Mathematics practise english 2 pdf


Answers and Explanations
1. c. Danny earned a total of 40($6.30) = $252. To
find the number of hours Erica would take to
earn $252, divide $252 by $8.40.
2.
c. Since m∠ACB = 90° and m∠CAD = 40°, then
m∠B = 180 − 90 − 40 = 50°. In BCD,m∠CDB =
90° and m∠B = 50°. Therefore, m∠DCB =
180 − 90 − 50 = 40.
3. e. If the class has x students and 5 students are
absent, then x − 5 students are present:
ᎏ
x −
5
5
ᎏ
4. b. If the tank is
ᎏ
1
3
ᎏ
full, it is
ᎏ
2
3
ᎏ
empty. Let x = the
capacity of the tank;
ᎏ
2

3
ᎏ
x = 16, so x = 16 ÷
ᎏ
2
3
ᎏ
=
16 ×
ᎏ
3
2
ᎏ
= 24.
5.
c. Let x = the length of the ramp. Use the
Pythagorean theorem to obtain the equation:
x
2
= 12
2
+ 16
2
= 144 + 256 = 400
x = ͙400
ෆ
= 20
6. c. 48 half-pints = 24 pints. Since 8 pt. = 1 gal.,
24 pt. = 3 gal., 3($3.50) = $10.50.
7. d. If x is replaced by the answer choices, only 2 and

−3 make the expression true.
(2)
2
+ 2 − 6 = 0 (−3)
2
+ −3 − 6 = 0
4 + −4 = 0 9 + −3 − 6 = 0
9 + −9 = 0
0 = 0 0 = 0
8.
c. To find the perimeter of the figure, find the sum
of the lengths of its sides.
2a + a + b + 2a + b + a + 2b = 6a + 4b
9.
e. Let x = the width of the room; 23x = 322; x =
322 ÷ 23 = 14. Perimeter = 23 + 14 + 23 + 14 =
74 feet.
10.
a. The perimeter of the figure is
x + 2y + 3x − y + 2x + 3y + 5x + y = 11x + 5y.
5x + y
3x − y
2x + 3
y
x
+ 2y
A = 322 square feet 23 feet
a + b
a + 2b
2a + b

2a
Ramp
12 ft.
16 ft.
B
D
A
C
– GED MATHEMATICS PRACTICE QUESTIONS–
445
11. d. Set up an equation with Oliver’s money as the
unknown, and solve. Oliver = x, Henry = 5 + x,
and Murray = 5 + x. Therefore,
x + 2(5 + x) = 85
x + 10 + 2x = 85
3x + 10 = 85
3x = 75
x = 25
12.
IF YOUR TAXABLE INCOME IS:
But Not Your Tax
At Least More Than Is
0 $3,499 2% of amount
$3,500 $4,499 $70 plus 3%
of any amount
above $3,500
$4,500 $7,499 $100 plus 5%
of any amount
above $4,500
$7,500 $250 plus 7%

of any amount
above $7,500
d. $5,800 − $4,500 = $1,300. Tax is $100 + 5% of
$1,300 = 100 + 0.05(1,300) = 100 + 65 = $165.
13. e. You cannot compute the cost unless you are told
the number of days that the couple stays at the
bed and breakfast. This information is not
given.
14.
c. m∠CBD = 125
m∠ABC = 180 − 125 = 55
m∠A + m∠ABC = 90
m∠A + 55 = 90
m∠A = 90 − 55 = 35
15. c. Let n = number. Then n
2
= square of a number,
and n
2
+ n + 4 = 60.
16.
b. Meat department sales = $2,500
Dairy department sales = $1,500
Difference = $1,000
17. b. Because the coupon has double value, the
reduction is 2(.15) = 30 cents. The cost of the
cereal is x − 30 cents.
30
Hundreds of Dollars
Baked

Goods
Groceries Dairy Produce Meat
25
20
15
10
5
C
A
B
D
– GED MATHEMATICS PRACTICE QUESTIONS–
446
18.
e. Let x,2x, and 3x be the measures of the three
angles. Then:
x + 2x + 3x = 180
6x = 180
x = 180 ÷ 6 = 30
3x = 3(30) = 90
19.
d. Let x = m∠3 and 2x = m∠2
m∠1 + m∠2 + m∠3 = 180
36 + 2x + x = 180
3x + 36 = 180
3x = 180 − 36 = 144
x = 144 ÷ 3 = 48 degrees
20. c. The beef costs 4($2.76) = $11.04. The chicken
costs $13.98 − $11.04 = $2.94. To find the cost
per pound of chicken, divide $2.94 by 3

ᎏ
1
2
ᎏ
or by
ᎏ
7
2
ᎏ
; 2.94 ÷
ᎏ
7
2
ᎏ
= 2.94 ×
ᎏ
2
7
ᎏ
= 0.84.
21.
d. Forty percent of the total expenses of $240,000
went for labor: 0.40($240,000) = $96,000.
22. d. To express a number in scientific notation,
express it as the product of a number between 1
and 10 and a power of 10. In this case, the num-
ber between 1 and 10 is 6.315. In going from
6.315 to 63,150,000,000, you move the decimal
point 10 places to the right. Each such move
represents a multiplication by 10

