Geometry 2nd Semester Final Exam

You may use your scientific calculator for the entire exam. There will also be patty paper, rulers, and scratch paper available.

It is strongly recommended that you spend quality time reviewing all tests and quizzes as well as looking through the notes you took during class. Don’t procrastinate!!

Test Dates:

Monday June 10, 2019 and Tuesday June 11, 2019. You will take the final during your geometry class period.

Topics:

Chapter 7: Similarity

Definition of Similar Ratios & ProportionsAA, SAS, and SSS triangle similarity shortcuts

Trapezoid & Triangle Midsegment Properties Apply Similar Triangles to solve real world problems

Chapter 8: Right Triangles and Trigonometry

Sine, Cosine, &TangentFinding Missing SidesFinding Missing Angles

Solving Word ProblemsLaw of CosinesLaw of Sines

Angles of Elevation/DepressionPythagorean Theorem

Chapter 10: Circles

Area of SectorsArc LengthProperties of Tangents lines

Properties of ChordsInscribed AnglesProperties of Secant lines and segments

Chapter 11: Volume

Find Volume Given Volume find a missing pieceSurface Area

All the above for the following shapes: Prisms, Cylinders, Pyramids, Cones, Spheres, Hemispheres

Word problems Cross Sections

Chapter 12: Probability

Basic Probability Tables of OutcomesTree DiagramsVenn Diagrams

Conditional Probability Counting Using: Counting Principle, Combinations & Permutations

After the geometry final, we will do a unit preparing for algebra 2. You will have the algebra test on the day of your scheduled final. June 24, 2019 – Periods 1 and 2. June 25, 2019 – Periods 3 and 4. June 26, 2019 – Periods 5 and 6.

Geometry – 2nd Semester Review

Chapter 7 – Similarity

1.For a dilation with a scale factorless than 1, how do the angles andside lengths of the preimage relateto the angles and side lengths ofthe image?

AAngles are proportional;side lengths are larger.

BAngles are proportional;side lengths are smaller.

CAngles are congruent;side lengths are larger.

DAngles are congruent;side lengths are smaller.

2.What is the scale factor of thedilation shown?

3.What are the coordinates of theimage D0.5 (2, 4)?

4.Graph .

5.Which best describes thecomposition of transformationsthat maps ΔLMN to ΔL′M′N′?

A

B

C

D

6.What are the coordinates of U′ forthe transformation of T(−7, −6), U(−8, 3),and V(2, 1)?

7.Label each statement True or False.

· A similarity transformation thatmaps one circle onto another mustinclude a reflection.

· There is no similaritytransformation that will mapone circle onto another.

· All circles are similar.

8.Given ΔSTU and ΔDEF,what is m∠D?

9.Given ΔLMN ∼ ΔRST, which mustbe true? Select all that apply.

AC

BDMN = ST

10.Which condition would proveΔDEF ∼ ΔJKL?

AEF : KL = 2 : 1

BDF : JL = 2 : 1

CDE : JK = 1 : 2

DDF : JL = 1 : 2

11.Given ΔVXY and ΔVWZ,what is VW?

12.What is JL?

13.What is BD?

14.Which are similar to ΔMKL?

Yes

No

ΔLKJ

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ΔLMK

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ΔMLJ

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15.What is the value of x?

16.Which conclusion does the diagramsupport?

AC

BD

17.What is EF?

18.Given ΔABC, what is the value of x?

Chapter 8 – Right Triangles and Trigonometry

1.What is BC?

2.Do line segmentswith the givenlengths form aright triangle?

3.The hypotenuse of a 30°-60°-90°triangle has a length of 15 cm.Which could be the length of a legof the triangle? Select all that apply.

A9 cmC12 cm

B cmD7.5 cm

4.Which is the area of the rectangle?

5.Which is the sine ratio of ∠A?

AC

BD

6.Which is equal to ? Select all thatapply.

Asin 30°Dcos 60°

Bsin 45°Etan 30°

Ccos 45°Ftan 45°

7.To the nearest tenth, which is theperimeter of ΔABC?

8.What is m∠A to the nearest tenth?

9.The ratios of the ______ of theangles in a triangle to the lengthsof their ______________ sidesare equal.

10.Find the value of x to the nearesttenth.

11.Use the Law of Sines to write anexpression that represents anglemeasure x.

12.What is the perimeter of ΔABC tothe nearest whole number?

13.Use the Law of Cosines to write anexpression equivalent to a.

14.Find BC to the nearest tenth.

15.What is x to the nearest tenth?

16.What measurementof ΔABC can bedeterminedby just using theLaw of Cosines?

Yes

No

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17.What is the angle of depressionfrom the start of a 3-foot-highaccess ramp that ends at a point20 feet away along the ground?

18.The angle of elevation from aviewer to the top of a flagpole is50°. If the viewer is 20 feet awayand the viewer’s eyes are 5 feetfrom the ground, how high is thepole, to the nearest tenth of a foot?

19.What is the angle of elevation, tothe nearest tenth of a degree, tothe top of a 45-foot building from85 feet away?

20.Given that the area of ΔABC is D,write an expression you could useto find the measure of ∠A.

Chapter 10 – Circles

1.What is the length of ?

2.What is the lengthof expressed interms of ?

3.Write an expressionin terms of thatrepresents the areaof the shaded partof ⊙N.

4. is tangent to ⊙U at point Y.Is each statement true for ⊙U?

Yes

No

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is tangent to ⊙U at point V.

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For Items 5 and 6, use ⊙A.

5. is tangent to⊙A at point B.What is thevalue of x?

6.What is the area of ⊙A?

7.Given ⊙D and , what is?

8.In ⊙H, Whichstatement must be true? Select allthat apply.

