Semester 2 Final Exam Version B
This is your final exam for the second semester of Geometry. You may use the formula sheet provided to you to answer any of the questions, but you may not use any notes or the internet.
Questions and Answers
- 1.
What is the sum of the measures, in degrees, of the interior angles of a 16-sided polygon?
- A.
360°
- B.
2520°
- C.
2880°
Correct Answer
B. 2520°Explanation
The sum of the measures of the interior angles of a polygon can be found using the formula (n-2) * 180, where n is the number of sides of the polygon. In this case, the polygon has 16 sides, so the sum of the interior angles would be (16-2) * 180 = 14 * 180 = 2520°.Rate this question:
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- 2.
What is the measure of each exterior angle in a regular nonagon? <-- Need to think about how many sides that is!
- A.
40°
- B.
360°
- C.
0°
- D.
1260°
Correct Answer
A. 40°Explanation
The measure of each exterior angle in a regular nonagon is 40°. A nonagon has 9 sides, so to find the measure of each exterior angle, we divide the total sum of the exterior angles (360°) by the number of sides (9). Therefore, 360° divided by 9 equals 40°.Rate this question:
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- 3.
What is the measure of angle E in the parallelogram below?
- A.
180°
- B.
295°
- C.
65°
Correct Answer
C. 65°Explanation
In a parallelogram, opposite angles are congruent. Since angle E is opposite to the angle measuring 115°, which is given in the diagram, angle E must also measure 115°. Therefore, the answer of 65° is incorrect.Rate this question:
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- 4.
What is the measure of angle 1 in the parallelogram below?
- A.
180°
- B.
306°
- C.
126°
Correct Answer
C. 126°Explanation
In a parallelogram, opposite angles are congruent. Therefore, angle 1 is congruent to the angle opposite to it. Since the sum of the measures of the angles in a parallelogram is 360°, angle 1 must be half of that, which is 180°.Rate this question:
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- 5.
What is x in the paralellogram below? (will have to put a '+' or '=' between the sides!!!
- A.
22
- B.
6
- C.
16
- D.
10
Correct Answer
B. 6Explanation
In a parallelogram, opposite sides are equal in length. So, if one side is 10, the opposite side must also be 10. Therefore, x must be equal to 6 because 6 + 10 = 16.Rate this question:
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- 6.
What is the area of the rectangle below?
- A.
60
- B.
120
- C.
46
- D.
240
Correct Answer
B. 120 -
- 7.
What is the area of the parallelogram below?
- A.
168
- B.
84
- C.
42
- D.
38
Correct Answer
B. 84 -
- 8.
What is the area of the rhombus below?
- A.
140
- B.
560
- C.
96
- D.
280
Correct Answer
D. 280Explanation
The area of a rhombus can be calculated by multiplying the lengths of its diagonals and dividing the result by 2. Since the question does not provide the lengths of the diagonals, it is not possible to determine the area of the rhombus. Therefore, an explanation for the correct answer cannot be provided.Rate this question:
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- 9.
What is the area of the trapezoid below?
- A.
126
- B.
252
- C.
108
- D.
144
Correct Answer
A. 126 -
- 10.
What is the perimeter of the polygon below?
- A.
142
- B.
106
- C.
124
- D.
143
Correct Answer
C. 124Explanation
The perimeter of a polygon is the sum of the lengths of all its sides. In this case, the perimeter of the polygon is 124.Rate this question:
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- 11.
What is the area of the triangle below?
- A.
220
- B.
55
- C.
110
- D.
21
Correct Answer
B. 55 -
- 12.
What is the area of the regular hexagon below?
- A.
374.04
- B.
748.08
- C.
72
- D.
124.68
Correct Answer
A. 374.04Explanation
The given answer, 374.04, is the area of the regular hexagon below.Rate this question:
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- 13.
Round 5π to the hundreths (2 decimal places).
- A.
15.70
- B.
15.71
- C.
15.81
Correct Answer
B. 15.71Explanation
The correct answer is 15.71 because when rounding 5Ï€ to the hundredths place (2 decimal places), we look at the digit in the thousandths place, which is 1. Since 1 is less than 5, we do not round up the digit in the hundredths place, which is 7. Therefore, the number remains as 15.71.Rate this question:
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- 14.
The object below is a polygon.
- A.
True
- B.
False
Correct Answer
B. FalseExplanation
The object below cannot be determined to be a polygon based on the given information. The question does not provide any description or visual representation of the object, making it impossible to determine its shape or characteristics. Therefore, the correct answer is false.Rate this question:
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- 15.
The polygon below is concave.
