Geometry H Semester 2 Practice Exam

Transcription

1 1. tire has a radius of 15 inches. What is the approximate circumference, in inches, of the tire?. 47 in.. 94 in in. D. 707 in. 2. In the figure below, adjacent sides of the polygon are perpendicular What is the perimeter of the figure? rectangular garden is to be edged with decorative brick as shown by the shaded region in the figure. The flower garden is 4 feet by 12 feet. The trapezoids are 2 feet high. 4 ft What is the area of the decorative edge (the shaded region) in square feet?. 20 ft ft ft 2 D. 48 ft 2 8 ft 12 ft 2 ft D The length of a rectangular patio is 32 feet. Its area is 800 square feet. What is the perimeter of the patio in feet?. 25 ft. 57 ft. 114 ft D. 368 ft GO ON

2 5. Given the figure below: V H F D What is the best description of VF?. altitude. base edge. lateral edge D. slant height 6. The surface area of a cylinder is 2 (rea of ase) + (ircumference of the ase) height. In the cylinder below, the radius is 4 centimeters and surface area is 72π square centimeters. What is the height of the cylinder?. 4 cm. 5 cm. 6 cm D. 9 cm GO ON

3 7. regular pyramid has height of 6 inches and the measure of the base edge is 7 inches. Volume = 1 3 (rea of ase) height 6 in. 7 in. What is the volume of the pyramid?. 49 in in in. 3 D. 294 in What is the volume of the cone below? Volume = 1 3 (rea of ase) height 12 in. 4 in.. 192π in π in π in. 3 D. 48π in GO ON

4 9. group of students wants to make a fabric toy ball to donate to the canine rescue. The diameter of the ball is 3 inches. Surface area = 4 (rea of a Great ircle). pproximately how many square inches of fabric will they need for each ball?. 29 in in in. 2 D. 114 in cereal box is 18 inches by 3 inches by 12 inches. fter breakfast, the box is one-third full. Volume = (rea of ase) height How many cubic inches of cereal are left inside?. 36 in in in. 3 D. 648 in GO ON

5 11. Two similar rectangular prisms have a scale factor of 4:1. The smaller prism has a volume of 6 cubic centimeters. What is the volume of the larger prism in cubic centimeters?. 24 cm cm cm 3 D cm Which accurately describes a tangent?. segment whose endpoints are on the circle.. line that intersects a circle in two points and passes through the center of the circle.. segment having an endpoint on the circle and an endpoint at the center of the circle. D. line that intersects a circle at exactly one point. 14. Use the figure below. 12. pizza parlor has two different sizes of circular pizzas. The smaller one has a diameter of 12 inches and the larger one has a diameter of 20 inches. E G What is the ratio of their areas?. 9:25. 3:5. 2 3:2 5 D. 6 : 10 Which of the following represent a secant?. G D. E. D. D GO ON

6 15. In circle S below, Q 32 P 17. In K, mxy ( 7x 9) 3( 2x 15) =, mwz = +, and m XLY = 148. S W X T R K L The m QPT = 32, what is the measure of QRT? Z Y D Use ircle J below D. 27 L What is the value of x? J ( 3x 6) 156 K D. 350 What is the value of x? 18. In the figure below, m = 75 and md= 135, What is m P? D. 60 D R Q P GO ON

7 19. Two tangents are drawn from point P to circle H. N 21. In K, NK = 3x + 4, KW = 5x 8, S = 5x 4. R N H P K R W What conclusion is guaranteed by this diagram? 1. mnr m NPR 2 =. ΔHNR is a right triangle.. HNPR is a rhombus. D. HNPR is a kite. What is N? D. 26 S 20. ll of the segments shown in the figure below are tangents to N. 6 cm T N 10 cm W 4 cm D V U 3 cm Given the measures in the figure above, what is the perimeter of quadrilateral D?. 23 cm. 40 cm. 46 cm D. 52 cm GO ON

8 22. K is the diameter of O, = ( 19x ), and ( 9( x 2) 6) mj mjk = +. O 24. How many lines of symmetry does a square have? D Which figure contains two similar triangles that are not congruent? J K L. What is the value of x? D Determine the transformation that has mapped Δ to Δ.. ' D. ' '. dilation. reflection. rotation D. translation GO ON

9 26. The following figures are similar. W What is the scale factor of WXYZ to D?. 1 to 2. 3 to 1. 3 to 2 D. 4 to 3 Z 56 D Two plasma screen TVs are similar rectangles. Their scale factor is 8:5. The perimeter of the smaller TV is 70 inches. The lengths of the sides of the larger TV are represented by the variable expressions shown in the diagram below. (3x 4) in. 24 X 32 Y (2x) in. 28. The measures of the angles of a triangle have the ratio 4:6:7. What type of triangle is it?. acute. isosceles. obtuse D. right 29. The perimeter of a right triangle is 90 feet. The ratio of the legs is 5:12. What is the length of the longest leg of the triangle?. 12 ft. 32 ft. 36 ft D. 90 ft 30. Pat measures the length of the shadow of a tree to be 54 feet long. t the same time he measures his own shadow to be 12 feet long and his height to be 5 feet. How tall is the tree in feet? feet. 25 feet feet D. 20 feet What is the value of x? D GO ON

