ACT 60 Pre Work Questions

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FOIL METHOD
6.
The expression (4z + 3)(z – 2) is
equivalent to:
-F. 4z2 – 5
-G. 4z2 – 6
-H. 4z2 – 3z – 5
-J. 4z2 – 5z – 6
-K. 4z2 + 5z – 6
PRETEST
midpoints
In the standard (x,y) coordinate plane,
point M with coordinates (5,4) is the
midpoint of AB, and B has coordinates
(7,3). What are the coordinates of A.
9.
-A. (17, 11)
-B. (9, 2)
-C. (6, 3.5)
-D. (3, 5)
-E. (-3, -5)
PRETEST
AREAS
16. In
square ABCE shown below, D is the
midpoint of CE. Which of the following is the
ratio of the area of ADE to the area or ADB.
E
-F. 1:1
-G. 1:2
-H. 1:3
-J. 1:4
-K. 1:8
A
D
C
B
PRETEST
RATIOS
Janelle cut a board 30 feet long into 2
pieces. The ratio of the lengths of the 2
pieces is 2:3. What is the length, to the
nearest foot, of the shorter piece.
18.
-F. 5
-G. 6
-H. 12
-J. 15
-K. 18
PRETEST
EXPONENTS.
22.
For all a > 1, the expression 3a4 equals:
3a6
-F. 1/2
-G. –a2
-H. a2
-J. -1/a2
-K. 1/a2
PRETEST
26.
If 3√7 = 3√7 is true, then a = ?
a√7 7
-F. 1
-G. √7
-H. 7
-J. 21
-K. 49
PRETEST
RADICALS
PATTERNS
A hot-air balloon 70 meters above the ground
is falling at a constant rate of 6 meters per second
while another hot-air balloon 10 meters above
the ground is rising at a constant rate of 15 meters
per second. To the nearest tenth of a second,
after how many seconds will the 2 balloons be the
same height above the ground?
27.
-A. 8.9
-B. 6.7
-C. 2.9
-D. 0.4
-E. 0.2
PRETEST
PROBABILITIES
A hiking group will go from a certain town to
a certain village by van on 1 of 4 roads, from the
village to a waterfall by riding bicycles on 1 of 2
bicycle paths, and then from the waterfall to
their campsite by hiking on 1 of 6 trails. How
many routes are possible for the hiking group to
go from the town to the village to the waterfall
to their campsite?
28.
-F. 6
-G. 12
-H. 24
-J. 48
-K. 220
PRETEST
RATIOS.
29. Cube A has an edge length of 2
inches. Cube B has an edge length
double that of Cube A. What is the
volume, in cubic inches, of Cube B?
-A. 4
-B. 8
-C. 16
-D. 32
-E. 64
PRETEST
AREA
31. A right circular cylinder is shown in the figure
below, with dimensions given in centimeters.
What is the total surface area of this cylinder, in
square centimeters.
(Note: The total surface area of a cylinder is given
by 2r2 + 2rh where r is the radius and h is the
height.)
20
-A. 300
-B. 400
-C. 500
-D. 600
-E. 1,600
20
PRETEST
32. Given f(x) = 4x + 1 and
FUNCTIONS
g(x) = x2 - 2, which of the following is
an expression for f(g(x))?
2
-x
-F.
+ 4x + 1
-G. x2 + 4x - 1
-H. 4x2 - 7
-J. 4x2 - 1
-K. 16x2 + 8x - 1
PRETEST
ANGLES
34. Lines a, b, c, and d are shown
below and a ll b. Which of the
following is the set of all angles that
must be supplementary to <x ?
a
-F. {1, 2}
-G. {1, 2, 5, 6}
-H. {1, 2, 9, 10}
-J. {1, 2, 5, 6, 9, 10}
-K. {1, 2, 5, 6, 9, 10, 13, 14}
b
x 1 8 9
2 3 10 11
13
12
4 5
15
14
7
6
c
d
PRETEST
EXPONENTS.
35.
3
3
(3x )
-A. x
-B. 9x6
-C. 9x9
-D. 27x6
9
-E. 27x
is equivalent to:
PRETEST
38. For right triangle
what is sin <M ?
