Practice Test Student Answer Document

Practice Test Student Answer Document Record your answers by coloring in the appropriate bubble for the best answer to each question. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 Mastering the EOI, Geometry 37

Practice Test 1 Which of the following can serve as a counterexample to the assertion that two lines that are not parallel always intersect? A intersecting lines B parallel lines C perpendicular lines D skew lines 3 If a and b are both negative numbers, which of the following expressions must also be negative? A a _ b B a + b C a - b D 3ab 2 The net of a cylinder is shown below as two congruent circles and a square. 4 Transversal t cuts parallel lines a and b. a b 1 2 5 4 t If the radius of the circles is 1 cm, then what is the surface area to the nearest tenth of a square centimeter? (Use π 3.14.) F 16.2 cm 2 G 18.8 cm 2 H 45.8 cm 2 J 59.2 cm 2 SA = 2π r 2 + 2πrh What is m 4 if m 1 = 80? F 10 G 80 H 90 J 100 5 Which of the following is another name for a regular triangle? A an obtuse triangle B a right triangle C an equilateral triangle D a scalene triangle Mastering the EOI, Geometry 39

6 A pentagonal prism has how many faces? F 5 G 7 H 10 J 15 10 Trey placed a rectangular box in an empty cylindrical can. 30 in. 6 in. 24 in. 10 in. 7 A triangle has a base 12 inches long and an area of 36 square inches. What is the length of the altitude to the base side? A 3 in. B 4 in. C 5 in. D 6 in. 8 The diagonals of a rhombus are perpendicular. If the slope of one diagonal is -_ 3, what is the slope of 2 the other diagonal? F -1 H _ 2 3 G -_ 3 J _ 3 2 2 9 The hypotenuse of a 30-60 -90 right triangle measures 30 inches. What is the length of the side opposite the 60 angle? A 10 3 in. B 15 in. C 15 2 in. D 15 3 in. 8 in. What is the volume of the empty space in the can to the nearest cubic inch? (Use 3.14 for π.) V (cylinder) = π r 2 h V (rectangular prism) = lwh F 3,840 in 3 G 13,085 in 3 H 16,800 in 3 J 53,779 in 3 11 What is the measure of each exterior angle of a regular octagon? A 8 B 45 C 135 D 1080 40 Mastering the EOI, Geometry

12 Triangles ABC and DEC are similar with AD = 6, DC = 12, AB = 6, and BE = 4. 14 A truck tire has a diameter of 3 feet. How far will the truck travel with 20 rotations of the tire? What is the perimeter of DCE? F 24 G 28 H 32 J 36 15 F 30π ft G 60π ft H 120π ft J 180π ft C = 2πr 13 All rectangles are parallelograms. Which of the following is the conditional form of the above statement? A If a figure is a parallelogram, then it is a rectangle. B If a figure is a rectangle, then it is a parallelogram. C A figure is a parallelogram if and only if it is a rectangle. D If a figure has 4 sides, then it is both a rectangle and a parallelogram. 24 ft What is the height of the flagpole shown above to the nearest tenth of a foot? A 16.0 ft B 19.9 ft C 29.7 ft D 36.0 ft cos x 0.55 sin x 0.83 tan x 1.50 Mastering the EOI, Geometry 41

16 18 A conical pile of sand has a height of 5 meters and a diameter of 12 meters. How many cubic meters of sand are in the pile? V = 1 _ 3 π r 2 h If triangle EFG is rotated 270 clockwise about the origin, what are the coordinates of G? F (-2, 4) G (-2, -4) H (-4, 2) J (2, -4) F 20π cubic meters G 50π cubic meters H 60π cubic meters J 240π cubic meters 19 A rectangular prism has 12 edges. What is the maximum number of edges parallel to each other? 17 Point G is the midpoint of FH. Given F (-2, 3) and G(1, 4), what are the coordinates of point H? Midpoint between 2 points P 1 (x 1, y 1 ) and P 2 (x 2, y 2 ): (_ x 1 + x 2,_ y 1 + y 2 2 2 ) A (-0.5, 3.5) B (3.5, -0.5) C (4, 5) D (5, 4) 20 A 12 edges B 8 edges C 4 edges D 2 edges 12 37 35 Which ratio represents cos P? F _ 12 H _ 35 35 37 G _ 12 J _ 35 37 12 42 Mastering the EOI, Geometry

