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GPS GEOMETRY

SAMPLE EOCT TEST - STUDY GUIDE

CROSSROADS

GPS Geometry Formula Sheet

Below are the formulas you may find useful as you work the problems. However, some of the formulas may not be used. You may refer to this page as you take the test.

Area Pythagorean Theorem

Rectangle/Parallelogram A =bh a2 + b2 ::::: c2

Triangle A::::: ~ bh 2 Population Standard Deviation

Circle A::::: n,.2

N

Circumference Sample Standard Deviation C=mi n z 3.14

Volume

Rectangular Prism/Cylinder V =Bh

1 Pyramid/Cone Trigonometric Relationships V = :3 Bh

Sphere 4 3

V:= ­ m'­3

oppsin (8) =-;

hyp

adj opp cos (8)::::: _.; tan (8) :::::-.

hyp a~

Snrface Area

Rectangular Prism SA::::: 2lw + 2wh + 2lh

Cylinder SA::::: 2nr2 + 2nrh

Sphere SA::::: 4n,.2

Special Right Triangles

45°- 45°_ 90° Triangle 30°- 60°- 90° Triangle

xx

x

- -

GPS Geometry EOCT UNIT 1: GEOMETRY GALLERY

EOCT Practice Items

ill In b.ECD, mLE = 136°, mLC = 17°, and mLD = 27c• Which statement must be true?

A. CD<DE

B. DE<CD C. CE>CD D. DE>CE

@ Which set could be the lengths of the sides of a triangle?

A. 15 em, 18 em, 26 em B. 16 em, 16 em, 32 em C. 17 em, 20 em, 40 em D. 18 em, 22 em, 42 em

(}) The first three angles in a pentagon each have the same measure. The other two angles each measure 10° less than each of the first three angles.

What is the measure of one of the first three angles in the pentagon?

A. 1020

B. 104° C. 112° D. 114°

(!to.. Which set of relationships is sufficient to prove that the triangles in this figure are congruent?

Q T [f

A. PR~SU,PQ~ST,LQ~LU

B. PQ~PR,ST~SU,RQ~TU

C. RQ~TU,LR~LU,LP?!:.LS

D. LP~LS,LR~LU,LQ~LT

p s

Use this diagram of a kite to answer the question.

Q

T P "c----....------» II

s

Which statement can be proved by using the HL postulate?

A. D.PQR ~D.PSR

B. D.PTS ~ D.TQR

C. D.QPS ~D.SRQ

D. D.QTP ~D.QTR

A student wants to inscribe a circle inside of a triangle. Which of the following should the student construct to locate the incenter of the triangle?

A. the medians of the triangles B. the altitudes of the triangles C. the angle bisectors of the triangle D. the perpendicular bisectors of the sides of the triangle

Jay constructed a line segment from each vertex that was perpendicular to the line containing the opposite side of a triangle. At what point of concurrency did the Hues meet?

A. the incenter B. the centroid C. the orthocenter D. the circumcenter

@.. Which of the following proves that quad rilateral GHJK is a parallelogram?

~~14-6-0----~--3-4-0-----yG

~ 146V J,L----------~

H

A. L.G is supplementary to L.H and LX B. L.J is complementary to L.G C. GH 1- HJ and JK 1- KG

D. GH~HJ~JK~KG

GJ' '! This diagram shows isosceles trapezoid QRST.

Q R

T S

What is the length, in units, of QS?

A. 2 B. 6 C. 7 D.9

GPS Geometry EOCT UNIT 2: COORDINATE GEOMETRY

15- 'i---'>--' ..+... +"'---"-j-,_.-i- ­

EOCT Practice Items

(10"; L On this coordinate grid, the library is located at point T, the music store is located at ~ point S, and the pet store is located at point R.

y

t14· .+ _......---+---+...._~---+--"'t- ..--.,.­

:13 j·--.-···j----·..·.·-j-.---.;-·-0·---+·---'--·.· ;...

12··· J I . ,10 ..

·9 ,8 .

7­

~. 61-··-·+---+---;--····;-,--··-j----;.......·-;..···.."..···--,

, 5 I---+--+--l-""'--+--r--~""""---+-~--'i- ...-...­L 4. R.i ; _ ; , , ,.

. 3

,-2 , I

1 2 .........!..•......_ -....••- .

Each grid line represents 1 mile. How much farther, to the nearest tenth of a mile, is the music store from the library than it is from the pet store?

A. 3.3 miles B. 8.0 miles C. 11.3 miles D. 13.6 miles

fjl)~ ­~ In isosceles.6PQR, PQ '"'-' QR. Point P is located at (1, 1). The centroid of the triangle is

located at (6, 2).

Which coordinate pair could represent the location of point R of the triangle?