A

B

C

D

E

For Items 9–11, use ⊙P with m∠KPH = 100, and

9.Which angle iscongruent to∠JPH?

10.If = 60, what is

11.Which segment is congruentto

For Items 12 and 13, use ⊙T with

12.What is SR?

13.What is the radius of ⊙T?

For Items 14 and 15, use ⊙F.

14.What is m∠HJK?

15.What is

16.Given is tangent to ⊙S atpoint V, which statement must betrue? Select all that apply.

Am∠TUV = m∠TVW

Bm∠TSV = m∠UVX

Cm∠UVX = m∠VTU

Dm∠TVW = m∠TSV

Em∠TVX = m∠TVX

17.In ⊙Q, what is m∠1?

18.For ⊙A with secants and tangent what is an expression for r in terms p and q?

19.What is m∠1?

Chapter 11 – Two- and Three-Dimensional Models

1.Given a polyhedron with 6 verticesand 12 edges, how many facesdoes it have?

2.Match each solid to the spacefigure formed by rotating aboutthe axis of rotation shown.

PolygonSpace Figure

A i.cone

B ii.cylinder

Ciii.hemisphere

3.A plane intersectsthe prism parallel tothe base. Which bestdescribes the cross-section?

ArectangleCpentagon

BtrapezoidDtriangle

4.What is the radius of a hemispherewith a volume of 281,250 cm3?

5.A plane intersects the center ofa sphere with a volume of about9,202.8 m3. What is the area of thecross section? Round to the nearesttenth.

6.For each row in the table, could apolyhedron exist with the givennumber of faces, vertices, andedges?

Faces

Vertices

Edges

Yes

No

8

10

14

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14

9

21

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6

8

12

□

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7.Assuming a soap bubble is a perfectsphere, what is the diameter of abubble containing 1,200 cm3 of air,to the nearest tenth of a centimeter?

8.Which best compares the volumesof the two cylinders?

AThe volume of cylinder A isthe same as the volume ofcylinder B.

BThere is not enoughinformation to compare thevolumes of the cylinders.

CThe volume of cylinder A is lessthan the volume of cylinder B.

DThe volume of cylinder A isgreater than the volume ofcylinder B.

9.A steel pipe 100 cm long has anoutside diameter of 2 cm and aninside diameter of 1.8 cm. If thedensity of the steel is 7.8 grams percm3, what is the mass of the pipe,to the nearest gram?

10.The volume of prism A is 48, andthe volume of prism B is half thevolume of prism A. What is thevalue of a?

11.A stack of one dozen cookies ofdiameter 5 in. exactly fits in acylindrical container of volume176.715 in.3. Which is the thicknessof each cookie?

12.The height of a square pyramid isone half the length of each side.The volume of the pyramid is4,500 in.3. What is the heightof the pyramid?

13.For the regularoctahedron,each edge haslength 3 cm and What isthe volume of theoctahedron? Roundto the nearest hundredth.

14.What is the volume of the cone?

15.Which best compares the volumesof cone A and cone B?

AThe volume of A is half thevolume of B.

BThe volumes of A and B areequal.

CThe volume of A is twice thevolume of B.

DThe volume of A is 4 times thevolume of B.

16.A pile of earth removed from anexcavation is a cone measuring 6 fthigh and 30 ft across its base. Howmany trips will it take to haul awaythe earth using a dump truck witha capacity of 9 cubic yards?

17.A basketball with diameter 9.5 in.is placed in a cubic box with sides10 in. long. How many cubic inchesof packing foam are needed to fillthe rest of the box? Round to thenearest tenth.

18.The ________ of the numberof ________ and vertices ofa polyhedron is equal to thenumber of edges ________.

Chapter 12 – Probability

1. Geologists conclude that there is a 62% probability of a large magnitude earthquake striking the San Francisco Bay region before 2032, and a 17% probability of a large magnitude earthquake striking the Seattle area before 2032.

A. Sketch a tree diagram that gives all possible outcomes.

B. What is the probability that both earthquakes happen?

C. What is the probability that only 1 earth quake happens?

D. What is the probability that neither earthquake happens?

E. Given that one of the earthquakes happens, what is the probability that it will occur in San Francisco?

2.Four percent of the students atWashington High School are inMath Club, 7% are in ComputerClub, and 3% are in both. If astudent is selected at random, whatis the probability that the studentis in Math Club or Computer Club?

A7%C11%

B8%D14%

3.How many different committees with 4 members can be formed from a group of 8 people? (Order is not important.)

4.In a survey of students, 80% weregirls and 20% were boys. Of thegirls surveyed, 40% were wearingsneakers. If a surveyed student isselected at random, what is theprobability that the student is a girlwearing sneakers?

A8%B16%C32%D40%

5. A math class is composed of 34 students.

a How many different general groups of 4 students can be made in this class?

b If each group has a specific Editor, Recorder, Timekeeper, and Spokesperson, how many possible groups can be made?

_______________________________

6. A password for a website must have 5 different digits. If a password is chosen at random, what is the probability that it is 76543?

_______________________________

7. In a recent survey of 100 Skyline orchestra students, 35 students liked Mozart, 75 students liked Bach, and 19 students liked both.

a) Sketch a complete Venn diagram of this problem.

b) What is the probability that a student likes Mozart, given that they like Bach?

c) What is the probability that a student likes neither Mozart nor Bach?

d) Who is better: Mozart or Bach?

__________________________________

8. You roll a standard number cube 5 times. Assume that each number is equally likely to come up each time you roll. To the nearest tenth of a percent, what is the probability that a number greater than 4 comes up exactly 2 of the 5 times?

A. 0.3%

B. 16.5%

C. 31.3%

D. 32.9%

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