Geometry Sample Test

1.In the figure, JL = JK, QK = QS,

SRL = 105o, QRS and QLK are straight lines. Q = Xo. X = ?

(A) 10 (B) 30 (C) 70 (D) 75 (E) 85

2. The sum of all but one of the interior angles of a convex polygon is 2570o. The remaining angle is:

(A) 90o (B) 105o (C) 120o (D) 130o (E) 144o

3.Which of the following statements about the diagonals of a rectangle is (are) true?

i They are perpendicular

ii They are congruent

iii They bisect each other

(A) just ii (B) just i and ii (C) just i and iii (D) just ii and iii
(E) all three

4.A seesaw is balanced at its center at a point 3 feet above the ground. What is the highest that either end can rise above the ground?

(A) 3 ft. (B) ft. (C) 4 ft. (D) 5 ft. (E) 6 ft

5. A rectangular fish tank 25" by 9" has water in it to a level of 2". This water is carefully poured into a cylindrical container with a diameter of 10". How high, in terms of p, will the water reach in the cylindrical container?

(A) 18p (B) p / 18 (C) 18 / p (D) 9 / 2p (E) 9p / 2

6. Sides AB, BC, CD, and DA of convex quadrilateral ABCD have lengths 3, 4, 12, and 13, respectively. If angle CBA is a right angle, what is the area of the quadrilateral?

(A) 32 (B) 36 (C) 39 (D) 42 (E) 48

7.In the diagram, POS is a line through the center, O, of a circle with radius r cm. The line PQR is drawn so that PQ is of length r cm. If ROS has a measure of 60o , then what is the degree measure of OPQ?

(A) 10 (B) 15 (C) 25 (D) 30 (E) 20

8. A plane figure consists of a circle and two lines that are parallel tangents to the circle. How many points are equidistant from the circle and the two lines?

(A) 1 (B) 2 (C) 3 (D) infinite (E) none of these

Check your answers

Answers

1.A, 2.D, 3.D, 4.E, 5. C, 6.B, 7.E, 8.C