Download Estimation

Estimation
1.
In RST shown below, RS  RT , and the measure of R is 40. What is the
measure of S ?
A.
B.
C.
D.
E.
2.
20
40
50
70
Cannot be determined from the given information
A recipe calls for 23 cup sugar to make 24 two-inch cookies. According to this
recipe, how many cups of sugar should be used to make 60 two-inch cookies?
A.
B.
C.
D.
E.
5
9
1
1 15
1 23
3 16
3.
In the figure below, F and E are points on GD . What is the ratio of the area of
square ABEF to the area of the parallelogram ACDG ?
A.
B.
C.
D.
E.
4.
1:14
1:7
7:1
7:2
2:7
The scales on both axes of the standard (x,y) coordinate plane below are the same.
Of the following, which is the best estimate for the slope of AB ?
A. 4
B. 34
C. 14
D. - 14
E. -4
5.
In the regular hexagon below, vertices B, C, and D are labeled; OA is perpendicular
to CD ; A is the midpoint of CD ; and O is the midpoint of BC . What is the degree
measure of AOC ?
F.
G.
H.
J.
K.
6.
15
20
30
45
60
Theo polygon below was a square with 12-inch sides before a triangle was cut off.
What is the perimeter, in inches, of this polygon?
F.
G.
H.
J.
K.
41
43
46
48
53
7.
In triangle ABD below, points D, C, and B are collinear, AD is perpendicular to
DB , and AC bisects DAB. If the measure of CBA is 40, what is the measure
of ACB ?
F.
G.
H.
J.
K.
8.
115
112.5
110
107.5
105
The area of the trapezoid below is 16 square inches, the altitude is 2 inches, and the
length of one base is 3 inches. What is the length, b, of the other base, in inches?
A. 2 23
B. 5
C. 11
D. 13
E. 15
9.
The radio station WEST is erecting a new transmitting tower that is 280 feet tall. A
support wire will be attached to the ground at point A and to the tower 250 feet up at
point B, as shown below. The wire must be at least as long as AB . Which of the
following expresses the length of AB , in feet?
F. 250 cos 70
G. 250 sin 70
H. 250 tan 70
J. cos250
70
K.
250
sin 70
10. In the diagram shown below, lines m and n are parallel. The lengths of AB and
AC are equal, and one angle measures 70, as shown. What is the measure of
ACD ?
F.
G.
H.
J.
K.
110
130
140
150
160
11. In the figure below, PQ is perpendicular to QR , and points Q, R, and S are
collinear. If the measure of PRS is 145, what is the measure of QPR ?
F.
G.
H.
J.
K.
27.5
35
45
55
72.5
12. In trapezoid ABCD below, BAD and ADC are both right angles. If AB is 10
units long, DC is 15 units long, and AD is 12 units long, how many units long is
BC ?
A.
B.
C.
D.
E.
119
5 5
13
2 61
17
13. In the figure below, OB bisects 70 angle AOC and is perpendicular to AC . What
is the degree measure of ACD ?
A.
B.
C.
D.
E.
105
125
135
140
160
14. (2 - 3 2 )(3 + 2 2 ) = ?
A.
6-6 2
B. -6
C.
6 - 11 2
D. -6 - 5 2
E. -16
15. In right triangle ABD below, AC is perpendicular to the hypotenuse BD . If the
length of AD is 6 units and that of AB is 8 units, then how many units long is AC
?
A. 10.0
B. 7.5
C. 6.4
D. 4.8
E. 2.4
16. In the figure below, m is parallel to n and the measures of angles are as marked.
What is the measure, in degrees, of x ?
A.
B.
C.
D.
E.
80
75
65
55
35
17. Two transversals intersect at R, a point between the 2 parallel lines m and n. The
measures of angles are as marked on the figure below. What is the measure, in
degrees, of PQR ?
F.
G.
H.
J.
K.