21 Which of the following could be the lengths of the three sides of a right triangle? A 11, 11, and 22 B 3, 5, and 8 C 2, 4, and 10 D 3, 5, and 8 23 A triangle cannot have an obtuse angle. Which of the following could provide a counterexample to the above statement? A scalene triangle B right triangle C equilateral triangle D acute triangle 22 In the circle, m BD = 24, m BAD = 32, secants BC and DE intersect at point A. 24 Quadrilateral LMNP is a parallelogram. What is m CE? m QPS = 1 _ 2 ( m RT - m QS ) F 4 G 40 H 68 J 88 What are the coordinates for the midpoint of either diagonal? Midpoint between two points P 1 (x 1, y 1 ) and P 2 (x 2, y 2 ): (_ x 1 + x 2,_ y 1 + y 2 2 2 ) F (6, 4) G (3, 2) H (2.5, 2) J (2.5, 0) Mastering the EOI, Geometry 43

25 In the figure, AE bisects BD. 1 2 3 4 5 Which of the following is not sufficient to prove that ABC and EDC are congruent? A AC CE B 2 5 C AB DE D 1 2 6 27 If the sum of the measures of two angles equals 90, then the two angles are complementary. If m A = 20 and m B = 70, which of the following is a logical conclusion? A m A + m B = m C B A and B are interior angles of a triangle. C A and B are vertical angles. D A and B are complementary. 28 Line a cuts across lines b and c. b c 26 The hypotenuse of a right triangle has a length of 8 and one leg has a length of 5. What is the exact length of the other leg? F 3 G 13 H 39 J 89 (3) (2 17) For what value of x will lines b and c be parallel? F 3.4 G 17 H 32.6 J 51 a 44 Mastering the EOI, Geometry

29 Triangle ABC is a right triangle and AC = 8. 31 Point C is the center of the circle, and m CAB = 25. What is the exact value of x? A 2 B 4 2 C 16 2 D 8 What is m ADB? A 25 B 100 C 130 D 230 30 Triangle ABC is to be translated to A B C by using the following rule. (x, y) (x - 2, y + 3) What will be the coordinates of point B? F (-3, 5) G (2, 0) H (1, 5) J (2, 0) 32 In right triangle DEF, e = 4 3 and m D = 30. 30 What is the value of f? F 8 G 12 H 8 3 J 16 Mastering the EOI, Geometry 45

33 Quadrilateral WXYZ is a kite. 35 In the figure, DE AC. 14 8 26 What is the length of ZY? A 14 in. B 16 in. C 26 in. D 29.5 in. Which could be used to prove that ABC is similar to DBE? A ASA B SSA C AA D SSS 34 A kite is flying so that the string makes a 55 angle with the ground. 400 ft 55 How high above the ground, to the nearest foot, is the kite if 400 feet of string has been released? F 228 ft G 328 ft h sin 55 0.82 cos 55 0.57 tan 55 1.43 H 488 ft J 572 ft 36 Each face on a cubical block of ice has an area of 81 square inches. A salt block is in the shape of a cube congruent to the block of ice. What is the volume of the salt block? F 9 in 3 G 27 in 3 H 81 in 3 J 729 in 3 V = s 3 46 Mastering the EOI, Geometry

37 The base of a pyramid is a square. 5 cm 6 cm What is the volume of the pyramid? V = 1 _ 3 Bh 39 In a model of the solar system, Earth has a diameter of 15 inches and Mars has a diameter of 9 inches. What is the ratio of their surface areas? A 5 to 3 B 25 to 9 C 125 to 27 D 8 to 1 A 10 cm 3 B 30 cm 3 C 50 cm 3 D 150 cm 3 40 Chords EF and GH intersect at K, EK = 3, FK = 10, and HK = 12. 12 3 10 38 What is the degree measure of 2 if m 1 = (3x + 9) and m 2 = (5x + 3)? F 18 G 21 H 72 J 108 1 2 What is the value of GK? F 1 G 2.5 H 4.5 J 6 Mastering the EOI, Geometry 47

