Act Math Practice

Front 1

The length of a rectangle with area 54 squarecentimeters is 9

centimeters. What is the perimeter ofthe rectangle, in centimeters?

F. 6

G. 12

H. 15

J. 24

K. 30

Back 1

K. 30

Front 2

In the figure below, C is the

intersection of line segment AD and line segment BE.If it can be determined, what is the measure

of ∠BAC?

A. 80°

B. 100°

C. 110°

D. 115°

E. Cannot be determined from the given information

Back 2

B. 100°

Front 3

Antwan drew the circle graph

below describing histime spent at school in 1 day. His teacher said that thenumbers of hours listed were correct, but that thecentral angle measures for the sectors were not correct.What should be the central angle

measure for the Coresubjects sector?

F. 072°

G. 080°

H. 160°

J. 200°

K. 288°

Back 3

H. 160°

Front 4

A. 43°

B. 47°

C. 94°

D. 133°

E. 137°

Back 4

D. 133°

Front 5

For trapezoid ABCD shown below, AB || DC , themeasures of the

interior angles are distinct, and themeasure of ∠D is x°. What is the

degree measure of ∠A in terms of x?

Back 5

Front 6

In the figure shown below, the measure of ∠BAC is(x + 20)° and the measure of ∠BAD is 90°. What is the measure of ∠CAD?

F) (x − 70)°

G) (70 − x)°

H) (70 + x)°

J) (160 − x)°

K) (160 + x)°

Back 6

G) (70 − x)°

Front 7

What is the perimeter, in inches, of the isosceles righttriangle shown below, whose hypotenuse is 8√2 incheslong?

A. 8

B. 8+ 8√2

C. 8+16√2

D. 16

E. 16+ 8√2

Back 7

E. 16+ 8√2

Front 8

The radius of the base of the right circular cone shownbelow is 5 inches, and the height of the cone is7 inches. Solving which of the following equationsgives the measure, θ, of the angle formed by a slantheight of the cone and a radius?

F) tan θ= 5/7

G) tan θ= 7/5

H) sin θ= 5/7

J) sin θ= 7/5

K) cos θ= 7/5

Back 8

G) tan θ= 7/5

Front 9

Gianna is converting a

12-foot-by-15-foot room in herhouse to a craft room. Gianna will install tile herself butwill have CC Installations build and install the cabinets.The scale drawing shown below displays the location of thecabinets in the craft room (0.25 inch represents 2 feet).

Cabinets will be installed along one of the 12-foot wallsfrom floor to ceiling, and 4 cabinets that are each 3 feet tallwill be installed in the middle of the room. These are theonly cabinets that will be installed, and each of them willbe 2 feet wide and 2 feet deep. CC Installations has

givenGianna an estimate of $2,150.00 for building and

installingthe cabinets.

Gianna will install tile on the

portion of the floor that will NOT be covered by cabinets. What is the area, in square feet, of the portion of the floor that will NOT be covered by cabinets?

F. 072

G. 090

H. 140

J. 156

K. 164

Back 9

H. 140

Front 10

Which of the following vertical lines cuts ABCD into2 trapezoids with equal areas?

A. x=2.5

B. x=3.5

C. x=4.5

D. x=5.5

E. x=6.5

Back 10

E. x=6.5

Front 11

You can find the volume of an irregularly shaped solidobject by completely submerging it in water andcalculating the volume of water the object displaces.You completely submerge a solid object in a

rectangular tank that has a base 40 centimeters by30 centimeters and is filled with water to a depth of20 centimeters. The object sinks to the bottom, and thewater level goes up 0.25 centimeters. What is the

volume, in cubic centimeters, of the object?

F) 300

G) 240

H) 200

J) 150

K) 75

Back 11

F) 300

Front 12

A formula for the surface area (A) of the rectangularsolidshownbelowisA=2lw+2lh+2wh where

lrepresents length; w, width; and h, height. By doublingeach of the dimensions (l, w, and h), the surface areawill be multiplied by what factor?

A. 2

B. 4

C. 6

D. 8

E. 12

Back 12

B. 4

Front 13

The functions y=sin,x and y=sin(x+a)+b, forconstants a and b, are graphed in the standard (x,y)coordinate plane below. The functions have the same

maximum value. One of the

following statementsabout the values of a and b is true. Which statement isit?

A. a<0 and b=0

B. a<0 and b>0

C. a=0 and b>0

D. a>0 and b<0

E. a>0 and b>0

Back 13

A. a<0 and b=0

Front 14

The sides of an acute triangle measure 14 cm, 18 cm,and 20 cm, respectively. Which of the followingequations, when solved for θ, gives the measure of thesmallest angle of the triangle?

Back 14

Front 15

In the 8-sided figure below,

adjacent sides meet atright

angles and the lengths given are in meters. Whatis the perimeter of the figure, in meters?

A. 40

B. 80

C. 120

D. 160

E. 400

Back 15

B. 80

Front 16

What is the length, in feet, of the hypotenuse of a righttriangle with legs that are 6 feet long and 7 feet long,respectively?

