Transcript Educational Talent Search and Upward Bound Forward Service Corporation

Educational Talent Search and Upward Bound
Forward Service Corporation
Question 15
Points N and J have coordinates (-1, -1) and (3,3) respectively.
What is the length of line NJ ?
(the distance between ( x1 , y1 )and ( x2 , y2 ) )
Distance Formula =
A.
4
B.
8
C. 6
( x2  x1 )2  ( y2  y1 )2
(3  (1))2  (3  (1))2
42  42
32  16 2  4 2
D. 8
E. 4 2
CORRECT ANSWER: E
5
2x

4
6
3x y
Calculator or Zoom?
34  53
Calculator or Zoom?
73  54
5
2
3
(3
–
3
4)
2
4
2
7x y (2x
(3x –
–
2
2
5y )
4
7xy
+ 3xy)
Question 7
What is the value of x in the solution
for the system of equations below?
2x + 5y = 20
6x – ½ y = 29
A. 4
B. 5
C. 6
D. 15
E. 20
ZOOM?
What is the value of x in the solution
for the system of equations below?
2x + 5y = 20
6x – ½ y = 29
2x + 5y = 20
6x – ½ y = 29 multiply by 10
add equations together
solve for x
2x + 5y = 20
60x - 5y = 290
62x = 310
x=5
What is the value of x in the solution for the system of
equations below?
CORRECT ANSWER: B
2x + 5y = 20
6x – ½ y = 29
solve for y
substitute into 1st equation
solve for x
12x – y = 58
-y = 58 – 12x
y = -58 + 12x
2x + 5(-58+12x) = 20
2x + -290 + 60x = 20
62x + -290 = 20
62x = 310
x=5
2x – 4 = 8
2x – 4 < 8
2x – 4 > 8
√576
4√1296
6√64
Cos A=
Sin A=
Tan A=
Cos C=
Sin C=
Tan C=
A
5
3
B
4
C
Will you be asked for Sin B?
Use Sin to find
Angle A
A
5
3
B
4
Use Cos to find
Angle A
C
Use Sin to find
Angle C
A
5
B
13
12
Use Cos to find
Angle C
C
Use Sin to find
Angle A
A
5
B
13
12
Use Cos to find
Angle A
C
Imaginary Numbers
1. i14 Calculator or zoom?
2. i7
3. i20
1. i21
1. i(2 + i)
2. 6i(5 – 4i)
3. (2 + 8i) + (-3 – 9i)
4. (6 – 5i) – (3 + 12i)
5. (2 – i)(4 + 3i)
Question 6
If the area of a circle is , what is the length
of its circumference?
A. 1
B. 2
C. 
D. 2
E. 3
Areacircle = r2
Circumference = 2r
 = r2
C = 2(1)
1 = r2
C = 2
1=r
CORRECT ANSWER: D
GUESSTIMATE (cont.)
In the right triangle below, how many meters long is AB ?
A
F.
G.
H.
J.
K.
12
7
5
3
?
4 meters
7
B
3 meters
12, 7, and 5 are longer than the hypotenuse –
eliminate answers F, G, and H
C
GUESSTIMATE (cont.)
In the right triangle below, how many meters long is AB ?
a b  c
2
F.
G.
H.
J.
K.
12
7
5
3
7
2
32  b 2  42
9  b  16
2
A
2
?
4 meters
b 7
2
b 7
B
CORRECT ANSWER: K
3 meters
C
EYEBALL
By looking at the figure:
thetoo
ACT,
diagrams
are “not
necessarily”
drawn
XOne
looks
bigthe
to be
5°- eliminate
answer
A
to scale, but usually they’re quite accurate, so you could
X looks too small to be either 60° or 55° - eliminate
eliminate certain answer choices by sizing things up with
answers E and D
your eyes
In the figure below, what is the value of x?
A. 5°
x
B. 30°
C. 40°
D. 55°
E. 60°
125°
85°
EYEBALL (cont.)
In the figure below, what is the value of x?
x
A. 5°
B. 30°
C. 40°
D. 55°
E. 60°
125° 55° 95° 85°
180 –125 = 55
180 - 85 = 95
180 – 55 – 95 = 30
CORRECT ANSWER: B
Question 1
In the figure below, CA is perpendicular to AB and CB is
perpendicular to BD; AB is 3 units long, AC is 4 units long,
and BD is 12 units long. How many units long is CD ?
D
C
A. 13
B. 17
4
A
12
3
C. 19
D. 24
B
E. 25
a b  c
2
2
5  12  CD
2
2
3  4  CB
2
2
9  16  CB
25  CB
2
2
169  CD
2
2
13  CD
5  CB
13
CORRECT ANSWER: A
D
5
4
A
2
25  144  CD
2
C
2
12
3
B
ABC is a 3-4-5 right triangle and BCD is a 5-12-13 right triangle
Question 2
In the figure below, line m is parallel to line n, and line t is
a transversal crossing both m and n. Which of the
following lists has 3 angles that are all equal in measure?
a
b
c
d
e
t
m
n
A. a,b,d
B. a,c,d
C. a,c,e
D. b,c,d
E. b,c,e
CORRECT ANSWER: A
Question 3
A shirt that originally cost $35 is on sale at 20% off. If
the sales tax on shirts is 5% of the purchase price, how
much would it cost to buy the shirt at its sale price?
CORRECT ANSWER: D
35 (.20) = 7
A. $ 7.35
35 – 7 = 28
28 (.05) = 1.40
B. $20.00
28 + 1.40 = 29.40
C. $26.60
D. $29.40
35 (.80) = 28
E. $29.75
28 (1.05) = 29.40
Question 4
What is the slope of the line x = 2y +3?
CORRECT ANSWER: A
A.
B.
C.
D.
1
2
1
3
2
2
E. 3
x = 2y + 3
x – 3 = 2y
x 3
y
2
x 3
 y
2 2
1
3
x  y
2
2
y = mx + b
1
m
2
3
b
2
Question 5
In the figure below, A, C, and D are collinear.
If the measure of A is 30 and the measure
ofBCD is 120, what is the measure of B?
A. 30
B
B. 60
C. 90
A
D. 120
C
D
E. 150
In the figure below, A, C, and D are collinear. If
the measure of A is 30 and the measure of
BCD is 120, what is the measure of B?
CORRECT ANSWER: C
B
90
A
30
180 – 30 – 60 = 90
60
120
C
D
180 – 120 = 60
Question 8
1 2 3 4 5
      ?
2 3 4 5 6
1  2 3   20 
   
