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1/22

Straight LinesX

Z

Y

x

If XYZ in the figure above is a right angle, what is the

value ofx?

(A) 155 (D) 125(B) 145 (E) 110

(C) 135

55


2/22

Parallel Lines

k

m

y

xz

In the figure above, if the lines k and m are parallel, what is the

value of x?

(1) y = 120

(2) z = 60


3/22

DegreesS T

R USquare RSTU shown above is rotated in a plane about its center

in a clockwise direction the minimum number of degrees

necessary for T to be in position where S is now shown. The

number of degrees through which RSTU is rotated is:(A) 135 (D) 270

(B) 180 (E) 315

(C) 225


4/22

Right Triangle 1

Which of the following groups of numbers could be the lengths

of the sides of a right triangle?

I. 1, 4,

II. 4,7,

III. 4,9,6

(A) I only (D) II and III only

(B) I and II only (E) I, II, and III

(C) I and III only

17

11


5/22

Right Triangle 2

In the triangle above, does a2 + b2 = c2?

(1) x + y = 90

(2) x = y

ca

b

y

x


6/22

Right Triangle 3

In HGM, what is the length of sideHM?

(1) HG = 5

(2) GM= 8


7/22

Right Triangle 4

AB

C

X

If the figure above, three squares and a triangle have areas of

A, B, C and X as shown. If A = 144, B = 81 and C = 225, then

X =

(A) 150 (C) 80 (E) 36

(B) 144 (D) 54


8/22

3:4:5 Right Triangle 1

Dan and Karen, who live 10 miles apart, meet at a caf that is

directly east of Karens house. If the caf is 2 miles closer to Dans

house than to Karens house,and Dan lives directly north of the caf,

how many miles is the caf from Karens house?(A) 6

(B) 7

(C) 8(D) 9

(E) 10


9/22


A ladder 25 feet long is leaning against a wall that is

perpendicular to level ground. The bottom of the ladder is 7 feet

from the base of the wall. If the top of the ladder slips down 4

feet, how many feet will the bottom of the ladder slip?(A) 4

(B) 5

(C) 8(D) 9

(E) 15


10/22


In XYZ, what is the length of YZ?

(1) The length of XY is 3.

(2) The length of XZ is 5.


11/22

Isosceles Triangle

x

D

3050

A

B

C

In the figure above, DA = DB = DC. What is the value ofx ?

(A) 10

(B) 20(C) 30

(D) 40

(E) 50


12/22

30-60-90 Triangle

In JKL shown above, what is the length of segment JL?

(1) JK = 10

(2) KL = 5

J

K

L30

60


13/22

45-45-90 Triangle

6045

T R V

U

S

In the figure above, segments RS and TU represent two positions

of the same ladder leaning against the side SV of a wall. The

length TV is how much greater than the length of RV?

(1) The length of TU is 10 meters

(2) The length of RV is 5 meters


14/22

Similar Triangle 1

A

BC

x

In the figure above, line AC represents a seesaw that is touching

level ground at point A. If B is the midpoint of AC, how far

above the ground is point C ?

(1) x = 30

(2) Point B is 5 feet above the ground.


15/22

Similar Triangle 2

3

4P

Q

S

R

In PQSto the right, ifPQ = 3 and PS = 4, then PR =

(A) 9/4

(B) 12/5

(C) 16/5

(D) 15/4

(E) 20/3


16/22

Area Rectangle

The figure above represents a rectangular desk blotter in a holder

with dimensions shown. Ifx = 8 centimeters, what is the area, in

square centimeters, of the shaded portion of the blotter?(A) 4200 (D) 4072

(B) 4184 (E) 3944

(C) 4124

50 cm

84 cm

x

x x

x

xx x

x


17/22

Area Circle 1

The figure above represents the floor of a square foyer with a

circular rug partially covering the floor and extending to the

outer edges of the floor as shown. What is the are of the foyer

that is not covered by the rug?

(1) The area of the foyer is 9 square meters.

(2) The area of the rug is 2.25 square meters.


18/22

Area Circle 2

If the circumference of a circular region is c, which of the

following represents the area of that circular region?

(A) (D)

(B) (E)

(C)

2

2c

4

2c

2

2c

4

2c

2

2

4

c


19/22

Area Circle 330 m

The figure above represents a rectangular parking lot that is 30

meters by 40 meters and an attached semicircular driveway that

has an outer radius of 20 meters and an inner radius of 10 m. If the

shaded region is not included, what is the area, in square meters, ofthe lot and driveway?

(A) 1350 (C) 1200 + 300 (E) 1200 + 150

(B) 1200 + 400

(D) 1200 + 200


20/22

Perimeter Cone

The outline of a sign of an ice-cream store is made

by placing 3/4 of the circumference of a circle with

radius 2 ft on top of an isosceles triangle with

height 5 feet, as shown to the right. What is theperimeter, in feet of the sign?

(A)

(B)(C)

(D)

(E)

333

363

3323

334

364


21/22

Coordinate Geometry

O

y

x

R (1,0)

S(a,b)

T (c,0)

In the rectangular coordinate system to the right, the area of

RSTis

(A) bc/2

(B) b(c - 1)/2

(C) c(b -1)/2

(D) a(c - 1)/2

(E) c(a -1)/2


22/22

Coordinate Geometry

x

y

P(a, b)

Q(c, d)

R

In the figure on the right, segments PR and QRare each parallel to one of the rectangular

coordinate axis. Is the ratio of the length ofQR

to the length ofPR equal to 1?

(1) c = 3 and d= 4.

(2) a = -2 and b = -1

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