Select the best answer. 1. Simplify: + ( 8) + ( 1) + 8 a. b. 4 c. 8 d. e. 4. Compute: 4 1 + 8 a. 1 b. 1 10 c. 40 d. 40 e. 8 40. Divide: 14 1 a. 8 b. 1 c. 10 d. 1 e. 1 1 4/00
4. Simplify: a. 1 1 b. 1 9 10 c. 1 11 0 d. 0 e. 1 1 4 + 10 4 1. Jill is making bookmarks for a fund-raising sale. Each bookmark costs $1.00 to make. If she sells the bookmarks for $1.0 each, how many will she have to sell to make a profit of exactly $0.00? a. 10 b. 1 c. 0 d. e. 40. What is the average (arithmetic mean) of 11, 8, 4,,, and? a. 4 b. 4 c. d.. e.. Simplify: 4 + 4 a. 1 b. c. d. 40 e. 48 4/00
8. Simplify: 4 1 a. 1 4 b. 9 1 8 c. 8 d. 4 e. 0 9. John pays $0 for a new coat, which is % of the original cost. What was the original cost? a. $4 b. $10 c. $00 d. $10 e. $1 10. A dress has been marked down % and now sells for $. What was the original price? a. $.00 b. $4.00 c. $. d. $40. e. $.00 11. The amount for food at a local restaurant is $.4. If tax is 1 %, what is your total bill without the tip? a. $1.09 b. $.4 c. $. d. $.11 e. $4. 1. If three pounds of apples cost $1.80, what is the cost of 1 pounds? a. $1.0 b. $1.40 c. $.0 d. $1.0 e. $.40 1. The largest prime factor of 80 is: a. b. c. d. 8 e. 11 4/00
14. What is the least common multiple of, 8 and 18? a. 1 b. 18 c. 4 d. e. 144 1. How many yards of material remain from a 0-yard length after two pieces, each 1 yards long, and four pieces, each 1 4 yards long, are removed? a. 4 yards b. 1 yards c. 1 1 4 yards d. 4 yards e. 18 yards 1. Ben is making wooden toys for an arts and crafts sale. Each toy costs Ben $1.80 to make. If he sells the toys for $.00 each, how many will he have to sell to make a profit of $.00? a. $1.0 b. 1 c. 0 d. 0 e. 40 1. What is the meaning of? a. b. 1 c. d. e. 18. Multiply (1.8)( 8.) a. 1.4 b. 1 c..1 d. 1. e. 1. 19. What is 40% of 90? a. 18 b. 0 c. 4 d. e. 4 4 4/00
0. Five pieces of wire are cut from a length of wire that is 0 feet long. One of the pieces is 1 feet long. Two of the pieces are 1 4 feet long each. Two of the pieces are 1 feet long each. How many feet of wire are left from the original length? a. 1 feet b. feet c. 1 feet d. 14 feet e. 14 feet 1. Find the missing number, x, that makes this proportion true. a. 4 9 b. x 9 11 c. 4 9 d. 1 11 e. 9. A man, feet tall, is standing 4 feet from a street light. The length of his shadow produced by the street light is 4 feet. Find the height of the street light. a. 1 feet b. 4 feet c. 4 feet d. 9 feet e. 18 Feet. Donna drives her delivery van 800 miles in days. At this rate, how far will she drive in 1 days? a.. miles b. 1,000 miles c. 4000 miles d.. miles e. 10 miles 4/00
4. It takes 0 oz of grass seed to seed 000 sq ft of lawn. What is the rate in ounces per square foot? a. oz sq ft b. 180,000 ounces sq ft c. 0 d. 00. oz oz sq ft e. 0 oz sq ft. According to the 1980 census, the population of Los Angeles County was approximately. million. In 1990 the population was approximately 9 million. Find the percent of increase of the population. a. 1. million b. 8. % c. 1. % d.. % e. 0 %. An 8-lb turkey breast contains servings of meat. How many pounds of turkey breast would be needed for 4 servings? a.. lbs b. 4. lbs c. 4 lbs d. 1 lbs e.. lbs. The temperature in Minneapolis was 4 on December. In the next days, the temperature dropped, then dropped, and then dropped 10. What was the temperature on December? a. - 1 b. - 10 c. - d. 1 e. 8. Add these numbers and give the result in scientific notation:,40,000 and 0,000 a. 4. 10 b. c. d. e. 4. 10. 10 4. 10. 10 4/00
9. If x pairs of shoes cost n dollars, how much will y pairs cost? ny a. x b. nx c. ny xy d. n nx e. y 0. What is the least common denominator of these fractions: a. b. 10 c. 80 d. 800 e. 40 1. Four adult tickets to a show cost $8.00 each. Six child tickets cost $.00 each. What was the average cost of the tickets? a. $.0 b. $.00 c. $1.00 d. $.00 e. $.0. 10% of a class received an A on a test. Half of those remaining received a B on the test. What percent of the class received a C, D, or F? a. 9% b. 40% c. 0% d. 4% e. %. Four specific and complete lengths of fabric are needed for a project:. yds., ½ yds., ¼ yds., 4.1 yds. If the fabric comes in only 8 yd. lengths, how many of the 8 yd. lengths should be purchased? a. 18.4 b. 4 c. 4 d. 1 e. 4, 1,, 10? 8 4/00
