Geometry 2 nd 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 & Proportions AA, 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, & Tangent Finding Missing Sides Finding Missing Angles

Solving Word Problems Law of Cosines Law of Sines

Angles of Elevation/Depression Pythagorean Theorem

Chapter 10: Circles

Area of Sectors Arc Length Properties of Tangents lines

Properties of Chords Inscribed Angles Properties of Secant lines and segments

Chapter 11: Volume

Find Volume Given Volume find a missing piece Surface 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 Outcomes Tree Diagrams Venn 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?A Angles are proportional;

side lengths are larger.

B Angles are proportional;

side lengths are smaller.

C Angles are congruent;

side lengths are larger.

D Angles are congruent;

side lengths are smaller.

_______________________________2. What is the scale factor of the

dilation shown?

_______________________________3. What are the coordinates of the

image D0.5 (2, 4)?_______________________________

4. Graph D2 (Δ XYZ ) .

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

A (T ⟨1 , 3⟩∘D2 ) (ΔLMN )

B (T ⟨−1 ,−2⟩∘D 12 ) (ΔLMN )

C (D2∘Rx−axis ) (ΔLMN )

D (D 12

∘R x−axis ) (ΔLMN )

_______________________________6. What are the coordinates of U′ for

the transformation (T ⟨−3, 1⟩∘D4) (ΔTUV ) of T(−7, −6), U(−8, 3),and V(2, 1)?

_______________________________7. Label each statement True or False.

o A similarity transformation that

maps one circle onto another must

include a reflection.

o There is no similarity

transformation that will map

one circle onto another.

o All circles are similar.

_______________________________8. Given ΔSTU and ΔDEF,

what is m∠D?

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

A

m∠ Lm∠R=m∠M

m∠S C m∠N=m∠T

B

LMRT

= LNRS D MN = ST

_______________________________10. Which condition would prove

ΔDEF ∼ ΔJKL?A EF : KL = 2 : 1

B DF : JL = 2 : 1

C DE : JK = 1 : 2

D DF : 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 □ □

ΔLMK □ □

ΔMLJ □ □

_______________________________15. What is the value of x?

_______________________________16. Which conclusion does the diagram

support?

AABBC

= FEED C

BECD

= AFBE

B AF= 12CD D BE= 1

2CD

_______________________________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 segments

with 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.A 9 cm C 12 cm

B 7 .5√3 cm D 7.5 cm

_______________________________4. Which is the area of the rectangle?

_______________________________5. Which is the sine ratio of ∠A?

A195197 C

28195

B28197 D

19528

6. Which is equal to 12 ? Select all that

apply.A sin 30° D cos 60°

B sin 45° E tan 30°

C cos 45° F tan 45°

_______________________________7. To the nearest tenth, which is the

perimeter of ΔABC?

_______________________________8. What is m∠A to the nearest tenth?

_______________________________9. The ratios of the ______ of the

angles in a triangle to the lengthsof their ______________ sidesare equal.

_______________________________10. Find the value of x to the nearest

tenth.

Yes No

28, 45, 53 □ □

33, 56, 64 □ □

36, 77, 85 □ □

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

_______________________________12. What is the perimeter of ΔABC to

the nearest whole number?

_______________________________13. Use the Law of Cosines to write an

expression 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

m∠A □ □

m∠B □ □

m∠C □ □

AC □ □

_______________________________17. What is the angle of depression

from the start of a 3-foot-highaccess ramp that ends at a point20 feet away along the ground?

_______________________________18. The angle of elevation from a

viewer 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, to

the 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 length

of expressed interms of ?

_______________________________3. Write an expression

in terms of thatrepresents the areaof the shaded partof ⊙N.

_______________________________

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

Yes No

m∠VUW=m∠UXY □ □

m∠VWU=m∠YXU □ □

V⃗W is tangent to ⊙U at point V.□ □

For Items 5 and 6, use ⊙A.

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

6. What is the area of ⊙A?_______________________________

7. Given ⊙D and EF≃FG , what is?

_______________________________

8. In ⊙H, ∠JHK≃∠ LHM . Whichstatement must be true? Select allthat apply.A ΔLHK≃ΔJHKB ML≃JKC

D ΔLHM≃ΔLHKE Δ JHK≃Δ LHM

For Items 9–11, use ⊙P with m∠KPH = 100, HK≃LN , and JK≃LM .9. Which angle is

congruent to∠JPH?

10. If = 60, what is

11. Which segment is congruent

to

MN ?

_______________________________

For Items 12 and 13, use ⊙T withPQ≃SR .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 W⃗X is tangent to ⊙S atpoint V, which statement must betrue? Select all that apply.

A m∠TUV = m∠TVW

B m∠TSV = m∠UVX

C m∠UVX = m∠VTU

D m∠TVW = 12 m∠TSV

E m∠TVX = 12 m∠TVX

_______________________________17. In ⊙Q, what is m∠1?

_______________________________

18. For ⊙A with secants BC and tangent BD , 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 space

figure formed by rotating aboutthe axis of rotation shown.

Polygon Space Figure

A i. cone

B ii. cylinder

C iii. hemisphere

_______________________________3. A plane intersects

the prism parallel tothe base. Which bestdescribes the cross-section?A rectangle C pentagon

B trapezoid D triangle

_______________________________4. What is the radius of a hemisphere

with a volume of 281,250 cm3?_______________________________5. A plane intersects the center of

a 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 □ □

14 9 21 □ □

6 8 12 □ □

_______________________________7. Assuming a soap bubble is a perfect

sphere, what is the diameter of abubble containing 1,200 cm3 of air,to the nearest tenth of a centimeter?

_______________________________8. Which best compares the volumes

of the two cylinders?

A The volume of cylinder A is

the same as the volume of

cylinder B.

B There is not enough

information to compare the

volumes of the cylinders.

C The volume of cylinder A is less

than the volume of cylinder B.

D The volume of cylinder A is

greater than the volume of

cylinder 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, and

the volume of prism B is half thevolume of prism A. What is thevalue of a?

_______________________________11. A stack of one dozen cookies of

diameter 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 is

one half the length of each side.The volume of the pyramid is4,500 in.3. What is the heightof the pyramid?

_______________________________13. For the regular

octahedron,each edge haslength 3 cm andh=3 √2

2 cm. What is

the volume of theoctahedron? Roundto the nearest hundredth.

14. What is the volume of the cone?

_______________________________15. Which best compares the volumes

of cone A and cone B?

A The volume of A is half the

volume of B.

B The volumes of A and B are

equal.

C The volume of A is twice the

volume of B.

D The volume of A is 4 times the

volume of B.

_______________________________16. A pile of earth removed from an

excavation 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 number

of ________ 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

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 the

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 at

Washington 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?A 7% C 11%

B 8% D 14%

_______________________________3. How many different committees with 4

members can be formed from a group of 8 people? (Order is not important.)

probability that the student is a girlwearing sneakers?A 8% B 16% C 32% D 40%

_______________________________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%