Unit 1 Practice Test Answer Key

1 If each of the integers 5, 3, and 2 is used only once in the expression (a – b)  c, then what is the largest possible value? (a – b)  c (5 – 3)  2 (2)  2 4 (5 – 2)  3 (3)  3 9 (3 – 2)  5 (1)  5 5

2 In the correctly worked multiplication problems, L, M, and N are single-digit integers. What is the value of N – M? M  L Factors of 28 and 21 N  L : 1,2,4,7,14,28 21: 1, 3, 7, 21 Greatest Common Factor = 7 =7 =4=3 N – M = 3 – 4 = –1

If n is a negative integer, what is the ordering of p, t, and r from greatest to least? 3 p = n 2 – 2.1 ; t = n ; r = (n – 2.1) 2 Substitute: n = –1 p = (–1) 2 – 2.1 p = 1 – 2.1 p = –1.1 t = (–1) t = – t = 1.1 r = (–1 – 2.1) 2 r = (–3.1) 2 r = 9.61 r > t > p

4 In a hospital parking lot, the rate is $1.50 for the first 2 hours and $0.75 for each additional hour or part of an hour. What does it cost to park a car for 4 hours and 15 minutes? 2 Hours$ Hours$ Hours$ Minutes$0.75 Total $3.75

5 P is a two-digit number. Q is a two-digit number, with P’s digits reversed. What is the largest possible value of P so that P and Q fit the given description and also have a difference of 54? P: 97Q: 7997 – 79 = 18NO P: 96Q: 6996 – 69 = 27NO P: 93Q: 3993 – 39 = 54YES Try E. 97 Try D. 96 Try C. 93 Difference

If x, y, and z are three prime numbers, and 19 < x < y < z < 35, find x + y – z. 6 x = 23, y = 29, z = 31 x + y – z – – 31 21

7 If N is an odd or even integer, which of the following will always be an odd integer? Answer: 2N + 1 2(3) + 12(4) + 1 Substitute odd integer Substitute even integer

8 If m and p are positive integers, which expression must be negative? 2 – 5 = –3 A.m – p B.p – m C.m + p D.–(m + p) E.–(m – p) No –(2 + 5) = – = 7 Yes Substitute: m = 2 p = 5 5 – 2 = 3 Subtraction with positive numbers can be positive or negative No

What is the value of x for which ? 9 Rewrite the fractions as decimals. Test A. Test B. Test C. NO YES

10 Least Common Denominator = 8

11 If a cake is cut into thirds and each third is cut into fourths, how many pieces of cake are there? 3 pieces  4 pieces = 12 pieces

12 Amy spent of the money in her savings account on clothes. The next month she spent of the remainder of her money on a weekend in Montauk. If she then had $3,600 left, how much was in her savings account originally? Strategy: Multiply each answer times. Find amount remaining. Multiply remaining amount times. Find remaining amount. It should equal $3,600.

12 Amy spent of the money in her savings account on clothes. The next month she spent of the remainder of her money on a weekend in Montauk. If she then had $3,600 left, how much was in her savings account originally? Test C. $4,900 4,900 – 980 = 3,920 3,920 – 980 = 2940 No Test E. $6,000 6,000 – 1200 = 4, – 1200 = 3600 Yes

13 There are b boys and g girls at the Jericho Academy. Girls make up what fractional part of the student body? Assume there are 8 girls and 5 boys.

