ACT PREP. . MATH. Educational Talent Search and Upward Bound Forward Service Corporation. Content. 14 questions dealing with Pre-Algebra 10 questions from Elementary Algebra 9 questions based on Intermediate Algebra 9 questions from Coordinate Geometry
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14 questions dealing with Pre-Algebra
10 questions from Elementary Algebra
9 questions based on Intermediate Algebra
9 questions from Coordinate Geometry
14 questions from Plane Geometry
4 Trigonometry questions
The questions assume knowledge of basic formulas and computational skills but do not require memorization of complex formulas or extensive computation
60 minutes
Don’t waste time on any one problem, spend your dftime doing as many problems as you can
The questions are arranged in order of difficulty
RELAX: answering only half of the questions right onwill give you a score of 20 on the Math Section
Go Through The Test Twice
Answer the questions you skipped
ALL PROBLEMS ON THE ACT CAN BE SOLVED WITHOUT USING A CALCULATOR
Get Stuck
Take advantage of the multiple-choice format and try each answer until you find the one that works.
WARNING: Doing it this way will take more time.
The greatest common divisor of 84, 90, and 66 (that is, the largest exact divisor of all three numbers) is:
84 = 2٠2٠3٠7 90 = 2٠3٠3٠5 66 = 2٠3٠11
2٠3 = 6
90 does not go into 84 – eliminate answer E
36 does not go into 84 – eliminate answer D
18 does not go into 84 – eliminate answer C
12 does not go into 90 – eliminate answer B
6 must be the correct answer and it checks
CORRECT ANSWER: A
If you can estimate the correct answer, then you should be able to eliminate at least one or two answer choices.
What is 2% of 60?
60 x 0.02 = 1.2
120 is greater than 60 – eliminate answer A
12 is too large – eliminate answer B
CORRECT ANSWER: C
0.012 is too small – eliminate answer E
A
? 4 meters
B 3 meters C
12, 7, and 5 are longer than the hypotenuse – eliminate answers F, G, and H
By looking at the figure:
X looks too big to be 5°- eliminate answer A
X looks too small to be either 60° or 55° - eliminate answers E and D
One the ACT, the diagrams are “not necessarily” drawn to scale, but usually they’re quite accurate, so you could eliminate certain answer choices by sizing things up with your eyes
In the figure below, what is the value of x?
x
125° 85°
In the figure below, what is the value of x?
x
125° 85°
55°
95°
180 –125 = 55
180 - 85 = 95
180 – 55 – 95 = 30
CORRECT ANSWER: B
By looking at the figure:
A looks larger than 99°– eliminate answer F
A looks smaller than 240° – eliminate answer K
Lola is making the circle graph below showing the number of students at each grade level in her high school. What should be the measure of A?
F. 99°
G. 120°
H. 133°
J. 167°
K. 240°
240 freshmen
A
200 sophomores
130 seniors
150 juniors
Total number of students = 720
Total number of freshmen = 240
Total number of degrees in a circle = 360°
CORRECT ANSWER: G
Some problems are hard because they’re general or abstract, so replace variables with specific numbers
If kx + k = 0, and k>1, then x = ?
Pick a value for k that is greater than 1
Let k = 2
kx + k = 0
2x + 2 = 0
2x = -2
x = -1
Let k = 5
kx + x = 0
5x + 5 = 0
5x = -5
x = -1
If kx + k = 0, and k>1, then x = ?
kx + k = 0
k(x+1) = 0
k= 0 OR x+1 = 0
k= 0 OR x = -1
CORRECT ANSWER:B
For all a 0, what is the slope of the line segment connecting (a,b) and (-a,b) in the usual (x,y) coordinate plane?
For all a 0, what is the slope of the line segment connecting (a,b) and (-a,b) in the usual (x,y) coordinate plane?
CORRECT ANSWER: F
Questions
13
D
C
5
4
12
A
3
B
ABC is a 3-4-5 right triangle and BCD is a 5-12-13 right triangle
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
m
n
b c
d
e
t
CORRECT ANSWER: A
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?
35 (.20) = 7
CORRECT ANSWER: D
35 – 7 = 28
28 (.05) = 1.40
28 + 1.40 = 29.40
35 (.80) = 28
28 (1.05) = 29.40
In the figure below, A, C, and D are collinear. If the measure of A is 30 and the measure ofBCD is 120, what is the measure of B?
B
A
C D
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
180 – 30 – 60 = 90
90
30
60
120
A
C D
180 – 120 = 60
Question 6 measure of
If the area of a circle is , what is the length of its circumference?
Areacircle = r2 Circumference = 2r
= r2
1 = r2
1 = r
C = 2(1)
C = 2
CORRECT ANSWER: D
Question 7 measure of
What is the value of x in the solution for the system of equations below?
