If sin and cos X , what is the value of tan X - Miss Cao's …kttmc.weebly.com/uploads/2/1/2/7/21275598/im_2... · · 2016-06-03and cos∠X = 7, what is the value of tan∠X?

1 What is the value of x?

A. 36 2 B. 18 2 C. 18 D. 9 2

2

If sin∠X =2425 and cos∠X =

725 , what is the value of tan∠X?

A. B. C. D.

Copy of IM 2 for End-of-Course Exam - Geometry Assessment ID: ib.666818

Directions: Answer the following question(s).

Illuminate Itembank™ Continue: Turn to the next page.Generated On May 28, 2016, 2:29 PM PDT Page 1

3 Triangle FLR is similar to triangle MBT.

Select the two angles whose sine equals 1237 .

A. B. C. D.

E. F.

4 Determine the length of BC asumming that AB is a tangent to cicle C. using the figure below:

A. 13cm B. 5cm C. 26cm D. 22cm

5 Write the equation of a circle with a radius of 10 and a center of (-2,5).

A. (x+2)2-(y+5)2 = 100 B. (x-2)2-(y-5)2 = 100 C. (x+2)2+(y+5)2 = 100 D. (x+2)2+(y-5)2 = 100




6 Calculate the total surface area of the cone and round to the nearest tenth.

A. 269.5 in2 B. 382.6 in2 C. 446.7 in2 D. 721.9 in2

7 If ΔPQR ~ ΔSTU, find the value of x .

A. 35 B. 24.6 C. 7 D. 4.4




8 Calculate the height of the Parallelogram.

A. 4.22 B. 5.00 C. 9.06 D. 21.45

9 Calculate the surface area of a square-based pyramid with a slant height of 5 ft and base edges of 6ft.

A. 48 ft2 B. 72 ft2 C. 96 ft2 D. 180 ft2

10 Calculate the probabilty that a dart thrown at the given target will hit the shaded region. Assume the dart isequally likely to hit any point inside the target.

A. 9.3% B. 5.1% C. 21.5% D. 31.4%




11 Examine the properties listed below. Determine which of the following properties are true for allrhombi or rhombuses. Select three that apply.

A. four right angles B. diagonals bisect eachother

C. diagonals arecongruent

D. opposite angles arecongruent

E. diagonals intersect atright angles

12 A fountain is located between two trees. Each tree has a height of 60 feet. The angles of elevationfrom the base of the fountain to the top of each tree are 64° and 48° as shown below.

What is the horizontal distance between the two trees (rounded to the nearest foot)?

A. 54 ft B. 83 ft C. 29 ft D. 90 ft




13 The diagram below shows a student using a clinometer to measure the height of a flagpole. Whenthe student stands 40 feet away from its base and the clinometer is exactly 5 feet above the ground,the clinometer shows a 35° angle of elevation to the top of the pole. What is the approximate height(h) of the flagpole? The diagram is not to scale.

A. 28.0 ft B. 33.0 ft C. 37.8 ft D. 62.1 ft

14 The steps in the construction result in a line (m) through the given point (A) that is parallel to the given line(n). Which statement justifies why the constructed line is parallel to the given line?

15 Look at this rectangular prism. What could be the dimensions of a rectangular prism that is similar to thisrectangular prism?

16 This diagram represents a tower. The tower is in the shape of a cone on top of a cylinder. Whichmeasurement is closest to the total volume of the tower?

17 If the side of a square is tripled, then by how much will the area the square increase?

A. The area will increaseby a multiple of 9.

B. The area will increaseby a mutliple of 6.

C. The area will increaseby a multiple of 3.

D. The area will stay thesame.




18 What is the area of the shaded region?

A. 25 - 5𝜋 B. 100 - 25𝜋 C. 10𝜋 D. 25𝜋

19 A circular in-ground pool has a diameter of 15 feet. To the nearest dollar, how much would it cost to put aconcrete walk 3 feet wide around the pool if a mason charges $3.20 per square foot? Use 3.14 for Pi.

