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 2128: 1,2,4,7,14,28

21: 1, 3, 7, 21

Greatest 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 – 2.1

p = 1 – 2.1

p = –1.1

t = (–1)3 + 2.1

t = –1 + 2.1

t = 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 – 31

21

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 ?91 1

3 2x

Rewrite the fractions as decimals.

Test A.

4

13

Test B. 4

12

0.33 0.5x

0.310.33 0.5

0.330.33 0.5

Test C. 5

120.420.33 0.5

NO

NO

YES

105

8 2

m m

4

4

5

8 2

m m

Least Common Denominator = 8

5 4

8 8

m m

8

m

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 girls

8 5 13

Number of girlsFraction of girls

Total number of students

g

g 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.

1

0.0D

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

150

0.0

2100

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 100

Original 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 Price

Percent 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 = 22

Test x = 2

z = 4x < y < z

2 < 3 < 4

z = 02

Test x = 0

z = 0x < y < z

0 < y < 0

z = (–1)2

Test 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?

12

3BD – BC = CD1 2

2 13 3

7 5

3 3

2

3

A B C D

21

3

12

3

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 100

AC

4 100

8 = 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