Download Test - FloridaMAO

January Regional
Geometry Individual Test
1. Find the sum of a + b + c + d
a
52
51
b
d
c
A. 167
B. 103
C. 257
D. Cannot be determined
E. NOTA
2. If Izzi lives in Chicago, then she lives in Illinois. If a person lives in Illinois, then she lives in the Midwest.
Given these conditionals, according to the law of syllogism, what must be true?
A. If Izzi lives in Illinois, then she lives in the Midwest.
B. If Izzi doesn’t live in Chicago then she lives in the Midwest.
C. If Izzi lives in Chicago, then she lives in the Midwest.
D. If Izzi lives in Chicago, then she does not live in the Midwest.
E. NOTA
3. An isosceles trapezoid has legs of length 30 cm each, two diagonals of length 40 cm each and the longest
base is 50 cm. What is the height of the trapezoid?
A. 25
B. 30
C. 40
4. Triangle ABC has measured sides of
A. Obtuse
B. Right
C. Acute
D. 24
E. NOTA
23 , 2 6 , and 7. Classify the triangle.
D. Not a triangle
E. NOTA
5. A rectangle has the following measurements. One side must be an odd integer. Find the perimeter.
4y + 8
y
x2
20x-16
A. 56
B. 106
C. 138
D. 122
E. NOTA
6. The sum of all of the interior angles of seven polygons is 180(17). Find the total number of sides of the
seven polygons.
A. 19
B. 30
C. 15
D. 62
E. NOTA
7. The measure of a complement of an angle is 222 degrees less than twice the measure of its supplement.
What is the difference between the supplement and the compliment of the original angle?
A. 42
B. 132
C. 90
D. 48
E. NOTA
8. Given the perimeter of the symmetric shape below is 50, find the area.
x+9
x
x+3
2x+10
A.
B.
C.
D.
E. NOTA
9. In the figure below, what is the length of x?
A.
B. 6
C.
D.
E. NOTA
10. An equilateral triangle has sides that are 1 inch long. An ant walks around the triangle maintaining a
distance of 1 inch from the triangle at all times. How far in inches does the ant walk?
A. 9
B. 3 + π
C. 9 + π
D. 3 + 2 π
E. NOTA
11. A lattice point is a point on the coordinate plane with integer values for x and y. How many lattice points
lie on a circle with radius 25 and center at the origin?
A. 4
B. 8
C. 12
D. 15
E. NOTA
12. What is the slope of the line passing through (3,7) and (11, 23)?
A. .5
B. 2
C. – 2
D. -.5
E. NOTA
13. A regular polygon has 1484 diagonals. How many sides does it have?
A. 53
B. 56
C. 28
D. 742
E. NOTA
14. In the diagram below, the outer circle has radius 3, and the inner circle has radius 2.
What is the area of shaded region?
A. 2 2
B. 10
C. 4 2
D. 3 2
E. NOTA
15. If two angles are obtuse, then both are not supplementary. This is the inverse of the converse of what
conditional?
A. If two angles are supplementary, then they are obtuse.
B. If two angles are obtuse, then they are supplementary.
C. If two angles are supplementary, then both are not obtuse.
D. If two angles are not supplementary, then both are obtuse.
E. NOTA
16. A parallelogram has 3 of its vertices at (1,2), (3,8), and (4,1). Compute the sum of the possible xcoordinates for the 4th vertex.
A. 0
B. 8
C. 11
D. 16
E. NOTA
17. If there are 12 people sitting around a table, how many different pairs of people can have conversations
during dinner, assuming they can all talk to each other?
A. 24
B. 132
C. 68
D. Not enough information
E. NOTA
18. Given triangle PQR with measure angle P = 90º, PQ = 20 inches and PR = 15 inches, find the sum of the
area of the triangle, the length of the hypotenuse and the length of the altitude to the hypotenuse.
A. 331
B. 337
C. 787
D. 187
E. NOTA
19. AGH, ABFG and BCDEF are all regular polygons with side congruency as shown. Find the measure of
angle HFD.
E
G
F
D
H
A
B
C
A. 132º
B. 101º C. 147º D. 76º
E. NOTA
20. Jorge was having a grand time balancing his obtuse triangle on the point of his pencil. At which point of
concurrency would Jorge’s pencil have to be located to accomplish this feat?
A.
Centroid
B. Incenter
C. Circumcenter
21. Given square ABCD of side length 1, with E on
perpendicular to
and
A.
E. NOTA
and F on the interior of the square so that
C.
D.
E. NOTA
is tangent to circle Q. The measure of arc BC is 84º. What is the measure of
angle AQB?
B
A
C
Q
A. 76º
B. 90º
C. 84º
D. 6º
E. NOTA
23. ABCDE is a regular pentagon. ABFG is a square. Find the measure of angle GAD.
D
F
G
E
C
B
A
A. 18º
B. 36º
C. 72º
D. Not enough information
24. If b = 2a + 1, then a > ?
M
a
b
34
N
L
K
A. 10
B . 11
is
. Find the area of quadrilateral ADEF.
B.
22. In the figure below,
D. Orthocenter
C. 12
D. 17
E. NOTA
E. NOTA
25. John stands against one wall of a square room with walls of length 4 meters each. He kicks a frictionless,
perfectly elastic ball in such a way that it bounces off the three other walls once each and returns to him. How
many meters does the ball travel?
A. 16
B. 16
C. 64
D. 8
E. NOTA
26. What is the area of the incircle of a triangle with side lengths 10040, 6024, and 8032?
A. 4032064π
B. 2008π
C. 4016
D. 2008²
E. NOTA
27. An equilateral triangle has perimeter numerically equal to its area, which is not zero. Find its side length.
A. 1
B. 4
C.
D. 4
E. NOTA
28. A rectangular field has a length that is 2 more than 6 times its width. The field has a perimeter of 242
feet. In order for the field to be used for a horseshoe tournament, the width must be narrowed by 10 feet.
What is the area (in square feet) of that part of the field that will be used for the tournament?
A. 1598
B. 728
C. 1728
D. 119
E. NOTA
29. Find the measure of each internal angle of a 20-gon.
A. 180
B. 81
C. 160
D. 162
E. NOTA
30. Quadrilateral ABCD located at A(-5, -2), B(10, 3), C(6, 5), D(-3, 2) is a
A. Trapezoid
B. Rectangle
C. Parallelogram
D. Rhombus
E. NOTA