76
54
46
44
32
18. In the figure below, all distances are in centimeters and all angles are right angles. A
straight line drawn from point A to point D would be how many centimeters long?
F.
G.
H.
J.
K.
5
12
13
16
17
19. A ramp goes from the edge of a dock to the edge of a ship’s deck. If the ramp is 25
feet long and the deck of the ship is 7 feet above the dock, how many feet away from
the dock is the ship?
A. 674
B. 576
C.
674
D. 24
E. 18
20. In the figure below, Q lies on PR , PQS and PSR are each right angles, and the
measure of QRS is 30. If PS is 4 units long, how many units long is QS ?
F.
2 3
3
G. 4 3 3
H. 3
J. 2 3
K. 4
21. In a certain rural school district, exactly 60% of the students live on farms. If there
are 7,345 students in the district, how many do NOT live on farms?
F.
294
G.
447
H. 2,938
J. 4,407
K. 6,898
22. Given: m and n are parallel lines
t is a transversal crossing lines m and n
a measures 30
What is the measure of f below?
A. 30
B. 60
C. 120
D. 130
E. 150
23. In the figure below, where the 3 lines intersect at the indicated angles, x = ?
F.
G.
H.
J.
K.
25
52.5
65
70
75
24. In the figure below, AB and CD bisect each other at E. The measure of CAE is
80 and the measure of BDE is 60. What is the measure of CEA ?
F.
G.
H.
J.
K.
10
30
40
60
Cannot be determined from the given information
25. At a certain company, 240 of the employees belong to a union while the other 160 do
not. What percent of the company’s workers are nonunion?
F.
G.
H.
J.
K.
25%
33 13 %
40%
60%
66 23 %
26. A circle has a circumference of 10 inches. What is the radius, in inches, of the
circle?
5
A.

10
B.

C. 10
D. 20
E. 100
27. What is the area, in square inches, of the figure shown below?
F.
G.
H.
J.
K.
18
30
36
44
60
28. If the lengths of the sides of the triangle below are shown in inches, how many
inches long is side AB ?
F.
G.
H.
J.
K.
12
40
70
4 3
4 5
29. Two 30-60-90 triangles are shown below. The hypotenuse of the larger triangle is
18 centimeters long. If the perimeter of one triangle is 3 times that of the other
triangle, how many centimeters long is the shortest of the 6 sides?
A.
B.
C.
D.
E.
3
3 3
6
9
9 3
30. In the diagram below, AED and BCD each measure 135, DF is an altitude of
CDE and ABCE is a rectangle. What is the area, in square meters, of pentagon
ABCDE ?
A. 28 + 8 2
B. 96
C. 112
D. 120
E. 140
31. A line passes through the points (2,4) and (3,8) in the standard (x,y) coordinate
plane. What is the value of y if (6,y) is also on this line?
A.
B.
C.
D.
E.
12
13
16
20
32
32. Below, in right triangle ABC, AB is 4 inches long and BC is 5 inches long. What
is the area, in square inches, of square ACDE ?
F. 9
G.
41
H.
82
J. 4 41
K. 41
33. In the figure below, rectangle CDFG is contained in rectangle ABCD. If equilateral
triangle CDE divides FG into 3 equal-length segments FT , TW , and WG , what is
the ratio of the widths of these rectangles (that is, FD:AD) ?
A.
B.
C.
D.
E.
1:3
1:2
1: 3
1:1
2:3
34. The figure below is a regular pentagon. What is the measure of A ?
F.
G.
H.
J.
K.
72
108
120
135
144
35. It is estimated that, from the beginning of 1980 to the end of 1986, average milk
consumption in the United States decreased from 30 gallons per year to 22 gallons
per year. During the same time period, soft drink consumption rose from an average
of 24 gallons per year to 34 gallons per year. Assuming that in each case the change
was linear, during what year were the 2 consumption rates equal?
A.
B.
C.
D.
