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Name: ________________________ Class: ___________________ Date: __________
CCGeometryB Final Exam Practice
Multiple Choice (1 point each)
Identify the choice that best completes the statement or answers the question.
____
1. ABCD ~ WXYZ. AD = 8, DC = 2, and WZ = 30. Find YZ. The figures are not drawn to scale.
a.
19
b.
120
c.
60
d.
7.5
____
2. Given: PQ Ä BC . Find the length of AQ. The diagram is not drawn to scale.
____
a. 9
b. 6
c. 12
d. 8
3. The dashed triangle is a dilation image of the solid triangle. What is the scale factor?
a.
1
4
b.
1
2
c.
1
2
3
d.
2
ID: A
Name: ________________________
____
____
____
ID: A
4. Write an equation of a parabola with a vertex at the origin and a focus at (3, 0).
1
1
c. x = − y 2
a. y = x 2
9
12
1 2
1 2
y
b. y = − x
d. x =
12
12
1
5. Identify the focus and the directrix of the graph of y = − x 2 .
8
a. focus (–2, 0), directrix at y = –2
c. focus (0, –2), directrix at y = 2
d. focus (–2, 0), directrix at y = 2
b. focus (0, –2), directrix at y = –2
6. Find the area of the shaded region. Leave your answer in terms of π and in simplest radical form.
a.
b.
ÊÁ
ˆ
ÁÁ 120π + 6 3 ˜˜˜ m2
Ë
¯
ÊÁ
ˆ
ÁÁ 142π + 36 3 ˜˜˜ m2
Ë
¯
c.
ÊÁ
ˆ
ÁÁ 120π + 36 3 ˜˜˜ m2
Ë
¯
d.
none of these
Assume that lines that appear to be tangent are tangent. O is the center of the circle. Find the value of
x. (Figures are not drawn to scale.)
____
7. m∠P = 25
a.
50
b.
115
c.
2
65
d.
32.5
Name: ________________________
ID: A
Find the value of x. If necessary, round your answer to the nearest tenth. The figure is not drawn to
scale.
____
____
8.
a. 13.6
b. 7.5
c. 94.3
d. 9.7
9. A low-wattage radio station can be heard only within a certain distance from the station. On the graph below,
the circular region represents that part of the city where the station can be heard, and the center of the circle
represents the location of the station. Which equation represents the boundary for the region where the
station can be heard?
a.
(x – 6) 2 + (y – 1) 2 = 32
c.
(x – 6) 2 + (y – 1) 2 = 16
b. (x + 6) 2 + (y + 1) 2 = 32
d. (x + 6) 2 + (y + 1) 2 = 16
____ 10. ∠1 and ∠2 are supplementary angles. m∠1 = x − 40, and m∠2 = x + 76. Find the measure of each angle.
a. ∠1 = 72, ∠2 = 118
c. ∠1 = 32, ∠2 = 158
b. ∠1 = 32, ∠2 = 148
d. ∠1 = 72, ∠2 = 108
____ 11. M(6, 7) is the midpoint of RS . The coordinates of S are (7, 9). What are the coordinates of R?
a. (12, 14)
b. (6.5, 8)
c. (5, 5)
d. (8, 11)
3
Name: ________________________
ID: A
____ 12. At the curb a ramp is 11 inches off the ground. The other end of the ramp rests on the street 77 inches straight
out from the curb. Write a linear equation in slope-intercept form that relates the height y of the ramp to the
distance x from the curb.
1
1
c. y = − x + 77
a. y = x + 77
7
7
1
b. y = 7x + 11
d. y = − x + 11
7
____ 13. Plans for a bridge are drawn on a coordinate grid. One girder of the bridge lies on the line y = –7x + 3. A
perpendicular brace passes through the point (–6, 1). Write an equation of the line that contains the brace.
1
a. y – 1 = (x + 6)
c. y – 1 = –7(x + 6)
7
1
b. x – 1 = –7(y + 6)
d. y – 6 = − (x + 1)
7
Find the surface area of the cylinder in terms of π .
____ 14.
a.
230π in. 2
b.
200π in. 2
c.