10
and
63,150,000,000 = 6.315 × 10
10
.
23.
b. Slope =
ᎏ
x
y
1
1
−
−
y
x
2
2
ᎏ
; in this case, y
1
= 4, y
2
= 3, x
1
= 5,
and x
2
= 0. Slope =
ᎏ

4
5
−
−
3
0
ᎏ
=
ᎏ
1
5
ᎏ
.
24. e. 1 km = 1,000 m and 1 m = 100 cm. So 1 km =
100,000 cm and 1 km = 1,000,000 mm.
0
x
y
B (0,3)
A (5,4)
Operating
Expenses
20%
Raw
Materials
33  %
Labor
40%
Net
Profit

6  %
1
2
3
CBA
D
E
C
B
A
ЄA:ЄB:ЄC = 3:2:1
– GED MATHEMATICS PRACTICE QUESTIONS–
447
25.
d. Let x = DC
ឈ
៮
៬
. Since ᭝ABE is similar to ᭝CED, the
lengths of their corresponding sides are in
proportion.
ᎏ
6
x
0
ᎏ
=
ᎏ
8
4

0
8
ᎏ
48x = 80(60) = 4,800
x = 4,800 ÷ 48 = 100
100 feet is the answer.
26.
e. Add the amounts given: 11 + 6 + 5 + 40 + 30 =
$92. $100 − $92 leaves $8 for profit.
27. c. Let x = number of points scored by Josh, x + 7 =
number of points scored by Nick, and x − 2 =
number of points scored by Paul.
x + x + 7 + x − 2 = 38
3x + 5 = 38
3x = 33
x = 11
28. c. Use the formula V = lwh. In this case, l = 5,
w = 5, and h = h. Therefore, V = 5 × 5 × h = 25h
and 25h = 200.
29.
29.
d. Since 3
2
= 9 and 4
2
= 16, ͙12
ෆ
is between 3 and 4.
Only point D lies between 3 and 4.
30.

d. Divide the floor space into two rectangles by
drawing a line segment. The area of the large
rectangle = 20 × 15 = 300 sq. ft. The area of the
small rectangle = 10 × 15 = 150 sq. ft. The total
area of floor space = 150 + 300 = 450 sq. ft.
Since 9 sq. ft. = 1 sq. yd., 450 sq. ft. ÷ 9 = 50 sq.
yd.
31. c. If you don’t see that you need to divide y by x,
set up a proportion. Let z = number of dollars
needed to purchase y francs.
ᎏ
d
fr
o
a
ll
n
a
c
r
s
s
ᎏ
=
ᎏ
1
x
ᎏ
=
ᎏ

y
z
ᎏ
y(
ᎏ
1
x
ᎏ
) = (
ᎏ
y
z
ᎏ
)y
ᎏ
x
y
ᎏ
= z
32. e. Replace the variables with their given values.
(−2)
2
(32 − [−2]) = 4(34) = 136
33. e. Since
ᎏ
1
4
ᎏ
in. represents 8 mi, 1 in. represents 4 × 8
= 32 mi., and 2 in. represents 2 × 32 = 64 mi.,

ᎏ
1
8
ᎏ
in. represents 4 mi. Then 2
ᎏ
1
8
ᎏ
in. represent
64 + 4 = 68 mi.
10′
15′
25′
20′
012
ACBED
345
Profit
?
Materials
$40
Insurance
$5
Misc.
$6
Salaries
$30
Taxes
$11

60′
48′
80′
AB
E
CD
– GED MATHEMATICS PRACTICE QUESTIONS–
448
34.
c. Use the formula for the area of a triangle.
A =
ᎏ
1
2
ᎏ
bh
ᎏ
1
2
ᎏ
(4)(8) = 16
35. c. Let x = height of steeple. Set up proportion:
ᎏ
le
h
n
e
g
ig
t

h
h
t
o
o
f
f
s
o
h
b
ad
je
o
c
w
t
ᎏ
:
ᎏ
2
x
8
ᎏ
=
ᎏ
6
4
ᎏ
4x = 6(28) = 168

x = 168 ÷ 4 = 42 ft.
36.
d. As you can see from the figure, to find the area
of the walkway, you need to subtract the area of
the inner rectangle, (20)(30) sq. ft., from the
area of the outer rectangle, (26)(36) sq. ft.:
(26)(36) − (20)(30) sq. ft.
37. e. Since the average depth of the pool is 6 ft., the
water forms a rectangular solid with dimensions
30 by 20 by 6. The volume of water is the prod-
uct of these three numbers: (30)(20)(6) =
3,600 ft.
3
38. d. Taken together, the pool and the walkway form
a rectangle with dimensions 36 by 26. The total
area is the product of these numbers: (36)(26) =
936 sq. ft.
39. c. 6 × 10
5
= 600,000
4 × 10
3
= 4,000
600,000 ÷ 4,000 = 600 ÷ 4 = 150
40. d. Let x = cost of lot and 3x = cost of house.
x + 3x = 120,000
4x = 120,000
x = 120,000 ÷ 4 = 30,000
3x = 3(30,000) = $90,000
41. e. Find the interest by multiplying the amount

