Unit 4
Practice Test
Answer Key
Tuesday, March 22, 2016
1 The number of students
who watch less than
1 hour or more than
7 hours of television is
approximately what
percent of the number of
students who watch
television each night?
Percent
9
7
2
Students watch
Students watch
less than 1 hour  more than 7 hours

Total number of students
23
5


=
0.24
≈
25%
=
24%
2973
21
3
2 The graph shows the number of people in the family
of each student enrolled at the local high school.
About how many students live in a family of fewer
than 4 people?
Total Percentage
= 11.7% + 13.3%
= 25%
Number of students
= 25% of 1,500
= 0.25  1,500
= 375
3
Harrison has grades of 87, 83, 74, and 89.
What grade must he get on his fifth test so
that his average will be 85?
Method #1
Let x = Fifth test score
Sum of Five Scores
Average 
Number of scores
87  83  74  89  x
85 
5
333  x
85 
5
85 333  x

1
5
(1)(333+x) = (85)(5)
333 + x = 425
x = 92
3
Harrison has grades of 87, 83, 74, and 89.
What grade must he get on his fifth test so
that his average will be 85?
Method #2
Test each answer
A. 85 ? NO
Sum of Five Scores
Average 
B. 88
C. 90
D. 92
E. 93
Number of scores
87  83  74  89  85

5
418

= 83.6 ≠ 85
5
3
Harrison has grades of 87, 83, 74, and 89.
What grade must he get on his fifth test so
that his average will be 85?
Method #2
Test each answer
A. 85 ? NO
Sum of Five Scores
Average 
B. 88 ? NO
C. 90
D. 92
E. 93
Number of scores
87  83  74  89  88

5
421

= 84.2 ≠ 85
5
3
Harrison has grades of 87, 83, 74, and 89.
What grade must he get on his fifth test so
that his average will be 85?
Method #2
Test each answer
A. 85 ? NO
Sum of Five Scores
Average 
B. 88 ? NO
C. 90 ? NO
D. 92
E. 93
Number of scores
87  83  74  89  90

5
423

= 84.6 ≠ 85
5
3
Harrison has grades of 87, 83, 74, and 89.
What grade must he get on his fifth test so
that his average will be 85?
Method #2
Test each answer
A. 85 ? NO
Sum of Five Scores
Average 
B. 88 ? NO
C. 90 ? NO
D. 92 ? YES
E. 93
Number of scores
87  83  74  89  92

5
425

= 85
5
4 Tom and Karen ate lunch at the ballpark. Tom ordered
a frankfurter, fries, and a soda. Karen ordered a
hamburger and a soda. They divided the total bill
evenly. What was the difference between what Karen
paid and what she should have paid?
4
Tom
Frankfurter
Fries
Soda
Total
$2.00
$1.50
$1.00
$4.50
Karen
Hamburger $2.50
Soda
$1.00
Total
$3.50
Total Bill = $4.50 + $3.50 = $8.00
Bill divided evenly = $8.00  2 = $4.00
What Karen paid – What Karen should have paid
$4.00
–
$3.50
= $0.50
5
The graph shows students in the twelth-grade
honor roll from 1992 to 1996. What was the
percent increase in the number of students who
made honor roll from 1993 to 1995?
Increase amount
= 135 – 125
= 10
Percent Increase
Increase Amount

Starting Amount
10

= 0.08 = 8%
125
135
125
6
The average grade on a class test taken by 11 students
is 85. When James (who was absent) took the test, his
score raised the class average by 1 point. What was
James’ score?
Average  Sum of 11 tests
of 11 tests Number of tests
Sum of 11 tests
85 
11
85 Sum of 11 tests

1
11
(1)(Sum of 11 tests) = (85)(11)
Sum of 11 tests = 935
6
The average grade on a class test taken by 11 students
is 85. When James (who was absent) took the test, his
score raised the class average by 1 point. What was
James’ score?
Sum of 11 tests = 935
Let x = Jame’s test score
Average with
Jame’s test =
Average with Jame’s test
85 + 1 = 86
Sum of
Jame’s
+
11 tests
test
Number of tests
935  x
86 
12
6
The average grade on a class test taken by 11 students
is 85. When James (who was absent) took the test, his
score raised the class average by 1 point. What was
James’ score?
Sum of 11 tests = 935
Let x = Jame’s test score
935  x
86 
12
86 935  x

