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WorksheetsGeo Final Review
Total questions: 121
Worksheet time: 7hrs 31mins
Name
Class
Date
1.
The definition of radius is
a)
distance from one point to another point
b)
distance around the circle
c)
distance from the center to any point on the circle
d)
distance across the circle through the center
2.
The definition of radius is
a)
distance from one point to another point
b)
distance around the circle
c)
distance from the center to any point on the circle
d)
distance across the circle through the center
3.
The definition of diameter is
a)
distance from the center of any point on the circle
b)
distance across the circle through the center
c)
distance from one point to another
d)
distance around the circle
4.
Write the equation of a circle with center (h,k) and radius r.
a)
x2 + y2 = r2
b)
(x + h)2 + (y + h)2 = r2
c)
(x - h)2 + (y - k)2 = r2
d)
(x - h)2 - (h - k)2 = r
5.
What is the equation of the circle?
a)
(x+1)2 + (y +1)2 = 3
b)
(x+1)2 + (y -1)2 = 3
c)
(x+1)2 + (y +1)2 = 9
d)
(x-1)2 + (y -1)2 = 9
6.
Write the equation of a circle with center (7, 0) with radius 3.
a)
(x - 7)2 + y2 = 9
b)
x2 + (y -7)2 = 9
c)
(x - 7)2 + y2 = 3
d)
x2 + (y -7)2 = 3
7.
Find the center if the endpoints of the diameter are at (-12, -7) and (3, 5).
a)
(-4.5, -1)
b)
(-7.5, -6)
c)
(4.5, 1)
d)
(7.5, 6)
8.
What is the equation for the circle, if it has diameter endpoints at (3,-4) and (-5,-4)?
a)
(x+1)² + (y-4)² = 4
b)
(x+1)² + (y+4)² = 16
c)
(x-1)² + (y-4)² = 16
d)
(x+1)² + (y+4)² = 4
9.
What is the radius of the circle with this equation of (x-5)²+(y+7)²=8?
a)
4
b)
8
c)
4√2
d)
2√2
10.
What is the equation of this circle?
a)
(x + 3)2 + (y - 1)2 = 9
b)
(x - 3)2 + (y + 1)2 = 9
c)
(x - 3)2 + (y + 1)2 = 3
d)
(x + 3)2 + (y - 1)2 = 3
11.
Write the equation of a circle with center (7, 0) with radius 3.
a)
(x - 7)2 + y2 = 9
b)
x2 + (y -7)2 = 9
c)
(x - 7)2 + y2 = 3
d)
x2 + (y -7)2 = 3
12.
In the equation (x-3)2+(y-2)2=16, the center of the circle is...
a)
(3,2)
b)
(-3, -2)
c)
(-2, -3)
d)
(2, 3)
13.
What is the equation for this circle?
a)
(x+1)+(y+1)=9
b)
x²+y²=9
c)
x+y=9
14.
What is the center and radius in this image?
a)
C(-7,3) ; r=3
b)
C(7,-3) ; r=3
c)
C(7,-3) ; r=9
d)
C(-7,3) ; r=9
15.
What is the correct graph for the equation x²+y²=4?
a)
b)
c)
Answer is in none of the given
d)
16.
Does the point (4,5) lie on the circle whose center is (-2,-2) and radius 9?
a)
yes
b)
No
17.
Circle O has a center at (3,1) and a diameter of 10 units. Which point lies on circle O?
a)
(3,-4)
b)
(-3,-1)
c)
(5,1)
d)
(8,0)
18.
Circle O has a center at (3,1) and a diameter of 10 units. Which point lies on circle O?
a)
(3,-4)
b)
(-3,-1)
c)
(5,1)
d)
(8,0)
19.
Which of the following equations of circle in general form given the center at (3, 4) and radius of 5 units?
a)
(x – 3)2 - (y – 4)2 = 25
b)
(x – 3)2 + (y – 4)2 = 25
c)
x2 + y2 + 6x - 8y - 25 = 0
d)
x2 + y2 - 6x - 8y = 0
20.
In order to convert from general form to center-radius form, you must ___________.
a)
Multiply out
b)
expand
c)
factor
d)
complete the square
21.
