2006 ACTM STATE GEOMETRY EXAM
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- Roxanne Jacobs
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1 2006 TM STT GOMTRY XM In each of the following you are to choose the best (most correct) answer and mark the corresponding letter on the answer sheet provided. The figures are not necessarily drawn to scale. 1. The length of a rectangle is 3 more than its width. If its perimeter is 24, what is its area? Not enough information. None of these 2. In the figure l, m, n are parallel lines with transversals s and t. If = 3, = 4, = 2x 3 and = x + 5 then = s t None of these l m n Problem 2 3. In the figure at the right, with angle measures indicated, what is the measure of?. 86 o. 94 o. 96 o. 104 o. None of these 4. ngle and angle are complementary angles and angle and angle are supplementary angles. Which of the following is/are true? Problem 3 I. m > m II. m m = 90 o III. m + m = 180 o. I and II only. I and III only. II and III only. I, II and III. None of these 5. In the figure = 4, = = and the area of Δ = 6. ind to the nearest hundredth None of these Problem 5
2 6. is the perpendicular bisector of and is the perpendicular bisector of. Which of the following is/are true? I. = II. III. bisects. I and II only. I and III only. II and III only. I, II, and III. None of these Problem 6 7. In the figure at the right, if and then m =. 36 o. 72 o. 108 o o. Not enough information Problem 7 8. How many vertices and edges does a prism have if it has 12 faces? nswers are written as (vertices, edges).. (18, 28). (20, 30). (22, 32). (16, 26). None of these 9. The contrapositive of the statement If is congruent to then = is. If is not congruent to then.. If = then is congruent to.. If then is congruent to.. If then is not congruent to.. None of these 10. The area of the polygon at the right is. 25½ ½. 25. None of these 11. The number of lines of symmetry in a regular octagon is Problem None of these
3 12. Δ is an isosceles triangle with. Which of the following is/are true? I. The centroid of the triangle lies on the angle bisector of. II. The altitude from vertex is a median of the triangle. III. The center of the circle that is tangent to the three sides of the triangle lies on the median drawn from.. I and II only. I and III only. II and III only. I, II, and III. None of these 13. regular polygon has 20 sides. The measure of an exterior angle of this polygon is. 36 o. 153 o. 18 o. 162 o. None of these 14. polygon on a geoboard has an area of If it has eleven pegs touching the geoband, how many pegs are in its interior? None of these 15. The diagonals of the quadrilateral are perpendicular. Which of the following could be true?. is a square. is a rhombus. is a kite. ither,, or might be true. None of these are true 16. The diagonals of the quadrilateral bisect each other. Which of the following is the most accurate?. is a rectangle. is a rhombus. is a parallelogram. is a kite. None of these 17. onsider the trapezoid at the right with and midpoints of and, respectively. If = 36, = 17, = 15, = 10 then = None of these Problem 17
4 18. and are chords in a circle intersecting at. If the measure of the arc P = 32 o and the measure of arc Q = 80 o then m is Q. 80 o. 56 o. 48 o. 24 o. None of these P Problem dart board consists of three concentric circles with diameters of 6 inches, one foot, and 18 inches. If a dart is thrown at and hits the board, what is the probability it lands in the shaded region? None of these. 1 4 Problem In Δ, and are medians intersecting at. The ratio of the area of Δ to the area of Δ is. 1 to 2. 2 to 3. 1 to 4. 1 to 3. None of these Problem In the figure at the right and are perpendicular to. If = 10, = 20, and = 18, then the area of Δ to the nearest hundredth is None of these Problem 21
5 22. In Δ, is an altitude, = 10, m = 60 o and m = 45 o. The perimeter of Δ, to the nearest hundredth, is None of these Problem What is the area, to the nearest hundredth, of the triangle at the right? Not enough information. None of these Problem cylinder has a radius of 3 inches and a height of 4 inches sits on a table. If a cone whose height is 12 inches is placed over the cylinder so that the top of the cylinder touches the inside of the cone and the base of the cone is on the table, what is the volume of the cone?. 24π in 3. 64π in 3. 81π in 3. 36π in 3. None of these Problem In the figure m G > m G andg. Which of the following is/are true? I. m G > m G II. G > III. > G.. I and II only. I and III only. II and III only. I, II, and III G. None of these Problem 25
6 Geometry Tie reaker Questions Name _ School _ The following questions will be used only in breaking ties for first, second or third place. e sure you answer all the questions on the test before attempting these questions. They will be used in the order given to break the ties. 1. In the figure at the right, what is the length of, to the nearest tenth of an inch? 54 in 32 Tie reaker #1 47
7 Geometry Tie reaker Questions Name _ School _ 2. In the figure at the right and. = 5, = 7, = 15, = 8, = 4. ompute. Tie reaker #2
8 Geometry Tie reaker Questions Name _ School _ 3. The edges of a pyramid with a square base are all equal. plane parallel to the base passes through the pyramid at the midpoint of the altitude of the pyramid. If an edge of the pyramid is 12 inches, what is the volume of the part of the pyramid that lies below the plane (the shaded portion)? 12 in Tie reaker #3
9 KY GOMTRY
10 GeometryTie reaker Questions Name KY _ School _ The following questions will be used only in breaking ties for first, second or third place. e sure you answer all the questions on the test before attempting these questions. They will be used in the order given to break the ties. 1. In the figure at the right, what is the length of, to the nearest tenth of an inch? = 54sin 32 o = 54sin 32 o /tan 47 o = 54cos 32 o = = 19.1 in in Tie reaker # In the figure at the right and. = 5, = 7, = 15, = 8, = 4. ompute. Δ Δ 4( 15) =. = = Tie reaker #2 8( 12) =. = = = = 24 5 = The edges of a pyramid with a square base are all equal. plane parallel to the base passes through the pyramid at the midpoint of the altitude of the pyramid. If an edge of the pyramid is 12 inches, what is the volume of the part of the pyramid that lies below the plane (the shaded portion)? The dimensions of the top square will be 6 x 6. The altitude of the pyramid on top is 3 2. The altitude of the large pyramid is 6 2. Volume (top pyramid) = 36(3 2 )/3 = 36 2 in 3. Volume(large pyramid) = 144(6 2 )/3 = in 3. Volume (bottom) = = in 3 Tie reaker #3 12 in
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