Geometry Semester 2 Exam Review 1. The diameter of a circle is 12 meters. If point P is in the same plane as the circle, and is 6 meters from the center of the circle, which best describes the location of point P? A. Point P must be on the circle. B. Point P must be inside the circle. C. Point P may be either outside the circle or on the circle. D. Point P may be either inside the circle or on the circle. 2. A right triangle’s hypotenuse has length 5. If one leg has length 2, what is the length of the other leg? 3. The rectangle shown has length 20 4. What is the area, in square inches 5
5. In the figure, if sin(x)= , what are 13
meters and width 10 meters. If four (in.), of the triangle? cos(x) and tan(x)? triangles are removed from the rectangle as shown, what will be the area of the remaining figure? 6. A diagram from a proof of the Pythagorean theorem is pictured. Which statement would not be used in the proof of the Pythagorean theorem? A. The area of a triangle equals ½ab. B. The four right triangles are congruent. C. The area of the inner square is equal to half of the area of the larger square. D. The area of the larger square is equal to the sum of the areas of the smaller square and the four congruent triangles. 7. Approximately how many feet tall is the streetlight? Given: sin(40°)≈0.64 cos(40°)≈0.77 tan(40°)≈0.84 8. In the accompanying diagram, m∠A=32° and AC=10. Which equation could be used to find x in ΔABC? A. x =10 sin(32°) B. x =10 cos(32°) C. x =10 tan(32°) D. x =
10. Nara created two right triangles. She started with ΔJKL and drew an altitude from point K to side JL . The diagram below shows ΔJKL and some of its measurements, in centimeters (cm). Based on the information in the diagram, what is the measure of x to the nearest tenth of a centimeter? 10
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cos 32°
9. ΔJKL is shown. Which equation should be used to find the length of segment JK? JK
28
A. sin 24° =
B. sin 24° =
28
JK
!
JK
28
C. cos 24° =
D. cos 24° =
28 JK
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11. What is the approximate height, in feet, of the tree in the figure below? Given: sin(50°)≈0.766 cos(50°)≈0.643 tan(50°)≈1.192 12. What is the value of x, in inches? 13. Mr. Rose is remodeling his house by adding a room to one side, as shown in the diagram below. In order to determine the length of the boards he needs for the roof of the room, he must calculate the distance from point A to point D. What is the length, to the nearest tenth of a foot, of !AD ? 14. Kayla inscribed quadrilateral ABCD 15. In the figure, what is the value of x? ∫
in a circle, as shown. If m!ADC is 255° in Kayla’s design, what is the measure, in degrees, of ∠ADC ? 17. To the nearest square meter, what 18. The sectors of the spinner are is the area of the shaded sector? congruent. What is the probability the pointer will stop in a sector other than 1 or 4? 16. This target is a circle, with a radius of 16 inches, that has a square inscribed in it. A dart thrown at random lands inside the circle. To the nearest hundredth, what is the probability that the dart lands in the shaded area? 19. To the nearest hundredth of a centimeter, what is the length of ∫
!ABC ? 20. A square is circumscribed about a circle. What is the ratio of the area of the circle to the area of the square? 21. What is the length of a chord that is 30 inches from the center of a circle whose diameter is 68 inches long? 22. The consecutive vertices of a parallelogram ABCD are A(1,2), B(1,0), and C(4,0). What are the coordinates of the fourth vertex D? 2
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23. What is the equation of the circle? 24. The equation of a circle is (x+3) +y =9. What are the center and radius of the circle? Draw a sketch of the circle on the graph. 25. Give the coordinates of point O without using any additional variables. 26. What is the area, in square meters, of the trapezoid that is shown? 27. What are the area and perimeter of the figure? 28. What are the area and perimeter of the figure? 29. A plastic tray is shown below, with the dimensions labeled. The tray does not have a cover on top. The bottom and two of the sides are rectangles. The remaining two sides are congruent isosceles trapezoids. What is the total area of the outer surface of the tray? 30. What is the equation of the line through the point (1,5) that is parallel to the line that passes through (2,1) and (0,–5)? 31. Prove or disprove that the quadrilateral determined by the points A(–3,1), B(3,3), C(4,–1), and D(–2,–3) is a rectangle. 32. What is the equation of the line through the point (4,3) that is perpendicular to the line y–2x=1? 33. What is the approximate surface area of a right hexagonal prism with a base perimeter of 96 meters and a height of 10 meters? (Use S=ap+ph, where a is the apothem of the base, p is the perimeter of the base, and h is the height of the prism.) 34. The ratio of the height of the pyramid to the edge of the square base is 1.5 to 1. The height of the pyramid is 3 meters. What is the approximate length of the slant height of the pyramid? 35. Name the plane figure that is formed by intersecting a cube with a plane that passes through a pair of opposite faces and is parallel to the face that intersects those opposite faces. 36. To the nearest cubic foot, what is the volume of a right circular cone whose circular base has a diameter of 12 feet and whose height is 12 feet? 37. The length and width of a right rectangular prism whose surface area is 292 square centimeters are 4 centimeters and 5 centimeters, respectively. What is the height of the prism? 38. A cone-­‐shaped funnel with a height of 30 centimeters and a radius of 20 centimeters is used to fill a container with liquid. The container is a cylinder with a height of 15 centimeters and a radius of 40 centimeters. How many times must the funnel be completely filled in order to fill the container? 39. A box printing company needs to wrap boxes that are 6 inches long, 6 inches wide, and 4 inches tall. What is the surface area of the box? 40. Jason jogs on a path equidistant from the parallel sides of two buildings. His jog path is represented by y = 4 and the side of building 1 is represented by y = 1. Which equation represents the side of building 2? 41. Two parallel lines are 10 units apart. Point A is located on one of the parallel lines. How many points are equidistant from the two parallel lines and are also 5 units from point A? 42. What is the equation(s) of the locus of points equidistant from the lines x = –15 and x = 3? 43. A is at -­‐6 and B is at 9. Find the point, T, so that T is three-­‐fifths of the distance from A to B. 44. Find the coordinate, T, that is three-­‐fifths of the distance from A(2, -­‐2) to B(-­‐3, 8). 46. On the set of axes, graph the locus of points that are 4 units from the line x=3 and the locus of points that are 5 units from the point (0,2). Label with an X all points that satisfy both conditions. 45. Find the coordinate, T, that divides AB into a ratio of 2:1 if A is at (-­‐1, 2) and B is at (5, 12). 47. A size 7 basketball has a circumference of 29.5 inches. A size 6 basketball has a circumference of 28.5 inches. To the nearest hundredth, what is the ratio of the volume of a size 7 basketball to the volume of a size 6 basketball? 48. A box printing company needs to wrap boxes that are 4 inches long, 4 inches wide, and 1 inch tall. What is the surface area of each box? 49. A new cylindrical container will have a volume that is double the volume of the old container it is replacing. The height of the new container is the same as the height of the old one. To the nearest tenth, by what factor must the radius of the new cylinder be increased? 50. An equilateral triangle has vertices (0, 0) and (4, 0). The third vertex lies above the x-­‐axis. What is the ordered pair of the third vertex?