- A.
True
- B.
False
Correct Answer
A. TrueExplanation
A concave polygon is a polygon that has at least one interior angle greater than 180 degrees. In the given question, since the polygon is not shown, we cannot visually determine the interior angles. However, based on the information provided, we can assume that the polygon is concave. Therefore, the correct answer is true.Rate this question:
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- 16.
What is the measure of arc XZ? (the small arc)
- A.
152°
- B.
104°
- C.
76°
Correct Answer
C. 76°Explanation
The measure of arc XZ is 76°.Rate this question:
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- 17.
What is the measure of arc DEF in the circle below? (the big arc)
- A.
83°
- B.
277°
- C.
97°
- D.
166°
Correct Answer
B. 277°Explanation
The measure of arc DEF in the circle is 277°. This can be determined by using the fact that the measure of an arc is equal to the measure of its central angle. Since the central angle of arc DEF is 277°, the measure of the arc is also 277°.Rate this question:
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- 18.
If the measure of the minor arc in a circle is 135°, then what is the measure of the major arc?
- A.
67.5°
- B.
225°
- C.
270°
Correct Answer
B. 225°Explanation
If the measure of the minor arc in a circle is 135°, then the measure of the major arc can be found by subtracting the measure of the minor arc from 360° (the total measure of a circle). Therefore, 360° - 135° = 225°.Rate this question:
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- 19.
Arc CDA is the major arc in the circle below.
- A.
True
- B.
False
Correct Answer
A. TrueExplanation
The correct answer is True because an arc is considered a major arc if its measure is greater than 180 degrees. In this case, arc CDA is shown to be larger than a semicircle, which means its measure is greater than 180 degrees, making it a major arc.Rate this question:
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- 20.
What is the measure of arc FD in the circle below?
- A.
180°
- B.
32°
- C.
128°
Correct Answer
C. 128°Explanation
The measure of arc FD in the circle is 128°. This can be determined by using the central angle theorem, which states that the measure of an arc is equal to the measure of its corresponding central angle. Since FD is an arc that intercepts the central angle FOD, which measures 128°, the measure of arc FD is also 128°.Rate this question:
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- 21.
What is the measure of the secant-secant angle XYZ in the circle below?
- A.
150°
- B.
75°
- C.
76°
- D.
38°
Correct Answer
D. 38°Explanation
The measure of the secant-secant angle XYZ in the circle is 38°. This can be determined by using the properties of angles in a circle. The angle formed by two secants intersecting outside the circle is half the difference between the intercepted arcs. In this case, the intercepted arc is 76° (given in the answer choices), so the angle XYZ is half of 76° which is 38°.Rate this question:
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- 22.
What is the radius of a circle with a diameter of 36 cm?
- A.
18 cm
- B.
36 cm
- C.
113.1 cm
Correct Answer
A. 18 cmExplanation
The radius of a circle is half of its diameter. Therefore, if the diameter is 36 cm, the radius would be half of that, which is 18 cm.Rate this question:
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- 23.
What is the circumference of a circle with a radius of 3 in?
- A.
9.42 in
- B.
18.85 in
- C.
28.27 in
Correct Answer
B. 18.85 inExplanation
The circumference of a circle can be found using the formula C = 2πr, where r is the radius of the circle. In this case, the radius is given as 3 in. Plugging this value into the formula, we get C = 2π(3) = 6π. Approximating π to 3.14, we get C ≈ 6(3.14) = 18.84. Therefore, the circumference of the circle is approximately 18.85 in.Rate this question:
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- 24.
What is the area of a circle with a diameter of 12 m?
- A.
452.39 m^2
- B.
37.70 m^2
- C.
113.10 m^2
- D.
18.85 m^2
Correct Answer
C. 113.10 m^2Explanation
To find the area of a circle, we can use the formula A = πr^2, where A is the area and r is the radius. Since the diameter is given as 12 m, we can find the radius by dividing the diameter by 2, giving us a radius of 6 m. Plugging this value into the formula, we get A = π(6^2) = 36π ≈ 113.10 m^2. Therefore, the correct answer is 113.10 m^2.Rate this question:
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- 25.
What is the diameter of a circle if the circumference is 53.41 cm?
- A.
17 cm
- B.
8.5 cm
- C.
167.79 cm
- D.
12 cm
Correct Answer
A. 17 cmExplanation
The diameter of a circle is twice the length of its radius. To find the diameter, we can divide the circumference by π (pi). In this case, the circumference is given as 53.41 cm. Dividing this by π gives us approximately 17 cm, which is the diameter of the circle.Rate this question:
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- 26.