A. (1,4) B. (5, 1) C. (7,3) D. (11,1)

·18 ,17-···.·· !l6

f1S :·J4 lJ l2j·_······!··+···'·····f·· j: ! ; .;. ,. .

q1t-·~-;----·-+-·-'---j--"T'-+--+---+--i·-,·_··,_··

,] Of·····:···········+·.. ·,···· , , 1.. . f········

- 9 f--~---_···~---i--~··_---_·_-+·-···.··_--+··

. ,

@ Wesley is walking with his dog along High Street. He wants to go from High Street to his house located at point T on this grid.

y

,~+-_...:--'--'---i--_---'-----.;..----!-:__=- x 2 3 4 5 6 7 8 9 101112

Once Wesley leaves High Street, he will have to walk across a rocky field. His dog refuses to walk across the field, so Wesley will have to carry him.

At what point on High Street should Wesley turn and walk toward his house so that he carries his dog the shortest possible distance?

A. (0, 7) B. (7, 7) C. (8,7) D. (10,7)

(Q71 "The vertices of quadrilateral EFGH have the coordinates E(2, - 2), F(4, 3), G(-1, 5),

and H(-3, 0). Which of the following describes quadrilateral EFGH?

A. a square B. a rectangle that is not a square C. a rhombus that is not a square D. a parallelogram that is not a rectangle

GPS Geometry EOCT UNIT 3: STATISTICS

EOCT Practice Items

This table shows the scores of the first six games played in a professional basketball league.

The winning margin for each game is the difference between the winning score and the losing score. What is the standard deviation of the winning margins for these data?

A. 3.8 points B. 8.3 points C. 9.5 points D. 12.0 points

ttf! This frequency table shows the heights for Mrs. Quinn's students.~;Y .

Heightfin inches) Frequency 42 1 43 2 44 4 45 5

46 4 47 2 48

_.

1

What is the approximate standard deviation ofthese data?

A. 1.0 inches B. 1.5 inches C. 2.5 inches D. 3.5 inches

Kara took 10 random samples of the winning margins for each of two professional basketball teams. The sample size was 4. The distributions of the sample means are shown in these histograms.

Mean Winning Margins Mean Winning l'vLargins Team 1 Team 2

6 .r----------;

5 f-----------;

2

4 8 12 16 20

6 f-----------;

5 1-'----------1

4 8 12 16 20

Sample M.ean Sample Mean (points) (p.oints)

Which is the best estimate of the standard deviation for both samples?

A. Team 1; 3.75 points; Team 2: 2.2 points B. Team 1: 7.4 points; Team 2: 4.4 points C. Teaml: 15 points; Team 2: 8.8 points D. Team 1: 10 points; Team 2: 10 points

John took 10 random samples of the winning margins for each of two professional basketball teams. The distributions of the sample means are shown in these histograms.

Mean 'W'inning Margins Mean Winning Margins Team 1 Team 2

6 -- - -- - - .. 6 _ -.-- _ - --- .

5 f-----------j 51-------------1

2

4 8 12 16 20 4 8 12 16 20

Sample Mean Sample Mean (points) (points)

Based on John's data, which statement is MOST likely true?

A. Both the sample mean and the sample standard deviation are greater for Team 1 than for Team 2.

B. The sample means for both teams are equal, but the sample standard deviation for Team 1 is greater.

C. The sample means for both teams are equal, but the sample standard deviation for Team 2 is greater.

D. Both the sample mean and the sample standard deviation are greater for Team 2 than for Team 1.

Mary took 10 random samples of the winning margins for each of two professional basketball teams. The samples were taken from all 82 games in one season. The distributions of the sample means are shown in these histograms.

Mean Winning Margins Mean Winning M.argins Team 1 Team 2

6 1-----------1 6 f---------j

5 1-------------15 .,., u § 4

2

4 8 12 l6 4 8 12 16 20

Sllmplc Mean Sample Mean (points) (points)

Which question can be answered based on Mary's data?

A. Which team had the greater number of all-star players? B. Which team won more games? C. Which team won by a more consistent margin? D. Which team lost more games by a narrow margin?

In a set of 10 random samples of winning scores for games played in a professional basketball league, the sample size is 6, the sample mean is 97.5 points, and the sample standard deviation is 5.2 points. Which expression represents the estimated standard deviation of all the winning scores?

5.2A.

J10 B. 5_2M

5.2 C.

J6 D. 5.2J6

GPS Geometry EOCT UNIT4; RIGHT TRIANGLE TRIGONOMETRY

@ . . The length of one diagonal of a rhombus IS 12 em. The measure of the angle 0pp0s-Ite

that diagonal is 60°.

What is the perimeter of the rhombus?

A. 24em

B. 48 em

C. 1213 em

D. 24f3 em

(£,)l': ., Angle J and angle K are complementary angles in a right triangle. The value of tan J

. 15 IS -.

8

What is the value of sin J?

8 A. ­

17

8 B. ­

15

15 C. ­

17

17D. ­15

@. Triangle RST is a right triangle with right angle S, as shown.

R

I I

I6 in. I

I I

I I

I I

s T

What is the area of triangle RST?

A. 6.15 sq. in. B. 6.54 sq. in. C. 46.47 sq. in, D. 49.45 sq. in.

GPS Geometry EOCT UNIT 5: CIRCLES AND SPHERES

@) In circle 0, PS is a diameter. The measure of Pi<.. is 72°.

s nol drawn lo scale

What is the measure of LSPR?