A. $169.56 B. $176.63 C. $346.19 D. $542.59

20 Find the area of a circle with a Circumference of 20π .

A. 400π B. 10π C. 100π D. 25π

21 Calculate the area.

A. 510 B. 686.7 C. 598.4 D. 622.4

22 Which of the following pairs of numbers have a geometric mean of 10? Select all that apply.

A. 4 and 50 B. 4 and 25 C. 25 and 75 D. 5 and 20

E. 2 and 50 F. 5 and 25




23 To prove that the area of a circle is equal to pi times the radius squared, Sonia drew a regularhexagon. She found the area of the hexagon to be 6 times the area (A) of the triangle shown in the

hexagon below, or A = 6 · 1

2s · r, where s is a side length and r is the distance from the center of a

side of the hexagon to the center of the hexagon.

She then drew a 12–sided regular figure and found the area to be A = 12 · 1

2s · r.

In the formula, A = 12 · 1

2s · r, what should Sonia replace with the circumference of a circle (2π · r) to

find the area of a circle?

A. 12 · s B.12 ·

1

2s

C. 12 · s · r D.12 ·

1

2 · s · r




24

In the diagram above NK = 8, LN = 3, and MN = 9 then what is the length of JN?

A. 24 B. 3.375 C. 4 D. 2.67

25 In the figure below, ∠HFG ≅ ∠HKJ and HF ≅ HK.

Select the triangle congruence criterion that can be used to prove that ΔHFG ≅ ΔHKJ.

A. angle–angle–side(AAS)

B. angle–side–angle(ASA)

C. side–angle–side(SAS)

D. side–side–angle(SSA)




26 Katherine wants to prove that the measures of the interior angles of a triangle have a sum of 180°. She draws a triangle and extends one of the sides through a vertex. She then draws a line throughthis vertex that is parallel to the opposite side, as shown in the diagram below.

Which of the following statements must be true and could be used as part of Katherine's proof? Select all that apply.

A. m∠1 = m∠5 B. m∠2 = m∠4 C. m∠3 = m∠4 + m∠5 D. m∠3 + m∠4 + m∠5= 180°

E. m∠1 + m∠2 + m∠4+ m∠5 = 180°

27 Mikhail draws triangles ABC and DEF, as shown below, and claims that the two triangles are similar.

Select all methods that can be used to justify the claim.

A. show that ∠C ≅ ∠Dand that allcorresponding sidesare congruent

B. show that ∠C ≅ ∠Dand that allcorresponding sidesare proportional

C. show that a sequenceof rotations,reflections, andtranslations carriestriangle ABC ontotriangle DEF

D. show that a sequenceof rotations,reflections,translations, anddilations carriestriangle ABC ontotriangle DEF




28 Parallelogram RSTU is shown below.

Ilan needs to prove that RS ≅ TU and RU ≅ TS. His proof is shown in the table below.

Step Statement

1 RSTU is a parallelogram

2 RS is parallel to TU and RU is parallel to TS

3 ∠RSU ≅ ∠TUS and ∠RUS ≅ ∠TSU

4 SU ≅ US

5 ΔRSU ≅ ΔTUS

6 RS ≅ TU and RU ≅ TS

Select all reasons that support one or more statements in the proof.

A. symmetric property B. definition of aparallelogram

C. alternate interiorangles are congruent

D. opposite sides of aparallelogram arecongruent

E. corresponding partsof congruent trianglesare congruent




29 Triangle PRT and triangle QRS are shown below.

Kirby claims that the missing side lengths PT and QS are parallel because they seem to be drawnthat way in the diagram. Which of the following statements best explains whether PT and QS areparallel?

A. Line segment PT isparallel to linesegment QS because

2

3 =

4

9.

B. Line segment PT isparallel to linesegment QS because

2

4 =

3

9.

C. Line segment PT isparallel to linesegment QS because

2

6 =

3

9.

D. Line segment PT isnot parallel to linesegment QS because

2

4 ≠

3

9.

30 Given ΔADE ≅ΔCDB, which of the following statements must be true?

Select all that apply!

