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2 A A A A A A A A A 2 MATHEMATICS TEST

60 Minutes—60 Questions DIRECTIONS: Solve each problem, choose the correct answer, and then fill in the corresponding oval on your answer document. Do not linger over problems that take too much time. Solve as many as you can; then return to the others in the time you have left for this test. You are permitted to use a calculator on this test. You may use your calculator for any problems you choose,

but some of the problems may best be done without using a calculator. Note: Unless otherwise stated, all of the following should be assumed. 1. Illustrative figures are NOT necessarily drawn to scale. 2. Geometric figures lie in a plane. 3. The word line indicates a straight line. 4. The word average indicates arithmetic mean.

1. Joe's weekly salary is $150.00. If 15% must be deducted for taxes, what will be his take-home pay?

DO YOUR FIGURING HERE.

A. B. C. D . E.

$100.00 $115.00 $127.50 $130.43 $135.00

2. Your toy company produces stuffed penguins and an iceberg "home"for them. In analyzing your production plans, you would like an expression for the total production cost, in dollars, for P penguins and / icebergs. The cost of producing each penguin is $5, and it costs your company $6 to produce each iceberg. Which of the following expressions gives the total production cost? F. 5 ^ + 6 / G. 6P+57 H . 11 J. \\(P+I) K. 30Pr

3. In a group of 64 students, 40 are freshmen. What percentage of the group are freshmen? A. 1.6% B. 16% C. 25% D . 40% E. 62.5%

ACT-52A-SAMPLE 14 GO ON TO THE NEXT PAGE.

2 A A A A A A A A A 2 4. I f 3 x - 4 = - 2 ( ; c - 3 ) , t h e n x = ? DO YOUR FIGURING HERE.

H . 1

J. 2

K. 10

5. Henry took an old soup can (right circular cylinder) and cut off and threw away the top and the bottom. Then he cut the rest of the can at a constant angle with respect to the bottom edge, as shown below. On flattening out the piece, what shape did he have?

cut

A. A circle B. An ellipse but not a circle C. A square D . A rectangle but not a square E. A parallelogram but not a rectangle

6. Which of the following is a good first step in solving {x+ 5)(x+ 1) = 21 F. Set the sum of the factors equal to 21. G. Set (jc+5) equal to 3, and set (jc + 1) equal to 7. H . Set each factor equal to 0. J. Set each factor equal to 21. K. Multiply to remove the parentheses.

7. What is the value of - Ixy - y when x - -l and J. = -2 ? A. -1 B. -4 C. -5 D. -19 E. -23


2 A A A A 8. Rudi has 5 pairs of slacks, 6 blouses, and 2 sweaters in

her closet. How many different outfits, composed of a pair of slacks, a blouse, and a sweater, can she choose from this closet? F. 60 G. 32 H . 13

• J. 6 K. 2

9. Two weeks before the election, the school board commissioned a poll of 300 eligible voters to see how public opinion stood on the school tax levy. They thought that if 60% of these persons were in favor, that would signal a reasonably sure passage of the levy. The next week, the local paper reported that the results of the poll fell 15 favorable responses short of this mark. How many of the people polled responded in favor of the school tax levy? A. 135 B. 165 C. 180 D. 185 E. 195

10. The graph below represents the solution of an inequality. Which of the following specifies the same solution in an algebraic form?

2 DO YOUR FIGURING HERE.

I 0 I I i I I I • I -4 -3 -2 - 1 0 1 2 3 4 5 x

¥. -3 = x = 4 G. -3 < X < 4 H . - 3 < : > : < 4 J. - 3 < x < 4 K. - 3 < x < 4

11. In the figure below, which is drawn to scale, exactly 1 of the following subfigures is a parallelogram. Which one?

H

A. ADEH B. BCGH C. BDEH D. BDFH E. CDFG


A.

