7 8 9 10 Distance (miles) 2. TEXT MESSAGING Many cell phones have a tet messaging option in addition to regular cell phone service. The function for the monthly cost of tet messaging service from Noline Wireless Company is f() 0.10 2, where is the number of tet messages that are sent. Find f(10) and f(30), the cost of 10 tet messages in a month and the cost of 30 tet messages in a month. 3. GEOMETRY The area for any square is given by the function y 2, where is the length of a side of the square and y is the area of the square. Write the equation in function notation and find the area of a square with a side length of 3.5 inches. 4. TRAVEL The cost for cars entering President George Bush Turnpike at Beltline road is given by the relation 0.75, where is the dollar amount for entrance to the toll road and y is the number of passengers. Determine if this relation is a function. Eplain. CONSUMER CHOICES For Eercises 5 7, use the following information. Aisha just received a \$40 paycheck from her new job. She spends some of it buying music online and saves the rest in a bank account. Her savings is given by f() 40 1.25, where is the number of songs she downloads at \$1.25 per song. 5. Graph the function. 6. Find f(3), f(18), and f(36). What do these values represent? Lesson 3-2 7. How many songs can Aisha buy if she wants to save \$30? Chapter 3 17 Glencoe Algebra 1

3-3 Linear Functions 1. FOOTBALL One football season, the Teas Tech Red Raiders won 4 more games than they lost. This can be represented by y 4, where is the number of games lost and y is the number of games won. Write this linear equation in standard form. 2. TOWING Pick-M-Up Towing Company charges \$40 to hook a car and \$1.70 for each mile that it is towed. The equation y 1.7 40 represents the total cost y for miles towed. Determine the -intercept and y-intercept. Describe what these values mean. 3. SHIPPING The OOCL Shenzhen, one of the world s largest container ships, carries 8,063 TEUs (1280 cubic feet containers). Workers can unload a ship at a rate of a TEU every minute. Using this rate, write and graph an equation to determine how many hours it will take the workers to unload half of the containers from the Shenzhen. TEUs on Ship (thousands) 9 8 7 6 5 4 3 2 1 y 0 10 20 30 40 50 60 70 80 Time (hours) 4. BUSINESS The equation y 1000 5000 represents the monthly profits of a start-up dry cleaning company. Time in months is and profit in dollars is y. The first date of operation is when time is zero. However, preparation for opening the business began 3 months earlier with the purchase of equipment and supplies. Graph the linear function for -values from 3 to 8. 3000 2000 1000 1000 2000 3000 4000 5000 6000 7000 8000 y O 1 2 3 4 5 6 7 8 BONE GROWTH For Eercises 5 7, use the following information. The height of a woman can be predicted by the equation h 81.2 3.34r, where h is her height in centimeters and r is the length of her radius bone in centimeters. 5. Is this is a linear function? Eplain. 6. What are the – and y-intercepts of the equation? Do they make sense in the situation? Eplain. 873946 Alg1 CH03 EP7 7. Use the function to find the approimate height of a woman whose radius bone is 25 centimeters long. Chapter 3 24 Glencoe Algebra 1

3-4 1. POSTAGE In 2002, the price for first class mail was raised to 37 cents for the first ounce and 23 cents for each additional ounce. The table below shows the cost for weights up to 5 ounces. Weight (ounces) Postage (cents) Source: www.prc.gov Arithmetic Sequences 1 2 3 4 5 37 60 83 106 129 How much did a letter weigh that cost \$1.98 to send? 2. SPORTS Wanda is the manager for the soccer team. One of her duties is to hand out cups of water at practice. Each cup of water is 4 ounces. She begins practice with a 128-ounce cooler of water. How much water is remaining after she hands out the 14th cup? 3. THEATER A theater has 20 seats in the first row, 22 in the second row, 24 in the third row, and so on for 25 rows. How many seats are in the last row? 4. NUMBER THEORY One of the most famous sequences in mathematics is the Fibonacci sequence. It is named after Leonardo de Pisa (1170-1250) or Filius Bonacci, alias Leonardo Fibonacci. The first several numbers in the Fibonacci sequence are: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, Does this represent an arithmetic sequence? Why or why not? SAVINGS For Eercises 5 and 6, use the following information. Inga s grandfather decides to start a fund for her college education. He makes an initial contribution of \$3000 and each month deposits an additional \$500. After one month he will have contributed \$3500. 5. Write an equation for the n th term of the sequence. 6. How much money will Inga s grandfather have contributed after 24 months? 873946 Alg1 CH03 EP7 Chapter 3 32 Glencoe Algebra 1

