ccgeometryb final exam practice - mrs. durante's math...

Name: ________________________ Class: ___________________ Date: __________ ID: A

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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

4b.

1

2c.

2

3d. 2

Name: ________________________ ID: A

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____ 4. Write an equation of a parabola with a vertex at the origin and a focus at (3, 0).

a. y = 19

x2 c. x = − 112

y2

b. y = − 112

x2 d. x = 112

y2

____ 5. Identify the focus and the directrix of the graph of y = −18

x2.

a. focus (–2, 0), directrix at y = –2 c. focus (0, –2), directrix at y = 2b. focus (0, –2), directrix at y = –2 d. focus (–2, 0), 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. 120π + 6 3ÊËÁÁÁ

ˆ¯˜̃̃ m2 c. 120π + 36 3

ÊËÁÁÁ

ˆ¯˜̃̃ m2

b. 142π + 36 3ÊËÁÁÁ

ˆ¯˜̃̃ m2 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. 65 d. 32.5

Name: ________________________ ID: A

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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 = 158b. ∠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)

Name: ________________________ ID: A

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____ 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.

a. y = 17

x + 77 c. y = −17

x + 77

b. y = 7x + 11 d. y = −17

x + 11

____ 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.

a. y – 1 = 17

(x + 6) c. y – 1 = –7(x + 6)

b. x – 1 = –7(y + 6) d. y – 6 = −17

(x + 1)

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 ft2 b. 88 ft2 c. 26 ft2 d. 160 ft2

Name: ________________________ ID: A

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____ 16.

a. 341 m2 b. 252 m2 c. 682 m2 d. 325 m2

Find the volume of the sphere shown. Give each answer rounded to the nearest cubic unit.

____ 17.

a. 524 mm3 b. 105 mm3 c. 314 mm3 d. 262 mm3

Explain why the triangles are similar. Then find the value of x.

____ 18.

a. AA Postulate; 1313

c. SAS Postulate; 1313

b. SSS Postulate; 1915

d. AA Postulate; 1915

Name: ________________________ ID: A

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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. w = 7.7, x = 44 c. w = 7.7, x = 54b. w = 6.4, x = 54 d. w = 6.4, x = 44

Name: ________________________ ID: A

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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. 80.0 in.2 d. 483.0 in.2

Name: ________________________ ID: A

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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 ft2.

a. 9384 ft2 b. 784 ft2 c. 63 ft2 d. 64 ft2

____ 27. Use the Law of Sines. Find b to the nearest tenth.

a. 93.9 b. 83.6 c. 28.9 d. 32.3

Name: ________________________ ID: A

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____ 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

placed on a large coordinate grid with its center at (0, 0), the equation x2

1369+

y2

3481= 1 models the path of

the track. The units are given in yards. How long is the major axis of the track? Explain how you found the distance.

Name: ________________________ ID: A

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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?

ID: A

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CCGeometryB Final Exam Practice

Answer Section

MULTIPLE CHOICE

1. ANS: D PTS: 1 DIF: L2 REF: 7-2 Similar PolygonsOBJ: 7-2.1 Similar Polygons NAT: NAEP 2005 G2e | NAEP 2005 M1k | ADP I.1.2 | ADP J.5.1 | ADP K.7TOP: 7-2 Example 3 KEY: corresponding sides | proportion

2. ANS: B PTS: 1 DIF: L2 REF: 7-5 Proportions in TrianglesOBJ: 7-5.1 Using the Side-Splitter Theorem NAT: NAEP 2005 G2e | ADP I.1.2 | ADP J.5.1 | ADP K.3 TOP: 7-5 Example 1KEY: Side-Splitter Theorem

3. ANS: B PTS: 1 DIF: L2 REF: 9-5 DilationsOBJ: 9-5.1 Locating dilation images NAT: NAEP 2005 G2c | ADP K.7TOP: 9-5 Example 1 KEY: dilation | reduction | scale factor

4. ANS: D PTS: 1 DIF: L2 REF: 10-2 ParabolasOBJ: 10-2.1 Writing the Equation of a Parabola TOP: 10-2 Example 2KEY: equation of a parabola | focus of a parabola | parabola | vertex of a parabola

5. ANS: C PTS: 1 DIF: L2 REF: 10-2 ParabolasOBJ: 10-2.2 Graphing Parabolas TOP: 10-2 Example 4 KEY: directrix | equation of a parabola | focus of a parabola | parabola | graphing

6. ANS: C PTS: 1 DIF: L3 REF: 10-7 Areas of Circles and SectorsOBJ: 10-7.1 Finding Areas of Circles and Parts of Circles NAT: NAEP 2005 M1h | ADP I.4.1 | ADP J.1.6 | ADP K.4 | ADP K.8.2 TOP: 10-7 Example 3 KEY: sector | circle | area | central angle