41 43 Transversal p cuts parallel lines m and n. 3 1 2 4 n What type of polyhedron is shown above? A pentagonal pyramid B pentagonal prism C hexagonal prism D octagonal pyramid 42 What is the distance between point H and point J? Distance between two points P 1 (x 1, y 1 ) and P 2 (x 2, y 2 ): F 50 G 34 H 32 J 10 ( x 2 - x 1 ) 2 + ( y 2 - y 1 ) 2 p 5 7 8 6 Which of the following names all the angles that must be congruent to 7? A 6, 4, 2 B 8, 4 C 5, 3, 1 D 6, 3, 2 44 The net of a triangular prism is composed of which shapes? m F 3 rectangles and 2 triangles G 2 rectangles and 3 triangles H 4 rectangles and 2 triangles J 3 rectangles and 1 triangle 45 What type of triangle is formed by the points P(3, 4), Q(2, 1), and R(4, 1)? A isosceles B right C scalene D equilateral 48 Mastering the EOI, Geometry

46 Triangle ABC is similar to XYZ. 8 10 16 What is the length of XY? F 8 G 10 H 12.8 J 20 47 In the right triangle, m Q = 17 and NP = 23. 23 17 Which equation could be used to find the value of x? 23 A x = _ sin 17 23 B x = _ cos 17 tan 17 C x = _ 23 D x = 23 tan 17 48 The measure of two complementary angles are given by (2x - 7) and (5x - 1). What is the measure of the larger angle? F 14 G 21 H 69 J 133 49 If B is between A and C, then AB + BC = AC. Which of the following is the inverse of this statement? A If B is not between A and C, then AB + BC AC. B If AB + BC = AC, then B is between A and C. C If AB + BC AC, then B is not between A and C. D If B is not between A and C, then AB BC. 50 Which could be the measurements for the three sides of an obtuse triangle? F 8 m, 12 m, 17 m G 21 cm, 28 cm, 35 cm H 7 ft, 8 ft, 71 ft J 20 in., 20 in., 26 in. Mastering the EOI, Geometry 49

51 In the figure below, BC DC and AC EC. 53 In circle O, AB is a diameter, CB is a chord, and m BC = 120. What theorem or postulate can be used to prove ABC EDC? A AAA B SSS C SAS D AAS 52 In the figure, line l is the perpendicular bisector of AB and AP BP. Suppose Q is another point on l. Which is a reasonable conjecture about this situation? F AQ AP G BQ BP H AQ BQ J APB AQB What is the measure of ABC? A 15 B 30 C 60 D 120 54 In the figure, BD is perpendicular to AC. 20 12 15 What is the length of AC? F 9 G 25 H 42.5 J 59 50 Mastering the EOI, Geometry

55 45 58 1 4 2 3 5 6 If a = 2 2, then what is the value of c? A 2 B 2 2 C 4 D 4 2 Which of the following would be sufficient to prove that ABC and DEF are similar? F AB DE G 1 6 H BC EF J 1 4 56 The top of a swimming pool is congruent to the circle at midcourt of a basketball court. If the midcourt circle has a radius of 6 feet, what is the circumference of the top of the swimming pool to the nearest tenth of a foot? (Use 3.14 for π.) F 12.0 ft G 18.8 ft H 37.7 ft J 113.0 ft 57 What is the slope of a line parallel to the line through (-4, -2) and (-1, 2)? A -_ 4 C _ 3 3 4 B -_ 3 D _ 4 4 3 59 10 cm 8 cm What is the surface area of this cylinder? A 96π cm 2 B 112π cm 2 C 160π cm 2 D 208π cm 2 SA = 2π r 2 + 2πrh Mastering the EOI, Geometry 51