A. DE ≅ DB B. AB ≅ CD C. D is the midpoint

of ACD. ∠A ≅ ∠B

E. ∠EDA ≅ ∠BDC




31

Given the triangles below, ∠S ≅ ∠U and SR ≅ UT

Which of the folliwing triangle congruence postulates proves that ΔTRS ≅ ΔRTU?

A. side-side-angle B. side-angle-side C. side-side-side D. not enoughinformation




32

Given:Line segment WZ bisects line segment XYLine segment XY bisects line segment WZ

To prove:Triangles WAX and ZAY are congruent

Statements: Reasons:

1. Segment WZ bisects XY 1. given

2. Segments XA and AY are congruent2. When a segment is bisected the resulting segments are

congruent

3. Segment XY bisects WZ 3. given

4. _____________________4. When a segment is bisected the resulting segments are

congruent

5. Angles WAX and YAZ are congruent 5. Vertical angles of intersecting lines are equal

6. Triangles WAX and ZYA are congruent6. Triangles with two sides and an included angle equal are

congruent

What should be in statement 4 to complete the proof?

A. Statement 4 is not needed the proof works without it.

B. Segments WA and AZ are congruent.

C. Segments WX and YZ are congruent.

D. Angles WXA and ZYA are congruent.




33 A home owner wants to landscape her backyard. She decides to lay sod for her new lawn. Sheneeds to work around an established tree with a base diameter of 8 feet. The distance from theretaining wall to the house is about 20 feet. The distance from one fence to the other is about 30feet.

Select all of the information that will help the homeowner make a reasonable estimate of the area ofthe new lawn.

A. A circle with a radiusof 4 ft should be usedto estimate the areathat the tree willoccupy.

B. A circle with adiameter of 20 ftshould be used toestimate the area ofthe new lawn.

C. A 20 ft × 30 ftrectangle should beused to model thearea of the new lawn.

D. An 8 ft × 30 ftrectangle should beused to model thearea of the new lawn.

E. With the giveninformation, theestimated area will begreater than theactual area.




34 A grain silo is approximately 85% full. A 55 lb sack of grain measures 2 cubic feet.

What is the best estimate of the number of bags of grain that can be filled using all the grain in thesilo?

A. 1708 bags B. 2010 bags C. 6833 bags D. 8038 bags

35 Prove that Circle P and Circle Q are similar.

Circle P: Center (–1, 4) and radius of 8 units.Circle Q: Center (3, 6) and a radius of 2 units.

Select the option that best shows the necessary transformations from Circle P to Circle Q.

A. move left 4 units;down 2 units; and nochange in the radius

B. move right 4 units; up2 units; radii ratio of4; increase in theradius

C. move left 4 units;down 2 units; radiiratio of 4; increase inthe radius

D. move right 4 units; up2 units; radii ratio of

1

4; reduction in the

radius




36 Find the area of the shaded sector. Round your answer to the nearest tenth. Use 3.14 for π.

A. 141.3 m2 B. 70.7 m2 C. 22.5 m2 D. 3.8 m2

37 Find the value of each variable.

A. x = 75° and y = 78° B. x = 78° and y = 65° C. x = 102° and y = 115° D. x = 71.5° and y =71.5°

38 Which quadrilaterals can always be inscribed in a circle? Select all that apply.

A. rectangle B. isosceles trapezoid C. kite D. parallelogram

E. rhombus F. square




39 A driveway is shown below with all of the dimensions given in feet.

The driveway needs to be resurfaced. What is the best estimate of the area of the driveway?

A. 100π ft2 B. 125π ft2 C. 225π ft2 D. 500π ft2

40 Marcus has been working on a large rubber band ball. When Marcus first measured the ball it had adiameter of 5 inches. Over the course of one year Marcus continued to add more rubber bands tothe ball. After one year Marcus measured the rubber band ball, and it had a diameter of 15 inches.

How much volume was added on to the rubber band ball? Round your answer to the nearest tenth.

A. 20.8π inches3 B. 541.7π inches3 C. 562.5π inches3 D. 4333.3π inches3




41 Maria claims that ΔABE is similar to ΔACD.

Select all of the transformations or series of transformations that supports Maria's claim and mapsΔABE to ΔACD.