-F. 10 / 12
-G. 12 / 10
-H. √44 / 10
-J. 10 / √44
-K. √44 / 12
M
TRIG RATIOS.
KLM below,
K
10 cm
L
PRETEST
42. What rational number is
MIDPOINTS
halfway between 1 and 1 ?
5
-F.
-G.
-H.
-J.
-K.
1/2
1/4
2 / 15
4 / 15
8 / 15
3
PRETEST
.TOTAL PIES
47. Tom has taken 5 of the 8 equally
weighted tests in his U.S. History class this
semester, and he has an average score of
exactly 78.0 points. How many points does he
need to earn on the 6th test to bring his
average score up to exactly 80.0 points?
-A.
-B.
-C.
-D.
-E.
90
88
82
80
79
PRETEST
EXPONENTS
2.1)
3x3 ∙2x2y ∙ 4x2y is equivalent to:
-F. 9x7y2
-G. 9x12y2
-H. 24x7y2
-J. 24x12y
12
2
-K. 24x y
PRETEST
.PROBLEM SOLVING
3.1) Mr. Dietz is a teacher whose salary is
$22,570 for this school year, which has 185 days.
In Mr. Dietz’s school district, substitute teachers
are paid $80 per day. If Mr. Dietz takes a day off
without pay and a substitute teacher is paid to
teach Mr. Dietz’s classes, how much less does the
school district pay in salary by paying a substitute
teacher instead of paying Mr. Dietz for that day?
-A. $42
-B. $80
-C. $97
-D. $105
-E. $122
PRETEST
4.1) So far, a student has earned the
TOTAL PIE
following scores on four 100-point tests this
grading period: 65, 73, 81, and 82. What
score must the student earn on the fifth test
of the grading period to earn an average test
grade of 80 for the 5 tests?
-F. 75
-G. 76
-H. 78
PRETEST
-J. 99
-K. The student cannot earn an average of 80.
CONSECUTIVE INTEGERS
9.1) What 2 numbers should be placed in
the blanks below so that the difference
between consecutive numbers is the
same?
17, ___ , ___ , 41
-A. 23, 29
-B. 24, 34
-C. 25, 33
-D. 26, 35
-E. 27, 31
PRETEST
SQUARE AND SQUARE ROOTS
10.1) If
x is a real number such that
x3 = 64, then x2 + √x = ?
-F. 4
-G. 10
-H. 18
-J. 20
-K. 47
PRETEST
VOLUME
A formula for the volume V of a
sphere with radius r is V = 4/3 r3. If the
radius of a spherical rubber ball is 1 ¼
inches, what is its volume to the nearest
cubic inch?
11.1)
-A. 5
-B. 7
-C. 8
-D. 16
-E. 65
PRETEST
MATRIXES
13.1) The number of students participating in fall sports at a
certain high school can be shown by the following matrix.
Tennis
Soccer
Cross-Country
Football
[ 40
60
80
80 ]
The athletic director estimates the ratio of the number of sports
awards that will be earned to the number of students
participating with the following matrix.
Tennis
0.3
Soccer
0.4
Cross-Country 0.2
0.5
Football
Given these matrices, what is the athletic director’s estimate for the
number of sports awards that will be earned for these fall sports?
-A. 80
-B. 88
-C. 91
-D. 92
-E. 99
PRETEST
LIKE EXPRESSIONS
16.1) What expression must the center cell
of the table below contain so that the
sums of each row, each column, and each
diagonal are equivalent?
-F. 6x
-G. 4x
-H. 2x
-J. -2x
-K. -4x
x
-2x
7x
8x
?
-4x
-3x
6x
3x
PRETEST
.RATIOS
19.1) At a refinery, 100,000 tons of sand
are required to produce each 60,000
barrels of a tarry material. How many
tons of sand are required to produce
3,000 barrels of this tarry material?
