Download 04.22.12 notes act practice test all 24 questions

ACT Practice test
Hamilton
Qtr 3 2011
WARM UP ACT PRACTIC
1. Find the value of x so that
the distance between points
P(3, 5) and Q(x, 11) is 10
Which equations represent the
locus of all points in a
coordinate plane that are
equidistant from the points
(1, -2) and (2, -5)?
3. Find the standard form of
the equation of the parabola.
1. What is 4% of 1,100
2. For all x,
A.4
(x + 4)(x – 5)
3. If
x+y=1
and
x – y = 1,
then y =?
B.4.4
F. x2 -20
A.-1
C.40
G. x2 - x – 20
B.0
D.44
H. 2x – 1
C.½
E.440
J. 2x2 - 1
D.1
K. 2x2 – x + 20
E.2
1. What is 4% of 1,100
2. For all x,
(x + 4)(x – 5)
1,100
x.04
44.00
(x + 4)(x – 5)
x2 + 4x - 5x - 20
x2 – x - 20
If you answered B
or E, you may
have used rules
about moving
decimal points and
moved the wrong
number of places.
Should have used
the distributive
property (FOIL)
If you got F, you
probably just
multiplied the
first and the last
terms.
3. If
x+y=1
and
x – y = 1,
then y =?
x-y=1
x=y+1
x +y = 1
(y+1)+y=1
2y + 1 = 1
2y = 0
y=0
If you chose D,
you probably found
x instead of y.
4. What is the slope of
the line containing ?
the points (-2, 7) and
(3, - 3)
F. 4
G. ¼
H. 0
J. – ½
K. -2
5. If the measure of
an angle is 37 ½ ,
what is the measure
of its supplement,
shown in the figure
below?
37 ½ °,
?
A.52 ½
B.62 ½ 
C.127 ½ 
D.142 ½ 
E.Cannot be
determined from the
given information.
6. What is the sine
of A in the triangle
below?
C
6
10
B
8
F. 0.30
G. 0.50
H.0.60
J. 0.75
K. 0.80
A
4. What is the slope of
the line containing ?
the points (-2, 7) and
(3, - 3)
y1  y2

x1  x2
7   3
 2
 23
If you answered J,
you probably got
the expression for
slope upside
down.
5. If the measure of
an angle is 37 ½ ,
what is the measure
of its supplement,
shown in the figure
below?
37 ½ °,
?
°
180 – 37 ½ = 142.5
If you answered A,
you found the
complementary angle.
6. What is the sine
of A in the triangle
below?
C
10
6
B
A
8
opp
sin A 
hyp
6
 0.6
10
If you answered
something other than
H, you either did not
know the trig
functions or which
ones to use.
7. What is the total
cost of 2.5 pounds
of bananas at $0.34
per pound and 2.5
pounds of tomatoes
at $0.66 per pound?
A.$1.00
B.$2.40
C.$2.50
D.$3.50
E.$5.00
8. The relationship
between temperature
expressed in Degrees
Fahrenheit (F) and
degrees Celsius (C) is
given by the formula
9. Amy drove the 200
miles to New Orleans at
an average speed of 10
miles per hour faster
than her usual average
speed. If she completed
9
the trip in 1 hour less
F  C  32
5
than usual, what is her
If the temperature
is 14 usual driving speed, in
°
degrees Fahrenheit,
miles per hour?
what is it in degrees
Celsius?
A.20
F. -10°
B.30
G. -12 °
C.40
H. -14 °
D.50
I. - 16°
E.60
K. -18°
7. What is the total
cost of 2.5 pounds
of bananas at $0.34
per pound and 2.5
pounds of tomatoes
at $0.66 per pound?
8. The relationship
between temperature
expressed in Degrees
Fahrenheit (F) and
degrees Celsius (C) is
given by the formula
9. Amy drove the 200
miles to New Orleans at
an average speed of 10
miles per hour faster
than her usual average
speed. If she completed
9
the trip in 1 hour less
F  C  32
2.5(0.34) + 2.5(0.66)
5
than usual, what is her
or
If the temperature
° is 14 usual driving speed, in
2.5(0.34 + 0.66) degrees Fahrenheit, what miles per hour?
is it in degrees Celsius?
200
200