A. A dilation with a scalefactor of 3 about pointA.

B. A dilation with a scalefactor of 2 about pointB.

C. A dilation with a scalefactor of 2 about pointA followed by atranslation of 4 unitsdownward.

D. A dilation with a scalefactor of 3 about pointB followed by atranslation of 4 unitsdownward.

E. A dilation with a scalefactor of 3 about pointA followed by atranslation of 8 unitsto the right.

F. A dilation with a scalefactor of 2 about pointB followed by atranslation of 8 unitsto the right.

42 A company is packing a box with basketballs to ship to the stores to sell. There are 36 balls, in a3 × 3 × 4 formation, packed into one box. If each ball has a diameter of 29.5 inches, what are thedimensions of the box?

A. 1062 in. B. 924,200 in3 C. 88.5 in. × 88.5 in. ×88.5 in.

D. 88.5 in. × 88.5 in. ×118 in.

43 A contractor is building a tower. He is told that the dimensions of the tower must be50 ft × 80 ft × 250 ft. The building is to have 20 floors with a 2.5 ft tall portion between each floor andfor the roof. What is the volume of each floor?

A. 40,000 ft3 B. 50,000 ft3 C. 800,000 ft3 D. 1,000,000 ft3




44

Keith is attempting to solve the Pythagorean Theorem by using similar triangles. After Keith has setup the appropriate ratios and solved, he ended up with two equations:

a2 = cdb2 = ce

What must Keith do next in order to complete the theorem?

A. Subtract the twoequations.

B. Multiply the twoequations.

C. Add the twoequations.

D. Divide the twoequations.

45

Thomas is attempting to prove the Pythagorean Theorem using similar triangles. Which of thefollowing could be Thomas's first ratio that he sets up?

A. AB

AC =

AD

AB

B. AB

AC =

DC

BC

C. BD

AB =

CD

BC

D. AB

BC =

BD

DC




46 A candle maker purchased packaging boxes to ship cylindrical candles to customers. The boxesmeasure 6 in. by 6 in. by 10 in. To keep the candles from damaging, foam inserts with a thickness of1

2in. are placed between the candle and the inside of the box on all sides. What is the volume of the

largest candle that can be shipped out?

A. 360 in3 B. 282.6 in3 C. 225.6 in3 D. 176.6 in3

47 A proof that the interior angles of a triangle have a sum of 180° is shown below.

Given: Triangle ABCProve: m∠1 + m∠2 + m∠3 = 180°

The reasons for Steps 4–6 are not shown in the proof. Which of the following definitions could beused as reasons in Steps 4–6? Select two that apply.

A. Definition of parallel lines

B. Definition of supplementary angles

C. Definition of congruent angles




48 A right circular cylinder is shown below.

Which of the following could be a two–dimensional figure that results when a plane intersects thisright circular cylinder? Select three that apply.

A. circle B. ellipse C. triangle D. rectangle

49 A square pyramid has a height of 12 feet and a base with a length of 5 feet. In order to double thevolume of this pyramid, which measurements could be changed? Select two that apply.

A. The length of thebase could beincreased to 10 feet.

B. The area of the basecould be increased to50 feet2.

C. The width of the basecould be increased to25 feet.

D. The height of thepyramid could beincreased to 24 feet.

50 In the drawing below, lines a and b are parallel lines cut by the transversal c. Jeremiah wishes tofind angles that are congruent to ∠7 in order to prove that ∠7 ≅ ∠3

Which angles are congruent to ∠7? Why are they congruent to ∠7? Select two that apply.

A. ∠8 because linearpairs are congruent

B. ∠6 because verticalangles are congruent

C. ∠4 because alternateinterior angles arecongruent

D. ∠3 becausecorresponding anglesare congruent




51 A student wants to prove that opposite angles of a parallelogram are congruent. The student drawsthe parallelogram below, where the sides of the parallelogram have been extended.