E.
1981
1982
1983
1984
1985
36. In a group of 64 students, 40 are freshmen. What percentage of the group are
freshmen?
A.
B.
C.
D.
E.
1.6%
16%
25%
40%
62.5%
37.
Of the 50 people in a music store, 35 of them own a cassette tape player. If 1 of
those 50 people is randomly selected to win a cassette tape, what is the probability
that the person chosen will already own a cassette tape player?
A.
B.
C.
D.
E.
.70
.65
.35
.30
.15
38. The volume of a certain gas at constant pressure is equal to a fixed number multiplied
by the absolute temperature. If that gas occupies 500 cubic centimeters when the
absolute temperature is 300, what is the volume, in cubic centimeters, when the
temperature rises 30 and the pressure kept constant?
F.
G.
H.
J.
K.
18
50
198
550
883 1/3
39. Given the information in the diagram below, including the fact that BCD is
isosceles, how many feet long is AB ?
F.
G.
H.
J.
K.
5 6
10
10 2
10 3
20
40. A parabola can be defined as the set of points equidistant from a focus point and a
directrix line. What is the distance, in units, between the focus F and the point P that
are graphed in the standard (x,y) coordinate plane below?
A.
B.
C.
D.
E.
4
2 5
6
4 5
20
41. If the radius of the circle below is 4 feet, what is the area of the shaded portion of the
circle, in square feet?
F.
G.
H.
J.
K.

4
6
8
12
16
42. Points A, B, C, and D are on the circle below with center at X and radius of 12
inches. The length of DB equals the length of XB . What is the length, in inches, of
arc DCB?
A.
B.
C.
D.
E.

4
8
20
24
48
43. In the figure below, A lies on CQ , P lies on QB , and AP is parallel to CB . If AP
is 5 units long, PQ is 3 units long, and CB is 15 units long, how many units long is
PB ?
F.
G.
H.
J.
K.
5
6
9
12
15
44. In the figure below, l1 is parallel to l2, l3 is parallel to l4, and the lines intersect as
shown. What is the measure of angle z?
A.
B.
C.
D.
E.
110
120
130
140
Cannot be determined from the given information
45. What is the number of degrees the hour hand of a clock moves in 10 hours?
A.
B.
C.
D.
E.
100
120
150
220
300
46. In the standard (x,y) coordinate plane below, POQ and SRQ are isosceles right
triangles with equal areas. Points O, P, Q, and R are located on the axes as shown.
Which of the following could be the coordinates of point S?
F.
G.
H.
J.
K.
( 0,14)
( 7, 0)
( 7,14)
(14, 0)
(14, 7)
47. Two strips of tape are to be used to wrap a box, as shown below. Both strips must go
completely around the box. What is the minimum length of tape, in centimeters
(cm), required to wrap the box?
F.
G.
H.
J.
K.
102
112
144
204
244
48. In the figure below, 3 parallel lines are crossed by 2 transversals as shown. the
points of intersection and some distances, in inches, are labeled. What is the length,
in inches, of YX ?
F. 1
G. 2
H. 3
J. 32
K. 52
49. The figure below shows square OABC and also shows the circle centered at O with
radii OC and OA . If the area of the square is 36 square units, what is the area of the
circle, in square units?
A.
B.
C.
D.
E.
12
18
36
72
81
50. A forest begins 300 feet from the center of the base of a vertical television tower,
across level ground. If the tower is 400 feet tall, how many feet is it from the top of
the tower to the nearest edge of the forest at ground level?
A.
B.
C.
D.
E.
100 7
200 3
500
700
120,000
51. Trapezoid ABCD below is isosceles, with side lengths as marked. Its diagonals
intersect at E. What is the ratio of the length of AE to DE ?
F.
x
y
G. xz
H. 1
J. yz
K. zy
52. Vivian made 63 throws out of 89 attempts during the basketball season. What
percentage, to the nearest percent, of her free throws did she make during this season?
