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Straight Lines. X. x. Y. 55 °. Z. 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. Parallel Lines. y. k. z. x. m. In the figure above, if the lines k and m are parallel, what is the value of x? (1)y = 120

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Straight Lines

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Straight lines

Straight Lines

X

x

Y

55°

Z

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


Parallel lines

Parallel Lines

y

k

z

x

m

In the figure above, if the lines k and m are parallel, what is the value of x?

(1)y = 120

(2)z = 60


Degrees

Degrees

S

T

U

R

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

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

  • I only(D) II and III only

  • I and II only (E) I, II, and III

  • I and III only


Right triangle 2

Right Triangle 2

y

c

a

x

b

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

(1)x + y = 90

(2)x = y


Right triangle 3

Right Triangle 3

In HGM, what is the length of side HM ?

(1)HG = 5

(2)GM = 8


Right triangle 4

Right Triangle 4

A

B

X

C

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 1

3:4:5 Right Triangle 1

  • Dan 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?

  • 6

  • 7

  • 8

  • 9

  • 10


3 4 5 right triangle 2

3:4:5 Right Triangle 2

  • 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?

  • 4

  • 5

  • 8

  • 9

  • 15


3 4 5 right triangle 3

3:4:5 Right Triangle 3

In XYZ, what is the length of YZ?

(1)The length of XY is 3.

(2)The length of XZ is 5.


Isosceles triangle

Isosceles Triangle

B

x

D

30

50

C

A

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

30-60-90 Triangle

K

60

30

J

L

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

(1)JK = 10

(2)KL = 5


45 45 90 triangle

45-45-90 Triangle

S

U

45

60

V

T

R

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

Similar Triangle 1

C

B

x

A

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

Similar Triangle 2

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

Q

R

3

S

P

4


Area rectangle

Area Rectangle

x

x

x

x

50 cm

x

x

x

x

84 cm

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


Area circle 1

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

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)


Area circle 3

Area Circle 3

30 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

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)

5 ft


Coordinate geometry

y

S (a,b)

x

O

T (c,0)

R (1,0)

Coordinate Geometry

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 geometry1

y

Q(c, d)

x

P(a, b)

R

Coordinate Geometry

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


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