Practice Test ISSUE SKILLS REVIEW Before heading to a mountain, a climber buys one 1 pair of shoes (s), one belay (b), and two carabiners (c). Which expression below describes the total amount of gear that the climber bought? A s + b + c B 2(s + b + c) C s + b c D s + b + 2c A pair of climbing shoes (s) costs five times as much 2 as a belay. Which expression describes the total cost of one pair of shoes and two belays? A 6s B s + 2( 5 s ) C s + 2s D 12s Which of the following numbers does 3 4.24 5 10 6 represent? A 42,400,000 B 4,240,000 C 424,000 D 42,400 4Which of the following numbers is 0.00074 in scientific notation? A 7.4 5 10-4 B 7.4 5 10-3 C 7.4 5 10 4 D 7.4 5 10-5 6Of the 25 exotic animals to escape in the U.S. in the first half of 2014, 14 were mammals. What percent of escaped exotic animals were not mammals? 7 Write the prescription for 20/40 vision as a decimal. 8Use what you ve learned about vision ratios (like 20/30, 20/40, etc.) to determine which of the following decimals represents the strongest eyesight. A 0.25 B 0.5 C 0.75 D 1 9-4 5 (-4) = 0 10 16 4 5 (-2) = 5In 9 out of 50 U.S. states, residents are forbidden from owning certain types of exotic pets. What percent of U.S. states is that?
Exponents HOW MUCH SPACE? In Planet Hunters on page 6, you read about how to write very large and very small numbers in scientific notation. When you express a number in scientific notation, you multiply a power of 10 by a number greater than or equal to 1 and less than 10. In a power of 10, the base is 10 and the exponent exponent is an integer: 10 n base The exponent tells you how many times to use the base in multiplication. So you can rewrite the number 4.71 x 10 6 as: 4.71 5 10 5 10 5 10 5 10 5 10 5 10 10 is multiplied 6 times The standard notation of this number is 4,710,000. 1A. Fill in the missing parts of the pattern below. You may use your calculator. 4.71 5 10 4 = 4.71 5 10 5 10 5 10 5 10 = 47,100 4.71 5 10 3 = 4.71 5 = 4.71 5 10 2 = 4.71 5 = 4.71 5 10 1 = 4.71 5 = B. Find a pattern in the final products. What do you think the final product of 4.71 5 10 0 will be? C. Extend the pattern. What do you think the final product of 4.71 5 10-1 will be? D. What do you think the final product of 4.71 5 10-2 will be? 2A. To find the product of 4.71 5 10 5, how many times do you move the decimal in 4.71 to the right? B. To find the product of 4.71 5 10-1, how many times do you move the decimal in 4.71 to the left? 3As Earth and Mars orbit the sun, the distance between the two planets varies. The greatest distance between Earth and Mars is about 4.01 5 10 8 kilometers. Write this distance in standard notation. 4The moon s mass is 1.2 5 10-2 Earth masses. What is this in standard notation?
Scientific Notation exoplanet exponents In Planet Hunters on page 6, you read about scientific notations. Now use that information to solve more problems about some more exoplanets discovered by Kepler. 1The exoplanet Kepler-42b is 9.95 5 10 6 meters in diameter. What is that written in standard form? 2Kepler-106b weighs 0.0005 Jupiter masses. What is that written in scientific notation? 3The diameter of exoplanet Kepler-364c is about 27,400,000 meters. What is that written in scientific notation? 4Kepler-407b weighs 9.0 5 10-3 Jupiter masses. What is that written in standard notation? 5A. Kepler-47c is one of the most massive exoplanets Kepler has found to date. It weighs 5.315 5 10 28 kilograms. What is that written in standard notation? B. At what place value do you think it is most convenient to start writing numbers in scientific notation?
