Math 074 Final Exam Review. REVIEW FOR NO CALCULATOR PART OF THE EXAM (Questions 1-14)

Transcription

1 Math 074 Final Exam Review REVIEW FOR NO CALCULATOR PART OF THE EXAM (Questions -4) I. Can you add, subtract, multiply and divide fractions and mixed numbers?. Perform the indicated operations. Be sure that your answers are in lowest terms. a. + b c d. e f g. 4 h. 6 7 i. 5 II. Can you add, subtract, multiply and divide signed numbers?. Perform the indicated operations. a. 8+ ( ) b. 8 ( ) + c. 8+ d. ( 8)( ) e. ( 8)( ) f. 8 ( ) g. 8 ( ) h. 8 i. 8 ( ) j. 8 ( ) k l. 0 7 m. n. 5 o p. 5 q. r. 5 5 III. Can you simplify expressions using order of operations?. Simplify: a. 8 + b. 4 + c. d. ( 5) + 7 e. ( )( 4) + ( ) f. g. h. ( ) i ( ) ( 5) 5 + ( ) Modified November 07

2 IV. Can you answer questions using information from histograms and pie charts? 4. The bar graph below lists the monthly production costs in dollars of a local manufacturing company. a. What is the total amount of production costs per month? b. What did the company spend the least on? Monthly Production Costs,440,640,90,60,60 c. What did the company spend the most on? d. What percent of total production costs were supplies? 5. The following circle graph describes the ages of the 00 men and women of the Glover City police force. Glover City police force a. What percent of the police force is between and 50 years old? b. What percent of the police force is years old or younger? c. What fraction of the police force is under? d. What percentage of police force is between the age -50? e. What is the ratio of police officers under to police officers over 50? - 50, 48% Over 50 % -, 0% Under, 0% V. Comparison of numbers 6. Which of the following fractions 6,,,, does not reduce to 4? 7. Which of the following fractions ,,,, does not reduce to ? 8. Write the following numbers,,, from smallest to largest Write the following numbers,,, from largest to smallest Arrange the following numbers, 4,,0,, from largest to smallest. 4. Arrange the following numbers,0,, 4,,, from smallest to largest. 4 Modified November 07

3 VI. Can you evaluate an algebraic expression?. Evaluate each expression for the given value of the variable. a. x + when x = 4 c. 5( + x) + when b. x when x = 6 x = d. ( x + ) when x = 4 VII. Can you determine if a number is a solution to an equation?. Determine if the given number is a solution for the given equation. a. Is n = a solution of n + = 5? b. Is x = 6 a solution of 4 x =? VIII. Can you simplify algebraic expressions? 4. Simplify: 7 x + b. x 5 x 9 a. ( ) + c. ( x+ 4) 6( x ) d. 5 8( x + ) REVIEW FOR CALCULATOR PART OF THE EXAM (Questions 5-4) IX. Can you solve linear equations involving one step, two steps, removing parentheses, combining like terms and having a variable on both sides? 5. Solve each equation. a. x + = b. 7= x 4 c. 4x = 5 d. 4 6 x + = e. x 4x+ 6= 8 f. 4( x ) = 8 g. x+ 5= 7x h. 5 x = 7 i. 5+ x = 8 j. 7 x = 5 X. Write and solve an equation that best describes the given situation. k. 9 x = 6. Ten subtracted from twice a number is Five more than seven times a number is eight times the number. XI. Can you solve application problem using fractions 8. Culinary arts students Lauren, Troy and Shane decided to bake a huge birthday cake. They need 6 lbs of flour to bake the cake. Troy brought lb of flour and Lauren brought lb 5 of flour. How much flour should Shane bring so they have enough flour? Modified November 07

