12.00 Semester 2 Exam QUESTION 1 A recipe for a strawberry smoothie requires a fourth cup of sugar for every 2 cups of strawberries. Which of the following is not the ratio of sugar to strawberries? 0.25 : 2 0.125 2 : 0.25 2 points QUESTION 2 Which of the following is an example of a ratio? number of dogs who like Good Boy treats number of chocolates per bag number of people who like math all of the above 2 points QUESTION 3 You counted 217 licks to get to the tootsie roll of 5 tootsie pops. How many licks does it take to get to one tootsie roll of one tootsie pop? 43.4 licks 39.8 licks 42.5 licks 45.7 licks 2 points QUESTION 4 Solve: x = 55.75 x = 55.50 x = 67.55 x = 60.75 2 points QUESTION 5 A racecar can travel 4 laps in 5 minutes. At this rate, it will take the racecar 93.25 minutes to complete 75 laps (in minutes). True False 2 points QUESTION 6 Determine whether each pair of triangles is similar. If similarity exists, write a similarity statement relating to the two triangles. Give a justification for your answer. because their angles are proportional to each other. using the Angle-Angle Similarity Postulate. using the Side-Side-Angle Similarity Postulate. is not similar to 2 points QUESTION 7 Scalene triangles are never similar to each other. True False 2 points QUESTION 8 At a certain time of day, a 5.5 foot tall man has a 6 foot shadow. If a tree is 19 feet tall, what is the length of the shadow of the tree? 21.31 ft 19.86 ft 20.73 ft 20.45 ft 2 points QUESTION 9 If two polygons are similar, the corresponding angles are congruent. True False 2 points QUESTION 10 Are the polygons similar? If so, justify your answer. because the corresponding sides are proportional because the corresponding sides are congruent ABCD is not similar to EFGH because the corresponding sides are not proportional. ABCD is not similar to EFGH because the corresponding sides are not congruent. QUESTION 11 Given , calculate the value of MH 4.8 3.7 4.2 5.2 2 points QUESTION 12 Given the two polygons are similar, calculate the value of x. 4.1 5.98 6.43 6.98 2 points QUESTION 13 A regular octagon has side length 10.9 in. The perimeter of the octagon is 87.2 in and the area is 392.4 in 2. A second octagon has side lengths equal to 16.35 in. Find the area of the second octagon. 461.60 in2 882.9 in2 717.06 in2 642.66 in2 2 points QUESTION 14 Given the figures are similar, calculate the area of EFGH 54 486 42 48 2 points QUESTION 15 Two triangular roofs are similar. The ratio of the corresponding sides of these roofs is 2:3. If the altitude of the bigger roof is 7.5 feet, find the corresponding altitude of the smaller roof. 4.5 ft 5 ft 3.75 ft 6 ft 2 points QUESTION 16 Two triangular roofs are similar. The ratio of the corresponding sides of these roofs is 2:3. If the altitude of the bigger roof is 3.25 feet, find the corresponding altitude of the smaller roof. 3.547 ft 2.167 ft 3.75 ft 6.5 ft 2 points QUESTION 17 If the diameter of a circle is 4, what is the radius? 25 2.5 2 8 2 points QUESTION 18 If the radius of a circle is 15 cm, what is the diameter? 7.5 cm 20 cm 60 cm 30 cm 2 points QUESTION 19 In the diagram below, AE = 12, EB = 6, and CE = 4. Find DE. 12 6 19 18 2 points QUESTION 20 Using the diagram below, calculate the length of 25 in 4 in 7 in 5 in 2 points QUESTION 21 is a secant to circle O. True False 2 points QUESTION 22 Calculate the length of AD given AB = 4 cm, AC =10 cm, and AD = 5. Find AE. 6 8 7 9 QUESTION 23 If AB = 10, CD = 12, and FE = 20, calculate the values of the circle are tangent to the circle. and . All lines that appear to be tangent to AE = 31 and CE = 33 AE = 32 and CE = 30 AE = 33 and CE = 31 AE = 30 and CE = 32 2 points QUESTION 24 If AB = 2.5, CD = 3, and FE = 5, calculate the values of the circle are tangent to the circle. and . All lines that appear to be tangent to AE = 7.5 and CE = 8 AE = 8 and CE = 7.5 AE = 8.25 and CE = 7.75 AE = 7.75 and CE = 8.25 2 points QUESTION 25 Name the corresponding major arc to . 2 points QUESTION 26 m = 45; then m = 135. True False 2 points QUESTION 27 Calculate the 42 145 149 113 2 points QUESTION 28 Calculate the m if is the diameter. 75.89 75.79 79.75 107 2 points QUESTION 29 If the = 94, what do you know about the and the ? is half is half 2 points QUESTION 30 The measure of an inscribed angle is equal to the measure of its corresponding arc. True False 2 points QUESTION 31 Calculate the m , given m = 170 and m = 190. 