1. Lines l1 and l2 are parallel. Line l3 makes a 20 degree angle with
l1.
Line l3 cuts across line l2, making 4 angles. What is the sum of the two
largest of these 4 angles?
(A) 40 degrees
(B) 120 degrees
(C) 160 degrees
(D) 180 degrees
(E) 320 degrees
2. Lines l1, l2, and l3 form a triangle. Line l2 makes suplementary
angles with l3 that are equal to x and 5x. One of the angles of the
triangle is 40 degrees. The other two angles of the triangle are x and y.
What is the numerical value of y?
(A) 40 degrees
(B) 50 degrees
(C) 80 degrees
(D) 90 degrees
(E) 110 degrees
3. Sam is looking at two triangles. In one triangle, the 3 angles are 5x,
2x, and 3x. In the other triangle, the 3 angles are x,3x, and p. What is
the numerical value of p?
(A) 18 degrees
(B) 36 degrees
(C) 72 degrees
(D) 108 degrees
(E) 135 degrees
4. Draw a circle. Suppose D and A are two points on the circle so that
the arc D to A is 80 degrees. Draw the chord from D to A and draw a
diameter from D across the circle to a point M. What is the angle MDA?
(A) 40 degrees
(B) 50 degrees
(C) 60 degrees
(D) 70 degrees
(E) 80 degrees
5. The angle between two equal sides of a triangle is 80 degrees. What is
the angle opposite one of the equal sides?
(A) 100 degrees
(B) 50 degrees
(C) 40 degrees
(D) 20 degrees
(E) cannot be determined
6. Two lines cross forming 4 angles. Two of the angles are obtuse, and
two of the angles are acute. One acute angle is 9x - 10. The other acute
angle is 35 degrees. What is x?
(A) 15 degrees
(B) 10 degrees
(C) 9 degrees
(D) 5 degrees
(E) 4 degrees
7. A box has dimensions 30 inches by 12 inches by 7 inches. San has a lot
of cubes 3 inches on a side to put in the box. How many of these cubes
can Sam put in this box?
(A) 70
(B) 74
(C) 80
(D) 84
(E) 88
8. Sam has a cube that has surface area equal to 54 square inches. What
is its volume?
(A) 9 cubic inches
(B) 18 cubic inches
(C) 27 cubic inches
(D) 54 cubic inches
(E) 216 cubic inches
9. A circle has area equal to 2 pi. A square is inscribed in the circle.
What is the area of the square?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
10. The 5 angles of a pentagon are in the ratio 1:2:3:4:5. What is the
size of the smallest angle?
(A) 20 degrees
(B) 24 degrees
(C) 30 degrees
(D) 36 degrees
(E) 42 degrees
11. A small circle touches a larger circle in one point. The radius of
the smaller circle is 5. Draw the line connecting the centers of the
circles. Now in the smaller circle draw a radius perpendicular to this
line. This perpendicular radius meets the smaller circle at a point p. The
distance from p to the center of the larger circle is 13. What is the
area of the larger circle?
(A) 144 pi
(B) 100 pi
(C) 81 pi
(D) 64 pi
(E) 49 pi
12. A circle is inscribed in a square. The area of the circle is
36 pi square inches.
What is the perimeter of the square?
(A) 24 inches
(B) 48 inches
(C) 60 inches
(D) 72 inches
(E) 84 inches
13. Sam is required to add water to an empty cylindrical tank until it is
2/3 full.
The tank's height is 9 feet and its diameter is 12 feet.
How many cubic feet of water will be needed?
(A) 144 pi
(B) 216 pi
(C) 256 pi
(D) 324 pi
(E) 720 pi
14. Draw a quadrilateral by connecting the points (0,0),(5,0),
(2,4), (0,5), and back to (0,0). What is the area of this
quadrilateral?
(A) 15
(B) 18
(C) 21
(D) 24
(E) 27
15. Two right triangles have a side in common. This side is equal to 4.
In one of the triangles, the hypotenuse is given equal to 5. In the other
triangle, the length of the other leg is given as 3.
What is the perimeter of one of the triangles?
(A) 10
(B) 11
(C) 12
(D) 13
(E) 14
16. A square and a rectangle have the same perimeter. The Rectangle has
sides of length 2 and of length 16. What is the area of the square?
(A) 4
(B) 9
(C) 16
(D) 36
(E) 81
17. A regular hexagon is inscribed in a circle. The length of one side of
the hexagon is 10 inches. What is the diameter of the circle?
(A) 10 inches
(B) 12 inches
(C) 14 inches
(D) 18 inches
(E) 20 inches
18. In a triangle, the sum of two angles is 100 degrees. The third angle
is bisected. How many degrees is each bisected part?
(A) 30
(B) 40
(C) 50
(D) 60
(E) 70
19. A triangle is drawn in a circle, with one side being the diameter of
the circle. The radius of the circle is 5 inches, and one side of the
triangle is 8 inches. Find the shortest side of the triangle.
(A) 3
(B) 4
(C) 6
(D) 8
(E) cannot be determined
20. Two right triangles share an hypotenuse. The two legs of one
triangle are 6 inches and 8 inches.
The other triangle is a 60-30 right triangle. What is the length of the
shortest side of the other triangle?
(A) 3 inches
(B) 4 inches
(C) 5 inches
(D) 6 inches
(E) 7 inches
21. What is the distance between the points (3,10) and (9,4)?
(A) 7.5
(B) 8.5
(C) 9
(D) 10
(E) 12.5
22. Sam asked directions to Wallytown. He was told, "Go straight down
this road 16 miles, and take a 45 degree diagonal road for one mile. You
will be there. But Don't take that 90 degree left turn which is 8 miles
down the road. Because if you do you will have to go 6 miles before you
can turn right onto the same diagonal road where it begins."
Sam was confused by this advice, and took the left turn 8 miles down
the road. All the roads were absolutely straight lines. How many miles
out of the way did he go?
(A) 7
(B) 8
(C) 10
(D) 19
(E) 30
23. A tin can is an example of a cylinder. The radius of the circular
base of a tin can is the number r. The height of the can is the number h.
What is the surface area of the can, both inside and outside?
(A) 2 pi r (r + h)
(B) 2 pi r (2 r + h)
(C) 2 pi r ( r^2 + h)
(D) 2 pi r^2 (2 + h)
(E) 2 pi r^2 h
24. Sam was hired to cut a circular area in a large field. When he came
to collect his payment, he was told: "You cut a circular area only 10 feet
in diameter. I said I wanted a circular area with a 10 foot radius. Here
is $10 for the work you did so far. If you finish the job I'll pay you
the porportional amount."
Sam finished the work. How much more was he paid at the end of his
work. Assume the payment is in proportion to the area of grass cut.
(A) $10
(B) $20
(C) $26.67
(D) $30
(E) $36
25. A circle has radius r. Its area is given by the number F. Another
circle has radius equal to 2 r. What is its area?
(A) 2 pi r F
(B) 2 F
(C) 3.1416 F
(D) 4 F
(E) 6 F