Determine the center and radius: x2 + y2 + 14x - 2y = -1
a)
center= (-7,2) radius= 3
b)
center= (-7,1) radius= 7
c)
center= (-4,1) radius= 5
22.
Determine the equation of the circle in standard form: x2 + y2 + 6x - 12y + 20 = 0
a)
(x-3)2 + (y+6)2 = 25
b)
(x+3)2 + (y-6)2 = 25
c)
(x-3)2 + (y+6)2 = 45
d)
(x+3)2 + (y-6)2 = 5
23.
What does (h,k) stand for in the standard circle equation?
a)
(h,k) is the center of the circle
b)
(h,k) is a point on the circle.
c)
(h,k) is a point that we guess and find
d)
(h,k) is the distance of the circle
24.
What are the coordinates of the center and the radius of the circle with equation:
(x - 4)2 + (y - 3)2 = 25 ?
(x - 4)2 + (y - 3)2 = 25 ?
a)
Center (4,3)
Radius = 5 units
Radius = 5 units
b)
Center (4,3)
Radius = 25 units
Radius = 25 units
c)
Center (-4,-3)
Radius = 25 units
Radius = 25 units
d)
Center (-4,-3)
Radius = 5 units
Radius = 5 units
25.
a)
(x + 3)2 + (y - 1)2 = 9
b)
(x - 3)2 + (y + 1)2 = 9
c)
(x - 3)2 + (y + 1)2 = 3
d)
(x + 3)2 + (y - 1)2 = 3
26.
Which graph corresponds to
x2+ (y-6)2=9
a)
A
b)
B
c)
C
d)
D
27.
What similarity theorem would prove that these triangles are similar?
a)
SAS∼
b)
SSS∼
c)
AA∼
d)
Side Splitter
28.
Are the triangles similar?
a)
Yes
b)
No
29.
A triangle has sizes measuring 11 cm, 16 cm, and 16 cm. A similar triangle has sides measuring x cm, 24 cm, and 24 cm. What is x?
a)
x = 19 cm
b)
x = 24 cm
c)
x = 3 cm
d)
x = 16.5 cm
30.
Solve for f.
a)
6
b)
4
c)
3
d)
8
31.
State the postulate that proves these triangles are similar.
a)
SSS
b)
AA
c)
SAS
d)
Not similar
32.
Find side length X.
a)
16
b)
18
c)
2.4
d)
15
33.
How do these triangles appear to be similar?
a)
AA
b)
SAS
c)
SSS
d)
Not Similar
34.
How do these triangles appear to be similar?
(Hint: Look for non-labeled parts!)
(Hint: Look for non-labeled parts!)
a)
AA
b)
SAS
c)
SSS
d)
Not Similar
35.
How do these triangles appear to be similar?
(Hint: Look for non-labeled parts!)
(Hint: Look for non-labeled parts!)
a)
AA
b)
SAS
c)
SSS
d)
Not Similar
36.
Solve for X.
a)
2 ft
b)
3 ft
c)
4 ft
d)
6 ft
37.
Find x.
a)
54/7
b)
56/3
c)
11
d)
21/2
38.
The triangles are similar, solve for the question mark.
a)
8
b)
12.5
c)
18
d)
24
39.
Choose the similarity statement for the triangles.
a)
ΔMNL ∼ ΔOPQ
b)
ΔNOM ∼ ΔPQL
c)
ΔLMN ∼ ΔPQO
d)
ΔMLN ∼ ΔPQO
40.
Find the value of x.
a)
6.92
b)
18.67
c)
2.625
d)
13.71
41.
Triangle SQR is similar to triangle SPT. Which segment corresponds to segment QR?
a)
A) SP
b)
B) ST
c)
C) PR
d)
D) PT
42.
Complete each proportion.
CB / DM = AC / ?
CB / DM = AC / ?
a)
BM
b)
MA
c)
BC
d)
AD
43.
Solve for X
a)
7.5
b)
4.8
c)
13.33
d)
5
44.
If ABCD is a parallelogram, what is the length of BD?
a)
10
b)
11
c)
7
d)
5
45.
