ACT MATH TEST
• You are given 60 minutes to answer 60
questions. That’s 60 seconds or less per
question.
• You should memorize the instructions for
the Math Test before you arrive to take the
test. (see handout) You don’t want to
waste a single second looking at the
directions on test day.
ACT MATH TEST
• All questions are printed in the left half of
the page.
• The right half of the page is for “your
figuring and your drawings.” USE IT!
ACT MATH TEST
• Five, not four, multiple choice answers. Be
careful filling in the bubbles on the answer
sheet.
• Guess on any question you can’t answer.
But, your best bet is always to try to
eliminate whatever answer choices you
can and then guess.
ACT MATH TEST
• Try to answer the easier questions first.
They should take you less than 60
seconds.
ACT MATH TEST
• If you skip a question be sure to put a
mark by it in your test booklet.
It’s often suggested that you go ahead
and bubble a “best guess” answer on
your answer sheet. This would help
keep you in order on the answer sheet
and you would have a best guess in
case you ran out of time and couldn’t
get back to that question.
ACT MATH STRATEGIES
ACT MATH STRATEGY
Draw a picture.
o Many of the word problems become much
easier when you can draw a picture of the
situation.
o The visual representation may remind you of
properties related to the problem.
o Be sure to label your drawing accurately to
assist with setting up your computations.
o This strategy is especially helpful with geometry
problems.
• Let’s use this strategy on the following
problem.
Problem
Four points, A, B, C, and D lie on a circle having a
circumference of 15 units. B is 2 units
counterclockwise from A. C is 5 units clockwise
from A. D is 7 units clockwise from A and 8 units
counterclockwise from A. What is the order of the
points, starting with A and going clockwise around
the circle?
F. A, B, C, D
G. A, B, D, C
H. A, C, B, D
J. A, C, D, B
K. A, D, C, B
• Answer is J
• Did drawing a picture work for you?
• Did anyone use a different method to
solve this problem?
ACT MATH STRATEGY
Eliminate two or three answer choices.
o In many problems, information is provided that
will make two or three of the answers impossible
to be the correct answer.
o Eliminate these answers and then use the
additional information to choose between the
remaining answer choices.
• Let’s use this strategy on the following
problem.
Problem
What is the least common multiple of 70, 60, and
50?
F.
60
G.
180
H.
210
J.
2,100
K. 210,000
• Answer is J
• Which answers could you immediately
eliminate? Why?
•
•
•
•
Couldn’t be 60 because of 70.
Couldn’t be 180 – not divisible by 50 evenly.
Couldn’t be 210 – not divisible by 50 or 60 evenly.
210,000 is a multiple of all 3 numbers but it is not the
least common multiple.
ACT MATH STRATEGY
Substitute numbers for variables.
o Many problems are particularly confusing
because they only contain variable expressions
and few, if any, numbers.
o Numbers can be substituted in for the variables
to provide more information about the answer to
the problem.
• Let’s use this strategy on the following
problem.
Problem
The length of a rectangle is 3 times the length of a
smaller rectangle. The 2 rectangles have the same
width. The area of the smaller rectangle is A
square units. The area of the larger rectangle is kA
square units. Which of the following is the value of
k?
F.
G.
H.
J.
K.
1/9
1/3
1
3
9
• Answer is J
• How did you solve this problem? Did you
substitute a number? Draw a picture?
• Assume area of rectangle A is 1. Width and height would
each be 1 (area=w*h). Width is the same on both
rectangles so could determine length of larger rectangle
as 3 times the length of smaller or in this case (3)(1).
• Picture would be an easy representation.
ACT MATH STRATEGY
Substitute answers into the problem.
o Start with an answer in the middle of the
choices. Substitute it into the problem.
o If that answer doesn’t work, try to decide if you
can eliminate the higher or lower answers. (The
numbers are usually listed in numerical order.)
o Continue substituting each of the remaining
answers until the correct answer is found.
• Let’s use this strategy on the following
problem.
Problem
For 2 consecutive integers, the result of adding the
smaller integer and triple the larger integer is 79.
What are the 2 integers?
A. 18, 19
B. 19, 20
C. 20, 21
D. 26, 27
E. 39, 40
• Answer is B
• Did you solve this problem by substituting
in the pairs?
• Did you start with the pair in the middle
thereby able to eliminate higher or lower?
• Did you solve another way?
– Maybe you realized quickly that 3 times 20 in answer
B would give you 60 + the 19 would then give you 79
ACT MATH STRATEGY
Determine what the question is asking.
o Word problems often contain many pieces of
information that could be confusing.
o It is necessary to read the problem carefully to
determine exactly what information the problem
is asking you to find.
• Let’s use this strategy on the following
problem.
Problem
Lines p and n lie in the standard (x,y) coordinate
plane. An equation for line p is y = 0.12x + 3,000.