Back 16

Front 17

Hexagon ABCDEF shown below was drawn on a gridwith unit squares. Each vertex is at the

intersection of2 grid lines. What is the area of the hexagon, in squareunits?

A) 18

B) 19

C) 20

D) 22

E) 25

Back 17

C) 20

Front 18

line segment AD is perpendicular to line segment BD,

and line segment AC is

perpendicular to line segment BC,

and line segment AD is congruent to line segment BC,

Which of the following

congruences is NOT necessarily true?

Back 18

Front 19

In the figure below, A, D, B, and G are collinear. If∠CAD measures 76°, ∠BCD measures 47°, and ∠CBGmeasures 140°, what is the degree measure of ∠ACD ?

F. 12°

G. 14°

H. 17°

J. 36°

K. 43°

Back 19

H. 17°

Front 20

Which of the following trigonometric equations isvalid for the side measurement x inches, diagonal measurement y inches, and angle measurement w° in therectangle shown below?

A. cos w°= x/y

B. cot w°= x/y

C s e c w ° = x/y

D s i n w ° = x/y

E tan w°= x/y

Back 20

D s i n w ° = x/y

Front 21

The youth center has installed a swimming pool on levelground. The pool is a right circular

cylinder with a diameterof 24 feet and a height of 6 feet. A

diagram of the pool andits entry

ladder is shown to the left.

To the nearest cubic foot, what is the volume of waterthat will be in the pool when it is filled with water to adepth of 5 feet?

(Note: The volume of a cylinder is given by πr^2h,where r is the

radius and h is the height.)

A) 942

B) 1,885

C) 2,262

D) 9,047

E) 11,310

Back 21

C) 2,262

Front 22

A plastic cover is made for the pool. The cover willrest on the top of the pool and will include awedge-shaped flap that forms a 45° angle at the centerof the

cover, as shown in the figure

below. A zipperwill go along 1 side of the wedge-shaped flap and around the arc. Which of the following is closest to thelength, in feet, of the zipper?

F. 17

G. 22

H. 24

J. 29

K. 57

Back 22

G. 22

Front 23

The directions for assembling the pool state that theladder should be placed at an angle of 75°

relative tolevel ground. Which of the following expressions

involving tangent gives the distance, in feet, that thebottom of the ladder should be placed away from thebottom edge of the pool in order to comply with the

directions?

Back 23

Front 24

The parallel sides of the isosceles trapezoid shownbelow are 10 feet long and 16 feet long, respectively.What is the distance, in feet, between these 2 sides?

A. 3

B. 4

C. 5

D. 10

E. 16

Back 24

B. 4

Front 25

In the figure below, line l is

parallel to line m. Transversals t and u intersect at point A on l and intersect mat points C and B,

respectively. Point X is on m, themeasure of ∠ACX is 130°, and the measure of ∠BAC is80°. How many of the angles formed by rays of l, m, t,and u have

measure 50° ?

A. 4

B. 6

C. 8

D. 10

E. 12

Back 25

C. 8

Front 26

For the triangle in the figure, which of the following ratios of side lengths is equivalent to the ratioof the perimeter of triangle 􏰄ABC to the perimeter of 􏰄triangle DAB?

F . AB:AD

G. AB:BD

H. AD:BD

J. BC:AD

K. BC:BD

Back 26

F . AB:AD

Front 27

In the figure below, 2 nonadjacent sides of a regularpentagon (5 congruent sides and 5 congruent interiorangles) are extended until they meet at point X. Whatis the measure of ∠X ?

A. 18°

B. 30°

C. 36°

D. 45°

E. 72°

Back 27

C. 36°

Front 28

The edges of a cube are each 3 inches long. What is thesurface area, in square inches, of this cube?

F.9

G. 18

H. 27

J. 36

K. 54

Back 28

K. 54

Front 29

For a project in Home Economics class, Kirk ismaking a tablecloth for a circular table 3 feet indiameter. The finished tablecloth needs to hang down5 inches over the edge of the table all the way around.To finish the edge of the tablecloth, Kirk will foldunder and sew down 1 inch of the material all aroundthe edge. Kirk is going to use a single piece of rectan-gular fabric that is 60 inches wide. What is the shortestlength of fabric, in inches, Kirk could use to make thetablecloth without putting any separate pieces of fabrictogether?

F. 15

G. 24

H. 30

J. 42

K. 48

Back 29

K. 48

Front 30

Back 30

Front 31

F. 0

G. 1

H. 2

J. –tan x

K. sin 2x

Back 31

H. 2

Front 32

The triangle, 􏰄XYZ, that is shown below has side lengths of x, y, and z inches and is not a right triangle. Let X′ be the image of X when the triangle is reflected across YZ . Which of the following is an expression forthe perimeter, in inches, of quadrilateral X′YXZ ?

F) 2(y+z)+x

G) 2(x+y+z)

H) 2(x+y)

J) 2(x+z)

K) 2(y+z)

Back 32

K) 2(y+z)