\1

"3 L 1

le-'-'t

7

n

/

1

9 . 1 /

1

1 7 5 - 1

^7 6 2 ^

P (

^ of

OL f l o o -

1 I^r^ .A f^O

/ '-7 a / 3o =

C

<

i e e i T A > /

5 % 5 A w c S i ^ ; j ^ ^ ^ H

l a

2 A A A A A A A A A 2 12. How many meters long is the radius of a circle whose DO YOUR FIGURING HERE.

circumference is 67r meters? F. 6

G. 2V3

H . 3

•J. V6

K. 1 V 6

13. What is the smallest nonzero whole number that is divisible, separately, by each of 2, 3, 4, 5, and 8 (with no remainder)? A. 22 B. 40 C. 120 D. 160 E. 960

14. What is the value of/(2) where / ( x ) = ( 2 x - 7 ) ( x ' - 3 j f + 6)? F. -176 G. -48 H . -42 J. -18 K. -12

15. Of the 50 people in a music store, 35 of them own a cassette tape player. If I of those 50 people is randomly selected to win a cassette tape, what is the probability that the person chosen will already own a cassette tape player? A. -.70 B. .65 C. .35 . . • D . .30 E. .15

16. The legs of a right triangle measure 15 centimeters and 20 centimeters, respectively. How many centimeters long is the hypotenuse? F. 5

G. V 3 T H . 5V7 ' J. 25 K. 35

17. In the (x,y) coordinate plane, at which jc-value does the line 2.v + v - 6 inter.sect the A-axis? A. 3 B. 4 C. 6 D . 8 E. 12


2 A A A A A A A A A 2 18. For all JTand 7 where ^J{X- Y)(X* Y) is defined, j 0 0 YOUR FIGURING HERE.

the expression is equivalent to:

¥. X-Y

. G. X^Y

M.\X\^\Y\

3. V.Y' - 2 X 7 + Y^

K. sj X^-Y^

19. One side of a right triangle is {An - 2) feet long and the side perpendicular to it is {In + 4) feet long. Which of the following expressions must represent the area, in square feet, of the triangle? A. 4 r t - 4 B. 4 « - - 4 C. 4n^+ 6 « - 4 D . 4rj'+ 1 0 « - 4 E. 4n-+ 1 2 « - 8

20. A family uses ^ of a pound of cheese each week. How o

many weeks' worth of cheese are there in a 5-pound block of cheese?

F. 8 • .

G. 10

H . 16

••• 4

K. I • •

21. Which of the following is a polynomial factor of 4A-' + 13x - 12 ? A. (2A : - 3) B. (2x+3) C. (2x+4) D . ( 4 x - 3 ) ) E. (4A: + 3) '

22. By factoring the left side, the quadratic equation 2r + a:/ + 12 = 0 can be written as (/ - 4){2t - 3) = 0. What must be the value oi F. -11 G. -8 H . -4 J. -3 . K. -2

ACT-52A-SAMPLE 18 I I

GO ON TO THE NEXT PAGE.

2 a A A A A A A A A 2 23. If the lengths of the sides of one triangle are 8 inches,

10 inches, and 12 inches, respectively, what is the perimeter, in inches, of a similar triangle whose longest side is 4 inches? A. 10 . B. 12 C. 15 D . 30 E . 90

24. In right triangle ABC illustrated below, the cosine of lA is -|. What is the sine of ZA ?


G.

H .

J .

K.

F. VSS"

3 v/55-

55 sVsT

55 25. Sometimes it is more convenient to work with fractions

that have no square roots in the denominator. Which 5a o of the following is an equivalent form for

A. - V5a - c

B.

C.

v/5fl t c

5fl\/5g - c 2Sa^ -

5e + e

E. 5aVSa - c 5a - c

26. The volume of a certain gas at constant pressure is equal to a fixed number multiplied by the absolute temperature. If that gas occupies 500 cubic centimeters when the absolute temperature is 300°, what is the volume, in cubic centimeters, when the temperature rises 30° and the pressure is kept constant? F. 18 G. 50 H . 198 • J . 550 K. 883^

ACT-S2A-SAMPLE 19 GO ON TO THE NEXT PAGE.

2 2 27. What is the average of - | and .075 ?

A. .06875 B. .35000 C. .68750 D. .70000 E. .83750


28. Which of the following is a rectangle?

F. J.

G.

n70°

K.

