Unit 1Practice TestAnswer 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)

24

(5 – 2) 3 (3)

39

(3 – 2) 5 (1)

55

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

28 21 28: 1,2,4,7,14,28

21: 1, 3, 7, 21Greatest Common Factor = 7

=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 greatestto least?

3

p = n2 – 2.1 ; t = n3 + 2.1 ; r = (n – 2.1)2

Substitute: n = –1

p = (–1)2 – 2.1p = 1 – 2.1p = –1.1

t = (–1)3 + 2.1t = –1 + 2.1t = 1.1

r = (–1 – 2.1)2

r = (–3.1)2

r = 9.61

r > t > p

4In 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 $1.503 Hours $0.754 Hours $0.75

15 Minutes $0.75Total $3.75

5P 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: 97 Q: 79 97 – 79 = 18 NO

P: 96 Q: 69 96 – 69 = 27 NO

P: 93 Q: 39 93 – 39 = 54 YES

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

23 + 29 – 31

52 – 3121

7 If N is an odd or even integer, whichof the following will always be anodd integer?

Answer: 2N + 1

2(3) + 1 2(4) + 1

Substitute odd integer

Substitute eveninteger

6 + 17

8 + 19

8 If m and p are positive integers, which expression must be negative?

2 – 5 = –3A. m – p

B. p – m

C. m + p

D. –(m + p)

E. –(m – p)

No

–(2 + 5) = –7

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 1 13 2

x

Rewrite the fractions as decimals.

Test A.

413

Test B. 412

0.33 0.5x

0.310.33 0.5

0.330.33 0.5

Test C. 512 0.420.33 0.5

NO

NO

YES

1058 2m m

44

58 2m m

Least Common Denominator = 8

5 48 8m m

8m

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.

15

14

15

14

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

15

14

4,900 – 980 = 3,920

1 4900 9805

1 3920 9804

3,920 – 980 = 2940No

Test E. $6,000

6,000 – 1200 = 4,800

4800 – 1200 = 3600Yes

1 6000 12005

1 4800 12004

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.

8 8Fraction of girls8 5 13

Number of girlsFraction of girlsTotal number of students

gg b

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.

10.0D

Then, find the answer that is equal to the same result.

1 500.0

2

100 502

(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 Cars½ hour 11 hour 21 = 22 hours 22 = 424 hours 224 = 481 day 482 days 2 48 = 96

96 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. 100

8% of 1 No= .08 1 = 0.08

8% of 8 No= .08 8 = 0.64

8% of 10 No= .08 10 = 0.8

8% of 80 No= .08 80 = 6.4

8% of 100 Yes= .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 raisedAmount Kathy raised 100Total amount raised

10 10050

= 0.2 100

= 20%

19 If the average cost of making five copies on a copy machine has increased from 18ȼ to 20ȼ, what was the percent increase?

Amount of Increase = 20¢ – 18¢ = 2¢Increase AmountPercent Increase 100Original Amount

2 10018

= 0.11 100= 11%

20 If a $3.75 book was bought for $3.30, what was the percent discount?

Discount =Original

Price – SalePrice

Discount = $3.75 – $3.30 = $0.45Discount PricePercent Discount 100Original Price

0.45 1003.75

= 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?

SellingPrice =

PurchasePrice + Profit

= $270 + $62.10= $332.10

Profit = 23% of $270 = .23(270) = 62.10

If n is a negative integer, then nb must be positive whenever b is

22

n = –1

nb = (–1)b

(–1)2 = (–1)(–1) = +1

Answer: C Even integer

If x2 = 36, then what could be thevalue of 2x–2 ?

23

x2 = 36

x = 6

2x–2

26–2

24

16

362 x

x, y, and z are three consecutive integers and z > y > x. If z = x2, which of the following could be the value of x?

24

I. 2 II. 0 III. –1

z = 22Test x = 2

z = 4x < y < z2 < 3 < 4

z = 02Test x = 0

z = 0x < y < z0 < y < 0

z = (–1)2Test x = –1

z = 1x < y < z–1 < 0 < 1

If a and b are positive integers such that a2 = 25 and b2 = 36. Which of the following statements are true?

25

I. a + b = 61 II. b – a = 1 III. a b = 30

Find a and b.

2 25a

a2 = 25

a = 5

b2 = 36

b = 6

2 36b

If a and y are positive integers such that a2 = 25 and b2 = 36. Which of the following statements are true?

25

I. a + b = 61 II. b – a = 1 III. a b = 30

a = 5 b = 6

5 + 6 = 6111 61

No

6 – 5 = 11 = 1Yes

5 6 = 3030 = 30

Yes

Answer: D Only II and III

If , then what is the value of k?26

9 = 3k

81 3k

81 3k

32 = 3k

2 = k

27

= 3

3 729

3 2 7296 729

28 is a number that lies between

which two powers of 10.

48,400

48,400 220

102 103

100 1,000

Answer: B

29 In the figure, if B is the midpoint of segment AD, what is the length of segment CD?

123BD – BC = CD

1 22 13 3

7 5 3 3

2 3

A B C D

213

123

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.

4 4 4

BC 100AC

4 1008

= 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) = 10 + 8 = 1818 6 = 3

Number of units fromthe first to the last peg

Number of pegs after the first peg:

How many units are the pegs apart?

6

–5 741–2

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 = 11 + 18 = 29

M

511 18

RTotal

People24

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

36 5

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

33 2

Baseball

Total Boys = 18

10

Not on either team = Total Boys – (Football + Baseball + Both)= 18 – (3 + 2 + 3) = 18 – 8 = 10

33

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

x < –2

x > 1

Commonshadedareas

Empty Set

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

x > –2

x < 1 Combineshadedareas

Answer