If D is a nonzero digit in the decimal number 0.0D, which of the following must be equal to ? Substitute any number for D. Then, find the answer that is equal to the same result. (A) 15

If it takes ½ hour to wash a car, how many days will it take to wash 96 cars? 16 Time Number of Cars ½ hour 1 1 hour 2  1 = 2 2 hours 2  2 = 4 24 hours 2  24 = 48 1 day 48 2 days 2  48 =  48 = 2 days

17 If 8 is 8% of N, then what does N equal? Test each answer. Substitute for N. A. 1 B. 8 C. 10 D. 80 E % of 1No =.08  1 = % of 8No =.08  8 = % of 10No =.08  10 = 0.8 8% of 80No =.08  80 = 6.4 8% of 100Yes =.08  100 = 8

Kathy, Keri, and Kim raised $10, $15, and $25 respectively, during a fundraising drive. What percent of the money did Kathy raise? 18 Total raised = $10 + $15 + $25 = $50 Percent Kathy raised = 0.2  100 = 20%

19 If the average cost of making five copies on a copy machine has increased from 18 to 20, what was the percent increase? Amount of Increase = 20¢ – 18¢ = 2¢ = 0.11  100 = 11%

20 If a $3.75 book was bought for $3.30, what was the percent discount? Discount= Original Price – Sale Price Discount=$3.75 – $3.30= $0.45 = 0.12  100 = 12%

21 A CD player costs the store $270. If the store must make a 23% profit, what must be the selling price? Selling Price = Purchase Price + Profit =$270 + $62.10 = $ Profit =23% of $270=.23(270)= 62.10

If n is a negative integer, then n b must be positive whenever b is 22 n = –1 n b = (–1) b (–1) 2 = (–1)  (–1) = +1 Answer: C Even integer

If x 2 = 36, then what could be the value of 2 x–2 ? 23 x 2 = 36 x = 6 2 x–2 2 6–

x, y, and z are three consecutive integers and z > y > x. If z = x 2, which of the following could be the value of x? 24 I. 2 II. 0 III. –1 z = 2 2 Test x = 2 z = 4 x < y < z 2 < 3 < 4 z = 0 2 Test x = 0 z = 0 x < y < z 0 < y < 0 z = (–1) 2 Test x = –1 z = 1 x < y < z –1 < 0 < 1

If a and b are positive integers such that a 2 = 25 and b 2 = 36. Which of the following statements are true? 25 I. a + b = 61II. b – a = 1III. a  b = 30 Find a and b. a 2 = 25 a = 5 b 2 = 36 b = 6

If a and y are positive integers such that a 2 = 25 and b 2 = 36. Which of the following statements are true? 25 I. a + b = 61II. b – a = 1III. a  b = 30 a = 5b = =  61 No 6 – 5 = 1 1 = 1 Yes 5  6 = = 30 Yes Answer: D Only II and III

If, then what is the value of k? 26 9 = 3 k 3 2 = 3 k 2 = k

27 = 3

28 is a number that lies between which two powers of ,000 Answer: B

29 In the figure, if B is the midpoint of segment AD, what is the length of segment CD? BD – BC = CD ABCD

In the figure, points B and C divide the segment AD into three equal parts. BC is what percent of AC? 30 Substitute a number for the lengths of each line segment. 444 = 0.5  100 = 50%

31 In the figure, the tick marks are equally spaced and their coordinates are shown. Of these coordinates, which has the smallest positive value? 10edcba –8 10 – (–8) = =  6 = 3 Number of units from the first to the last peg Number of pegs after the first peg: How many units are the pegs apart? 6 –5741–2

32 Club M has 11 members and Club R has 18. If a total of 24 people belong to the two clubs, how many people belong to both clubs? Both Clubs = 29 – 24 = 5 Club Participants = M + R = = 29 M R Total People 24

There are 18 boys in the class: 6 play football, 5 play baseball, and 3 play on both teams. How many boys are not on either team? 33 Football 365 Baseball

There are 18 boys in the class: 6 play football, 5 play baseball, and 3 play on both teams. How many boys are not on either team? Football 332 Baseball Total Boys = Not on either team = Total Boys – (Football + Baseball + Both) = 18 – ( )= 18 – 8 = 10 33

34 The compound sentence {x 1} can also be written as {x 1}. Which of the following number line graphs illustrate this relationship?  x < –2 x > 1 Common shaded areas Empty Set

35 Set A = {x > –2} and set B = {x < 1}. Which of the following illustrates A  B ? x > –2 x < 1 Combine shaded areas Answer