10 31. Kris places a mirror on the ground. She stands so that she can see the reflection of the top of a flagpole in the mirror. G h 2 m 3 m 15 m What is the height (h) of the flagpole in meters?. 10 m. 12 m. 18 m D. 20 m 32. Given the two triangles pictured below. N H J 9 6 L O 15 What measure for HJ would make ΔNO ΔLJH? D GO ON

11 33. In the triangle below, D. 7 4 z 10.5 D 35. What is the geometric mean of 16 and 36? D Nan stands at the corner of the rectangular driveway shown below. What is the value of z? D ft D ft 34. In the triangle below, RT HS. M 4 R What is the value of x? H x T 15 S How far must Nan walk diagonally across the driveway ( to )?. 7 ft. 14 ft. 35 ft D. 49 ft D GO ON

12 37. box is shown below. 38. Use the dimensions given in the diagram below in. 6 in. 8 in. x 16 What is?. 26 in.. 38 in in. D. 8 10in. What is the value of x? D The three sides of a triangle are 3 centimeters, 5 centimeters, and 7 centimeters. What is the best description for this triangle?. acute triangle. equiangular triangle. obtuse triangle D. right triangle GO ON

13 40. jet is flying 7 miles above the ground. The pilot spots an airport as shown below. 42. In rectangle D, D = 12 and m D = 30. What is the length of the longer side of the rectangle? 7 mi d D. 6 3 What is the distance d from the plane to the airport?. 7 2 mi. 7 3 mi. 7 mi D. 14 mi Use the dimensions given in the diagram below. 43. Use the table and the dimensions given in the diagram below. r θ sin θ cos θ tan θ y What is the value of y? D What is the value of r? D GO ON

14 44. Use the dimensions given in the right triangle below. 46. Use the dimensions given in the diagram below What is the cosine of D ? 45. Use the table and the dimensions given in the diagram below. ngle of descent Which equation would be used to find the distance h from the hot air balloon to the ground?. h = 150 tan 53. h = 150sin 53. D h = tan h = sin ft h 3.4 mi 10 mi θ sin θ cos θ tan θ What is the approximate angle of descent? D GO ON

15 47. Use the table and the dimensions given in the diagram below. 48. In circle D below, is tangent to D at, and is tangent to D at. 2x 6 10 d 128 ft D 40 3( x 7) θ sin θ cos θ tan θ What is the approximate length d of the kite string?. 256 ft. 200 ft. 168 ft D. 100 ft D. 26 What is the length of D? 49. In the figure below, is tangent to D at and is tangent to D at. 6 2( x + 5) 1 D 5x What is the value of x? D GO ON

16 50. In the figure below, RP is tangent to the circle at R and SP is a secant. R x P 52. The concentric circles below have radii of 4 centimeters, 10 centimeters, and 18 centimeters. S 8 cm V 6 cm What is the value of x?. 48 cm. 84 cm. 4 3 cm D cm 51. The figure below is a regular hexagon with a side length of 8 centimeters.. What is the probability that a randomly thrown dart will land in the white region, assuming it hits the board? D What is the probability that a randomly thrown dart will land in the shaded region? D GO ON

17 53. In the square below, all adjacent circles are congruent, externally tangent to each other, and outer circles are tangent to the square. 16 cm What is the area of the shaded region?. ( 256 4π ) cm 2. ( π ) cm 2. ( π ) cm 2 D. ( π ) cm snow cone consisting of a cone and a half-sphere is shown below. The base of the cone is a great circle on the sphere. 3 cm 4 cm Surface area of a cone = (rea of ase) + π radius slant height Surface area of a sphere = 4 (rea of a Great ircle) What is the surface area of the three-dimensional object in square centimeters?. 30π cm 2. 33π cm 2. 39π cm 2 D. 42π cm GO ON

18 55. glass block is in the shape of a rectangular prism. It has a hole passing through it also in the shape of a rectangular prism. 2 in. What is the volume of glass needed in cubic inches?. 80 in in in. 3 D. 972 in in. 56. Use the dimensions given in the diagram of an isosceles trapezoid below in in. 9 in. 57. Given a triangle, what is the cosine of the 60 angle? D circle with a point ( 3, 2) is centered at ( 5, 4). What is the equation of the circle? 2 2. ( x ) ( y ) = ( x ) ( y ) = ( x ) ( y ) = D. ( x ) ( y ) = 100 What is the area of the trapezoid? D GO ON