4 9. Three sisters, Leena, Maura and Liz, decide to share mowing their lawn. Leena mowed of the lawn and Maura mowed of the lawn. How much of the lawn did Liz mow? 5 0. A recipe for 5 pies call for a flour?. A recipe for loaves of banana nut bread calls for a you make with 4 cups of flour? cups of flour. How many pies can you make with 4 cups of 4 cups of flour. How many loaves can XII. Can you write a ratio in simplest form, find a rate and find a unit price?. Write the ratio 56 to 4 in simplest form.. Find the rate: 6 feet in 5 seconds 4. Find the unit price: $4.95 for 5 ounces 5. Which is a better buy? hotdogs for $.94 or 8 hotdogs for $ Suppose out of 5 students who were enrolled in a MATH 074 class passed the class. What fraction of the students passed the class? 7. Suppose out of 5 students who were enrolled in a MATH 074 class passed the class. What fraction of the students did not pass the class? 8. Suppose the local market sells 6 cans Campbell soup for $9.5. Find the unit price per soup can? 9. Suppose the local market sells 5 pairs of socks for $5.86. Find the unit price per pair of socks? XIII. Can you solve a proportion? 0. Solve the following proportions. x a. = 5 b. x = 6 5 c. x = d. x = 4 Modified November 07 4

5 XIV. Can you solve application problems using proportions?. Set up a proportion and solve. a. A baseball player gets 8 hits in the first 8 games of the season. If he continues at the same rate, how many hits will he get in 45 games? b. The scale on a map indicates that inch on the map corresponds to an actual distance of 85 miles. Two cities are.5 inches apart on the map. What is the actual distance between the two cities? c. Of every 7 parts manufactured by a certain machine, will be defective. How many parts were manufactured by the machine if 8 defective parts were found? d. While cooking lentils, the ratio of lentils to water is to 5 cups. If you have cups of lentils, how many cups of water will you need? e. A truck travels 0 miles on 6 gallons of gas, how many gallons of gas will it take to drive 00 miles if the truck travels at the same rate? XV. Can you convert between fractions, decimals and percents?. Fill in the blanks with the equivalent percent, decimal or fraction. Percent Decimal Fraction 8.5 7% % Modified November 07 5

6 XVI. Can you solve percent problems using proportions?. Set up a proportion and solve. a. What is % of 4? b. 6% of what number is 55.8? c. What percent of 00 is 0? d. A family spends $450 every month on food. If the family spends 8% of their income on food, how much is their monthly income? e. A student reader was making $6.50 per hour. After getting a raise, she makes $6.80 per hour. What is the percent increase in pay? Round to the nearest tenth of a percent. f. Shoes that usually sell for $5 are on sale for $0. What is the percent discount? g. Suppose you paid $9.80 in sales tax for the purchase of a stereo system. If the sales tax rate is 5%, how much did the stereo system cost including the sales tax? h. A real estate agent gets a commission of % of the price of each house that she sells. If she sold a house for $89,500, what was her commission? i. Now Tom spends $0 a week on gas. If the gas price goes up about 4%, what would be the total amount Tom spends on gas per week? XVII. Can you find the mean, median and mode for a set of data? 4. The prices paid for the cameras sold yesterday at Acme Cameras are listed below. Find the mean, median, mode, and range. $0 $9 $ $45 $0 $540 $67 $5 $5 $ Find the mean, median, mode, and range of the given numbers. 5 7, 5,, 6,, 7, XVIII. Can you convert from one unit of measure to another? 6. Convert the following temperatures. Round your answer to the nearest tenth of a degree. a. c. 04 F = C b. 87 F = C d. 5 C = F 5 C = F Modified November 07 6

7 7. Convert the following quantities to the units indicated. a. 4 tons = lb b. 5 mg = g c. 6 mm = cm d. 04 fl oz = gal e. 65 lb = kg f. 7.5 cm = in g. 00 oz = kg h. 5 gal = ml i. ft = in j. 7 ft = m XIX. Can you find the perimeter, circumference, area and volume of common geometric shapes? 8. Find the perimeter and area for each figure. Be sure to include correct units in your answer. a.. m b. 0 yd 6. m 7 yd 5 yd c. d. 7 ft ft 0 ft 8 ft ft ft 4 ft ft Modified November 07 7