2x + 5y = 20
6x – ½ y = 29
What is the value of measure 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
2x + 5y = 20
60x - 5y = 290
multiply by 10
add equations together 62x = 310
solve for x x = 5
What is the value of measure of x in the solution for the system of equations below?
CORRECT ANSWER: B
2x + 5y = 20
6x – ½ y = 29
solve for y
12x – y = 58
-y = 58 – 12x
substitute into 1st equation
y = -58 + 12x
2x + 5(-58+12x) = 20
solve for x
2x + -290 + 60x = 20
62x + -290 = 20
62x = 310
x = 5
Question 8 measure of
CORRECT ANSWER: C
Question 9 measure of
For all y, 26y – (-10y) – 3y(-y+3) = ?
26y – (-10y) – 3y(-y+3)
26y +10y +3y2 – 9y
3y2 +27y
CORRECT ANSWER: E
C measure of
D
80°
100
50
50
30
A B
180 – 30 – 50 = 100
180 – 100= 80
m BDC = 80
CORRECT ANSWER: D
Question 11 measure of
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
4
x
R 3 S
In the figure below, measure of 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
a2 + b2 = c2
32 + 42 = c2
9 + 16 = c2
25 = c2
5 = c
5
4
x
CORRECT ANSWER: C
R 3 S
RST is a 3-4-5 right triangle
Question 12 measure of
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 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 F
AreaTriangle = ½ base x height
= ½ (12) (10)
= 60
CORRECT ANSWER: C
Question 13 given, in units. What is the area, in square units, of triangle DEG?
A
6
O
60
B
Circumference = 2 given, in units. What is the area, in square units, of triangle DEG?r
C = 26
C = 12
degrees = arc
60(12) = 360 x
720 = 360 x
2 = x
A
6
O
60
CORRECT ANSWER: B
B
a given, in units. What is the area, in square units, of triangle DEG?2 + b2 = c2
122 + b2 = 132
144 + b2 = 169
b2 = 25
b = 5
CORRECT ANSWER: A
A
13
5
C 12 B
Question 15 given, in units. What is the area, in square units, of triangle DEG?
CORRECT ANSWER: E
Question 16 given, in units. What is the area, in square units, of triangle DEG?
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
Arearectangle= length x width
= 3x(3y) = 9xy square feet
Total Cost = area x price
= 9xy (2) = 18xy
CORRECT ANSWER: E
Question 17 given, in units. What is the area, in square units, of triangle DEG?
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
Question 17 given, in units. What is the area, in square units, of triangle DEG?
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
12 = = 3.14
1
Areasquare = s2
22 = 4
Areapiece = Areasquare - Areacircle
4 – 3.14 = 0.86
CORRECT ANSWER: C
Question 18 given, in units. What is the area, in square units, of triangle DEG?
Which of the following is equal to 3.14 x 106?
3.1400000000
3140000.0000
CORRECT ANSWER: E
Question 19 given, in units. What is the area, in square units, of triangle DEG?
Find the last number in the series: 8, 4, 12, 6, 18, 9,?
84 8-4=4 or 82=4
412 4+8=12 or 4x3=12
126 12-6=6 or 122 = 6
6 18 6+12=18 or 6x3=18
189 18-9=9 or 182 = 9
9x3=27
CORRECT ANSWER: E
Question 20 given, in units. What is the area, in square units, of triangle DEG?
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?
Let x = the fifth test score
(91 + 88 + 86 + 78 + x ) 5 = 85
343 + x = 425
x = 82
CORRECT ANSWER: A
Question 21 given, in units. What is the area, in square units, of triangle DEG?
One angle, A, has 3 times the measure of its supplement, B. What is the degree measure of A?
Let x = the measure of B
then 3x = the measure of A
x + 3x = 180°
4x = 180°
x = 45°
B = 45°
A = 135°
CORRECT ANSWER: C
Question 22 given, in units. What is the area, in square units, of triangle DEG?
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?
Probability of drawing a green jelly bean
CORRECT ANSWER: D
Question 23 given, in units. What is the area, in square units, of triangle DEG?
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
II. a>c, so 2a>c – TRUE
III. If c=2, a=4, and b=10, then a+c<b - FALSE
CORRECT ANSWER: C
Question 24 given, in units. What is the area, in square units, of triangle DEG?
B
A
1
C
CORRECT ANSWER: C
CORRECT ANSWER: E given, in units. What is the area, in square units, of triangle DEG?
B
20-x
E
x
C
20
4
D
6
A
10
Things to Remember on the Math ACT given, in units. What is the area, in square units, of triangle DEG?
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 given, in units. What is the area, in square units, of triangle DEG?
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