180π in. 2
d.
380 in. 2
Find the surface area of the pyramid shown to the nearest whole number.
____ 15.
a.
72 ft 2
b.
88 ft 2
c.
4
26 ft 2
d.
160 ft 2
Name: ________________________
ID: A
____ 16.
a.
341 m 2
b.
252 m 2
c.
682 m 2
d.
325 m 2
Find the volume of the sphere shown. Give each answer rounded to the nearest cubic unit.
____ 17.
a.
524 mm 3
b.
105 mm 3
c.
314 mm 3
d.
Explain why the triangles are similar. Then find the value of x.
____ 18.
a.
b.
1
3
1
SSS Postulate; 19
5
AA Postulate; 13
c.
d.
5
1
3
1
AA Postulate; 19
5
SAS Postulate; 13
262 mm 3
Name: ________________________
ID: A
Find the length of the missing side. Leave your answer in simplest radical form.
____ 19.
a. 4 cm
b. 2 26 cm
c. 116 cm
d. 2 29 cm
____ 20. Find the lengths of the missing sides in the triangle. Write your answers as integers or as decimals rounded to
the nearest tenth.
a.
x = 5.7, y = 6.9
b.
x = 11.3, y = 8
c.
x = 6.9, y = 5.7
d.
x = 8, y = 11.3
Find the value of x. Round to the nearest tenth.
____ 21.
a. 11.5
b. 19.6
c. 11.8
d. 20.1
____ 22. Find the value of w and then x. Round lengths to the nearest tenth and angle measures to the nearest degree.
a.
b.
w = 7.7, x = 44
w = 6.4, x = 54
c.
d.
6
w = 7.7, x = 54
w = 6.4, x = 44
Name: ________________________
ID: A
Find the value of x. Round the length to the nearest tenth.
____ 23.
a.
7.5 yd
b.
13 yd
c.
26 yd
d.
8.7 yd
Find the area. The figure is not drawn to scale.
____ 24.
a. 77.2 in.2
b. 80 in.2
c. 75 in.2
d. 70 in.2
____ 25. Find the area of the regular polygon. Round your answer to the nearest tenth.
a.
176.6 in.2
b.
966.1 in.2
c.
7
80.0 in.2
d.
483.0 in.2
Name: ________________________
ID: A
The figures are similar. The area of one figure is given. Find the area of the other figure to the nearest
whole number.
____ 26. The area of the larger triangle is 766 ft 2 .
a. 9384 ft 2
b. 784 ft 2
c.
____ 27. Use the Law of Sines. Find b to the nearest tenth.
a.
93.9
b.
83.6
c.
8
63 ft 2
d.
64 ft 2
28.9
d.
32.3
Name: ________________________
ID: A
____ 28. Use the Law of Cosines. Find b to the nearest tenth.
a.
35.0
b.
80.6
c.
108.2
d.
21.5
Short Answer ( 3 points each) Please show all work required to obtain a solution in the box provided.
29. In the coordinate plane, draw a square with sides 10q units long. Give coordinates for each vertex, and the
coordinates of the point of intersection of the diagonals.
Consider the prism shown below.
a. Draw a net for the prism and label all dimensions.
b. Use the net to find the surface area of the prism.
30.
31. Howard is flying a kite and wants to find its angle of elevation. The string on the kite is 29 meters long and
the kite is level with the top of a building that he knows is 24 meters high.
a. Draw a diagram of the situation.
b. To the nearest tenth of a degree, find the angle of elevation. Show your work.
32. Skip designs tracks for amusement park rides. For a new design, the track will be elliptical. If the ellipse is
y2
x2
+
= 1 models the path of
placed on a large coordinate grid with its center at (0, 0), the equation
1369 3481
the track. The units are given in yards. How long is the major axis of the track? Explain how you found the
distance.
9
Name: ________________________
ID: A
Free Response
33. The owners of a restaurant have decided to build an outdoor patio to increase the number of customers
that they can serve in the summer. The patio design consists of a rectangle, two right triangles, and a
semicircle. The patio area will be made of interlocking paving stones with different stones along the border.