-A. 5,000
-B. 18,000
-C. 20,000
-D. 40,000
-E. 50,000
PRETEST
.RATIOS
For all positive integers x, y, and z, which
of the following expressions is
equivalent to x ?
y
21.1)
-A. xy ∙∙ zz
-B. x ∙ x
y∙y
-C. y ∙ x
-D.
-E.
x∙y
x-z
y-z
x+z
y+z
PRETEST
TRIG RATIOS
The hypotenuse of the right
triangle PQR shown below is 16
feet long. The sine of <P is 3/5. About
how many feet long is QR ?
28.1)
P
-F. 8.0
-G. 9.6
-H. 12.4
-J. 14.3
-K. 15.4
16
PRETEST
Q
R
EQUIVALENT EXPRESSIONS
What is the x-coordinate of the
point in the standard (x,y) coordinate
plane at which the 2 lines y = 2x + 6
and y = 3x + 4 intersect?
31.1)
-A. 1
-B. 2
-C. 4
-D. 6
-E. 10
PRETEST
EQUIVALENT EXPRESSIONS
For all pairs of real numbers
M and V where M = 3V + 6, V = ?
32.1)
-F. M/3 - 6
-G. M/3 + 6
-H. 3M - 6
-J. M – 6
3
-K. M + 6
3
PRETEST
EQUIVALENT EXPRESSIONS.
34.1)
If a = b + 2, then (b - a)4 = ?
-F. -16
-G. -8
-H. 1
-J. 8
-K. 16
PRETEST
RIGHT ANGLES
37.1) Members of the fire department lean a 30-
foot ladder against a building. The side of the
building is perpendicular to the level ground so
that the base of the ladder is 10 feet away from
the base of the building. To the nearest foot, how
far up the building does the ladder reach?
-A. 10
-B. 20
-C. 28
-D. 31
-E. 40
PRETEST
ANGLES.
In the figure below, ABCD is a
trapezoid, E lies on AD, and angle
measures are as marked. What is the
measure of < BDC ?
40.1)
-F. 15
-G. 25
-H. 30
-J. 35
-K. 45
B
C
30
60
A
?
105
D
PRETEST
E
.RATIOS
42.1) Of the 804 graduating seniors in a certain
high school, approximately 2/5 are going to
college and approximately 1/4 of those going to
college are going to a state university. Which of
the following is the closest estimate for how many
of the graduating seniors are going to a state
university?
-F. 80
-G. 90
-H. 160
-J. 200
-K. 320
PRETEST
EQUIVALENT EXPRESSIONS
48.1)
In the complex numbers,
where i2 = -1, 1
1+i
-F. i - 1
-G. 1 + i
-H. 1 – i
-J. 1 – i
2
-K. 1 + i
2
∙
1-i=?
1-i
PRETEST
RATIOS
53.1) Douglas wants to draw a circle graph showing
the favorite colors of his friends. When he polled his
friends asking each their favorite color, 25% of his
friends said red; 30% of his friends said blue; 20% of his
friends said green; 10% of his friends said purple; and
the remaining friends said colors other than red, blue,
green, and purple. The colors other than red, blue,
green, and purple will be grouped together in an Other
sector. What will be the degree measure of the Other
sector?
-A. 108˚
-B. 54˚
-C. 27˚
-D. 15˚
-E. 10˚
PRETEST
.CO-ORDINATE GEOMETRY
A triangle, ABC, is reflected across the
x-axis to have the image A’B’C’ in the
standard (x, y) coordinate plane; thus, A
reflects to A’. The coordinates of point A are
(c,d). What are the coordinates of point A’?
58.1)
-F. (c , -d)
-G. (-c , d)
PRETEST
-H. (-c , - d)
-J. (d, c )
-K. Cannot be determined from the given
information
.EQUIVALENT EXPRESSIONS
If x = 2t – 9 and y = 5 – t,
which of the following expresses
y in terms of x ?
59.1)
-A. y = (1 – x) / 2
-B. y = (19 – x) / 2
-C. y = 14 – 2x
-D. y = 5 - x
-E. y = 1 - x
PRETEST
.RATIOS
A poll of 200 registered voters was taken before the election for
mayor of Springdale. All 200 voters indicated which 1 of the 4
candidates for whom they would vote. The results of the poll are
given in the table below.