1
12
Average with Jame’s test
85 + 1 = 86
1(935 + x) = (86)(12)
935 + x = 1032
–935
–935
x = 97
7 The circle graphs shows how David’s monthly expenses
are divided. If David spends $450 per month for food,
how much does he spend per month on his car?
Let x = Total Monthly Expenses
25% of total monthly
expenses is food cost
25% of x = 450
.25x = 450
.25x 450
=
.25
.25
x = 1800
7 The circle graphs shows how David’s monthly expenses
are divided. If David spends $450 per month for food,
how much does he spend per month on his car?
Let x = Total Monthly Expenses
x = 1800
Car Expense
20% of 1800
= 0.20  1800
= 360
8
The average of 7 test scores is 86. Four of the scores
are 80, 83, 86, and 92. Which of the following could
NOT be the other scores?
Total Points = 7  Average = 7  86 = 602
Four scores total = 80 + 83 + 86 + 92 = 341
Total Points – Four scores total = Other scores total
–
=
602
341
261
Test A 80 + 90 + 91 = 261
YES
Test B 75 + 88 + 98 = 261
Test C 85 + 84 + 93 = 262
YES
NO
Based on the chart, which
9 best approximates the
total number of video
rentals by premium
members at Store B
during the years
2000–2002?
Premium Members
Store B / 2000 – 2002
Total Video Rentals
Store B / 2000 – 2002
12(500)+15(1000)
+20(1250) = 46,000
10
The average of a and b is 5, and the average of c, d,
and 10 is 24. What is the average of a, b, c, and d?
Average of a and b is 5
ab
5
2
 ab
2
  2  5
 2 
a  b  10
Average of c, d, and 10 is 24
c  d  10
 24
3
 c  d  10 
3
  3  24 
3


c  d  10  72
–10 –10
Average of a, b, c, and d
c  d  62
a  b    c  d  10  62 72




 18
4
4
4
11 Salespeople at Victory Motors give discounts based on
the retail price of the car to repeat customers, such as
Todd and Alyse. If Todd buys a car with a retail price
of $22,000 and Alyse buys a car for $14,500, what is
the difference in the discounted prices of the cars?
Todd $22,000
Discount
= 8% of $22,000
= 0.08  22,000 = $1760
Alyse $14,500
Discount
= 5% of $14,500
= 0.05  14,500 = $725
11 Salespeople at Victory Motors give discounts based on
the retail price of the car to repeat customers, such as
Todd and Alyse. If Todd buys a car with a retail price
of $22,000 and Alyse buys a car for $14,500, what is
the difference in the discounted prices of the cars?
Todd $22,000
Discount = $1760
Discount Price
= $22000 – $1760
= $20240
Alyse $14,500
Discount = $725
Discount Price = $14500 – $725 = $13775
11 Salespeople at Victory Motors give discounts based on
the retail price of the car to repeat customers, such as
Todd and Alyse. If Todd buys a car with a retail price
of $22,000 and Alyse buys a car for $14,500, what is
the difference in the discounted prices of the cars?
Todd $22,000
Discount = $1760
Discount Price = $20240
Alyse $14,500
Discount = $725
Discount Price = $13775
Difference in Discounted Prices
$20240 – $13775 = $6465
12
If x = 2 and y = 3, what is the value
of the median of the following set?
2x + y , 2y – x , 2(x + y) , 3x + y
2(2) + 3
4+3
7
2(3) – 2
6–2
4
Write numbers in order:
Median =
2(2 + 3)
2(5)
10
3(2) + 3
6+3
9
4 , 7 , 9 , 10
7 + 9 = 16 = 8
2
2
13
What was the average (arithmetic mean) amount
of money, rounded to the nearest dollar, raised by
all the clubs in 1996?






600 400 400 350 250 200
1996
600  400  400  350  250  200 2200


 367
Average
6
6
14 If a = 2b and b = 3c and the average of
a, b, and c is 40, what is the value of a?
a = 2b
a = 2(3c)
a = 6c
b = 3c
abc
Average 
3
6c  3c  c
40 
3
40 10c