The paving stones cost $49.95 per square meter. The border stones are priced according to the length of
the border and cost $13 per meter. How much will the materials for the patio cost?
10
ID: A
CCGeometryB Final Exam Practice
Answer Section
MULTIPLE CHOICE
1. ANS:
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9. ANS:
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10. ANS:
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11. ANS:
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KEY:
D
PTS: 1
DIF: L2
REF: 7-2 Similar Polygons
7-2.1 Similar Polygons
NAEP 2005 G2e | NAEP 2005 M1k | ADP I.1.2 | ADP J.5.1 | ADP K.7
7-2 Example 3
KEY: corresponding sides | proportion
B
PTS: 1
DIF: L2
REF: 7-5 Proportions in Triangles
7-5.1 Using the Side-Splitter Theorem
NAEP 2005 G2e | ADP I.1.2 | ADP J.5.1 | ADP K.3
TOP: 7-5 Example 1
Side-Splitter Theorem
B
PTS: 1
DIF: L2
REF: 9-5 Dilations
9-5.1 Locating dilation images
NAT: NAEP 2005 G2c | ADP K.7
9-5 Example 1
KEY: dilation | reduction | scale factor
D
PTS: 1
DIF: L2
REF: 10-2 Parabolas
10-2.1 Writing the Equation of a Parabola
TOP: 10-2 Example 2
equation of a parabola | focus of a parabola | parabola | vertex of a parabola
C
PTS: 1
DIF: L2
REF: 10-2 Parabolas
10-2.2 Graphing Parabolas
TOP: 10-2 Example 4
directrix | equation of a parabola | focus of a parabola | parabola | graphing
C
PTS: 1
DIF: L3
REF: 10-7 Areas of Circles and Sectors
10-7.1 Finding Areas of Circles and Parts of Circles
NAEP 2005 M1h | ADP I.4.1 | ADP J.1.6 | ADP K.4 | ADP K.8.2
10-7 Example 3
KEY: sector | circle | area | central angle
C
PTS: 1
DIF: L2
REF: 12-1 Tangent Lines
12-1.1 Using the Radius-Tangent Relationship
NAT: NAEP 2005 G3e | ADP K.4
12-1 Example 1
tangent to a circle | point of tangency | angle measure | properties of tangents | central angle
D
PTS: 1
DIF: L2
REF: 12-2 Chords and Arcs
12-2.2 Lines Through the Center of a Circle
NAT: NAEP 2005 G3e | ADP K.4
12-2 Example 3
bisected chords | circle | perpendicular | perpendicular bisector | Pythagorean Theorem
D
PTS: 1
DIF: L2
12-5 Circles in the Coordinate Plane
12-5.2 Finding the Center and Radius of a Circle
NAT: NAEP 2005 G4d | ADP K.10.4
12-4 Example 4
center | circle | coordinate plane | radius | equation of a circle | word problem
B
PTS: 1
DIF: L3
REF: 1-6 Measuring Angles
1-6.2 Identifying Angle Pairs
NAT: NAEP 2005 M1e | NAEP 2005 M1f | NAEP 2005 G3g
supplementary angles
C
PTS: 1
DIF: L2
REF: 1-8 The Coordinate Plane
1-8.2 Finding the Midpoint of a Segment
NAEP 2005 M1e | ADP J.1.6 | ADP K.10.3
TOP: 1-8 Example 4
coordinate plane | Midpoint Formula
1
ID: A
12. ANS:
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KEY:
13. ANS:
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14. ANS:
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19. ANS:
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20. ANS:
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21. ANS:
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TOP:
D
PTS: 1