90 40 20 10 2 points QUESTION 32 Calculate the m , given m = 110, and m = 38. m = 212 m = 74 m = 89 m = 168 2 points QUESTION 33 Find the value of x, if m = 5x - 10 and m = 3x + 30. x = 20 x = 40 x=8 x=6 2 points QUESTION 34 What is the standard equation of a circle at the origin? x2 - y2 = r2 x2 + y2 = r2 x2 + y2 = r x2 - y2 = r 2 points QUESTION 35 Pizza Planet delivers pizza within a 15 mile radius of their store. If this area is represented graphically, with Pizza Planet located at (2, 4), what is the equation that represents the delivery area? (x + 2)2 + (y + 4)2 = 15 (x - 4)2 + (y - 2)2 = 115 (x - 2)2 + (y - 4)2 = 225 (x + 4)2 + (y + 2)2 = 15 2 points QUESTION 36 The equation of a circle is (x - 3)2 + (y + 5)2 = 81. Determine the coordinates of the center of the circle and the length of the radius. Center (-3, -5), radius is 9 Center (3, -5), radius is 9 Center (-5, -3), radius is 81 Center (5, 3), radius is 81 2 points QUESTION 37 The graph of (x - 3) 2 + (y + 3)2 = 4 is illustrated below. True False 2 points QUESTION 38 The graph of (x - 2) 2 + (y + 1)2 = 2 is illustrated below. True False 2 points QUESTION 39 The Nygen family wants to put a circular fence around their pool. They want it to be exactly 10 feet from the center of the pool. How many feet of fencing do they need to buy? 65.83 ft 62.83 ft 64.51 ft 63.84 ft 2 points QUESTION 40 If the circumference of a circle is 42 in, find the diameter. 13.7 in 13.37 in 13.11 in 13.35 in 2 points QUESTION 41 Estimate the length of the radius, if the area of a circle is 275 mm2. 9.78 mm 24.97 mm 9.36 mm 7.87 mm 2 points QUESTION 42 The size of a bicycle is determined by the diameter of the wheel. You want a 22-in bicycle for your birthday. What is the area of one of the wheels? 385.47 in2 314.16 in2 484.37 in2 380.13 in2 2 points QUESTION 43 Calculate the area of the shaded sector. 11.73 11.2 11.4 11.83 2 points QUESTION 44 is the diameter. Calculate the area of the sector created by 84.47 337.9 168.95 122.34 2 points QUESTION 45 In circle A, the radius is 7.5 and the measure of = 125. Find the length of 16.4 19.6 10.6 21.2 2 points QUESTION 46 Identify the leg(s) of the right triangle below. and and and 2 points QUESTION 47 To get from your house to your grandparent's house you must avoid walking through a pond. To avoid the pond, you walk 0.5 miles south and 1.2 miles east. How many miles would be saved if it were possible to walk through the pond? 0.4 miles 1.69 miles 3.0 miles 6.4 miles QUESTION 48 You are helping your dad build a dog house for your dog. You tell him that it would be easy to build a dog house in the shape of a tent. The slanted sides are 13 feet long and the bottom of the house is 24 feet across. You draw him the following illustration to help him find the height of the dog house. What do you tell him the height of the dog house is? 10 ft 5 ft 25 ft 4.5 ft 2 points QUESTION 49 In the triangle below, determine the value of c. 12.3 11.5 8.6 12.5 2 points QUESTION 50 In the triangle below, what ratio is sin ? 2 points QUESTION 51 In the triangle below, determine the value of a. 8.6 11.5 4.1 6.1 2 points QUESTION 52 In the triangle below, what ratio is cos H? 2 points QUESTION 53 In the triangle below, what ratio is tan ? 2 points QUESTION 54 In the triangle below, determine the 62.2 21.54 64.98 12.5 2 points QUESTION 55 Calculate the value of a. 2.93 1.46 1.87 1.36 2 points QUESTION 56 In the triangle below, determine the value of c. 8.6 11.5 12.3 12.5 2 points QUESTION 57 Secant is the reciprocal of which other ratio? Sine Cosine Cotangent Cosecant 2 points QUESTION 58 In the triangle below, what ratio is sec H? 2 points QUESTION 59 In the triangle below, what ratio is cot G? 2 points QUESTION 60 Tangent is the reciprocal of which other ratio? Sine Cosine Cotangent Cosecant 2 points QUESTION 61 If the angle that the sun makes with the side of a building is 75, and the distance from the top of the building to the tip of its shadow is 50 feet, the length of its shadow is 12.94 feet. True False 2 points QUESTION 62 The angle of elevation of a ladder leaning against a wall is 45. If the distance from the base of the ladder to the wall is 15 feet, find the length of the ladder. 15 feet 21.2 feet 30.5 feet 42.4 feet 2 points QUESTION 63 A security light is being installed outside a loading dock. The light must be placed at a 65 angle so that it illuminates a parking lot. If the distance from the end of the parking lot to the loading dock is 125 feet, the height of the security light is 113.29 feet. True False 2 points QUESTION 64 Your parents surprise you with a hot air balloon ride above the city. From a hot air balloon, the angle between vertical (straight down) and a line directly to your house is 63, as shown below. If the distance between the radio antenna directly below you and home is 14 miles, the height of the balloon is 7.1 miles. True False QUESTION 65 What is the value of sin(x) when x = 30? 