90° 90'

H . X

4.088 - 1.64 _ 9 2 + 4(2.1 - 0 . 6 )

A. .272 B. .306 C. .36 D. .436 E. .4905

30. if 18 - 3(5 - x) = X - 7, then x - ? F. -8 G. -5 H . -1 J. 5 K. 10

ACT-52A.SAMPLE 20 GO ON TO THE NEXT PAGE.

a

X

f t3A =

\

3 . 3^ucr^^ ^

-2,

.1

7 ,

r-7 ,

4 - ^ rk

3

Oeor^- el'^3 6^,5 ( cX

no'

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2 2 MATHEMATICS TEST

60 Minutes—60 Questions DIRECTIONS: Solve each problem, choose the correct answer, and then fill in the corresponding oval on your answer document. Do, not linger over problems that take too much time. Solve as many as you can; then return to the others in the time you have left for this test. You are permitted to use a calculator on this test. You may use your calculator for any problems you choose,

but some of the problems may best be done without using a calculator. Note: Unless otherwise stated, all of the following should be assumed. 1. Illustrative figures are NOT necessarily drawn to scale. 2. Geometric figures lie in a plane. 3. The word line indicates a straight line. 4. The word average indicates arithmetic mean.

1. On a real number line, point S has coordinate -5 and point T has coordinate -7 . What is the coordinate of the midpoint of 5T ?

• A . -6 B. -1 C. 1 D. 2 E. 6


2. Given right triangle AABC below, how many units long is 5C ?

A

B

C

F. V 2 G. 2 H . 4 J. V 3 4 K. 8

ACT-55C-SAMPLE 14 GO ON TO THE NEXT PAGE.

2 3. A Fahrenheit temperature F can be approximated by

doubling the Celsius temperature C and adding 32. Which of the following expresses this approximation method?

(Note: The symbol ~ means "is approximately equal to.")

A . F = | C +32

B. F « | ( C +32)

C. F = 2C + 32


D. F== 2(C+ 32)

E. F==C' + 32

4. Malcolm has 3 striped ties and 4 solid-colored ties hanging together in his closet. In his haste to get to his appointment, he randomly grabs 1 of these 7 ties. What is the probability the tie that Malcolm grabs is striped?

I 3 F.

1 7 3_ 7

H .

3.

K .

5. The daily totals of lunch customers served at the Sunshine Cafe last Monday through Saturday were 256, 189, 204, 179, 166, and 218. W^hat w'as the average number of lunch customers served each day? A. 1,212 B. 256 • C. 202 D. 197 . E. 173

6. In the figure showing AABC below, line m is parallel to line n. Which one of the following angles must be congruent to Zx ?

C B in

F. Z l G. Z2 H . Z3 J. Z4 K. Z5

ACT-SSC-SAMPLE 15 GO ON TO THE NEXT PAGE.

2 2 7. A package of 10 ballpoint pens is priced at $1.50 now.

I f the pens go on sale for 20% off the current price, what wi l l be the sale price of the package?


A. B. C. D. E.

$0.30 $0.75 $1.00 $1.20 $1.30

8. When a triangle is isosceles, its parts are given special names, which are shown below for AABC where AB ~ CB. I f 2 isosceles triangles are similar, which of the following must be equal?

B

A base C

F. Their areas G. Their perimeters H . Their heights (measured from vertex to base) J. The measures of all 4 legs K . The measures of their vertex angles

9. Sherry won a cash settlement for a suit she had filed in court. Sherry paid her lawyer 25% of the original settlement and had $12,000 remaining. How much was the original settlement? A. $16,000 B. $21,000 C. $28,000 D. $37,000 E. $48,000

10. Carlotta had 2 more CDs (compact discs) than Mario. Then she bought 3 CDs from Mario. Now how many more CDs does Carlotta have than Mario? F. - 4 G. 2 H . 6 J. 8 K . 12

ACT^SSC-SAMPLE 16 GO ON TO THE NEXT PAGE.

2 2 1 1 . What is thevaiueof j 3 - x | i f . T = 6? DO YOUR FIGURING HERE.