DIF: L3
REF: 3-6 Lines in the Coordinate Plane
3-6.2 Writing Equations of Lines
NAEP 2005 A1h | NAEP 2005 A2a | ADP J.4.1 | ADP J.4.2 | ADP K.10.2
word problem | problem solving | slope-intercept form
A
PTS: 1
DIF: L2
3-7 Slopes of Parallel and Perpendicular Lines
3-7.2 Slope and Perpendicular Lines
NAEP 2005 A1h | NAEP 2005 A2a | ADP J.4.1 | ADP J.4.2 | ADP K.10.2
3-7 Example 6
word problem | problem solving | perpendicular lines | slopes of perpendicular lines
A
PTS: 1
DIF: L2
11-2 Surface Areas of Prisms and Cylinders
11-2.2 Finding Surface Area of a Cylinder
NAEP 2005 M1j | ADP I.4.1 | ADP J.1.6 | ADP K.8.2 | ADP K.9
11-2 Example 3
surface area of a cylinder | cylinder | surface area formulas | surface area
B
PTS: 1
DIF: L2
11-3 Surface Areas of Pyramids and Cones
11-3.1 Finding Surface Area of a Pyramid
NAEP 2005 M1j | ADP I.4.1 | ADP J.1.6 | ADP K.8.2 | ADP K.9
11-3 Example 1
surface area of a pyramid | surface area | surface area formulas | pyramid
A
PTS: 1
DIF: L2
11-3 Surface Areas of Pyramids and Cones
11-3.1 Finding Surface Area of a Pyramid
NAEP 2005 M1j | ADP I.4.1 | ADP J.1.6 | ADP K.8.2 | ADP K.9
11-3 Example 1
surface area of a pyramid | surface area formulas | pyramid
A
PTS: 1
DIF: L2
11-6 Surface Areas and Volumes of Spheres
11-6.1 Finding Surface Area and Volume of a Sphere
NAEP 2005 M1j | ADP I.4.1 | ADP J.1.6 | ADP K.8.2
TOP: 11-6 Example 3
volume of a sphere | sphere | volume formulas | volume
A
PTS: 1
DIF: L2
REF: 7-3 Proving Triangles Similar
7-3.2 Applying AA, SAS, and SSS Similarity
NAEP 2005 G2e | ADP I.1.2 | ADP K.3
TOP: 7-3 Example 3
Angle-Angle Similarity Postulate
D
PTS: 1
DIF: L2
8-1 The Pythagorean Theorem and Its Converse
OBJ: 8-1.1 The Pythagorean Theorem
NAEP 2005 G3d | ADP I.4.1 | ADP J.1.6 | ADP K.1.2 | ADP K.5 | ADP K.10.3
8-1 Example 2
KEY: Pythagorean Theorem | leg | hypotenuse
B
PTS: 1
DIF: L3
REF: 8-2 Special Right Triangles
8-2.1 45°-45°-90° Triangles
NAT: NAEP 2005 G3d | ADP I.4.1 | ADP J.5.1 | ADP K.5
8-2 Example 2
KEY: special right triangles | hypotenuse | leg
B
PTS: 1
DIF: L2
REF: 8-4 Sine and Cosine Ratios
8-4.1 Using Sine and Cosine in Triangles
NAEP 2005 M1m | ADP I.1.2 | ADP I.4.1 | ADP K.11.1 | ADP K.11.2
8-4 Example 2
KEY: cosine | side length using since and cosine | cosine ratio
2
ID: A
22. ANS: A
PTS: 1
DIF: L3
REF: 8-4 Sine and Cosine Ratios
OBJ: 8-4.1 Using Sine and Cosine in Triangles
NAT: NAEP 2005 M1m | ADP I.1.2 | ADP I.4.1 | ADP K.11.1 | ADP K.11.2
KEY: side length using since and cosine | angle measure using sine and cosine | problem solving | sine |
inverse of cosine and sine | sine ratio
23. ANS: D
PTS: 1
DIF: L2
REF: 8-5 Angles of Elevation and Depression
OBJ: 8-5.1 Using Angles of Elevation and Depression
NAT: NAEP 2005 M1k | ADP I.1.2 | ADP I.4.1 | ADP K.11.2
TOP: 8-5 Example 3
KEY: tangent | side length using tangent | tangent ratio | angles of elevation and depression
24. ANS: D
PTS: 1
DIF: L2
REF: 10-2 Areas of Trapezoids, Rhombuses, and Kites
OBJ: 10-2.1 Area of a Trapezoid