Which is NOT a property of a parallelogram?
a)
Diagonals bisect each other
b)
Diagonals are congruent
c)
Both pairs of opposite sides are parallel
d)
Both pairs of opposite angles are congruent
46.
The opposite angles of a parallelogram are ...
a)
complementary
b)
congruent
c)
supplementary
d)
perpendicular
47.
In a parallelogram, consecutive angles are __________.
a)
congruent
b)
supplementary
c)
corresponding
d)
parallel
48.
In a parallelogram, diagonals are __________.
a)
perpendicular
b)
bisected
c)
congruent
d)
parallel
49.
The figure is a parallelogram.
Solve for x.
Solve for x.
a)
1
b)
11
c)
7
d)
6
50.
3 angles of a quadrilateral are 110, 120 and 50. What is the measure of the 4th angle?
a)
60
b)
70
c)
80
d)
130
51.
The figure is a parallelogram.
Solve for x.
Solve for x.
a)
7
b)
1
c)
5
d)
2
52.
The figure is a parallelogram.
Solve for x.
Solve for x.
a)
7
b)
2
c)
0
d)
4
53.
Identify the transformation from ABCD to A'B'C'D'.
a)
Translation
b)
Reflection across the y-axis
c)
Reflection across the x-axis
d)
90o counter clockwise Rotation
54.
Identify the transformation from ABC to A'B'C'.
a)
90o clockwise rotation
b)
90o counter clockwise rotation
c)
Reflection across the y-axis
d)
Reflection across the x-axis
55.
Point (-5,2) is reflected over the y axis. Where is the new point located?
a)
(5,2)
b)
(-5,-2)
c)
(-5,2)
d)
(5,-2)
56.
Point (7,2) is translated vertically 2 units and horizontally -5 units. Where is the new point located?
a)
(9,-3)
b)
(2,4)
c)
(2,0)
d)
12,4)
57.
How many degrees was the figure rotated?
a)
90 degrees counterclockwise
b)
180 degrees
c)
90 degrees clockwise
58.
Reflect Point C over the y-axis:
a)
(-3, 2)
b)
(3,2)
c)
(-2,3)
d)
(3,0)
59.
Translations, reflections and rotations are all known as ________________________.
a)
Geometry
b)
Transformations
c)
Congruent
60.
Write a rule for the translation.
a)
(x -1, y + 2)
b)
(x -2, y + 1)
c)
(x +2, y - 1)
d)
(x +1, y - 2)
61.
Apply the following rule to the point (-5,6):
(x,y)-->(y,-x)
(x,y)-->(y,-x)
a)
(-5,-6)
b)
(5,-6)
c)
(6,5)
d)
(-6,5)
62.
Which rule would result in a translation of 2 units left and 3 units up?
a)
(x, y) → (2x, 3y)
b)
(x, y) → (x - 2, y + 3)
c)
(x, y) → (-x, -y)
d)
(x, y) → (x + 2, y - 3)
63.
Identify the transformation from ABC to A'B'C'.
a)
(x+8, y+4)
b)
(x-8, y-4)
c)
(x+4, y+8)
d)
(x-4, y-8)
64.
Determine where X' would be if you translated X 3 units to the left and 9 units down.
a)
(-4, 4)
b)
(-10, 2)
c)
(-4, -5)
d)
(-1, 5)
65.
The rule for reflection over the y-axis is
(x, y) --> _
(x, y) --> _
a)
(-x, y)
b)
(x, -y)
c)
(y, x)
d)
(-y, x)
66.
The rule for rotation of 270 degrees is
(x, y) --> _
(x, y) --> _
a)
(y, x)
b)
(-y, x)
c)
(y, -x)
d)
(x, -y)
67.
What would the new point be if you rotated the point (4,9) 180°about the origin?
a)
a. (-9,4)
b)
b. (-4,-9)
c)
c. ( 9, -4)
d)
d. (4,9)
68.
∆QRS contains the points: Q(4, 2) R(5, 1) S(3,7). If the triangle is reflected across the y-axis, what will S' be?
a)
S'(3, 7)
b)
S'(-3, 7)
c)
S'(-3, -7)
d)
S'(3, 7)
69.
Find the length of line segment AB given A(4, 3) and B(0, 6).
a)
3
b)
4
c)
5
d)
7
70.