7. ANS: C PTS: 1 DIF: L2 REF: 12-1 Tangent LinesOBJ: 12-1.1 Using the Radius-Tangent Relationship NAT: NAEP 2005 G3e | ADP K.4TOP: 12-1 Example 1 KEY: tangent to a circle | point of tangency | angle measure | properties of tangents | central angle

8. ANS: D PTS: 1 DIF: L2 REF: 12-2 Chords and ArcsOBJ: 12-2.2 Lines Through the Center of a Circle NAT: NAEP 2005 G3e | ADP K.4TOP: 12-2 Example 3 KEY: bisected chords | circle | perpendicular | perpendicular bisector | Pythagorean Theorem

9. ANS: D PTS: 1 DIF: L2 REF: 12-5 Circles in the Coordinate Plane OBJ: 12-5.2 Finding the Center and Radius of a Circle NAT: NAEP 2005 G4d | ADP K.10.4TOP: 12-4 Example 4 KEY: center | circle | coordinate plane | radius | equation of a circle | word problem

10. ANS: B PTS: 1 DIF: L3 REF: 1-6 Measuring AnglesOBJ: 1-6.2 Identifying Angle Pairs NAT: NAEP 2005 M1e | NAEP 2005 M1f | NAEP 2005 G3gKEY: supplementary angles

11. ANS: C PTS: 1 DIF: L2 REF: 1-8 The Coordinate PlaneOBJ: 1-8.2 Finding the Midpoint of a Segment NAT: NAEP 2005 M1e | ADP J.1.6 | ADP K.10.3 TOP: 1-8 Example 4KEY: coordinate plane | Midpoint Formula

ID: A

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22. ANS: A PTS: 1 DIF: L3 REF: 8-4 Sine and Cosine RatiosOBJ: 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.11.2KEY: 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 3KEY: 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 TrapezoidNAT: NAEP 2005 M1h | ADP J.1.6 | ADP K.8.2 TOP: 10-2 Example 1KEY: trapezoid | area

25. ANS: D PTS: 1 DIF: L2 REF: 10-3 Areas of Regular PolygonsOBJ: 10-3.1 Areas of Regular Polygons NAT: NAEP 2005 M1h | ADP K.8.2TOP: 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 SinesOBJ: 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 CosinesOBJ: 14-5.1 The Law of Cosines TOP: 14-5 Example 1 KEY: Law of Cosines

ID: A

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SHORT ANSWER

29. ANS:

drawing of the situation 1 pointplacing the correct coordinates 1 pointcalculation of midpoint 1 points

PTS: 1 DIF: L3 REF: 6-6 Placing Figures in the Coordinate PlaneOBJ: 6-6.1 Naming Coordinates NAT: NAEP 2005 G4d KEY: algebra | coordinate plane | square

30. ANS: a.

b. 456 m2 1 point, net 1 point, calculations 1 point

PTS: 1 DIF: L2 REF: 11-2 Surface Areas of Prisms and CylindersOBJ: 11-2.1 Finding Surface Area of a Prism NAT: NAEP 2005 M1j | ADP I.4.1 | ADP J.1.6 | ADP K.8.2 | ADP K.9 TOP: 11-2 Example 1 KEY: surface area of a prism | prism | surface area | net | multi-part question

ID: A

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31. ANS: a.

b. sinθ = 2429

definition of sine

θ = sin−1 2429

Ê

Ë

ÁÁÁÁÁ

ˆ

¯

˜̃˜̃˜ Use the inverse of the sine function.

θ ≈ 55.9°

diagram 1 point, work 1 point, answer 1 point

PTS: 1 DIF: L2 REF: 14-3 Right Triangles and Trigonometric RatiosOBJ: 14-3.2 Finding the Measures of Angles in a Right Triangle TOP: 14-3 Example 5 KEY: angle measure | trigonometric ratios | problem solving | sine function | multi-part question

OTHER

32. ANS:

When the equation for an ellipse is in the standard form x2

b 2+

y2

a2= 1, the major axis can be determined by

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

PTS: 1 DIF: L3 REF: 10-4 Ellipses OBJ: 10-4.1 Writing the Equation of an Ellipse TOP: 10-4 Example 2KEY: 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

ID: A

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ESSAY

33. ANS: 10 points 5 perimeter question, 5 area question

Perimeter Lengthsx = 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)

AreaRectangle 15 (1)Semicirlce 9.8 (1)Triangle 6 (1)Triangle 2.6 (1)Total 33.4 Answer 1768.53

PTS: 10

ccgeometryb final exam practice - mrs. durante's math...

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