1
3
(1)(10c) = (40)(3)
10c = 120
c = 12
14 If a = 2b and b = 3c and the average of
a, b, and c is 40, what is the value of a?
Substitute c = 12
a = 2b
b = 3c
b = 3(12)
b = 36
a = 2b
a = 2(36)
a = 72
15 The table shows the total number of copies of Book B
that were sold by the end of each of the first 5 weeks
of its publication. How many copies of the book
were sold during the 3rd week of its publication?
Total
Copies
Sold
End of 1st week
End of 2nd week
End of 3rd week
End of 4th week
End of 5th week
3200
5500
6800
7400
7700
Copies Sold Each Week
(Total Copies Sold present week
minus total copies sold previous week)
1st week
3200
2nd week
5500 – 3200 = 2300
6800 – 5500 = 1300
3rd week
16 A doll’s wardrobe consists of 40 possible outfits
consisting of a shirt, pants, and a pair of shoes.
If there are 5 shirts and 2 pairs of shoes, how
many pairs of pants are in the doll’s wardrobe?
Possible
Outfits
= Shirts  Pants  Shoes
40
=
40
= 10
4
=
5
 Pants 
 Pants
Pants
2
17 The diagram shows the Washington, D.C. attractions
visited by a social studies class. If 22 students visited the
Capitol, how many students visited the Smithsonian?
Capitol = x + 2 + 9 + 6
22 = x + 2 + 9 + 6
22 = x + 17
Smithsonian = 5 + 2 + 3 + 10
5=x
Smithsonian = 20
18
A bag contains 3 round blue pegs, 2 round red pegs,
5 square red pegs, 4 square yellow pegs, and
6 square blue pegs. One peg dropped out of the bag.
What is the probability that it was red or round?
P(red OR round)
P(red) OR P(round)
7
20
+
5
20
=
12
20
=
3
5
19
A circular target is inscribed in a square base.
The radius of the circle is 3. Assuming that a dart
randomly strikes the figure, what is the probability
that it lands in the circle?
area of circle
P(circle) 
area of square
Circle area
A = r2
A = 32
A = 9
A = 9
Square area
d=6
A = s2
A = 62
A = 36
6
9


P(circle) 
36
4
There are 30 students in Mary’s homeroom. Of
20
these students, 15 are studying Spanish, 10 are
studying Latin, and 3 are studying both
languages. How many students are studying
neither language?
Spanish
Latin
12
3
7
Students studying languages = 12 + 7 + 3 = 22
Students studying neither = 30 – 22 = 8
21 Each sector in the spinner is of equal size and there is
no overlap. The spinner is equally likely to stop on
any sector. What is the probability that the spinner
will land on a sector labeled with a prime number?
P(landing on prime number)
sectors with prime number

total number of sectors

5
6
22
In a class of 24 students, there are twice as many male
students as female students. Twelve students have a
driver’s license. One quarter of the male students have a
driver’s license. How many females in the class do not
have a driver’s license?
Females = x 8
Males = 2x 2(8) = 16
Students
24
24
8
= Males + Females
x
= 2x +
= 3x
= x
22
In a class of 24 students, there are twice as many male
students as female students. Twelve students have a
driver’s license. One quarter of the male students have a
driver’s license. How many females in the class do not
have a driver’s license?
Males with D.L. =
Males with D.L. =
Males with D.L. =
Females D.L.
Females D.L.
Females D.L.
¼
¼
 Males
 16
4
Females = 8
Males = 16
Females
Without
D.L. = 0
= Students D.L. – Males D.L.
4
–
12
=
8
=
23 A class roster lists 15 boys and 12 girls. Two students
are randomly selected to speak at a school assembly.
If one of the students selected is a boy, what is the
probability that the other student selected is a girl?
There are 15 boys.
One boy is selected.
There are now 14 boys.
P(selecting girl)
# girls
12
12
6




# girls + #boys 1214 26
13
A box contains colored jellybeans. There are 14 red,
24 6 yellow, and x blue jellybeans in the bag. If the
probability of drawing a yellow jellybean is 1 4 ,
what is the value of x?
1
number of yellow

P(yellow) 
total number of jellybeans 4
6
1

x  14  6
4
6
1

x  20
4
(1)(x + 20) = (6)(4)
x + 20 = 24
–20 –20
x
= 4
25
If a die is rolled twice, what is the probability
that is lands on 5 both times?
P(#5 on 1st roll AND #5 on 2nd roll)
P(#5 on 1st roll) AND P(#5 on 2nd roll)
1
6

1
6
=
1
36
26
A box contains 50 marbles. Twenty-five are red,
15 are white, and 10 are blue. Steve took a
marble without looking. What is the probability
that the marble is not blue?
P(not blue)
P(red OR white)
P(red) OR P(white)
25
50
+
15
50
=
40
50
=
4
5
27
A target is made up of concentric circles as shown
in the figure. Assuming that a dart randomly strikes
the target, what is the probability that it will strike
the shaded region?
Big area  Small area
P(shaded) 
Big area
Big area
A = r2
A = 32
A = 9 = 9
Small area
A = r2
A = 22
A = 4 = 4
9  4
5
5