The student outlines a proof, as follows:

"First, I'll show that ∠5 ≅ ∠2. Then, I'll show that ∠5 ≅ ∠4. It must follow that ∠2 ≅ ∠4.

Next, I'll show that ∠1 ≅ ∠6. Then, I'll show that ∠3 ≅ ∠6. It must follow that ∠1 ≅ ∠3.

Since ∠2 ≅ ∠4 and ∠1 ≅ ∠3, it follows that opposite angles of a parallelogram are congruent."

Which of the following congruence statements are based on the reasoning that alternate interiorangles are congruent when two parallel lines are cut by a transversal? Select two that apply.

A. ∠1 ≅ ∠3 B. ∠1 ≅ ∠6 C. ∠5 ≅ ∠2 D. ∠5 ≅ ∠4

52 A student wants to prove that the base angles of an isosceles triangle are congruent. The studentdraws isosceles triangle ABC with base angles B and C, as shown below.

Point M is drawn as the midpoint of BC.

Which of the following could be used as part of the proof that ∠B ≅ ∠C? Select three that apply.

A. AM ≅ AM becauseof the SymmetricProperty.

B. BM ≅ CM becauseof the definition of amidpoint.

C. AB ≅ AC because ofthe definition of anisosceles triangle.

D. ΔABM ≅ ΔACMbecause of the SAStriangle congruencecriterion.

E. ∠B ≅ ∠C becausecorresponding partsof congruent trianglesare congruent.




53 In the figure below, B is the midpoint of AC and D is the midpoint of CE.

Which of the following statements must be true? Select three that apply.

A. AB ≅ BC B. BC ≅ CD C. AB ≅ DE D.BD ≅

1

2 AE

E. BD || AE F. AC ⊥ AE

54 Examine parallelogram RSTU below.

Determine which of the following values are correct. Select three that apply.

A. x = 15 B. y = 23 C. m∠R = 27° D. m∠S = 135°

E. m∠T = 45° F. m∠U = 99°




55 Examine the figure below.

Determine which of the following angle measures are correct. Select two that apply.

A. m∠JKL = 37° B. m∠KJL = 73° C. m∠JLK = 86° D. m∠KLM = 126°

56 Examine the properties listed below. Determine which of the following properties are true for allparallelograms. Select three that apply.

A. four right angles B. diagonals bisect eachother

C. opposite sides arecongruent

D. opposite angles arecongruent

E. diagonals intersect atright angles

57 Examine ΔABC below.

Which of the following equations correctly represent the relationships between the segments? Select two that apply.

A. AG = 2GD B.GC =

1

2FG

C. BE = 2BG D.GA =

1

2AD

E. GF = 2CG F.GE =

1

2BG




58 In the figure below, line a || line b.

If m∠2 = 78°, which of the following angles also measure 78°? Select three that apply.

A. ∠3 B. ∠4 C. ∠5 D. ∠6

E. ∠7 F. ∠8

59 Mrs. McDonnell is making 25 paper cones to fill with popcorn for her daughter's birthday party.

Find the volume of one paper cone if the diameter is 4 inches and the height is 7 inches. Round youranswer to the nearest cubic inch.

A. 29 in3 B. 59 in3 C. 88 in3 D. 117 in3

60 Triangle PQR is shown below.

When triangle PQR is rotated about side QR, which of the following three–dimensional figures iscreated?

A. cone B. cylinder C. pyramid D. triangular prism




61

A student examines the triangle shown above. He notices that lines BE and CD look parallel. Thestudent claims that they are parallel by look alone.

Is the student correct?

A. Yes, because

6

3 =

12

9 .

B. Yes, because

6

12 =

3

9 .

C. Yes, because

6

9 =

3

12 .

D. No, because

6

3 ≠

12

9 .

62The radius of Earth is 20,903,520 feet. Mark wants to make a model globe of Earth that is

1

10,000,000

of its actual size. What would be the volume of Mark's globe? (Round to the nearest tenth. Useπ = 3.14.)