The slope of line n is 0.1 greater than the slope of
line p. What is the slope of line n?
F. 000.012
G. 000.02
H. 000.22
J. 001.2
K. 300
• Answer is H
• What is the question asking?
• Do you know what the slope of line p is?
(0.12)
• Do you know what the slope of line n is?
(0.1 > than slope of line p)
(0.12 + 0.1…0.22)
• Remember…Strategies are just that.
• They do not replace math skills.
• They are meant to support your
understanding of math.
• Good strategies can help you put your
knowledge of math and the ACT format to
the best possible use and help you
achieve your target score.
• Let’s try a few more problems.
Problem
Kaya ran 1-2/5 miles on Monday and 2-1/3 miles
on Tuesday. What was the total distance, in miles,
Kaya ran during those 2 days?
A. 3-2/15
B. 3-3/8
C. 3-2/5
D. 3-7/15
E. 3-11/15
• Answer is E
• Total distance = sum of 1-2/5 and 2-1/3
• To add mixed numbers, each fraction must have a
common denominator
• 3 and 5 do not have any common factors other than 1 so
the least common denominator is 3(5), or 15
• To convert 2/5, multiply by 3/3 = 6/15
• To convert 1/3, multiply by 5/5 = 5/15
• 1-6/15 + 2-5/15 = 1+2 and 6/15+5/15 = 3-11/15
Problem
(3x3)(2x2y)(4x2y) is equivalent to:
F. 9x7y2
G. 9x12y2
H. 24x7y2
J. 24x12y
K. 24x12y2
• Answer is H
• Multiply the constants (3)(2)(4)
• When have common base, use the base and add the
exponents.
• Combine the x terms (x3x2x2 – x3+2+2 – x7)
• Combine the y terms (yy – y1y1 – y1+1 – y2)
• Result is 24x7y2
If you didn’t get the correct answer, do you see where you
made your mistake?
Problem
If a rectangle measures 54 meters by 72 meters,
what is the length, in meters, of the diagonal of the
rectangle?
F. 48
G. 63
H. 90
J. 126
K. 252
• Answer is H
• Did you draw a picture?
• Could use the Pythagorean theorem because the sides
of the rectangle are the legs of a right triangle
• Diagonal of the rectangle is the hypotenuse of the right
triangle
72 meters
2
2
2
• Then h = 72 + 54 then h = 80
h
54 meters
Problem
If a = b + 2, then (b – a)4 = ?
F. -16
G. -8
H. 1
J. 8
K. 16
• Answer is K
• To find (b - a)4 given a = b+2, you could solve the
equation for b - a.
• Subtract a and 2 from both sides
• You get -2 = b – a
• Substitute -2 for b – a in (b – a)4
• (-2)4 or 16
Problem
Points B and C lie on AD as shown below. The
length of AD is 30 units; AC is 16 units long; and
BD is 20 units long. How many units long, if it can
be determined, is BC?
F. 4
G. 6
A
C
B
H. 10
J. 14
K. cannot be determined from the given
information
D
• Answer is G
• Did you use the line drawing to determine your
answer?
• If AD is 30 units and BD is 20 units then AB is 10
units
• If AC is 16 units then AC – AB is 6 units
Problem
A cord 24 inches long is 5 inches from the center of a circle,
as shown below. What is the radius of the circle, to the
nearest tenth of an inch?
A. 29.0
B. 24.5
C. 16.9
D. 13.0
E. 10.9
r
5
24
• Answer is D
• Use the right triangle shown on the diagram
• Half the length of the cord is 12 inches (the length of one
leg)
• The other leg is 5 inches long
• The hypotenuse is r inches long
• This is a right triangle because the distance between a
point and line must be measured perpendicular to the line.
• Pythagorean theorem r2 = 122 + 52 then r2 = 169
• r = 13 inches
Problem
The larger of two numbers exceeds twice the smaller
number by 8. The sum of twice the larger and 3 times the
smaller number is 65. If x is the smaller number, which
equation below determines the correct value of x?
F. 3(2x + 8) + 2x = 65
G. 3(2x - 8) + 2x = 65
H. (4x + 8) + 3x = 65
J. 2(2x + 8) + 3x = 65
K. 2(2x - 8) + 3x = 65
• Answer is J
• One strategy is to find equations.
• In the first part of the problem let y be the larger number
and get the equation y = 2x + 8.
• The second part of the problem says 2y + 3x = 65.
• Substitute 2x + 8 for y in the second equation.
• 2(2x + 8) + 3x = 65
To get better at taking the test…
– TAKE PRACTICE TESTS
– TAKE PRACTICE TESTS
– TAKE PRACTICE TESTS
Resources
• ACT website
• http://www.actstudent.org/
• Louisville Free Public Library
• http://www.lfpl.org/MyLibraryU/act.htm
•
The Real ACT Prep Guide
•
SparkNotes
• http://www.sparknotes.com/testprep/act/