P(shaded) 
9
9
9
28
Cake
Pie
6
5
2
3
0
1
4
Cookies
The Venn Diagram illustrates a relationship between
cake, cookie, and pie orders at a bakery.
28a
Cake
Pie
6
5
2
3
0
1
4
Cookies
How many people ordered
pies and cookies? 3 + 1 = 4
28b
Cake
Pie
6
5
2
3
0
1
4
Cookies
How many people ordered pies or cookies?
5 + 2 + 3 + 1 + 0 + 4 = 15
28c
Cake
Pie
6
5
2
3
0
1
4
Cookies
How many people ordered
cookies and no cake? 4 + 1 = 5
29
Find the number of ways you can arrange
two letters in the word MATH.
1st
letter
2nd
letter
4  ___
3 =
___
12
Number of choices
Answer: 12 arrangements
There are four black cats and five grey cats in a cage,
30
and none of them want to be in there. The cage door
opens briefly and two cats escape. What is the
probability that both escaped cats are black?
Each cat leaves the cage without replacement.
4 1

8 2
3 1

9 3
P(1st black AND 2nd black)
P(1st black) AND P(2nd black)
3
4

8
9
1
1
1
=

2
6
3
31
Find the 10th term of the sequence.
19, 25, 31, 37, …
Term 1st 2nd 3rd 4th
Method #1
5th
6th
19 25 31 37 43 49
+6 +6 +6 +6 +6
Term 6th 7th 8th 9th 10th
49 55 61 67 73
+6
+6
+6
+6
31
Find the 10th term of the sequence.
19, 25, 31, 37, …
Method #2
+6 +6 +6
First: Find formula
Next:
Find 10th term
an = a1 + d(n – 1)
an = 6n + 13
a1 = 19
d=6
an = 19 + 6(n – 1)
an = 19 + 6n – 6
an = 6n + 13
a10 = 6(10) + 13
= 60 + 13
= 73
32
Find the 12th term of the sequence.
4, 9, 14, 19, …
Term 1st 2nd 3rd 4th
Method #1
5th
6th
4 9 14 19 24 29
+5 +5 +5 +5 +5
Term 6th 7th 8th 9th 10th 11th 12th
29 34 39 44 49 54 59
+5
+5
+5
+5
+5
+5
32
Find the 12th term of the sequence.
4, 9, 14, 19, …
Method #2
+5 +5 +5
First: Find formula
Next:
Find 12th term
an = a1 + d(n – 1)
an = 5n – 1
a1 = 4
d=5
an = 4 + 5(n – 1)
an = 4 + 5n – 5
an = 5n – 1
a12 = 5(12) – 1
= 60 – 1
= 59
33
What term of the sequence is 25?
1, 4, 7, 10, …
+3 +3 +3
First: Find formula
an = a1 + d(n – 1)
a1 = 1
d=3
an = 1 + 3(n – 1)
an = 1 + 3n – 3
an = 3n – 2
Next: Let an = 25
an = 3n – 2
25 = 3n – 2
+2
+2
27 = 3n
9= n
34
Which set is not a geometric sequence?
A. {48, 24, 12, 6, …} Geometric
×½ ×½ ×½
B. {2, –6, 18, –54, …} Geometric
× –3 × –3 × –3
34
Which set is not a geometric sequence?
ìï 1 1 1 1 ü
ï
C. í ,
, , , ...ý
ïîï 32 16 8 4 ïþ
ï
×2
Geometric
×2 ×2
D. {4, 2, 0, –2, …}
–2 –2 –2
Not
Geometric
35
The 8th term of the geometric sequence
{243, 81, 27, 9, …} is
Term 1st
2nd
3rd
4th
243 81
27
9
1
×⅓ ×⅓ ×⅓
Term 4th
9
5th
3
6th
7th
8th
1
1
1
3
×⅓ ×⅓ ×⅓ ×⅓
9
9
36
What is the tenth term of the geometric
sequence ìïí - 1 , 1 , - 1, ...üïý
ïîï
Term 1st
1
4
2nd
1
2
ïþ
ï
4 2
3rd
4th
5th
6th
–1
2
–4
8
× -2 × -2 × -2 × -2 × -2
Term 6th 7th
8th 9th 10th
8 –16
32 –64 128
× -2 × -2
× -2 × -2
37 If {1, –2, 4, …} is a geometric sequence, what
is the sum of the first seven terms?
Term 1st
2nd
3rd
4th
5th
1
–2
4
–8
16
× -2 × -2 × -2 × -2
Term 5th 6th
7th
16 –32 64
× -2 × -2
Sum = 85 +(-42) = 43
Sum = 1 + (–2) + 4 + (-8) + 16 + (-32) +64