A. 36° B. 54° C. 72° D. 108°

Quadrilateral 1¥.X"YZ is inscribed ill this circle.

Which statement must be true?

A. LW and LY are complementary. B. LW and LY are supplementary. C. LZ and LY are complementary. D. LZ and LY are supplementary.

...~

(1-5) .' 'b d' thO 'rcle~-:. I celes triangle XYZ IS mscn e m IS CI •

,,"j;~ sos y

Xy"'IT• ..--. 0

mYZ=108•

What is the measure of LXYZ?

A. 48° B. 54° C. 72° D. 108°

In this diagram, segment QT is tangent to circle P at point T.

p T

Q

.­The measure of minor arc ST is 70°. What is mL.TQP?

A. 20° B. 25° C. 35° D. 40°

----. t!J)'·~ Points R, 5, T, and U lie on the circle. The measure of RU is represented by x.

R

55°

T

What is the value of x?

A.70 B. 85 C. 110 D. 140

(fj) " Points A, B, D and E lie on the circle. Point C is outside the circle.

84° ~-------:;t?-------~C

A B

• AE"'" DE

• mBD = 56°

• mLEAC=84°

What is the measure of LACE?

A.28° B. 42° C. 56° D. 84°

@'. The center of circle 0 is located at (3, 4) on the coordinate plane. The radius of circle 0

is J3 units. Point P is located at (7, 0).

What is the length of PT, the segment from point P that is tangent to circle 0 at point T?

A. J13 units

B. .JJ9 units

C. .J29 units

D. J35 units

(fi: " Points A, B, C, and D are on circle P as shown.

c

What is the value of x?

A. 7.5 B. 8 C. 9 D. 12

@.~-;. QuadrilateralABCD is a square in circleA.

A E

D

~---+-------t

+-----;11

F

If AE = 3cm, what is the length of DF?

A. li B. 3-312

3J2 c. - ­2

3J2 D. 3- ­

2

@ _'. A circular pizza with a diameter of 15 inches is cut into 8 equal slices. What is the area of one slice?

A. 5.9 sq. in, B. 22.1 sq in. C. 88.4 sq. in. D.120sq.in.

@ In this diagram, triangle OPQ is equilateral, with vertex 0 at the center of a circle and vertices P and Q on the circle.

o p

Q

The radius of circle 0 is 12 em. What is the area, in square units, of the shaded region?

A. 24n -18

B. 24n - 36J3 C. 48n-18

D. 48n - 36-J3

&l) ~. A map company makes a globe in the shape of a sphere. The company plans to make a

new model globe with a diameter that is 20% larger than the diameter of the original model.

By what percent will the surface area of the new model globe increase compared to the surface area of the original model?

A. 4% B. 20% C. 40% D.44%

A sphere has a volume of 39n cubic centimeters. What is the surface area of the sphere?

A. 3.0n sq. em B. 9.5n sq. em C. 38.0n sq. em D. 81.5n sq. em

GPS Geometry EOCT UNIT 6: EXPONENTIAL AND INVERSES

EXPONENTIAL FUNCTIONS

KEY IDEAS

1. There are five basic properties ofexponents:

Example:

5 2823.25 = 23 + = = 256

mb. (an)", = a n •

Example:

= 32 3(3 2)3 • = 36 = 729

Example:

SO = I

n a n-Ifl

d. -=a am

Example:

3 2 2~ = 25- = = 4

23

_II 1 e. a =­

an

Example:

r 2 =~=~ 32 9

Example:

1)-2 (4)2 2(4 ="1 = 4 = 16

Copynght © 2011 by the Georgia Deparunent of Education' All Rights Reserved

GPS Geometry EOCT UNIT 6: EXPONENTIAL AND INVERSES

EOCT Practice Items

(!j; - The function j(x) has these properties.

• As x increasesd(x) approaches 3. • As x decreases,j(x) increases. • The domain ofj(x) is all real numbers.

Which of the following could be the function?

A. f(x) = _2x-

3

(1"2r-3

B. f(x) =

c. f(x) = -Y +3

D. f(x) = (1"2r+3

(;:;7'\ [ 1]X+l~!'. , Which graph represents I(x) = 2" +3?

y

--5-4-},2-1 l 2 34 ~ ,x ~......" ,. ,..,1, - - " "" '; ,-,

:2 . -~-:r 1- j"

A. B. y y

T--'''''---'--",-,,-,

(~'-"·R\ :~Use this function to answer the question.

2f(x)=-+3

x What value is NOT included in the domain of the inverse of this function?

A. 0

B. 1

C. 2

D.3

® Use these functions to answer the question.

f(x)=4x-2

x+2g(x)=-­

4

f(g(x)) =x

Which statement about the functionsf(X) and g(x) is true?

A. They are inverse functions becausef(g(x)) is not equal to O.

B. They are inverse functions becausef(g(x)) is equal to x.

C. They are not inverse functions becausef(g(x)) is not equal to O.

D. They are not inverse functions because f(g(x)) is equal to x.