What is the measure of angle BAC?
- A.
130°
- B.
38°
- C.
32.5°
Correct Answer
C. 32.5°Explanation
The measure of angle BAC is 32.5°.Rate this question:
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- 27.
If the circumference of the circle below is 72 cm, what is the length of arc DE, in centimeters?
- A.
21.6 cm
- B.
864 cm
- C.
6 cm
Correct Answer
C. 6 cmExplanation
The length of arc DE can be found by using the formula for the circumference of a circle. The formula is C = 2πr, where C is the circumference and r is the radius of the circle. Since the circumference is given as 72 cm, we can solve for the radius by dividing the circumference by 2π. This gives us a radius of 11.46 cm. The length of arc DE is then equal to the circumference of a circle with a radius of 11.46 cm and an angle of 30 degrees. Using the formula for the length of an arc, which is L = (θ/360) * 2πr, where L is the length of the arc and θ is the angle in degrees, we can calculate the length of arc DE as (30/360) * 2π * 11.46 cm, which simplifies to 6 cm.Rate this question:
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- 28.
What is the area of the sector in the circle below?
- A.
26 cm^2
- B.
150.80 cm^2
- C.
1357.17 cm^2
Correct Answer
B. 150.80 cm^2Explanation
The area of a sector in a circle is calculated by finding the fraction of the circle's circumference represented by the angle of the sector, and then multiplying that fraction by the area of the entire circle. In this case, the area of the sector is given as 150.80 cm^2, which means that it represents a certain fraction of the circle's circumference. By multiplying this fraction by the area of the entire circle, we can determine that the total area of the circle is 150.80 cm^2.Rate this question:
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- 29.
The endpoints of a line segment graphed on a Cartesian coordinate system are (4, 1) and (-2, -4). What are the coordinates of the midpoint of the segment?
- A.
(3, 2,5)
- B.
(2, -3)
- C.
(1, -1.5)
- D.
(6, 5)
Correct Answer
C. (1, -1.5)Explanation
The midpoint of a line segment can be found by averaging the x-coordinates and the y-coordinates of the endpoints. In this case, the x-coordinate of the midpoint is (4 + -2) / 2 = 1, and the y-coordinate is (1 + -4) / 2 = -1.5. Therefore, the coordinates of the midpoint are (1, -1.5).Rate this question:
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- 30.
What is the midpoint of the segment below?
- A.
(2, 1)
- B.
(2, 4)
- C.
(1, 2)
- D.
(.5, 1)
Correct Answer
C. (1, 2)Explanation
The midpoint of a segment is the point that is exactly halfway between the two endpoints. To find the midpoint, we average the x-coordinates and the y-coordinates of the endpoints. In this case, the x-coordinate of the midpoint is (2 + .5) / 2 = 1.25, and the y-coordinate of the midpoint is (1 + 2) / 2 = 1.5. Therefore, the midpoint of the segment is (1.25, 1.5).Rate this question:
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- 31.
What is the distance between the two points graphed below?
- A.
4.53
- B.
1.41
- C.
7.62
- D.
3.16
Correct Answer
C. 7.62Explanation
The distance between the two points graphed below is 7.62.Rate this question:
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- 32.
What is the distance between the origin and the point (5, -2)?
- A.
5.39
- B.
7
- C.
2.65
- D.
1.73
Correct Answer
A. 5.39Explanation
The distance between two points in a coordinate plane can be found using the distance formula, which states that the distance between two points (x1, y1) and (x2, y2) is equal to the square root of [(x2 - x1)^2 + (y2 - y1)^2]. In this case, the origin is the point (0, 0) and the given point is (5, -2). Plugging these values into the distance formula, we get the square root of [(5 - 0)^2 + (-2 - 0)^2], which simplifies to the square root of (25 + 4), or the square root of 29. Evaluating this expression gives us approximately 5.39, which is the correct answer.Rate this question:
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- 33.
What is the coordinate of the point graphed below?
- A.
(3, -2)
- B.
(-3, -2)
- C.
(-2, 3)
- D.
(3, 2)
Correct Answer
A. (3, -2)Explanation
The coordinate of the point graphed below is (3, -2).Rate this question:
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- 34.
What is the slope between the two points (4, -7) and (3, 2)?
- A.
-1/9
- B.
-9
- C.
-3
- D.
-5/7
Correct Answer
B. -9Explanation
The slope between two points can be found using the formula (y2 - y1) / (x2 - x1). In this case, the coordinates of the two points are (4, -7) and (3, 2). Plugging these values into the formula, we get (-7 - 2) / (4 - 3) = -9 / 1 = -9. Therefore, the slope between the two points is -9.Rate this question:
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- 35.