3-5 Describing Number Patterns Alg1 CH03 EP7 873946 1. GEOMETRY A number that can be represented by a triangular array is called a triangular number. What are the net three numbers in the pattern? 2. FOOD It takes about four pounds of grapes to produce one pound of raisins. The graph shows the relation for the number of pounds of grapes needed,, to make y pounds of raisins. Write an equation in function notation for the relation shown. Pounds of Raisins 1 3 6 10 4.0 3.5 3.0 2.5 2.0 1.5 1.0 0.5 y 0 1 2 3 4 5 6 7 8 Pounds of Grapes 3. TECHNOLOGY Gordon wrote a computer program to control the lighting for a deejay. He sets the lighting so that only one color is on at a time. The lighting pattern is red, blue, violet, green, and rose. The pattern repeats and colors change every 10 seconds. After 1 minute, what color light is on? 4. MUSIC A measure of music contains the same number of beats throughout the song. The table shows the relation for the number of beats counted after a certain number of measures have been played in the si-eight time. Write an equation to describe this relationship. Measures Played () 1 2 3 4 5 6 Total Number of Beats (y) 6 12 18 24 30 36 Source: www.sheetmusicusa.com GEOMETRY For Eercises 5 7, use the following information. A fractal is a pattern containing parts which are identical to the overall pattern. The following geometric pattern is a fractal. 5. Complete the table. Term 1 2 3 4 Number of Smaller Triangles y 1 6. What are the net three numbers in the pattern? 7. Write an equation in function notation for the pattern. Lesson 3-5 Chapter 3 39 Glencoe Algebra 1

4-1 Rate of Change and Slope 1. HIGHWAYS Roadway signs such as the one below are used to warn drivers of an upcoming steep down grade that could lead to a dangerous situation. What is the grade, or slope, of the hill described on the sign? 4. REAL ESTATE The median price of an eisting home in the United States was \$139,000 in 2000. The median price had risen to \$191,300 by 2004. Find the average annual rate of change in median home price from 2000 to 2004. COAL EXPORTS For Eercises 5 7, use the following graph. The graph shows the annual coal eports from U.S. mines in millions of short tons. 100 2. AMUSEMENT PARKS The SheiKra roller coaster at Busch Gardens in Tampa, Florida, features a 138-foot vertical drop. What is the slope of the coaster track at this part of the ride? Eplain. Million Short Tons 90 80 70 60 50 40 Total Eports 30 0 1998 1999 2000 2001 2002 2003 2004 3. CENSUS The table shows the population density for the state of Teas in various years. Find the average annual rate of change in the population density from 1990 to 2000. Year Population Density People Per Square Mile 1930 22.1 1960 36.4 1980 54.3 1990 64.9 2000 79.6 Source: Bureau of the Census, U.S. Dept. of Commerce Source: www.eia.doe.gov/cneaf 5. What was the rate of change in coal eports between 2001 and 2002? 6. How does the rate of change in coal eports from 2003 to 2004 compare to that of 2001 to 2002? 7. Eplain the meaning of the part of the graph with a slope of zero. Chapter 4 10 Glencoe Algebra 1

4-2 Slope and Direct Variation 1. ENGINES The engine of a chainsaw requires a miture of engine oil and gasoline. According to the directions, oil and gasoline should be mied as shown in the graph below. What is the constant of variation for the line graphed? 4. SALARY Henry started a new job in which he is paid \$9.50 an hour. Write and solve an equation to determine Henry s gross salary for a 40-hour work week. 10 y Oil (fl oz) 9 8 7 6 5 4 SALES TAX For Eercises 5 7, use the following information. Amelia received a gift card to a local music shop for her birthday. She plans to use the gift card to buy some new CDs. 3 2 1 0 1 2 3 4 5 6 Gasoline (gal) 2. RACING In 2004, German driver Michael Schumacher won the United States Grand Pri at the Indianapolis Motor Speedway. His speed during the race averaged 113.523 miles per hour. Write a direct variation equation for the distance d that Schumacher drove in h hours at that speed. 3. CURRENCY The echange rate from U.S. dollars to British pound sterling ( ) was approimately \$1.79 to 1 in 2004. Write and solve a direct variation equation to determine how many pounds sterling you would receive in echange for US\$90. 5. Amelia chose 3 CDs that each cost \$16. The sales ta on the three CDs is \$3.96. Write a direct variation equation relating sales ta to the price. 6. Graph the equation you wrote in Eercise 5. 7. What is the sales ta that Amelia is paying on the CDs? Lesson 4-2 Chapter 4 17 Glencoe Algebra 1