60 In the figure, RS is a radius, ST is tangent to circle R at point S, and m RQS = 67. What is m QST? F 23 G 46 H 67 J 113 61 What is the most specific name for the quadrilateral represented by the points A(-3, -2), B(-2, 2), C(2, 1), and D(1, -3)? A parallelogram B rectangle C rhombus D square 62 The lengths of two similar rectangles are in a ratio of 1:2. If the area of the smaller rectangle is 12 square centimeters, what is the area of the larger rectangle? 63 F 12 cm 2 G 24 cm 2 H 36 cm 2 J 48 cm 2 32 cm 16 cm 12 cm A larger rectangular prism with a height of 40 centimeters is similar to the one above. What is the volume of the larger prism? A 6,144 cm 3 B 15,360 cm 3 C 64,000 cm 3 D 96,000 cm 3 52 Mastering the EOI, Geometry

64 ACB is inscribed in circle P, m AC = 70, and m CB = 160. What is the measure of ACB? F 35 G 65 H 80 J 130 66 The Ballerina is an 8 1 _ -foot tall statue 2 on display in the lobby of the Oklahoma City Civic Center. It honors Oklahoma s five American Indian ballerinas. If a spotlight is placed 4 feet perpendicular from its base, which ratio can be used to determine the angle of elevation, θ, to aim the light directly at the top of the statue? F sin θ = _ 4 8.5 G cos θ = 4_ 8.5 H tan θ = _ 4 8.5 J tan θ = _ 8.5 4 65 Consider the following two statements. (1) If a set is finite, then any subset of the set is finite. (2) The set of integers between -100 and 100 is finite. Which statement below follows logically from statements (1) and (2)? A The set of integers is finite. B The set of integers between -100 and 100 is not a subset of an infinite set. C A subset of the set of integers between -100 and 100 is also finite. D A subset of the set of integers between -100 and 100 is infinite. 67 A cone with a radius of 3 units is similar to a cone with a radius of 6 units. How many times greater is the volume of the larger cone than the volume of the smaller cone? A 2 B 4 C 8 D 216 Mastering the EOI, Geometry 53

68 Quadrilateral WXYZ is a square and XZ = 14 centimeters. 70 What is the perimeter of WXYZ? F 28 2 cm G 28 cm H 7 2 cm J 7 cm 69 Right triangles MNP and QRS are congruent. 5 17 12 What is the area of QRS? A 30 square units B 42.5 square units C 60 square units D 102 square units This figure is a net of which solid? F triangular-based pyramid G triangular prism H cone J rectangular prism 71 A cable is attached to a young tree to keep it perpendicular to the ground. The cable is attached to the tree 15 feet above the ground and tied to a stake that is placed 8 feet from the base of the tree. If an extra 2 feet of cable is needed to fasten the cable to the tree and the stake, then what is the minimum length of cable that is needed? A 14.7 ft B 17 ft C 19 ft D 25 ft 54 Mastering the EOI, Geometry

72 In the figure, AB AC. 74 Triangle QRS is isosceles. 1 4 90 2 3 5 6 Which of the following could be used to prove that ABD and ACD are congruent? F D is the midpoint of BC. G ABC is isosceles. H 1 5 J m 3 + m 5 = 180 16 What is the value of x? F 32 H 8 G 16 2 J 8 2 75 A 20-foot water slide at a local water park makes a 32 angle with the ground. 73 Maria and Kelly have glasses that are congruent cylinders 10 centimeters in diameter. If the volume of Maria s glass is 375π cubic centimeters, what is the height of Kelly s glass? A 3.75 cm B 15 cm C 37.5 cm D 75 cm V = π r 2 h 20 ft 32 What is the length of the ladder to the nearest tenth of a foot? A 10.6 ft B 12.4 ft sin 32 0.53 cos 32 0.85 tan 32 0.62 C 23.6 ft D 32.0 ft Mastering the EOI, Geometry 55