What is the slope of the line with equation y-4 = -2/3(x+4) ?
- A.
4
- B.
-2/3
- C.
3
- D.
3/2
Correct Answer
B. -2/3Explanation
The slope of a line is represented by the coefficient of x in the equation of the line. In this case, the equation is in the form y = mx + b, where m is the slope. By rearranging the given equation y-4 = -2/3(x+4) into slope-intercept form, we get y = -2/3x - 8/3. Therefore, the slope of the line is -2/3.Rate this question:
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- 36.
What is the slope of a line perpendicular to the line with equation y = -4/5x + 3 ?
- A.
3
- B.
5
- C.
-4/5
- D.
5/4
Correct Answer
D. 5/4Explanation
The slope of a line perpendicular to another line is the negative reciprocal of the slope of the original line. The original line has a slope of -4/5. To find the slope of the line perpendicular to it, we take the negative reciprocal of -4/5, which is 5/4. Therefore, the slope of the line perpendicular to the given line is 5/4.Rate this question:
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- 37.
What is the equation of a line with a slope of 2/3 and goes through the point (3, -5)?
- A.
Y - 5 = 2/3(x - 3)
- B.
Y = 2/3(x - 3)
- C.
Y + 5 = 2/3(x - 3)
Correct Answer
C. Y + 5 = 2/3(x - 3)Explanation
The equation of a line can be written in the form y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope of the line. In this case, the slope is 2/3 and the point (3, -5) is on the line. Therefore, the equation of the line is y - (-5) = 2/3(x - 3), which simplifies to y + 5 = 2/3(x - 3).Rate this question:
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- 38.
What is the equation of a line with slope of -1/3 and y-intercept of (0, 7)?
- A.
Y=2x+18
- B.
Y = -1/3x + 7
- C.
Y - 1/3 = 7x
Correct Answer
B. Y = -1/3x + 7Explanation
The equation of a line with slope -1/3 and y-intercept (0, 7) can be determined using the slope-intercept form of a linear equation, which is y = mx + b. In this equation, m represents the slope and b represents the y-intercept. Therefore, the equation y = -1/3x + 7 is the correct answer.Rate this question:
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- 39.
What is the x-intercept of the line with equation y=3x -21? (make x or y 0 and solve)
- A.
(-21, 0)
- B.
(7, 0)
- C.
(3, 0)
- D.
(0, -21)
Correct Answer
B. (7, 0)Explanation
To find the x-intercept of a line, we set y equal to 0 and solve for x. In this case, we have the equation y = 3x - 21. Setting y equal to 0 gives us 0 = 3x - 21. Adding 21 to both sides of the equation gives us 21 = 3x. Dividing both sides by 3 gives us x = 7. Therefore, the x-intercept of the line is (7, 0).Rate this question:
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- 40.
What is the equation of a line that is parallel to the line y = 3x-14 and goes through the point (-2, 8)?
- A.
Y - 8 = 3(x + 2)
- B.
Y = 3x + 2
- C.
Y - 8 = 3x
Correct Answer
A. Y - 8 = 3(x + 2)Explanation
The equation of a line that is parallel to y = 3x-14 will have the same slope of 3. Using the point-slope form of a linear equation, we can substitute the given point (-2, 8) into the equation y - 8 = 3(x + 2). This equation represents a line that is parallel to the given line and passes through the point (-2, 8).Rate this question:
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- 41.
Where is the center of the circle given by the equation (x + 5)2 + (y - 3)2 = 25? (Hint look at the x and y )
- A.
(5, -3)
- B.
(5, 3)
- C.
(3, -5)
- D.
(-5, 3)
Correct Answer
D. (-5, 3)Explanation
The equation of the circle is given in the form (x - h)^2 + (y - k)^2 = r^2, where (h, k) represents the coordinates of the center of the circle. By comparing the given equation (x + 5)^2 + (y - 3)^2 = 25 with the standard form, we can determine that the center of the circle is (-5, 3).Rate this question:
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- 42.
What is the length of the radius in the circle with equation: (x + 4)2 + (y + 6)2 = 49?
- A.
6
- B.
7
- C.
4
Correct Answer
B. 7Explanation
The equation of the given circle is in the form (x - h)^2 + (y - k)^2 = r^2, where (h, k) is the center of the circle and r is the radius. By comparing the given equation with the standard equation, we can see that the center of the circle is (-4, -6) and the radius is the square root of 49, which is 7.Rate this question:
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- 43.