4. 4 1 a. - b. 19 c. 14 d. 19 1 e. 8 4/00
Answers to Pre-Algebra COMPASS Review 1. d 1. c. e. d 14. d. d. b 1. b. a 4. c 1. d 8. b. e 1. d 0. e. c 18. e 1. e. d 19. d. d 8. b 0. c. e 9. c 1. c 4. b 10. e. c 11. e. c 1. c 4. d Solutions to Pre-Algebra COMPASS review 1. Simplify: + (-8) + (-1) + 8 Answer: d. + (-8) + (-1) + 8 14 + -(-1) + 8 14 + + 1 + 8 4 + 1 + 8 8 + 8 This problem is about signed numbers. Add two terms together at a time and check your work. Remember the opposite of -1 is +1.. Compute: 4 1 + Answer: d. 8 The Least Common Denominator is ()(8) 40. Change each fraction so that it has a denominator of 40. 4 8 1 + 8 8 + (Add numerators together.) 40 40 40 If possible, reduce fraction, but in this case the fraction is in reduced form. 9 4/00
. Divide: Answer: b. 1 14 14 14 (Remember to invert 14 and multiply it by ) 14 (Cancel common factor of ) 10 10 1 4. Simplify: + 4 Answer: c. 10 1 11 1 0 1 4 + (Multiply fractions. You do not need a common denominator to multiply 0 1 10 fractions.) (Find the Least Common Denominator and change all fractions to an equivalent form. LCD is 0 ) 1 1 + 1 0 4 1 4 4 (multiply fractions) 4 1 + (combine numerators) 0 0 0 4 + 1 0 1 11 1 0 0 10 4/00
. Jill is making bookmarks for a fund-raising sale. Each bookmark costs $1.00 to make. If she sells the bookmarks for $1.0 each, how many will she have to sell to make a profit of exactly $0.00? Answer: e. 40 Jill is making $.0 profit per bookmark. $0. 00 40 $. 0. What is the average (arithmetic mean) of 11, 8, 4,,, and? Answer: c. The average is the sum of the values divided by the total number of values. 11+ 8 + 4 + + + + 44 44. Simplify: 4 + 4 Answer: d. 40 4 + 4 4 + 4 order of operations (division before addition or subtraction) 4 + 4 40 8. Simplify: 4 1 Answer: b. 1 9 8 4 1 81 8 1 Order of operations, exponents first 81 8 1 1 9 8 8 8 9. John pays $0 for a new coat, which is % of the original cost. What was the original cost? Answer: c. $00 Percent equation: 0 % of x 0 (0.)(x) 0 x. x 00 10. A dress has been marked down % and now sells for $. What was the original price? Answer: e. $.00 If the dress has been marked down %, that means the current selling price is % of the original price. Therefore $ is % of what number? % of x (0.)(x) x. x $.00 11 4/00
11. The amount for food at a local restaurant is $.4. If tax is 1 %, what is your total bill without the tip? Answer: e. $4. The amount of tax is (.4)(.0). 109 or $.11 Total bill is amount for the food + tax. $.4 + $.11 $4. 1. If three pounds of apples cost $1.80, what is the cost of 1 pounds? Answer: c. $.0 $1.80 $0.0 Each pound costs $0.0 1 pounds would cost (1)($0.0) 1. The largest prime factor of 80 is: Answer: c. Write 80 as a product of prime factors: ()()()()() is the largest prime factor 14. What is the least common multiple of, 8 and 18? Answer: d. Write each number as a product of prime factors. ()() 8 ()()() 18 ()()() The least common multiple is ()()()()(). The factors of each number,, 8 and 18 must be represented in the least common multiple. 1. How many yards of material remain from a 0-yard length after two pieces, each 1 yards long, and four pieces, each 1 4 yards long, are removed? Answer: b. 1 yards 1 4 Total amount to start with is 0 yards. Total amount removed: ( ) + ( 4) + 1 (total amount at start) (total amount removed) (total amount remaining) 0 yards 18 yards 1 yards 1. Ben is making wooden toys for an arts and crafts sale. Each toy costs Ben $1.80 to make. If he sells the toys for $.00 each, how many will he have to sell to make a profit of $.00? Answer: d. 0 For each toy, Ben makes $1.0 ($.00 - $1.80) 18 Profit profit desired per toy number of toys $.00 $1.0 0 1 4/00
1. What is the meaning of? Answer: d. Repeat three times as a factor. 18. Multiply (1.8)( 8.) Answer: e. 1. 19. What is 40% of 90? Answer: d. Percent equation X (.40)(90) X 0. Five pieces of wire are cut from a length of wire that is 0 feet long. One of the pieces is 1 feet long. Two of the pieces are 1 4 feet long each. Two of the pieces are 1 feet long each. How many feet of wire are left from the original length? Answer: c. (Total amount at start) (total amount of pieces) amount left 8 1 1 + + 4 Total amount of pieces ( ) ( ) 1 feet 8 1 1 8 1 + ( ) + ( ) + + 1 Find the least common denominator ()() 4 Change fractions to an equivalent fraction with a denominator of 8 1 8 1 1 + + 1 + + 1 8 1 1 + + 1 + + 8 1 + + 8 1 1 This equals the total amount for the pieces. (Total amount at start) (total amount of pieces) amount left 0 feet - 1 feet 1 feet 1 4/00