19 59. The room shown below is to have crown molding installed around the ceiling s perimeter. 16 ft 10 ft 4 ft 4 ft 4 ft 2 ft pproximately how many feet of molding are needed to complete the room?. 40 ft. 52 ft. 54 ft D. 60 ft 60. lighthouse keeper spots a boat moving away from the lighthouse, first at 30 and then at 50. The height of the light house shown below is 100 feet above sea level. 100 ft θ sin θ cos θ tan θ d What is the approximate distance d the boat traveled?. 22 ft. 61 ft. 72 ft D. 89 ft

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21 Free Response 1. Given Δ with right angle at and altitude D, draw the picture and prove Δ ΔD GO ON

22 Free Response 2. Find the length of the altitude of an isosceles triangle with vertex angle 120 and a base length of x centimeters. Give answer in simplified radical form in terms of x. 3. Explain how to find the area of a regular hexagon if only the length of the apothem is known

23 GEOMETRY HONORS SEMESTER 2 EXM ITEM SPEIFITION SHEET & KEY Free Response # Objective Syllabus Objective NV State Standard 1 Prove that two triangles are similar Solve problems utilizing the ratios of the sides or special right triangles Solve problems using perimeters or areas of geometric figures Multiple hoice # Objective Syllabus Objective 1 Solve problems using perimeters or areas of geometric figures. 2 Solve problems using perimeters or areas of geometric figures. NV State Standard Practice Key Final Key D 3 Solve real world problems of perimeter and area Solve real world problems of perimeter and area ompare attributes of various geometric solids D 6 Solve surface area and volume problems of various geometric solids D 7 Solve surface area and volume problems of various geometric solids Solve surface area and volume problems of various geometric solids Solve real world problems of surface area and volume Solve real world problems of surface area and volume Solve area and volume problems of similar two and three dimensional figures Solve area and volume problems of similar two and three dimensional figures D 13 Differentiate among the terms relating to a circle D 14 Differentiate among the terms relating to a circle D 15 Solve problems involving angles, arcs, or sectors of circles Solve problems involving angles, arcs, or sectors of circles Solve problems involving arcs, chords, and radii of a circle Solve problems involving arcs, chords, and radii of a circle Explore relationships among circles and external lines or rays D D 20 Explore relationships among circles and external lines or rays D 21 Solve problems involving properties of circles using algebraic techniques Solve problems involving properties of circles using algebraic techniques D 23 Distinguish among the basic mapping functions: reflections, translations, and rotations Differentiate between examples of each type of symmetry D 25 Differentiate between similar and congruent Determine scale ratios and write appropriate proportions D 27 Solve proportion problems using algebraic techniques Solve proportion problems using algebraic techniques Solve proportion problems using algebraic techniques Page 1 of 2 Revised: 01/07/09 lark ounty School District

24 GEOMETRY HONORS SEMESTER 2 EXM ITEM SPEIFITION SHEET & KEY Multiple hoice # Objective Syllabus Objective 30 Formulate and solve real world problems using similar triangles. 31 Formulate and solve real world problems using similar triangles. NV State Standard Practice Key Final Key Prove that two triangles are similar Prove that two triangles are similar D 34 Explore geometric mean relationships within a right triangle D 35 Explore geometric mean relationships within a right triangle Solve problems using the Pythagorean Theorem Solve problems using the Pythagorean Theorem Solve problems using the Pythagorean Theorem Solve problems using the converse of the Pythagorean Theorem and related theorems for obtuse or acute triangles Solve problems using the converse of the Pythagorean Theorem and related theorems for obtuse or acute triangles D 41 Solve problems utilizing the ratios of the sides of special right triangles D 42 Solve problems utilizing the ratios of the sides of special right triangles D D 43 Define and apply basic trigonometric ratios of sine, cosine, and tangent Define and apply basic trigonometric ratios of sine, cosine, and tangent D D 45 Solve problems using the trigonometric ratios D 46 Solve problems using the trigonometric ratios D 47 Solve problems using the trigonometric ratios Solve problems involving secant segments and tangent segments for a circle D 49 Solve problems involving secant segments and tangent segments for a circle Solve problems involving secant segments and tangent segments for a circle D 51 Solve problems involving geometric probability Solve problems involving geometric probability D 53 Solve problems using perimeters or areas of geometric figures Solve problems involving surface areas and volumes of various geometric solids Solve real world problems of surface area and volume Solve problems using perimeters or areas of geometric figures Define and apply basic trigonometric ratios of sine, cosine, and tangent D 58 Graph a circle and determine its equation D 59 Solve real world problems of perimeter and area Solve problems using trigonometric ratios D Page 2 of 2 Revised: 01/07/09 lark ounty School District