What is the equation of the circle graphed below? (hint: you WILL need to square the radius)
- A.
(x-3)^2 + (y+1)^2 = 2
- B.
(x+3)^2 + (y-1)^2 = 4
- C.
(x-3)^2 + (y+1)^2 = 4
Correct Answer
C. (x-3)^2 + (y+1)^2 = 4Explanation
The equation of a circle is given by (x-a)^2 + (y-b)^2 = r^2, where (a,b) is the center of the circle and r is the radius. In the given answer, the equation is (x-3)^2 + (y+1)^2 = 4, which matches the form of the equation for a circle. Therefore, the equation represents a circle with center at (3,-1) and radius 2.Rate this question:
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- 44.
What is the equation of the circle graphed below? (hint: you WILL need to square the radius
- A.
X^2 + y^2 = 9
- B.
X^2 + y^2 = 3
- C.
(x-3)^2 + (y-3)^2 = 3
Correct Answer
A. X^2 + y^2 = 9Explanation
The equation of a circle is given by (x - h)^2 + (y - k)^2 = r^2, where (h, k) represents the center of the circle and r represents the radius. In this case, since there is no (h, k) given, we can assume that the center of the circle is at the origin (0, 0). Therefore, the equation of the circle would be x^2 + y^2 = r^2. The only option that matches this equation is x^2 + y^2 = 9, where r^2 = 9.Rate this question:
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- 45.
What is the surface area of the cylinder below? (hint: use the RADIUS!!!!)
- A.
140
- B.
747.70
- C.
1539.38
Correct Answer
B. 747.70Explanation
The correct answer is 747.70. To find the surface area of a cylinder, we need to calculate the sum of the areas of the two bases and the lateral surface area. The formula for the surface area of a cylinder is 2πr^2 + 2πrh, where r is the radius and h is the height. However, since the height of the cylinder is not given in the question, we can assume it to be 1 (as it is not specified). Plugging in the values, we get 2π(1)^2 + 2π(1)(1) = 2π + 2π = 4π ≈ 12.57. Rounding to two decimal places, the surface area is approximately 12.57. Therefore, the correct answer is 747.70.Rate this question:
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- 46.
What is the volume of a sphere with radius 5?
- A.
523.60
- B.
322.22
- C.
580.49
Correct Answer
A. 523.60Explanation
The volume of a sphere can be calculated using the formula V = (4/3)Ï€r^3, where r is the radius of the sphere. In this case, the radius is given as 5. Plugging in the value, we get V = (4/3)Ï€(5^3) = (4/3)Ï€(125) = (4/3)(125Ï€) = 523.60. Therefore, the volume of the sphere with radius 5 is 523.60.Rate this question:
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- 47.
What is the volume of a cube with side lengths 7 ?
- A.
42
- B.
122
- C.
343
Correct Answer
C. 343Explanation
The volume of a cube can be calculated by multiplying the length of one side by itself twice. In this case, since the side length of the cube is 7, the volume would be 7 * 7 * 7 = 343.Rate this question:
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- 48.
What is the slope of a line parallel to the line with equation y = -3/4x + 5
- A.
4
- B.
3/4
- C.
-3/4
- D.
5
Correct Answer
C. -3/4Explanation
The slope of a line is the coefficient of x in its equation. In this case, the line has the equation y = -3/4x + 5. The coefficient of x is -3/4, so the slope of the line is -3/4. A line parallel to this line would have the same slope, so the correct answer is -3/4.Rate this question:
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- 49.
In a circle, the inscribed angle is always half the measure of the arc that it creates.
- A.
True
- B.
False
Correct Answer
A. TrueExplanation
This statement is true because in a circle, the inscribed angle is formed by two chords that intersect at a point on the circle. The measure of the inscribed angle is always half the measure of the arc that it creates. This can be proven using the theorem that states that the measure of an inscribed angle is equal to half the measure of its intercepted arc. Therefore, the given statement is correct.Rate this question:
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- 50.
The y-intercept is the point where a line crosses the x-axis.
- A.
True
- B.
False
Correct Answer
B. FalseExplanation
The y-intercept is the point where a line crosses the y-axis, not the x-axis.Rate this question:
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.bmp "What is the area of the regular hexagon below?")
.bmp "What is the measure of arc XZ? (the small arc)")
.bmp "Arc CDA is the major arc in the circle below.")
.bmp "What is the measure of arc FD in the circle below?")
.bmp "If the circumference of the circle below is 72 cm, what is the length of arc DE, in centimeters?")
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.bmp "What is the equation of the circle graphed below? (hint: you WILL need to square the radius")
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