What is the center of MN given M(3, -1) and N(7, -5)
a)
(5, -2)
b)
(10, -6)
c)
(5, -3)
d)
(2, -2)
71.
What point is halfway between (3, -1) and (8, -6)?
a)
(11, -7)
b)
(-5.5, -3.5)
c)
(5.5, -3.5)
d)
(2, -2)
72.
Point M with coordinates (3,4) is the midpoint of the line AB and A has the point (-1,6). What is the point of B?
a)
(1,5)
b)
(2,10)
c)
(7,2)
d)
(1,2)
73.
Find the midpoint of the segment with the endpoints:(4, 12) and (-6, 14)
a)
(-1, 13)
b)
(13, 1)
c)
(13, -1)
d)
(5, 13)
74.
How far is point A from point B?
a)
7.1
b)
7.8
c)
8.7
d)
8.9
75.
What is the distance between the two points?
a)
6.3
b)
6.5
c)
6.7
d)
16
76.
Find the length between ( 1, 3) and (5, 6)
a)
3
b)
4
c)
5
d)
6
77.
What formula do you use to measure the entire length of a diagonal?
a)
midpoint formula
b)
slope
c)
distance formula
d)
midpoint theory
78.
The length between (3, 8) and (-2, -4) is ______?
a)
√17
b)
13
c)
17
d)
169
79.
If a rectangle is made up from points (-2,-1), (4,-1), (4,-3) & (-2,-3)
What is the perimeter of the rectangle?
What is the perimeter of the rectangle?
a)
12
b)
8
c)
16
d)
15
80.
What is the distance of JK, where J(4,3) and K(2, -3)?
a)
√ ̅3̅2̅
b)
40
c)
32
d)
√ ̅4̅0̅
81.
Find the distance between the points (4, 3) and (0, 6).
a)
3
b)
4
c)
5
d)
7
82.
What is the midpoint between (3, -1) and (7, -5)
a)
(5, -2)
b)
(10, -6)
c)
(5, -3)
d)
(2, -2)
83.
What is the midpoint between (3, -1) and (8, -6)
a)
(11, -7)
b)
(-5.5, -3.5)
c)
(5.5, -3.5)
d)
(2, -2)
84.
We can use SOH-CAH-TOA for...
a)
Any triangle ever
b)
Non-right triangles only
c)
Right Triangles only
d)
Never
85.
The ratio in a right triangle of adjacent to hypotenuse is _____
a)
sine
b)
cosine
c)
tangent
d)
inverse cosine
86.
The ratio in a right triangle of opposite to adjacent side is _____
a)
sine
b)
cosine
c)
tangent
d)
inverse cosine
87.
Choose the correct ratio.
a)
A
b)
B
c)
C
d)
D
88.
Choose the correct ratio.
a)
sin(37)=x/14
b)
cos(37)=x/14
c)
tan(37)=x/14
d)
sin(37)=14/x
89.
Find the length of side w.
a)
21.4 cm
b)
18.0 cm
c)
36.5 cm
d)
43.6 cm
90.
What is the cosine of angle P?
a)
p/q
b)
q/r
c)
p/r
d)
r/q
91.
Find x round to the nearest tenth.
a)
46.1
b)
4.9
c)
16.4
d)
26.9
92.
a)
6.99
b)
6.33
c)
13.59
d)
7.83
93.
a)
20.35
b)
12.72
c)
14.99
d)
21.83
94.
Find the length of side y.
a)
22.32 cm
b)
36.5 cm
c)
76.34 cm
d)
87.76 cm
95.
a)
44.55
b)
22.69
c)
41.66
d)
38.49
96.
The ratio in a right triangle of opposite and hypotenuse is
a)
Cosine
b)
Tangent
c)
Sine
d)
Pythagorean Theorem
97.
Find the length of the missing side.
a)
17 cm
b)
22 cm
c)
15 cm
d)
13 cm
98.
The Pythagorean Theorem is
a2 + b2 + c2
a)
false
b)
true
99.
Casey travels from her house directly west to the bank and then directly north from the bank to the mall. She then travels home on the road connecting the mall and her house. What is her total distance traveled?
a)
17 miles
b)
32 miles
c)
37 miles
d)
40 miles
100.