A.
B.
C.
D.
E.
41%
63%
71%
89%
98%
53. In the triangle shown below, what does the x represent?
F.
G.
H.
J.
K.
42
64
69
74
Cannot be determined from the given information.
54. If all angles in the figure shown below are right angles and each dimension given is in
inches, then what is the area of the figure, in square inches?
A.
B.
C.
D.
E.
35
44
62
83
96
55. The dimensions of parallelogram ABCD, shown below, are given in centimeters.
What is the area, in square centimeters, of parallelogram ABCD ?
F.
G.
H.
J.
K.
25
36
40
50
80
56. On the number line below, what is the coordinate of the point between A and B that is
twice as far from point A as from point B ?
57. Two lookout towers are located about 7 miles apart, at the same elevation. A fire is
sighted at angles of 37 and 42 from the line of sight between the towers, as
indicated in the diagram below. Which of the following expressions, if any, gives the
approximate distance, in miles, between the fire and tower A ?
(Note: The law of sines states that the ratio between the length of the side opposite an
angle and the sine of that angle is the same for all interior angles in the same triangle)
F.
G.
H.
J.
K.
The distance cannot be approximated without more information.
37 2  42 2
7 cos 42
cos101
7 tan 42
7 sin 42
sin101
58. In the figure below, the perpendicular bisectors of XY and XW meet at P.
Given the information above, a circle with center P and radius PX must pass through
which of the labeled points?
A.
B.
C.
D.
E.
X only
W and X only
Y and X only
W, X, and Y only
W, X, Y, and Z
59. to keep up with rising expenses, a motel manager needs to raise the $40.00 room rate
by 22%. What will be the new rate?
F.
G.
H.
J.
K.
$40.22
$42.20
$48.00
$48.80
$62.00
60. The total cost of renting a car is $30.00 for each day the car is rented plus 28 ½ ¢ for
each mile the care is driven. What is the total cost of renting the car for 5 days and
driving 350 miles?
(Note: No sales tax is involved.)
A.
B.
C.
D.
E.
$ 104.75
$ 159.98
$ 249.75
$ 300.00
$1,147.50
61. In the isosceles right triangle below, AB = 10 feet. What is the length, in feet, of AC ?
A.
B.
C.
D.
E.
5
10
20
20
10 2
62. In the standard (x,y) coordinate plane, a line segment has its endpoints at (3,6) and
(9,4). What are the coordinates of the midpoint of the line segment?
A.
B.
C.
D.
E.
( 3, -1)
( 3, 1)
( 6, 2)
( 6, 5)
(12,10)
63. The lengths of the corresponding sides of 2 similar right triangles are in the ratio of
2:5. If the hypotenuse of the smaller triangle is 5 inches long, how many inches long
is the hypotenuse of the larger triangle?
F.
2
G. 2.5
H. 7
J. 10
K. 12.5
64. In the figure below, ABCD is a square. Points are chosen on each pair of adjacent
sides of ABCD to form 4 congruent right triangles, as shown below. Each of these
has one leg that is twice as long as the other leg. What fraction of the area of square
ABCD is shaded?
A.
B.
C.
D.
E.
1
9
2
9
4
9
5
9
8
9
65. In ABC, shown below, the measure of B is 41, the measure of C is 34, and
AB is 25 units long. Which of the following is an expression for the length, in units,
of BC ?
(Note: The law of sines states that, for any triangle, the ratios of the sines of the
interior angles to the lengths of the sides opposite those angles are equal.)
A.
B.
C.
D.
E.
25 sin105
sin 41
25 sin105
sin 34
25 sin 75
sin 41
25 sin 41
sin105
25 sin 34
sin 75
66. In the pentagon ABCDE, shown below, A measures 50. What is the total measure
of the other 4 interior angles?
F.
G.
H.
J.
K.
130
200
310
432
490