Candidate
Number of voters
Blackcloud
Lue
Gomez
Whitney
50
80
40
30
13. What percent of the voters polled chose Whitney in the poll?
-A. 15%
-B. 20%
-C. 25%
PRETEST
-D. 30%
-E. 40%
RATIOS
A poll of 200 registered voters was taken before the election for mayor
of Springdale. All 200 voters indicated which 1 of the 4 candidates for
whom they would vote. The results of the poll are given in the table
below.
Candidate
Number of voters
Blackcloud
Lue
Gomez
Whitney
50
80
40
30
14. If the poll is indicative of how the 10,000 registered voters of
Springdale will actually vote in the election, which of the
following is the best estimate of the number of votes Lue will
receive in the election.
-F. 1,500
-G. 2,500
-H. 4,000
-J. 5,000
PRETEST
-K. 8,000
RATIOS
A poll of 200 registered voters was taken before the election for mayor
of Springdale. All 200 voters indicated which 1 of the 4 candidates for
whom they would vote. The results of the poll are given in the table
below.
Candidate
Number of voters
Blackcloud
Lue
Gomez
Whitney
50
80
40
30
15. If the information in the table were converted into a
circle graph (pie chart), then the central angle of the sector
for Gomez would measure how many degrees?
-A. 54˚
-B. 72˚
-C. 90˚
-D. 108˚
-E. 144˚
RATIOS
33. The table below shows the total number of goals
scored in each of 43 soccer matches in a regional
tournament. What is the average number of goals
scored per match, to the nearest 0.1 goal?
-A. 1.0
-B. 2.8
-C. 3.0
-D. 6.1
-E. 17.1
Total number of
goals in a match
Number of matches
with this total
0
1
2
3
4
5
6
7
4
10
5
9
7
5
1
2
ANGLES
39. In the figure below, B lies on AC, BD
bisects <ABE, and BE bisects <CBD. What is
the measure of <DBE ?
D
-A. 90˚
-B. 60˚
-C. 45˚
-D. 30˚
A
-E. Cannot be determined
from the given information
E
B
C
PRETEST
ANGLES
43. In isosceles trapezoid ABCD, AB is parallel
to DC, <BDC measures 25˚, and <BCA
measures 35˚. What is the measure of <DBC
?
A
-A. 85˚
-B. 95˚
-C. 105˚
-D. 115˚
-E. 125˚
B
35˚
25˚
D
C
.CO-ORDINATE GEOMETRY
59. In the figure below, the vertices of
ABC
have (x,y) coordinates (4,5), (5,3), and (1,3),
respectively. What is the area of ABC?
-A. 4
-B. 4√2
-C. 4√3
-D. 8
-E. 8√2
NEED PICTURE
PRETEST
A -PROBABILITIES
• A deck of cards for a children’s game contains 10
red cards, 10 blue cards, and 10 yellow cards. The
players take turns, each drawing a card at random
from the deck and placing the card on the table.
When it is the fourth player’s turn, there are 3
yellow cards on the table. What is the probability
that the fourth player will draw a yellow card?
–
–
–
–
–
A) 7/30
B) 7/27
C) 1/3
D) 4/10
E) 7/10
LOOK ALSO FOR
FRACTIONS WHICH
COULD OF BEN REDUCED
PRETEST
.A- PROBABILITY
• What is the probability of drawing a heart
from a well-shuffled standard deck of playing
cards.
– A) 1/4
– B) 1/52
– C) 1/13
– D) 4/13
– E) 1
4 DIFFERENT TYPES OF SUITS
16.9
A- Probability
• WHAT IS THE PROBABILITY OF GETTING A
SUM OF 8 ON ONE ROLL OF A FAIR PAIR OF
DICE:
– A) 1/4
– B) 1/6
– C) 8/36
– D) 5/36
– E) None of the above
PRETEST
If I rolled three
Dice , how many
Different possibilities ?
B -SLOPES
• What is the slope of the line whose equation
is x+2y=5 - (x+y)?