You need a ladder that will reach up a 25 foot tall house when placed 10 feet away from the house. How tall does the ladder need to be?
a)
25 feet
b)
26 feet
c)
27 feet
d)
28 feet
101.
Find the length of the missing side.
a)
20 in.
b)
68 in.
c)
16 in.
d)
80 in.
102.
Jake is 6 ft. tall. He is standing outside when the angle of elevation of the sun is 28 degrees. How long would his shadow be?
a)
5.3 feet
b)
2.8 feet
c)
3.2 feet
d)
11.3 feet
103.
A plane takes off at an angle of 30 degrees and reaches a height of 10 miles. What is the diagonal distance it has traveled from take off to it's current position?
a)
15 miles
b)
38 miles
c)
17 miles
d)
20 miles
104.
You are standing 10 feet away from a tree. There is a cat up in the tree. Your eyes make a 48 degree angle to look up at the cat. How high is the cat?
a)
11.1 ft.
b)
9 ft.
c)
7.4 ft.
d)
13.8 ft.
105.
Susan is flying a kite, which gets caught in the top of a tree. Use the diagram to estimate the height of the tree.
a)
63.6 ft
b)
1.59 ft
c)
74.2 ft
d)
86.9 ft
106.
a2 + b2 = c2
a = 9 b = 40
a = 9 b = 40
a)
c = 41
b)
c = 65
c)
c = 25
d)
c = 5
107.
Find the missing side
a)
9
b)
41
c)
6.4
d)
3
108.
What is the longest side of a right triangle called?
a)
Leg A
b)
Leg B
c)
Hypotenuse
d)
Pythagoras' Big Buddy
109.
State if the three sides lengths form an acute, obtuse, or right triangle:
6 mi, 14 mi, 17 mi
6 mi, 14 mi, 17 mi
a)
acute
b)
obtuse
c)
right
110.
You need a ladder that will reach up a 25 foot tall house when placed 10 feet away from the house. How tall does the ladder need to be?
a)
25 feet
b)
26 feet
c)
27 feet
d)
28 feet
111.
Find the length of the missing side.
a)
25 cm
b)
42 cm
c)
52 cm
d)
48 cm
112.
State if the three sides lengths form an acute, obtuse, or right triangle:
7 in, 11 in, 13 in
7 in, 11 in, 13 in
a)
acute
b)
obtuse
c)
right
113.
The size of a television screen is measured by the length of the diagonal of the screen. What size is a television screen that is 3 feet tall and 6 feet wide?
a)
18
b)
6.7
114.
Find the missing side
a)
11
b)
61
c)
61
d)
11
115.
Do the segment lengths 15, 9 and, 12 form a right triangle?
a)
Yes
b)
No
116.
The lengths of a triangle are given below. Is the the triangle obtuse, acute, or right?
4, 5, 6
4, 5, 6
a)
right
b)
obtuse
c)
acute
117.
Do the following squares form a right triangle? Why or why not?
a)
No, because 9+15 does not equal 16
b)
No, because the squares are not equal
c)
Yes, because the squares are all different sizes
d)
Yes, becuase 9+15=16
118.
Isabella has sticks that are 10cm, 11cm, and 13cm long. Can she place the sticks together to form a right triangle? Justify your answer.
a)
No, because 10+11 does not equal 13
b)
No, because 100+121 does not equal 169
c)
Yes, because there is a small side, medium side and long side
d)
Yes, because a triangle has 3 sides
119.
Alan made a small four-sided table for his office. The opposite sides of the table are 27 inches long and 36 inches long. If the diagonal of the table measures 40 inches, does the table have right angles at the corners? Why or why not?
a)
Yes, because it's a rectangle and rectangles have 90 degree angles in the corners
b)
Yes, because 27 and 36 are less than 40
c)
No, because 272+362 does not equal 402
d)
No, because 27+36 does not equal 40
120.
Find X
a)
1015
b)
25
c)
303
d)
150
121.
Is this Triangle Right, Acute, Straight or Obtuse?
a)
Acute
b)
Straight
c)
Right
d)
Obtuse
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