1 -1 2 points QUESTION 66 The value(s) of x when sin(x) = -1 are x = -90 and 270? True False 2 points QUESTION 67 What is the domain and range of f(x) = cos(x)? The domain is and the range is all real numbers. The domain is and the range is all real numbers. The domain is all real numbers and the range is The domain is all real numbers and the range is 2 points QUESTION 68 The y-value for y = cos(x) when x = 180 is 1. True False 2 points QUESTION 69 The y-value of y = tan(x) when x = -90 and x = 90 is 0. True False 2 points QUESTION 70 What is the y-value for y = tan(90)? - 1 undefined 2 points QUESTION 71 The in the illustration below is 29. True False 2 points QUESTION 72 Write an equation that could be used to find the value of b. 382 = 22 + 32 - 2(2)(3)(cos b) b2 = 22 + 32 - 2(2)(3)(cos 38) 22 = b2 + 32 - 2(b)(3)(cos 38) 32 = 22 + b2 - 2(2)(b)(cos 38) 2 points QUESTION 73 Find the surface area of the right triangular prism below. 108 in2 48 in2 51 in2 102 in2 2 points QUESTION 74 Find the height of a rectangular prism if the surface area is 458.17 in2, the width is 6.2 in and the length is 8.3 in. 12.5 in 16.5 in 8.9 in 12.25 in 2 points QUESTION 75 Find the surface area of a cylinder with diameter 40 mm and height 16 mm. 1055.58 mm2 2111.15 mm2 4523.89 mm2 1344.00 mm2 2 points QUESTION 76 Find the height of the figure below if the surface area is 694.35 mm2 12.4 mm 24. 5 mm 21.4 mm 11.7 mm 2 points QUESTION 77 The volume of the figure below is 56 mi3. True False QUESTION 78 Find the value of x in the figure below if the volume is 65.97 m3. x = 24.3 x = 2.71 x = 5.43 x = 12.15 2 points QUESTION 79 Find the volume of a cylinder with height 14 cm and diameter 12 cm. 549.78 cm3 2199.12 cm3 1099.56 cm3 1583.36 cm3 2 points QUESTION 80 Find the radius of a cylinder with a volume of 118.79 feet 3 and height of 5 feet. 3.45 ft 1.94 ft 2.52 ft 2.75 ft 2 points QUESTION 81 The surface area of the square pyramid below is 126 mm2. True False 2 points QUESTION 82 Find the surface area of the square pyramid below. 689 m2 744 m2 714 m2 728 m2 2 points QUESTION 83 Find the slant height of a cone with surface area 282.74 ft2 and diameter 10 ft. 13 ft 14 ft 12 ft 15 ft 2 points QUESTION 84 The surface area of the figure below is 50.80 m2. True False 2 points QUESTION 85 The volume of the figure below is 3441.24 in3. True False 2 points QUESTION 86 Find the height of a square pyramid with volume 126.97 ft 3 and dimensions of base 6 ft by 6 ft. 9.67 ft 11.78 ft 10.65 ft 10.58 ft 2 points QUESTION 87 The volume of the figure below is 14.21 units3. True False 2 points QUESTION 88 Find the radius of a cone with volume 45.19 cm3 and height 7.5 cm. 1.2 cm 2.4 cm 2.6 cm 4.8 cm 2 points QUESTION 89 The surface area of a sphere with radius 1.25 miles is 19.63 miles 2. True False 2 points QUESTION 90 Find the length of the radius of a sphere with a surface area of 64.62 km2. 1.125 km 2.25 km 2.27 km 3.375 km 2 points QUESTION 91 The length of the diameter of a sphere with a volume of 321.57 miles3 is 4.25 miles. True False 2 points QUESTION 92 The length of the radius of a sphere with a volume of 1463.76 in 3 is 18.69 in. True False 2 points QUESTION 93 Going down a slide is not an example of a translation. True False 2 points QUESTION 94 Triangle ABC is located at A (-4, 5), B (-4, -1), and C (-1, 1) and is translated 3 units to the left and 2 units down. The translation of the triangle is located at A' (-1, 7), B' (-1, 1), and C' (2, 3). True False 2 points QUESTION 95 Which of the following sets of points are reflections of each other across the x-axis? (4, -7) (4, 7) (4, -7) (-4, -7) (4, -7) (-4, 7) (4, -7) (-7, 4) 2 points QUESTION 96 Which of the following sets of points are reflections of each other across the origin? (-6, -9) (-6, -9) (-6, -9) (6, 9) (-6, -9) (-6, 9) (-6, -9) (-9, -6) 2 points QUESTION 97 A rotation is a type of transformation that can be defined as turning a figure about a fixed point with no change to the size and shape of the figure. True False 2 points QUESTION 98 When Point E (-2, -5) is rotated 270 counterclockwise about the origin, it becomes (-5, 2). True False 2 points QUESTION 99 Which of the following is an example of a dilation? 2 points QUESTION 100 The length of a rectangle is 3 in and the width is 4 in. The rectangle is then dilated to 9 in by 12 in by a scale factor of 3. True False 2 points