– A) 5/3
– B) -2
– C) -2/3
– D) -3/2
– E) -1
PRETEST
19.2%
C- Averages
• THE AVERAGE OF A SET OF 7 INTEGERS IS 24.
WHEN AN 8TH NUMBER IS INCLUDED IN THE
SET THE AVERAGE OF SET INCREASES TO 31.
WHAT IS THE 8TH NUMBER:
– A) 31
– B) 62
– C) 56
– D) 80
– E) 168
PRETEST
D-Y INTERCEPT
CAN WE MAKE A REASONABLE GUESS ?
• What is the y-intercept of the line in the
standard (x,y) coordinate plane that goes
through the points (-3,6) and (3,2)?
– A) 0
– B) 2
– C) 4
– D) 6
– E) 8
-3 AND 3 =ZERO
PRETEST
E -PERIMETER
• If the length of a rectangle is 1 foot less than
twice its width and its perimeter is 34 feet,
what is the length of the rectangle in feet?
– A) 6
– B) 11
– C) 11 2/3
– D) 22 1/3
– E) None of these
PRETEST
E-AREA OF SQUARE
• Shannon is planning to tile a rectangular kitchen
countertop that is 24 inches wide and 64 inches
long. She determined that 1 tile will be needed
for each 4-inch-by-4-inch region. What is the
minimum number of tiles that will be needed to
completely cover the countertop to its edges?
–
–
–
–
–
A) 44
B) 88
C) 96
D) 176
E) 384
PRETEST
6.9%
.E - Perimeter
• A CIRCULAR RUNNING TRACK IS BEING BUILT IN A
FENCED-IN ATHLETIC FIELD 100 FEET WIDE AND 150
FEET LONG. IF A BORDER OF 10 FEET IS NEEDED
BETWEEN THE OUTSIDE EDGE OF THE TRACK AND
BOTH FENCES, WHICH IS THE RADIUS OF THE
LARGEST TRACK THAT CAN BE BUILT?
– A) 40
– B) 45
– C) 65
PRETEST
– D) 90
– E) 110
G 3,4,5 TRIANGLE
5,12,13 TRIANGLE
• A ramp for loading trucks is 13 feet long and
covers 12 feet along the level ground. How
many feet high is the highest point on the
ramp?
– A) 1
– B) 2
– C) 4
– D) 5
– E) 6¼
PRETEST
54.6%
.G- 3,4,5 Triangle
• THE LENGTHS OF THE SIDES OF A TRIANGLE
ARE 3,4,5 INCHES. WHAT IS THE LENGTH IN
INCHES OF THE SHORTEST SIDE OF A SIMILAR
TRIANGLE THAT HAS A PERIMETER OF 36
INCHES:
– A.
– B.
– C.
– D.
– E.
9
12
13
15
18
PRETEST
H- AREA OF SQUARES
• The diagonal of a square quilt is 4√2 feet long.
What is the area of the quilt in square feet?
– A) 16√2
– B) 16
– C) 4√2
– D) 4
– E) √2
PRETEST
H -TRIANGLES
• Points A(1,0), B(8,0), and C(3,4) are the
vertices of a triangle. What is the area of this
triangle?
– A) 5
– B) 10.5
– C) 14
– D) 16
– E) 28
PRETEST
TIP—SAME VALUES FOR Y AXIS
H –TRIANGLES.
• On level ground, a vertical rod 12 feet tall
casts a shadow 4 feet long, and at the same
time a nearby vertical flagpole casts a shadow
12 feet long. How many feet tall is the
flagpole?
– A) 4
– B) 8
– C) 12
– D) 20
– E) 36
I -MIDPOINTS
• What is the distance, in coordinate units,
between the points (-3,5) and (4,-1) in the
standard (x,y) coordinate plane?
– A) √13
– B) √17
– C) √85
– D) 13
– E) 85
PRETEST
MADE EASY
• IN HOW MANY ORDERS CAN 6 DIFFERENT
BOOKS BE PLACED ON A SHELF:
– A.
– B.
– C.
– D.
– E.
21
30
720
1120
NONE OF THE ABOVE
PRETEST

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