8 9. Find the circumference and area for each circle. Be sure to include the correct units in your answer. a. b. 7 in. cm 40. Find the perimeter and area of the figure given below. Be sure to include correct units in your answer. 8 km 6 km 4 km 0 km 4. Find the volume for each figure. Use π =.4 where necessary. Be sure to include the correct units in your answer. a. 7 km 4 mm 6 mm 6 mm b. radius = 7m, height = 8m Modified November 07 8

9 Answers: ) a. 7 0 b. 5 c. 6 4 d. 6 e. 5 f. g. h. i ) a. 0 b. 6 c. 6 d. 6 e. 6 f. 4 g. 4 h. 0 i. 6 j. 0 k. 0 l. 7 4 m. 5 n. ) a. b. 4 c. 4 g. 4 h. 8 i. o Modified November 07 9 p. 5 q. 9 r d. 0 e. 0 f. 5 4) a. The production costs per month total $4,000. b. The company spent the least on utilities. c. The company spent the most on salaries. d. Supplies were 4% of total production costs. 5) a. 48% of the police force is between and 50. b. 40% of the police force is years or younger. c. /0 of police office are under the age of. d. 78% of police officers are between the age of and 50. e. The ratio of police officers under to police officers over 50 is ) /4 7) 4/6 8) ¼, ½, /5, / 9) /, /5, ½, ¼ 0), /, ¼, 0, /, 4 ) 4,, 0, /, ¾,, ) a. 0, b. c. d. 9 ) a. No b. Yes 4) a. 7x 7 b. 5x+4 c. x+4 d. 8x 9 5) a. x = b. x = c. x = ¾ d. x = 5 e. x = f. x = g. x = h. x = i. x = j. x = k. x = 6) x 0 = 5; x = ½ 7) 5 + 7x = 8x; x = 5 lb 8) 0 9) 4/5 of the lawn. 0) 8 pies ) 6 loaves of bread. ) 4 ) 7. ft/sec 4) $0. per ounce 5) hotdogs for $.94 6) /5 7) /5 8) $.54 per can 9) $.7 per pair of socks 0) a. x = 5 b. x = 4 c. x = d. x = 6 ) a. He will get 0 hits in 45 games. b. The actual distance between the cities is 97.5 miles. c. If 8 parts are defective then parts were manufactured by the machine. d. You will need 7.5 cups of water. e. 0 gallons of gas are needed to travel 00 miles.

10 ) Percent Decimal Fraction 7.5% %.5 7% % % 0.05 /0 0.% 0.00 /000 ) a..88 is % of 4 b. 6% of 55 is 55.8 c. 5% of 00 is 0 d. The family s income each month is $ e. The student got a 4.6% increase in pay. f. The discount was 0% g. The stereo system with tax costs $45.80 h. Her commission was $ i. He will spend $.0 4) mean = $64.0 median = $4.00 mode = $5.00 range = $80 7 5) mean = median = no mode range = ) a. 40 C b. 5.6 C c. 0.6 C d. 9 F 7) Depending on the conversion equations that you use, your answers may vary slightly. a. 500 lb b g c..6 cm d. 8 gal e. 75 kg f. 7 in g. 5.6 kg h. 9,000 ml i. 44 in j. 8.8 m 8) a. perimeter = 6.8m area = 75.0 m b. perimeter = 4 yd area = 50 yd c. perimeter = 48 ft area = 84 ft d. perimeter = 6 ft area = 47 ft 9) a. circumference =.98 in area = in b. circumference = 8.84 cm area = 8.6 cm 40) Perimeter = 66 km area = 46 km 4) a. volume = 84 mm³ b. volume = m³ Modified November 07 0