2006 Geometry Form A Page 1


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1 2006 Geometry Form Page 1 1. he hypotenuse of a right triangle is 12" long, and one of the acute angles measures 30 degrees. he length of the shorter leg must be: () 4 3 inches () 6 3 inches () 5 inches () 6 inches (E) 7 inches 2. he sum of the measures of all of the nonoverlapping angles formed by 7 rays drawn on the same side of a line from the same point of that line is (?) () 1260 () 1080 () 900 () 360 (E) How many degrees are there in an angle that measures oneninth of its complement? () 810 () 162 () 81 () 80 (E) 9 4. Each interior angle of a regular octagon is: () 120 () 144 () 135 () 140 (E) Which of the following is true if two given triangles are not similar? () their areas cannot be equal () they may be congruent () they are not congruent () their corresponding sides may be proportional (E) their corresponding angles may be equal 7. he points (1,2), ( 4,3) and (7, 6) are three vertices of a parallelogram. he fourth vertex is: () (12, 2) () (2, 11) () ( 11,5) () all of these 8. triangle and a rectangle have equal areas. he base and height of the triangle are 12 and 4, respectively. Find the width of the rectangle if its length is 8. () 3 () 4 () 5 () 6 (E) 7 5. is a rhombus with = 5, and = 6. What is the length of? () 8 () 9 () 10 () 11 (E) rectangle has length x units and width y units. he rectangle has the same perimeter as an equilateral triangle with a side of m units. Find x in terms of m and y. () m + y () 3m  2y () 1 2 m + y (E) 1 2 () m  y (3m 2y)
2 2006 Geometry Form Page he side of a cube is decreased by 50%. y how much does the volume decrease? () 12.5% () 25% () 50% () 75% (E) 87.5% 15. If a quadrilateral is inscribed in a circle, the opposite angles are: () congruent () complementary (E) supplementary () obtuse () acute 11. If the circumference of a circle is 12π feet, what is the number of square feet in its area? () 6π () 9π () 36π () 81π (E) 144π 12. What is the area of a circle inscribed in a square that has a side length of 8 cm? () 8π cm 2 () 16π cm 2 () 32 π cm 2 () 64π cm 2 (E) 48π cm In circle, minor arc XK is 1 / 3 of the circumference of the circle. If F is not on minor arc XK, what is the measure of inscribed angle XFK? () 60 () 30 () 15 () 120 (E) Find the area of the shaded part of the figure: () 25cm 2 () 50cm 2 () 35cm 2 () (E) circle can be inscribed in: () any triangle () any octagon () any trapezoid () any polygon (E) any parallelogram 17. he area of a trapezoid is 160 square units, one base is 26 units, and the height is 8 units. What is the length of the other base? () 7 () 14 () 56 () 6 (E) 80 / square piece of paper, with one side equal to 12 units, is folded so that the four corners of the square meet in the center of the square. his forms a new square. What is the side measure of the new square? () 5 () 5 3 () 6 2 () 6 (E) he diameter of the front wheel of a tricycle is 8" and the diameter of each rear wheel is 3". How many revolutions has each back wheel made while the front wheel has turned 1440 degrees? () () 4 () () 24 (E) 96
3 2006 Geometry Form Page circular track has a radius of 210 feet. pproximately how many times must a jogger circle the track in order to jog one mile? () 20 () 4 () 35 () 39 (E) he set of points in a plane at a fixed distance from a given point in that plane is: () a line () a circle () an angle () two lines (E) a point 21. he value of Β is: () 3.14 () () () he area of a circle inscribed in an equilateral triangle is 4π. What is the height of the triangle? () 2 () 4 () 6 () 8 (E) he sum of the exterior angles of any polygon will always be what measure? () 180 () 360 () (n 2) 180 () (n + 2) he area of a square 18 ft. on a side is equal to the area of a rectangle with a length of 3 yards. he width of this rectangle is: () 2 ft. () 9 ft. () 18 ft. () 36 ft. (E) 27 ft. 26. he radii of two circles are 3 cm and, respectively. Find the radius of the circle whose area is equal to the sum of the areas of the two given circles. () 8 () 34 () 34 () 34π 27. hree lines lie in one plane. Line m intersects line n which is parallel to line p. How many points are equidistant from all three lines at the same time? () 2 () 1 () 0 () 4 (E) sector of a circle has the same area as an equilateral triangle whose base is 12. What is the area of the sector? () 6 3 () 36 3 () 12 () he number of points on a circle that are equidistant from the endpoints of a given diameter is: () 1 () 2 () 3 () 4 (E) 5
4 2006 Geometry Form Page he radius of a circle is increased by 50%. y how much does the area increase? () 25% () 50% () 100% () 125% (E) 250% 33. Given line Q which goes through the center of a circle with center, whose radius is 4 and P lies on the circle. If P = 4 and Q =4 find the measure of the angle x = πpq. () x < 20 () 20 # x < 30 () 30 # x < 40 () 40 # x < 50 (E) x In the figure, =, =, π = ½ π, and π = 70. How many degrees are there in π? () 55 () 70 () 105 () 110 (E) QRS is a quadrilateral with Q S and QR RS as shown in the figure below. If Q = 70m, SR = 200m, and S = 240 m, how many square meters are there in quadrilateral QRS? S Q 34. wo sides of a triangle are 12 cm and 8 cm, respectively. he altitude to the 12 cm side is 4 cm. Find the altitude to the 8 cm side. () 3 cm () 24 cm () 12 cm () 6 cm (E) 8 / 3 cm 35. Given quadrilateral PQRS inscribed in a circle with side PQ extended beyond Q to point. How many degrees are in πqr if πqps = 110 degrees, & πpsr = 40 degrees? () 30 () 70 () 140 () 40 (E) In the figure below,,, = 8, = 5, = 4. What is the shortest distance from to? R () 2340 () () () (E) () 12 () 13 () 15 () 16 (E) 17
5 2006 Geometry Form Page What is the effect on the volume of a cylinder if the diameter is doubled and the height is cut in half? () the volume remains the same () the volume is doubled () the volume is cut in half () the volume increases by a factor of four 39. point P is selected at random on a semicircle with diameter RS. is the foot of the perpendicular from P to RS. If RS = 6 and R = x, then the length of P in terms of x is: R P S ( ) 6x x ( ) 6x 2x ( ) 3 x ( ) 3 2x ( E) 2x x What is the length of F in this cube that has edges 1 cm long? 40. In the figure below, the large circle has diameter. he two small circles have their centers on and are tangent to each other at the center of the large circle. Find the area of the shaded region, given that = 4. F () 3 () () () 2 O () 16π () 4π () 2π () 1π O
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