1
= $2.50
r  10
r
9
14  C  32
200
200  r

5
r  10
r
2
9
200
r


r
 190r  2000
 18  C
5
r 2  10r  2000  0
 10  C
(r  50)(r  40)  0
r  40
10. A map is laid out
in standard (x, y)
coordinate plane.
How long, in units, is
an airplane flies along
a straight line from
City A located at
(20, 14) to City B
located at (5, 10)?
11. A person 2
meters tall casts a
shadow 3 meters
long. At the same
time, a telephone
pole cast a shadow
12 meters long.
How many meters
tall is the pole?
F.
1200
A.4
G.
B.6
H.
241
209
J.
7
D.11
K.
19
E.18
12. The hiking path to the top
of a mountain makes, at the
steepest place, an angle of
20°, with the horizontal, and
it maintains this constant
slope of 500 meters, as
illustrated below. Which of
the following is the closest
approximation to the change
in elevation in meters, over
this 500-meter section?
F. 20
G. 170
H. 180
J. 250 K. 470
C.8
?
20°
You may use the follow 
cos 20° = .94, sin 20° = .34, tan 20°= .36
10. A map is laid out
in standard (x, y)
coordinate plane.
How long, in units, is
an airplane flies along
a straight line from
City A located at
(20, 14) to City B
located at (5, 10)?
11. A person 2
meters tall casts a
shadow 3 meters
long. At the same
time, a telephone
pole cast a shadow
12 meters long.
How many meters
tall is the pole?
AB  ( x1  x2 ) 2  ( y1  y2 ) 2 2
 ( 20  5) 2  (14  10) 2
3
 225  16
 241
h 8
?
20°
h
3 2

12 h
3h  24
12. The hiking path to the top
of a mountain makes, at the
steepest place, an angle of
20°, with the horizontal, and
it maintains this constant
slope of 500 meters, as
illustrated below. Which of
the following is the closest
approximation to the change
in elevation in meters, over
this 500-meter section?
12
h
500
h
.34 
500
170  h
sin 20 
13. IF 537102 were
14. If a < -1, which of
15. If
calculated it would have
the following best
 4
5
    
5
4
279 digits. What would
describes a general
Then n = ?
the digit farthest to the
relationship between
A.- 3/2
right be (the ones
a3 and a2
B.-1
digit)?
F. a3 > a2
C.-2/3
n
A.1
B.3
D.2/3
G. a3 < a2
C.4
H. a3 = a2
D.7
J. a3 = -a2
E.9
K.
a3 
1
a2
E.3/2
3
13. IF 537102 were
14. If a < -1, which of
15. If
calculated it would have
the following best
 4
5
    
5
4
279 digits. What would
describes a general
n
3
Then n = ?
the digit farthest to the relationship between. The fraction is
flipped so n will have
right be (the ones digit)?
a3 and a2
to be negative. To put
70 = 1, 71 = 7, 72 = 49,
If a is a negative the exponents into a
rational number put
73= 743, 74=2401, 75 =
number, when
he power on top and
16807, 76 = 117,649,…
squared it will be the root on the
bottom. n = -3/2
1’s digit 1 7 9 3
positive, when its
Power
0 1
2
3
4
6
7…
5
100 101 102
cubed, it will be
negative. Therefore
a3 < a2.
16. In the standard (x,y)
coordinate plane, the triangle
with vertices at (0,0), (0,k)
and (2, m), where m is a
constant. Changes shape as k
changes. What happens to
the triangle’s area, expressed
in square coordinate units, as
k increases starting from 2?
F. The area increases as k
increases
G. The area decreases as k
increases
H. The area always equals 2
J. The area always equals m.
K. The area always equals
2m.
17. In the figures below,
AB =AC and BC is 10
units long. What is the
area, in square inches of
ABC? A
B
C
D
A.12.5
B.25
C. 25 2
D.50
E.Cannot be determined
from the given
information.
18. A bag of pennies
could be evenly
divided among 6
children, 7 children,
or 8 children with
each getting the same
number, and with 1
penny left over in
each case. What is
the smallest number
of pennies that could
be in the bag?
F. 22
G. 43
H. 57
J. 169
K. 337
16. In the standard (x,y)
coordinate plane, the triangle
with vertices at (0,0), (0,k)
and (2, m), where m is a
constant. Changes shape as k
changes. What happens to
the triangle’s area, expressed
in square coordinate units, as
k increases starting from 2?
18. A bag of pennies
could be evenly
divided among 6
children, 7 children,
or 8 children with
each getting the same
number, and with 1
penny left over in
each case. What is
the smallest number
B
C
D
of pennies that could
Not enough information. be in the bag?
The drawing
25 2 may throw you off. It
F. 22
could also look like this.
G. 43
H. 57
A
J. 169
K. 337
B
C
D
h
(0,k)
17. In the figures below,
AB =AC and BC is 10
units long. What is the
area, in square inches of
ABC? A
b
(0,0)
A = ½ bh
As k increase, the base
gets larger, therefore the
area increases
19. There are n students 20. Starting at her doorstep,
21.An object on
Ramona walked down the
in a class. If, among sidewalk at 1.5 feet per second for radar is 5 miles to the
those students, p%
4 seconds. Then she stopped for 4 east, 4 miles to the
play at least 1 musical seconds, realizing that she had
north, and 1 mile
forgotten something. Next she
instrument, which of returned to her doorstep along the above the tracking
the following general same route at 1.5 feet per second. station. Among the
expressions represent Which graph of Ramona’s distance following, which is
(d) from her doorstep as a function
the number of student of time (t) would resemble which the closest
who play NO musical of the following?
approximation to the
d
d
instruments?
distance in miles,
A. Np
that the object is
from the tracking
F.
J.
t
t
B. .01np
d
d
station?
A. 6.5
(100  p)n
G.
K.
C. 100
B. 7.2
t
t
d
C. 9.0
(1  p) n
H.
D.
D. 10.0
.01
E. 100(1 – p)n
t
21.An object on radar is 5
19. There are n students 20. Starting at her doorstep,
Ramona walked down the
miles to the east, 4 miles to
in a class. If, among sidewalk at 1.5 feet per second for the north, and 1 mile above
those students, p%
4 seconds. Then she stopped for 4 the tracking station. Among
the following, which is the
play at least 1 musical seconds, realizing that she had
forgotten something. Next she
closest approximation to the
instrument, which of returned to her doorstep along the distance in miles, that the
the following general same route at 1.5 feet per second. object is from the tracking
expressions represent The graph of Ramona’s distance station?
(d) from her doorstep as a function
object
the number of student of time (t) would resemble which
who play NO musical of the following?
1 mi
Tracking
instruments?
station
100 – p = % none players
100  p
= % none players
100 (in decimal form)
(100  p)n