NAT: NAEP 2005 M1h | ADP J.1.6 | ADP K.8.2
TOP: 10-2 Example 1
KEY: trapezoid | area
25. ANS: D
PTS: 1
DIF: L2
REF: 10-3 Areas of Regular Polygons
OBJ: 10-3.1 Areas of Regular Polygons NAT: NAEP 2005 M1h | ADP K.8.2
TOP: 10-3 Example 3
KEY: regular polygon | area | apothem | radius | octagon
26. ANS: C
PTS: 1
DIF: L2
REF: 10-4 Perimeters and Areas of Similar Figures
OBJ: 10-4.1 Finding Perimeters and Areas of Similar Figures
NAT: NAEP 2005 M2g | NAEP 2005 N4c | ADP I.1.2 | ADP K.8.3
TOP: 10-4 Example 2
KEY: similar figures | area
27. ANS: D
PTS: 1
DIF: L2
REF: 14-4 Area and the Law of Sines
OBJ: 14-4.1 Area and the Law of Sines TOP: 14-4 Example 2
KEY: Law of Sines
28. ANS: D
PTS: 1
DIF: L2
REF: 14-5 The Law of Cosines
OBJ: 14-5.1 The Law of Cosines
TOP: 14-5 Example 1
KEY: Law of Cosines
3
ID: A
SHORT ANSWER
29. ANS:
drawing of the situation 1 point
placing the correct coordinates 1 point
calculation of midpoint 1 points
PTS: 1
DIF: L3
OBJ: 6-6.1 Naming Coordinates
KEY: algebra | coordinate plane | square
30. ANS:
a.
b.
REF: 6-6 Placing Figures in the Coordinate Plane
NAT: NAEP 2005 G4d
456 m 2 1 point, net 1 point, calculations 1 point
PTS:
OBJ:
NAT:
TOP:
KEY:
1
DIF: L2
REF: 11-2 Surface Areas of Prisms and Cylinders
11-2.1 Finding Surface Area of a Prism
NAEP 2005 M1j | ADP I.4.1 | ADP J.1.6 | ADP K.8.2 | ADP K.9
11-2 Example 1
surface area of a prism | prism | surface area | net | multi-part question
4
ID: A
31. ANS:
a.
24
29
ÊÁ 24 ˆ˜
θ = sin −1 ÁÁÁÁ ˜˜˜˜
Ë 29 ¯
b. sin θ =
definition of sine
Use the inverse of the sine function.
θ ≈ 55.9°
diagram 1 point, work 1 point, answer 1 point
PTS:
OBJ:
TOP:
KEY:
1
DIF: L2
REF: 14-3 Right Triangles and Trigonometric Ratios
14-3.2 Finding the Measures of Angles in a Right Triangle
14-3 Example 5
angle measure | trigonometric ratios | problem solving | sine function | multi-part question
OTHER
32. ANS:
y2
x2
+
= 1, the major axis can be determined by
b2
a2
the greater value of the denominator. In this case, the greater denominator is with the y2 term, so the ellipse
has a vertical major axis. The distance from the center of the ellipse to a vertex is a. In this case,
a = 3481 = 59. The length of the major axis of the track is twice a or 118 yards.
1 point knowing the major axis, 1 point correct answer, 1 point written explanation
When the equation for an ellipse is in the standard form
PTS: 1
DIF: L3
REF: 10-4 Ellipses
OBJ: 10-4.1 Writing the Equation of an Ellipse
TOP: 10-4 Example 2
KEY: co-vertex of an ellipse | ellipse | equation of an ellipse | major axis of an ellipse | minor axis of an
ellipse | problem solving | vertex of an ellipse | writing in math | word problem
5
ID: A
ESSAY
33. ANS:
10 points 5 perimeter question, 5 area question
Perimeter Lengths
x = 1.73
(1)
y=3.46
(1)
semicircle circumference 7.85 (1)
add 5, 4, 5 (from 3-4-5 triangle) (1)
Total 27.04 Cost 419.12 (1)
Area
Rectangle 15 (1)
Semicirlce 9.8 (1)
Triangle 6 (1)
Triangle 2.6 (1)
Total 33.4 Answer 1768.53
PTS: 10
6