Expressions EXPLAINING EXPRESSIONS On page 4 of Vertical Forces, you learned how to write algebraic expressions. You can write algebraic expressions to describe real-world situations and solve them. Example: Because of different gravitational pulls, objects weigh different amounts on various planets and satellites. For example, on the moon, a person would weigh 16.6% of what they weigh on Earth. Write an expression to describe how much a person would weigh on the moon. Step 1: Identify the constant information and the changing variable in the word problem. Constant information: on the moon, objects weigh 16.6% of what they weigh on Earth. Changing variable: a person s weight Step 2: Decide upon a letter for the variable. w = weight on Earth Step 3: Consider what operations must be used to relate the constant information to the changing variable. Step 4: Write an expression using the information you gathered in the previous steps. When you take a percent of a number, you multiply the percent by the number. 16.6% 5 w or 0.166 5 w To solve: Use the expression above. How much would a person who weighs 180 pounds on Earth weigh on the moon? 0.166 5 w, where w = 180 = 0.166 5 180 = 29.88 pounds 1A. Nina buys a rock-climbing gym membership for $135 per month. She visits the gym d days per month. What is the constant information in this? B. What is the variable? C. Write an expression to show how much Nina s membership costs per visit. D. In August, Nina went to the rock-climbing gym 15 times. How much did the membership cost Nina per visit? 2A. During the month of September, a rock-climbing gym has a sale on its classes. Each class is sold at an 18% discounted price. A class s original price is $p. What is the constant information? What is the variable? B. Write an expression to represent the sale price of a class during the September sale. C. The original price for a bouldering class is $75. How much money do climbers save if they take a bouldering class in September? 3A. In one visit to the climbing gym, Malcolm climbs 1.4 times as many walls as Curtis. Curtis climbs c walls. Write an expression that represents how many walls Malcolm climbs. B. Curtis climbs 15 walls. How many walls does Malcolm climb?
Algebraic Expressions VERTICAL VARIABLES In Vertical Forces on page 4, you learned how to write and evaluate algebraic expressions. Practice the skill with these extra questions. 1A. Many people hire guides when taking long climbing trips on unfamiliar mountains. Suppose a guide charges a group $25 per day. The group wants to give the guide a $200 tip at the end of the trip. Use the equation C = 25d + 200, where C = cost and d = number of days of the trip. Find the cost of the trip if the climb takes 6 days. 4A. Jack buys a rock-climbing gym membership for $125 per month. When he visits the gym d days per month, he also has to rent gear for $10 per visit. Write an expression to show how much Jack s membership and gear rental costs per visit. B. Find the cost of the trip if the climb takes 9 days. B. During the month of October, Jack went to the rockclimbing gym 20 times. How much did the membership and gear rental cost Jack per visit? 2A. Suppose a popular mountain opened to the public in September 1972. An average of 7,500 people have climbed the mountain each year since its opening. Use the equation n = 7,500(y 1972), where n is the total number of people who have climbed the mountain and y is the current year. About how many total people have climbed the mountain from its opening to the present? B. If people continue to visit at that rate, how many will have climbed the mountain by the end of 2020? 3A. A climber carries 3 liters of water every day during her climb. If she climbs for 6 hours on a given day, how much water can she drink per hour? Use the equation w = 3 h, where h is the number of hours climbed and w is the amount of water the climber can drink per hour. B. If she climbs for 11 hours on a given day, how much water can she drink per hour? (Round your answer to the nearest hundredth.) 5A. In one visit to the rock-climbing gym, Annie climbs 1.5 times as many walls as Julie. Annie climbs c walls. Write an expression that represents how many walls Julie climbs. B. Annie climbs 9 walls. How many walls does Julie climb?
Simplifying to Find Percents EXOTIC ESCAPES In Wild Pets on page 8, you learned how to convert fractions to percents. Most of the fractions you encountered had denominators that were factors of 100. Sometimes, however, you might encounter a fraction with a denominator that is not a factor of 100. In that instance, try simplifying the fraction. Sometimes the simplified fraction has a denominator that is a factor of 100. Example: What percent of Colorado s animal escape reports from 1995 to 2014 were either primates or bears? Step 1: Write the ratio of the number of primate and bear escape reports to the total number of escape reports as a fraction. Step 2: Simplify the fraction. Step 3: Scale the simplified fraction up so that the denominator is 100. Step 4: Write the fraction as a percent. 4 16 4 4 = 1 16 4 = 4 1 5 25 = 25 4 5 25 = 100 25 100 = 25 % Reports of Animal Escapes in Colorado: 1995 July 2014 Type of Animal Number of Incidents Reptile 6 Primate 3 Cat 2 Elephant 1 Bear 1 Other 3 SOURCE: BORN FREE USA (DATA AS OF JULY 2014) 1A. What fraction of the reports of animal escapes in Colorado were cats or reptiles? Simplify your answer. B. By what number do you need to multiply both the numerator and the denominator of the fraction to make the denominator 100? C. What percent of the reports of animal escapes in Colorado were cats? 2A. What fraction of the reports of animal escapes in Colorado were elephants, reptiles, cats, or primates? Simplify your answer. B. What percent of the reports of animal escapes in Colorado were elephants, reptiles, cats, or primates? 3A. List the simplified denominators of the fractions you wrote in questions 1 and 2. These denominators are factors of 100. You can multiply each of these denominators by a whole number to get 100. B. What other denominators can you multiply by a whole number to get 100?