2  3 4   30 
Regular calculator or ZOOM? 1   2  4    4 

  
2 3 3 6
1
A.
1 8 2
6
  
17
2 9 3
B.
27
1 8 6
  
13
C.
2 9 9
18
1 2
7

D.
2 9
9
9 4 13
5
 
E.
18 18 18
6
CORRECT
ANSWER:
C
Question 9
For all y, 26y – (-10y) – 3y(-y+3) = ?
A. 10y
26y – (-10y) – 3y(-y+3)
B. -3y2 + 25y
26y +10y +3y2 – 9y
C. 3y2 + 7y
3y2 +27y
D. 3y2 + 25y
E. 3y2 + 27y
CORRECT ANSWER: E
Question 10
In ABC shown below, BD bisects ABC. The measure of ABC
is 100, and A measures 30. What is the measure of BDC?
C
A. 65
D
B. 70
C. 75
D. 80
E. 85
30
A
100
B
In ABC shown below, BD bisects ABC. The measure of ABC
is 100, and A measures 30. What is the measure of BDC?
C
A. 65
B. 70
C. 75
30
D
80°
100 50
50
A
B
D. 80
180 – 30 – 50 = 100
E. 85
180 – 100= 80
m BDC = 80
CORRECT ANSWER: D
Question 11
In the figure below, S is a right angle, RS is 3 units
long, and ST is 4 units long. If the measure of R is
x, then sin x = ?
T
3
A.
5
3
B.
4
4
C.
4
5
5
D.
4
x
5
E.
R
3
S
3
In the figure below, S is a right angle, RS is 3 units
long, and ST is 4 units long. If the measure of R is
x, then sin x = ?
T
opposite
sin x 
hypotenuse
a2 + b2 = c2
32
+
42
=
5
c2
4
9 + 16 = c2
25 = c2
5=c
4
sin x 
5
x
R
3
RST is a 3-4-5 right triangle
S
CORRECT
ANSWER: C
Question 12
In the figure below, the lengths of DE, EF, and FG
are given, in units. What is the area, in square
units, of triangle DEG?
A.29
B.47.5
G
C.60
D.6 149
E.120
10
D
12
E
7
F
In the figure below, the lengths of DE, EF, and FG
are given, in units. What is the area, in square units,
of triangle DEG?
G
10
D
12
E
7
AreaTriangle = ½ base x height
= ½ (12) (10)
= 60
CORRECT ANSWER: C
F
Question 13
In the figure below, A and B lie on the circle centered at O,
OA is 6 units long, and the measure of AOB is 60°. How
many units long is minor arc AB?
A
6
A. 
B. 2
C. 6
D. 12
E. 36
O
60
B
Circumference = 2r
degrees = arc
C = 26
arc
circle
C = 12
60
x