A. -3 • • B. 3 • . • , C. 6

D. 9 • . • E. 18

12. For all x and y, (2x - y^x" + j ) = ? F. 2x^-y^ G. 2x'-yy H . Ix^+xy-y" J. Ix^ + 2xy - x V K . 2x^ - x'y + 2xy - /

13. For all x, 5 ~ 3(x - 4) = ? A . - 3 x + 17 B. - 3 x - 7 C. - 3 x + 1 D. 2 x - 4 E. 2 x - 8

14. ( x ' ) " is equivalent to:

F. , . G. x "

H . 12x' J. 12x= K . 60x •

15. What is the 311th digit after the decimal point in the repeating decimal 0.51246 ? A. 6 B. 5 C. 4 D. 2 - , E. 0 .

16. The area of a square is 36 square inches. What is its perimeter, in inches? , F. 6 • . G. 9 • ,

• H . 12 J. 18 ,

, K . 24 " . . •.


2 2 17. What is the sum of the 2 solutions of the equation

.f' + 2 x - 1 5 = 0? ' • A. -15

B. -5 C. -2 • D. 0 E. 3 •


18. Which of the fol lowing expressions is NOT a polynomial factor of x"* - 4 ? . " •

• - F. r - 2 . . • . G. X- + 2

. H . X - \ / 2 • . • " •, J. x + V'2 •. K . x - 2 „ - / .

19. When x = y what is the value o f ?

A . -20

B.

C.

D.

E.

-2

2

20. How many minutes would i t take a train to travel 90 kilometers at a constant speed of 120 kilometers per hour? F. 30 . . .G. 40 ' H . 45 J. 80 K . 90


2 21. The area of a trapezoid may be found by using the

formuia\ = + ^2), where h is the height and

fc, and o, are the lengths of the parallel bases. What is

the area, in square inches, of the isosceles trapezoid

below? 6 inches

12 inches

A. 15 B. 20 C. 27 D. 36 E. 45

22. For a certain quadratic equation, ax^ + bx + c •= Q,

the 2 solutions are x = y and x = - i . Which of the

following could be factors of ax" + bx + cl F. ( 5 x - 3 ) a n d ( 2 x + 1 ) G. (5x - 1) and (2x + 3) H . (5x+ 1) and ( 2 x - 3 ) • ' J. (5x + 3 ) a n d ( 2 x - l ) K . (5x + 3) and (2x + 1 )

23. A l l sides of a rhombus are the same length, as illustrated below.

I f one diagonal is 10 inches long and the other is 24 inches long, how many inches long is a side of the rhombus?

A. vT7 B. V ' M C. 13 D. 17 E. 26 • ,



2 2 24. A rectangular room that is 2 feet longer than it is wide

has an area of 120 square feet. How many feet long is the room? F. 10 G. 12 H . 22 J. 29 K . 31 .


25. In the standard (x,y) coordinate plane, what is the slope of the line joining the points (2,-7) and (5,4) ?

A- i "•A C. 1

»• ^ E. 9

26. What is the center of the circle with equation (X - 2f + (y + 2f = 2 in the standard ix,y) coordinate plane? •

F. (-V2,\/2) G. (-2,2)

, H . (V2,-V2) ' J. (2,-2)

K. ' (2,2)

27. The domain of a function / is the set of all values of x for which fix) is defined. One of the following sets is the domain for the function graphed below. Which set

, is that domain?

• • ' •

3--

A. { - 2 , - 1 , 0 , 1 , 2 , 3 , 4 } B. { - 1 , 0 , 1 , 2 } C. { x : - 2 < x < 4 } D. { x : - l < x < 2 } E. { x : - l < x < 4 }


2 2 28. la the standard (x,y) coordinate piane, what is the

midpoint of the line segment that has endpoints (-1,3) and (2,7)?

I I


F.

G.

H .

\

1,

,5

2) / 7, \

- 2

J. (1,4) K . (3,4)

29. As a salesperson, Onawa travels to a variety of locations during a day. The graph shows the relationship between time and total distance traveled on a particular day. What was Onawa's average speed, in miles per hour, for the parts of the day when she was traveling from one place to another?

A. B.

19 33

C. 45 D. 55 E. 110

330-j

BM 220^

| - s l lo^ J r

~ T — \ I — 1 — r — 2 4 6 8 10

working hours

30. I f -X

true?

^ = X " for all X 0, which of the following must be

F. G. H . J. K .

a-b • a + b-a^b-ax b

3 3

: 3 • 3 • 3


1, 23 t u (^-i)r5j

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