Fractions and Percents WILD PERCENTS In Wild Pets on page 8, you learned how to convert fractions to percents using equivalent fractions. Practice converting more fractions to percents with the information in the charts below. Reports of Animal Escapes in Illinois Year Incidents 2000 2 2001 0 2002 1 2003 4 2004 5 2005 1 2006 2 2007 1 2008 2 2009 1 2010 1 2011 3 2012 2 Reports of Animal Escapes in Virginia Year Incidents 2001 3 2002 1 2003 2 2004 0 2005 0 2006 1 2007 3 2008 2 2009 0 2010 1 2011 1 2012 6 SOURCE: BORN FREE USA 1A. What fraction of Illinois s reports of animal escapes occurred from 2000 through 2006? B. What is that as a percent? 2A. What fraction of the reports of animal escapes in Virginia were from 2007 through 2012? B. What is that as a percent? 3A. In which year did Illinois have the most animal escapes? B. What percent of the total escapes does that represent? SOURCE: BORN FREE USA 4A. In which year did Virginia have the most animal escapes? B. What percent of the total escapes does that represent? 5A. Find a combination of years that make up 20% of the animal-escape reports in Illinois. B. Find a combination of years that make up 40% of the animal-escape reports in Virginia.
Fraction Place-Value ANIMAL VISION In Vision Quest on page 14, you learned that you can use division to convert a fraction to a decimal. You can divide the numerator of a fraction by the denominator because the fraction bar represents division. In many cases, you can also use equivalent fractions and place value concepts to convert fractions to decimals. Example: Eagles have vision that is much better than human vision. An eagle s vision is sometimes as good as 20/5. These birds of prey need excellent vision to fly safely and track prey from great heights. What would the prescription decimal be for an eagle? Step 1: Rewrite the fraction as an equivalent fraction with either 10 or 100 as the denominator. Step 2: Read the equivalent fraction aloud. Identify the word name of the fraction. 20 5 or 20 5 20 5 2 = = 5 5 2 20 5 20 = = 5 5 20 40 10 400 100 forty tenths or four hundred hundredths So, an eagle s vision can be written either as 20/5 or as 4.00. 1A. Hawks have extraordinary vision. It can be as good as 20/2. Rewrite this prescription as an equivalent fraction with 10 as the denominator. B. Rewrite this prescription as an equivalent fraction with 100 as the denominator. C. What would the prescription decimal be for a hawk with 20/2 vision? Read the fractions from parts A and B aloud. Use the word names of the fractions to help you fill in the place-value chart below. tens. 2Doctors think that the best human vision possible is about 20/10. What would this be as a decimal? Use the place value chart below to help you. tens ones ones Step 3: Write the standard form of the word name in a place value chart. Decimal point tenths hundredths Decimal point tenths hundredths. tens ones Decimal point tenths hundredths 4. 0 0 3A. Drivers have to pass vision tests to get licenses. Many states allow people to drive without glasses or contacts if their vision is 20/40 or better. What is the prescription decimal of 20/40 vision? B. Some states will not allow people to get driver s licenses if their corrected vision is worse than 20/100. What is the prescription decimal of 20/100 vision? C. Look at your answers above. Describe how you can find which of two visions has a greater prescription decimal without first converting them to prescription decimals. 4A dog s vision is about 20/75. A horse s vision is about 20/33. Without converting to decimals, which animal has a greater prescription decimal?
Fractions to Decimals VISION DECIMALS In Vision Quest on page 14, you learned that you can use division to convert a fraction to a decimal. Use that information to solve more ratio-to-decimal problems. If necessary, round all answers to the nearest hundredth. 1Chelsea has 20/25 vision in her left eye. What is her prescription in decimals? 2Alessandra has 20/80 vision her right eye. What is her prescription in decimals? 3Dipti has 20/15 vision in her left eye. What is her prescription in decimals? 4Greg has 20/40 vision in his left eye and 20/100 in his right eye. What is his prescription in decimals for each eye? 5Mark s vision ratio is 20/75 in his left eye and 20/30 in his right eye. How much better is the vision in his right eye, in decimals?