100
d
Stopped for 4
seconds
5 mi
Walking away
from home
52  4 2  41
# of none players
Answer C
Walking back
home
t
Answer J
( 41) 2  12  42
Answer A
 6.5
Same graph for 22 – 24
50
40
Q
S
30
20
C
At both Quick Car rental
and speedy Car Rental, the
cost in dollars, of renting a
full–size car depends on a
fixed daily rental fee and a
fixed charge per mile that
the car is driven.
However, the daily rental
fee and the charge per mile
are not the same for the 2
companies. In the graph to
the right, line Q represents
the total cost for Quick
Car Rental and line S
represents the total cost for
Speedy Car Rental.
60
10
0
0 20 40 60 80 100
Miles driven
22. Robert plans to rent a
full-size car for 1 day
and drive only 50 miles.
If his only consideration
is to incur the least cost,
which company should
he choose?
23. If you rent a fullsize car from Quick
Car Rental for 1 day,
how much more
would the total rental
cost be if you drove
the car 78 miles than
F. Quick Car Rental, because if you drove it 77
miles?
the cost is $5 less.
G. Quick Car Rental, because
the cost is $15 less
H. Either company, because
the costs are equal.
J. Speedy Car Rental, because
the cost is $5 less
K. Speedy Car Rental,
because the cost is $15 less
A. $0.10
B. $0.15
C. $0.20
D. $0.40
E. $0.55
24. What would be
the total cost of
renting a full-size car
from Speedy Car
Rental for 1 day and
driving the car 150
miles.
F. $60
G. $75
H. $85
J. $90
K. $120
22. Robert plans to rent a
full-size car for 1 day
and drive only 50 miles.
If his only consideration
is to incur the least cost,
which company should
he choose?
Answer F
The lower line is for Q
and is saves about $5
60
50
40
Q
S
30
23. If you rent a fullsize car from Quick
Car Rental for 1 day,
how much more
would the total rental
cost be if you drove
the car 78 miles than
if you drove it 77
miles?
The slope of the Q
line gives you the
cost per mile.
24. What would be
the total cost of
renting a full-size car
from Speedy Car
Rental for 1 day and
driving the car 150
miles.
C = $30 + 150(.2)
= $60
Answer F
Pick two points,
(100, 55) and (0, 15)
C
20
10
0
0 20 40 60 80 100
Miles driven
Then find the slope
55  15
 $0.40
100  0 Answer D