A. 8.8 ft3 B. 18.3 ft3 C. 28.7 ft3 D. 38.2 ft3




63

A. 8.7 B. 10.8 C. 14.0 D. 16.3

64 A line segment with endpoints (–3, 4) and (5, –6) is used to perform a dilation with center (0, 0). Afterthe dilation, the new line segment has a length that is half as long as the original line segment. The

dilation has a scale factor of k. Annabelle claims that k must have been 1

2.

Which statement best describes Annabelle's claim?

A. Annabelle's claim isincorrect since thescale factor of dilation

was 2, not 1

2.

B. Annabelle's claim isincorrect since thescale factor of dilationcould have also have

been – 1

2.

C. Annabelle's claim iscorrect since a scale

factor of 1

2 results in

a line segment half aslong as the original.

D. Annabelle's claim iscorrect since adilation of a linesegment half as longas the original musthave a scale factor of

1

2.




65 A student states the following two conjectures.

Conjecture 1: If the corresponding angles of two triangles are congruent, then the triangles arecongruent since a sequence of rigid motions carries one triangle onto the other.

Conjecture 2: If two triangles are congruent, then the corresponding angles are congruent since asequence of rigid motions carries each angle onto its corresponding angle.

Which statement correctly classifies the student's conjectures?

A. Both Conjecture 1and Conjecture 2 arealways true for anypair of triangles.

B. Both Conjecture 1and Conjecture 2 aretrue for some pairs oftriangles, but not all.

C. Conjecture 1 isalways true, butConjecture 2 is truefor only some pairs oftriangles.

D. Conjecture 1 is truefor only some pairs oftriangles, whileConjecture 2 isalways true.

66

NOTE: Drawings are not necessarily to scale.

Are the two triangles above similar? (select the best response)

A. Yes, because theylook proportional.

B. Yes, becausecorresponding sidesare proportional.

C. Yes, because allisosceles trianglesare similar.

D. No, because we don’tknow whether ALLpairs ofcorresponding sidesare proportional.

E. No, because /D is not

proportional to /A .




67 Circle O is shown below.

What is the measure of arc ADC if the measure of arc BC is 52 degrees?

A. 28 degrees B. 218 degrees C. 225 degrees D. 270 degrees

68 A tree is standing next to a 40 foot high building. The tree has an 18 foot shadow, while the building has a 16foot shadow. How tall is the tree rounded to the nearest foot?

A. 42 feet B. 36 feet C. 45 feet D. 7 feet




69

Hypothesis:Given ΔABC, if m∠ABC = m∠ACB. AB = AC

Proof:

1. If AB ≠ AC, then AB > AC or AC > AB2. Suppose AB > AC, then make DB = AC. Join D to C3. Consider ΔDBC and ΔACB. Sides DB and BC = sides AC and CB and angle m∠DBC = m∠ACB4. Therefore base DC = base AB and ΔDBC = ΔACB

Conclusion: In ΔABC side AB = side AC

A. Step 2 is aconstruction so it is aproof by construction.

B. Step 3 shows that it isa proof by induction.

C. Step 4 is acontradiction so it is aproof bycontradiction.

D. Step 1 uses the lawof trichotomy so it is aproof by trichotomy.




70

What is the value of a in the figure above?

A. 4 B. 6 C. 8 D. 9

E. Not enoughinformation.

71 Which of the following pairs of figures MUST be similar? (select all that apply)

A. two squares B. two parallelograms C. two circles D. two pentagons

E. two right triangles




72 Find all the mistakes in the proof:

Statements Reasons1.

1. Given

2. 2. Two angles that form a linear pair are supplementary.

3. 3. Supplements of the same angle, or congruent angles, arecongruent.

4. 4. Reflexive Property

5. 5. (CPCTC) Corresponding parts of congruent triangles arecongruent.

6. 6. SAS

7. 7. An angle bisector is a ray whose endpoint is the vertex ofthe angle and which divides the angle into two congruentangles.

A. The statement in step4 should be: "AB ≅CB"

B. The reason in step 6should be: "ASA"

C. Step 7 should gobefore step 6.

D. Step 5 should go afterstep 6.




73 Find all the mistakes in the proof:

Statements Reasons

1.

