Straight LinesX

Z

Yx

If XYZ in the figure above is a right angle, what is the value of x?

(A) 155 (D) 125

(B) 145 (E) 110

(C) 135

55°

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

DegreesS T

R U

Square 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

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

Right Triangle 2

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

(1) x + y = 90

(2) x = y

ca

b

y

x

Right Triangle 3

In HGM, what is the length of side HM ?

(1) HG = 5

(2) GM = 8

Right Triangle 4

A B

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

3:4:5 Right Triangle 1Dan and Karen, who live 10 miles apart, meet at a café that is directly east of Karen’s house. If the café is 2 miles closer to Dan’s house than to Karen’s house,and Dan lives directly north of the café, how many miles is the café from Karen’s house?

(A) 6

(B) 7

(C) 8

(D) 9

(E) 10

3:4:5 Right Triangle 2A 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

3:4:5 Right Triangle 3In XYZ, what is the length of YZ?

(1) The length of XY is 3.

(2) The length of XZ is 5.

Isosceles Triangle

x

D30

50A

B

C

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

(A) 10

(B) 20

(C) 30

(D) 40

(E) 50

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

45-45-90 Triangle

6045T 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

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.

Similar Triangle 2

3

4P

Q

S

R

In PQS to the right, if PQ = 3 and PS = 4, then PR =

(A) 9/4

(B) 12/5

(C) 16/5

(D) 15/4

(E) 20/3

Area Rectangle

The figure above represents a rectangular desk blotter in a holder with dimensions shown. If x = 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

x

x xx

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.

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

4c

Area Circle 330 m

40 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, of the lot and driveway?

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

(B) 1200 + 400 (D) 1200 + 200

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 the perimeter, in feet of the sign?

(A)

(B)

(C)

(D)

(E)

333 363 3323 334 364

5 ft

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 RST is

(A) bc/2

(B) b(c - 1)/2

(C) c(b -1)/2

(D) a(c - 1)/2

(E) c(a -1)/2

Coordinate Geometry

x

y

P(a, b)

Q(c, d)

R

In the figure on the right, segments PR and QR are each parallel to one of the rectangular coordinate axis. Is the ratio of the length of QR to the length of PR equal to 1?

(1) c = 3 and d = 4.

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