borrowed ($1,300) by the time period in years
(1.5) by the interest expressed as a decimal
(0.09). To find the amount paid back, the
amount borrowed must be added to the interest.
$1,300 + ($1,300 × 0.09 × 1.5)
42. a. Simply multiply: $8,000 × 0.13 × 5 = $5,200
43. e. Tr y −5 for x in each equation. Only option e is
true when −5 is substituted for x.
12x = −60
12(−5) = −60
−60 = −60
44. b. When you subtract the check from the amount
in the checking account, the result will be the
current balance: $572.18 − c = $434.68
45. a. Solve: x + (2x + 12) = $174
3x + 12 = $174
3x = $162
x = $54
46. c. Let x = the price of an adult’s ticket and x − $6 =
the price of a child’s ticket. In the problem, the
cost of 2 adults’ tickets and 4 children’s tickets is
$48. Write and solve an equation:
2x + 4(x − 6) = $48
2
x + 4x − $24 = $48
6x − $24 = $48
6x = $72
x = $12
47. c. The median is the middle amount. Arrange the
amounts in order and find the middle amount,

$900.
48. b. The mode is the number that occurs most often.
Only 14 occurs more than once in the data set.
3 ft.
30 ft.
20 ft.
8 units
4 units
– GED MATHEMATICS PRACTICE QUESTIONS–
449
49. c. Find the amount of interest. For the time
period, use
ᎏ
1
9
2
ᎏ
, which equals
ᎏ
3
4
ᎏ
, or .75. Multiply.
$1,500 × 0.04 × 0.75 = $45. Add to find the
amount paid back. $1,500 + $45 = $1,545.
50. c. Multiply 3 lb. 12. oz. by 6 to get 18 lb. 72 oz.
Divide 72 oz. by the number of oz. in a pound
(16) to get 4 lbs. with a remainder of 8 oz.
Therefore, 18 lb. + 4 lb. 8 oz. = 22 lb. 8 oz.
51. a. If 80% of the audience were adults, 100% − 80%

= 20% were children.
20% = .20, and 0.20(650) = 130
52. b. Let x = number of inches between the towns on
the map. Set up a proportion:
ᎏ
6
1
0
i
m
n.
i.
ᎏ
=
ᎏ
22
x
5
in
m
.
i.
ᎏ
60x = 255
x =
ᎏ
2
6
5
0

5
ᎏ
= 4
ᎏ
1
4
ᎏ
53. b. 4 ft. 3 in. = 3 ft. 15 in. − 2 ft. 8 in. = 1 ft. 7 in.
54. d. v = lwh; the container is 5 ft. long × 3 ft. wide ×
2 ft. high. 5 × 3 × 2 = 30 ft.
3
55.
d. The top of the bar for Wednesday is at 6 on the
vertical scale.
56. e. The top of the bar for Monday is halfway
between 4 and 6, so 5 gal. were sold on Monday.
The top of the bar for Saturday is halfway
between 16 and 18, so 17 gal. were sold on Sat-
urday. The difference between 17 gal. and 5 gal.
is 12 gal.
57. d. The tops of the bars for Monday through Sun-
day are at 5, 4, 6, 5, 14, 17, and 9. These add up
to 60.
58.
a. Let x = m∠OAB. OA
ឈ
៮
៬
= OB
ឈ

៮
៬
since radii of the
same circle have equal measures. Therefore,
m∠OAB = m∠OBA.
x + x + 70 = 180
2x + 70 = 180
2x = 180 − 70 = 110
x = 110 ÷ 2 = 55
59. e. Let x = number of books on the small shelf, and
x + 8 = number of books on the large shelf.
Then, 4x = number of books on 4 small shelves,
and 3(x + 8) = number of books on 3 large
shelves.
4x + 3(x + 8) = 297
4x + 3x + 24 = 297
7x + 24 = 297
7x = 297 − 24
7x = 273 ÷ 7 = 39
60. a. 40 ft. = 40 × 12 = 480 in.
3 ft. 4 in. = 3(12) + 4 = 36 + 4 = 40 in. 480 ÷ 40
= 12 scarves.
61. b. $130,000 (catalog sales) − $65,000 (online sales)
= $65,000
62. b. $130,000 + $65,000 + $100,000 = $295,000,
which is about $300,000. Working with compat-
ible numbers, $100,000 out of $300,000 is
ᎏ
1
3

ᎏ
.
A
B
O
70°
20
Number of Gallons
Days of the Week
Paint Sales at Carolyn’s Hardware
M T W Th F Sa Su
18
16
14
12
10
8
6
4
2
– GED MATHEMATICS PRACTICE QUESTIONS–
450