1. Given

2. 2. Perpendicular lines meet to form right angles.

3. 3. Right angles are congruent.

4. 4. Reflexive Property

5. 5. SAS

A. The statement in step4 should be: "BC ≅CB"

B. The reason in step 5should be: "ASA"

C. The reason in step 4should be: "Definitionof Midpoint."

D. There are nomistakes.

74 While standing at the top of a lighthouse, Joel notices a boat approaching the shore. If the boat is250 ft from the base of the lighthouse and Joel needs to look down at 41° angle of depression inorder to see the boat, what is the approximate height of the lighthouse? (Assume the lighthouse isat a right angle to the ground.)

sin 41° ≅ 0.66

cos 41° ≅ 0.75

tan 41° ≅ 0.87

A. 165 ft B. 188 ft C. 218 ft D. 287 ft

75 In order for cos 53° = sin A, what must be the measure of ∠A?

A. 37° B. 53° C. 90° D. 127°




76 Sam claims that cos X = sin Y if X and Y are congruent angles. Is Sam correct?

A. Yes, Sam is correct. B. No, cos X = sin Y if Xand Y arecorrespondingangles.

C. No, cos X = sin Y if Xand Y arecomplementaryangles.

D. No, cos X = sin Y if Xand Y aresupplementaryangles.

77 In the figure below, ΔABC is similar to ΔDEF. Find the length of EF.

A. 10 B. 12 C. 18 D. 21

78 Solve for x.

A. 12 B. 14 C. 23 D. 30




79 Which pair of triangles below can be shown to be similar using AA similarity?

A. B. C. D.

80 ∠ABC of a triangle is a right angle. If Tania draws a line segment from vertex B of the triangle to thetriangle's hypotenuse, which of these statements must be correct?

A. The line segmentneither needs tobisect the hypotenusenor be perpendicularto it to prove that thetwo triangles formedare similar.

B. The line segmentmust bisect thehypotenuse, but itneed not beperpendicular to it toprove that the twotriangles formed aresimilar.

C. The line segmentmust beperpendicular to thehypotenuse, but itneed not bisect it toprove that the twotriangles formed aresimilar.

D. The line segmentmust bisect thehypotenuse and beperpendicular to it toprove that the twotriangles formed aresimilar.

81

What is the measure of angle W is the measure of arc VZ is 100 and the measure of arc AB is 30?

A. 30 B. 100 C. 35 D. 65




82

In the diagram above, the length of QS is six more than the length of QP. If the length of PR is 21, what isthe length of QS?

A. 4 B. 1.7 C. 10 D. 25

83

In the diagram above, the measure of angle LNJ is 64 degrees and the measure of arc JL is 10 degrees. What is the measure of arc MK?

A. 128 B. 118 C. 64 D. 10




84

In the diagram above, AZ= 2, VB = 11, and WB = 5. What is the length of AW?

A. 40.0 B. 8.0 C. 14.0 D. 27.5

85

In the diagram above, the sum of the measures of arcs SP and PR is equal to the measure of arc SR. If themeasure of SP is one third the measure of PR, what is the measure of angle SQP?

A. 60 B. 45 C. 67.5 D. There is not enoughinformation in thisproblem to determinethe measure of angleSQP.




86

In the diagram above, E is the center of the circle, GH = 5 and EF = 6.5, what is the length of HF?

A. 12 B. 10 C. 4.2 D. 14

87

In the diagram above, the measure of angle W is the same as the measure of arc AB. If the measure of arcVZ is 80 more than the measure of arc AB, what is the measure of angle W?

A. 160 B. 80 C. 40 D. 120




88

In the diagram above QS = 8 and PR = 12. What is the length of QP?

A. 8 B. 4 C. 5.3 D. 6




89

In the diagram above, A is the center of the circle and AE = 1 and BE = 4. What is the length of CE?

A. 5.0 B. 4.9 C. 2.5 D. There isn't enoughinformation in theproblem to figure thisout.




90

In the diagram above, the measure of angle ACD is 40 degrees, what is the measure of minor arc AD?