1. Find the missing number, x, that makes this proportion true. 4 Answer: c. 9 Cross multiply: 9x ()(11) x 9 11 9x x 9 4 9 9. A man, feet tall, is standing 4 feet from a street light. The length of his shadow produced by the street light is 4 feet. Find the height of the street light. Answer: c. 4 feet x Draw a picture: x 4 4 Use similar triangles and set up a proportion: height of total street length light height of man length of shadow x 8 4 Solve proportion using cross multiplication. 4x ()(8) 4x 18 x 18 4 x 4 feet 14 4/00
. Donna drives her delivery van 800 miles in days. At this rate, how far will she drive in 1 days? Answer: c. 4000 miles Set up a proportion: 800 miles x miles Cross multiply and solve for x. days 1 days x (800)(1) x 1,000 x 4000 miles 4. It takes 0 oz of grass seed to seed 000 sq ft of lawn. What is the rate in ounces per square foot? oz Answer: d. 00. sq ft To find the rate, set up the ratio with proper units of measurement in the numerator and denominator and divide so the numerical value in the denominator is 1. oz sq ft oz 0 sq ft 0 000 1 0 1 oz 0 sq. oz sq ft ft. According to the 1980 census, the population of Los Angeles County was approximately. million. In 1990 the population was approximately 9 million. Find the percent of increase of the population. Answer: e. 0 % To find the percent of increase calculate answer to a percent. new value old old value value and then change the decimal 9.... 0%. An 8-lb turkey breast contains servings of meat. How many pounds of turkey breast would be needed for 4 servings? Answer: d. 1 lbs 8 lbs x lbs Set up a proportion: Cross multiply and solve for x. servings 4 servings x (8)(4) x 4 x 1 lbs 1 4/00
. The temperature in Minneapolis was 4 on December. In the next days, the temperature dropped, then dropped, and then dropped 10. What was the temperature on December? Answer: a. - 1 4 10 4 + (-) + (-) + (-10) + (-) + (-10) (-) + (-10) -1 8. Add these numbers and give the result in scientific notation:,40,000 and 0,000 Answer: b. 4. 10,40,000 + 0,000 4,0,000 To put the number into scientific notation, place the decimal point after the first non-zero digit, 4. That means that the decimal point would move places to the right to get 4,0,000. So, multiply by 10. 4. 10 9. If x pairs of shoes cost n dollars, how much will y pairs cost? ny Answer: a. x Set up a proportion: x y n? (x) (?) (n) (y) ( x )(?) ( n)( y) x x ny? x 0. What is the least common denominator of these fractions? 4 1,,, 10 8 Answer: e. 40 State each denominator as the product of prime factors:,, 10 x, 8 x x The least common denominator must contain each of the prime factors. Each prime factor must be included as many times as necessary to be sure that each denominator is fully represented: There need to be three s. There needs to be one. x x x 8 x 40 is the least common denominator. 1 4/00
1. Four adult tickets to a show cost $8.00 each. Six child tickets cost $.00 each. What was the average cost of the tickets? Answer: e. $.0 4 x $8.00 $.00 for the adult tickets. x $.00 $0.00 for the child tickets. $.00 + $0.00 $.00 Divide $.00 by the ten people who have tickets, to get $.0. This is the average cost of the tickets.. 10% of a class received an A on a test. Half of those remaining received a B on the test. What percent of the class received a C, D, or F? Answer: d. 4% 100% 10% 90% that is left for grades B, C, D, or F. ½ of 90% is 4% that received a grade of B. 100% 10% 4% 4% remaining for those a C, D, or F.. Four specific and complete lengths of fabric are needed for a project:. yds., ½ yds., ¼ yds., 4.1 yds. If the fabric comes in only 8 yd. lengths, how many of the 8 yd. lengths should be purchased? Answer: e. ½. ¼.. +. +. + 4.1 1.4 yds are needed. Check to be sure that each of the 4 pieces of fabric will be complete: The first two,. and., add up to.1 yds., which can be taken from one of the 8 yd. pieces. Each of the other two pieces can each be taken from the other 8 yd. pieces. 4. 4 1 19 Answer: b. 4 1 9 4 49 1 4 4 1 19 1 4/00