360 12
60(12) = 360 x
A
6
O
720 = 360 x
2 = x
60
B
CORRECT
ANSWER:
B
Question 14
In the right triangle below, the length of AB is 13 units and
the length of CB is 12 units. What is the tangent of A?
A.
B.
C.
D.
E.
12
5
13
12
12
13
5
12
5
13
A
13
C
12
B
opposite
tan x 
adjacent
a2 + b2 = c2
122 + b2 = 132
144 + b2 = 169
b2 = 25
12
tan x 
5
b=5
CORRECT ANSWER: A
A
13
5
C
12
B
Question 16
What is the cost in dollars to carpet a room x yards long and
y yards wide if the carpet costs two dollars per square foot?
x yards = 3x feet
y yards = 3y feet
A. xy
B. 2xy
Arearectangle= length x width
C. 3xy
= 3x(3y) = 9xy square feet
Total Cost = area x price
D. 6xy
= 9xy (2) = 18xy
E. 18xy
CORRECT ANSWER: E
Question 17
In the figure below, the largest possible circle is cut out of a
square piece of tin. The area of the remaining piece of tin is
approximately (in square inches)
2 inches
A. 0.14
B. 0.75
C. 0.86
D. 1.0
E. 3.14
Question 17
In the figure below, the largest possible circle is cut out of a
square piece of tin. The area of the remaining piece of tin is
approximately (in square inches)
2 inches
Areacircle =  r2
A. 0.14
B. 0.75
 12 =  = 3.14
1
C. 0.86
Areasquare = s2
D. 1.0
E. 3.14
22 = 4
Areapiece = Areasquare - Areacircle
CORRECT ANSWER: C
4 – 3.14 = 0.86
Question 18
Which of the following is equal to 3.14 x 106?
Regular calculator or ZOOM or NEITHER?
A. 314
3.1400000000
B. 3140
C. 31,400
D. 314,000
E. 3,140,000
3140000.0000
CORRECT ANSWER: E
Question 19
Find the last number in the series:
8, 4, 12, 6, 18, 9,?
A. 19
B. 20
C. 22
D. 24
E. 27
84
8-4=4
or
82=4
412
4+8=12
or
4x3=12
126
12-6=6
or
122 = 6
6 18
6+12=18
or
6x3=18
189
18-9=9
or
182 = 9
9x3=27
CORRECT ANSWER: E
Question 20
Lyndsey receives grades of 91, 88, 86, and 78 on
four tests. What grade must she receive on her
fifth test to have an average test score of 85?
A. 82
Let
B. 83
(91 + 88 + 86 + 78 + x )  5 = 85
C. 84
343 + x = 425
D. 85
x = 82
E. 86
x = the fifth test score
CORRECT ANSWER: A
Question 21
One angle, A, has 3 times the measure of its
supplement, B. What is the degree measure of A?
A. 112 ½°
B. 120°
Let x = the measure of B
then 3x = the measure of A
C. 135°
x + 3x = 180°
D. 150°
4x = 180°
B = 45°
E. 157 ½°
x = 45°
A = 135°
CORRECT ANSWER: C
Question 22
A bag contains 4 red jelly beans, 5 green jelly beans,
and 3 white jelly beans. If a jelly bean is selected at
random from the bag, what is the probability that the
jelly bean selected is green?
A.
B.
C.
D.
E.
1
12
1
5
5
23
5
12
5
7
Probability of drawing a green jelly bean
number of green jelly beans 5

total number of jelly beans 12
CORRECT ANSWER: D
Question 23
For all positive values of a, b, and c with a<b and a>c,
which of the following MUST be true?
I. a+b>c
II. 2a>c
III. a+c>b
c<a<b
I.
a and b are both greater than c,
so their sum will also be – TRUE
A. I only
II.
B. II only
III. If c=2, a=4, and b=10,
then a+c<b - FALSE
C. I and II only
D. II and III only
E. I, II, and III
a>c, so 2a>c – TRUE
CORRECT ANSWER: C
Question 24
The scales on both axes of the standard (x,y) coordinate
plane below are the same. Of the following, which is
the best estimate for the slope of AB ?
A. 4
3
B.
4
1
C.
4
1
D. 4
E. -4
1
rise

slope =
run
4
A
B
1
C
CORRECT ANSWER: C
Question 25
In the figure below, D is a point on AB and E is a point
on BC such that DE AC. If DB = 4, AB = 10, BC = 20,
what is the length of EC ?
B
A. 4
B. 6
D
C. 8
E
D. 10
E. 12
A
C
CORRECT ANSWER: E
ABC and DBE are similar triangles,
so their sides are in proportion
4
10

20-x 20
4  20  10(20  x )
80  200  10x
120  10x
x  12
B
4
10
D
6
A
20
20-x
E
x
C
Things to Remember on
the Math ACT
Don’t read the directions
Bring a calculator that you know how to use
Read the question carefully
Pay attention to what the question asks you to find
Watch for unnecessary information
Draw a picture
Pace yourself (60 questions/60 minutes)
Things to Remember on
the Math ACT
Do the easy questions first, then try the hard ones
Show some work and circle your answers in your test booklet
Don’t waste too much time on one problem
Eliminate wrong answers before guessing
Answer every question
Check your work
Work for the whole 60 minutes