A. 140 degrees B. 80 degrees C. 40 degrees D. 100 degrees




91 Find the volume of the cylinder. Round the answer to the nearest hundredth.

A. 216.97 ft3 B. 324.59 ft3 C. 435.20 ft3 D. 681.64 ft3

92 Find the volume of the pyramid and round to the nearest tenth.

A. 33.3 cm3 B. 37.5 cm3 C. 66.7 cm3 D. 100 cm3

93

A. 360 – (m∠Q) B.360 –

1

2 (m∠Q)

C. 180 – (m∠Q) D.180 –

1

2 (m∠Q)




94

Which statement must be true in this figure?

A. ∠Q ≅ ∠S B. ∠Q ≅ ∠R C. TQ ≅ SR D. TQ ⊥ RS

95 What is the approximate volume of the right pyramid represented by this net?

A. 1365 cm3 B. 1182 cm3 C. 965 cm3 D. There is not enoughinformation to answerthis question.

96 What is the approximate volume of the cylinder represented by this net?

A. 297 cm3 B. 385 cm3 C. 1,539 cm3 D. There is not enoughinformation to answerthis question.




97 A sphere has a volume of 1,436.03 m3, what is the approximate length of its radius?

A. 4.9 m B. 7.0 m C. 10.7 m D. 18.5 m

98 The blades of a helicopter's propeller are perpendicular and congruent. The distance betweenconsecutive blade tips is 24 feet. Find the length (b) of each blade.

A. 12 √ 2 ft B. 24 √ 2 ft C. 12 ft D. 24 ft

99 The diagram below shows a central angle of θ radians in a circle of radius r. The angle intercepts anarc with an arc length of s.

Wesley wants to derive a formula for the arc length of a circle. Complete the proportion below with afraction in terms of s and r that can be used to derive the formula for the arc length of a circle.

θ

2π =




Knowformulasforthevolumesofcones,cylinders,andspheresandusethemtosolverealworldandmathematicalproblems.

100




A diameter of a circle has endpoints of (–5 , 6) and (–5 , –2). What is the equation of this circle?

A. (x + 5)2 + (y – 2)2 =16

B. (x – 5)2 + (y + 2)2 = 4 C. (x + 5)2 + (y – 2)2 = 4 D. (x + 5)2 + (y – 2)2 =64

101

Find the value of z. Round to the nearest hundredth.

A. 61.91 B. 10.20 C. 64.29 D. 56.28

102

Find the value of y.

A. 16 B. 36 C. 40 D. 44

103




Find the amount of empty space within a cylinder containing three solid spheres, where each sphere

has a radius of 3 cm. (Volume of a sphere = 4

3πr3)

A. 54π cm3 B. 72π cm3 C. 126π cm3 D. 378π cm3

104

NOPQ is a rhombus. Use coordinate geometry to find the length of side ON.

A. d B. a + d C. √ a + d D. √ a2 + d2

105




Jean is trying to prove parallelogram LMNO is a rhombus by using coordinate geometry.

Showing which of the following statements to be true would be sufficient to prove LMNO is arhombus?

A. (slope of MO )(slopeof LN ) = –1

B. (slope of MO)(slopeof LN) = 1

C. the midpoint of MO isthe midpoint of LN

D. the distance from Mto O = the distancefrom L to N

106

Determine the coordinates of point B that would prove quadrilateral ABCD is a parallelogram.

A. (a, c) B. (a – b, c) C. (a + b, c) D. (b – a, c)

107




Find the coordinates of point T in equilateral triangle RTS shown below.

A. (0, a) B. (0, 2a) C. (0, a √ 3 ) D. (0, 2a √ 3 )

108

Find the coordinates for point R that proves figure TRAP is an isosceles trapezoid.

A. (a, c – b) B. (2a, b) C. (c – a, b) D. (c – 2a, b)

109




Figure ABC is an equilateral triangle.

The coordinates of Point B are (4, 4 √ 3 ). What are the coordinates of point C?

A. (4 √ 3 , 0) B. (8, 0) C. (8 √ 3 , 0) D. (12 , 0)

110



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