Transcript Unit 1 Practice Test KEY

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
(3 – 2)  5
(1)  5
5
(5 – 3)  2
(2)  2
4
(5 – 2)  3
(3)  3
9
2 In the correctly worked multiplication
problems, L, M, and N are single-digit
integers. What is the value of N – M?
M=4
 L=7
28
N=3
 L =7
21
N–M
= 3 – 4 = –1
Factors of
28 and 21
28: 1,2,4,7,14,28
21: 1, 3, 7, 21
Greatest Common
Factor = 7
If n is a negative integer, what is the
ordering of p, t, and r from greatest
to least?
p = n2 – 2.1 ; t = n3 + 2.1 ; r = (n – 2.1)2
3
Substitute: n = –1
p = (–1)2 – 2.1 t = (–1)3 + 2.1 r = (–1 – 2.1)2
p = 1 – 2.1
t = –1 + 2.1
r = (–3.1)2
p = –1.1
t=
1.1
r>t>p
r = 9.61
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
3 Hours
4 Hours
15 Minutes
Total
$1.50
$0.75
$0.75
$0.75
$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?
Try E. 97 P: 97
Q: 79
Difference
97 – 79 = 18
Try D. 96 P: 96
Q: 69
96 – 69 = 27
Try C. 93 P: 93
Q: 39
93 – 39 = 54 YES
NO
NO
6
If x, y, and z are three prime
numbers, and 19 < x < y < z < 35,
find x + y – z.
x = 23 , y = 29 , z = 31
x + y – z
23 + 29 – 31
52 – 31
21
7
If N is an odd or even integer, which
of the following will always be an
odd integer?
Substitute odd
integer
2(3) + 1
Substitute even
integer
2(4) + 1
8+1
9
6+1
7
Answer: 2N + 1
8
If m and p are positive integers, which
expression must be negative?
Substitute: m = 2
A. m – p
B. p – m
C. m + p
2 – 5 = –3
5–2=3
No
p=5
Subtraction with
positive numbers can
be positive or negative
2 + 5 = 7 No
D. –(m + p) –(2 + 5) = –7 Yes
E. –(m – p)
1
1
9 What is the value of x for which  x  ?
3
2
Rewrite the fractions as decimals.
0.33  x  0.5
4
Test A.
13
0.33  0.31  0.5
NO
Test B. 4
12
0.33  0.33  0.5
NO
Test C. 5
12
0.33  0.42  0.5
YES
10
5m m

8
2
Least Common
Denominator = 8
5m  m 4 
  
8  2 4
5m 4 m m


8
8
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 15 of the money in her savings account
on clothes. The next month she spent 1 4 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?
1
Strategy: Multiply each answer times 5 . Find
amount remaining. Multiply remaining amount
times 1 4 . Find remaining amount. It should equal
$3,600.
12
Amy spent 15 of the money in her savings account
on clothes. The next month she spent 1 4 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
1  4900  980
5
4,900 – 980 = 3,920
1  3920  980
4
3,920 – 980 = 2940
No
Test E. $6,000
1  6000  1200
5
6,000 – 1200 = 4,800
1  4800  1200
4
4800 – 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.
8
8
Fraction of girls 

8  5 13
Number of girls
g
Fraction of girls 

Total number of students g  b
15
If D is a nonzero digit in the decimal number 0.0D,
1
which of the following must be equal to
?
0.0D
Substitute any number for D.
Then, find the answer that is
equal to the same result.
(A) 100  50
2
1
 50
0.02
16
If it takes ½ hour to wash a car, how many
days will it take to wash 96 cars?
Time
½ hour
1 hour
2 hours
24 hours
1 day
2 days
Number of Cars
1
21 = 2
22 = 4
224 = 48
48
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
8% of 1 = .08  1 = 0.08
No
B. 8
8% of 8 = .08  8 = 0.64
No
C. 10
8% of 10 = .08  10 = 0.8
No
D. 80
8% of 80 = .08  80 = 6.4
No
E. 100
8% of 100 = .08  100 = 8
Yes
18 Kathy, Keri, and Kim raised $10, $15, and
$25 respectively, during a fundraising drive.
What percent of the money did Kathy raise?
Total raised = $10 + $15 + $25 = $50
Amount Kathy raised
100
Percent Kathy raised 
Total amount raised
10

 100
50
= 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 Amount
Percent Increase 
 100
Original Amount
2

 100
18
= 0.11  100
= 11%
20
If a $3.75 book was bought for $3.30,
what was the percent discount?
Original
Sale
Discount = Price – Price
Discount = $3.75 – $3.30 = $0.45
Discount Price
Percent Discount 
 100
Original Price
0.45

 100
3.75
= 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?
Profit = 23% of $270 = .23(270) = 62.10
Selling
Purchase
+ Profit
=
Price
Price
+ $62.10
= $270
=
$332.10
22
If n is a negative integer, then nb
must be positive whenever b is
n = –1
nb = (–1)b
(–1)2 = (–1)(–1)
= +1
Answer: C
Even integer
23
If x2 = 36, then what could be the
value of 2x–2 ?
x2 = 36
x  36
x = 6
2
2x–2
26–2
4
2
16
24 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?
I. 2
II. 0
III. –1
Test x = –1
Test x = 2
Test x = 0
z = 22
z=4
z = 02
z=0
z = (–1)2
z=1
x<y<z
x<y<z
x<y<z
2<3<4
0<y<0
–1 < 0 < 1
25 If a and b are positive integers such that
a2 = 25 and b2 = 36. Which of the
following statements are true?
I. a + b = 61
II. b – a = 1
III. a  b = 30
Find a and b.
a2 = 25
b2 = 36
a  25
a =5
b  36
b =6
2
2
25 If a and y are positive integers such that
a2 = 25 and b2 = 36. Which of the
following statements are true?
a =5
b =6
I. a + b = 61
II. b – a = 1
III. a  b = 30
5 + 6 = 61
11  61
6–5=1
1=1
5  6 = 30
30 = 30
No
Yes
Answer: D Only II and III
Yes
26 If
81  3 , then what is the value of k?
k
81  3
k
k
3
9=
2
k
3 =3
2=k
27
3
729
3 2
729
6
729 = 3
28
48, 400 is a number that lies between
which two powers of 10.
48, 400  220
102
100
103
1,000
Answer: B
29 In the figure, if B is the midpoint of
segment AD, what is the length of
segment CD?
1
2
3
A
2
1
3
B
BD – BC = CD
1
2
7 5
2
2 1 
 
3
3
3 3
3
C
1
2
3
D
30 In the figure, points B and C divide the
segment AD into three equal parts.
BC is what percent of AC?
4
4
4
Substitute a number for the
lengths of each line segment.
4
BC
 100   100 = 0.5  100
8
AC
= 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?
–8
a
b
c
–5 –2 1
Number of units from
the first to the last peg
10 – (–8) = 10 + 8 = 18
d
4
e
7
10
Number of pegs after
the first peg: 6
How many units are the pegs apart? 18  6 = 3
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?
M
R
11
5
Club Participants
= M + R = 11 + 18 = 29
18
Total
People
24
Both Clubs
= 29 – 24 = 5
33
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
6
Baseball
3
5
33
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?
Total Boys = 18
Football
3
Baseball
3
2
10
Not on either team
= Total Boys – (Football + Baseball + Both)
= 18 – (3 + 2 + 3) = 18 – 8 = 10
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
Common
shaded
areas
x>1

Empty Set
35 Set A = {x > –2} and set B = {x < 1}.
Which of the following illustrates A  B ?
x > –2
x<1
Answer
Combine
shaded
areas