Download Name: Date: Bell: Math Part I Introduction The breakdown of the

Name:
Date:
Bell:
Math Part I
Introduction
The breakdown of the questions on the ACT Math Test is the
Topic
every time.
# of Questions
Pre-Algebra
Elementary Algebra
Intermediate Algebra
Coordinate Algebra
Plane Geometry
Trigonometry
Never leave a question
on the ACT.
Usually the first 10 questions are pretty
, and the last 10 are
The 2 Pass Approach:

Easy questions. Do these

Medium-to-hard questions. These are questions you can do, but which will take a good bit of
. You always want to get the easy points.
. Circle these and come back to them after you've gotten all the easy points.

Super-hard questions. Answer these
. You're not going to be able
to figure them out later, so just put a guess down now and be done with them.
is a great Process of Elimination (POE) tool. Before you start to solve
any math problem,
it first and take a look at the answers. If there are any answers
which you know are way too
or way too
Fundamentals
Terminology
Write the definition of each of the following terms:
Product
Sum
cross them off!
Difference
Quotient
Integer
Rational Numbers
Real Numbers
Remainder
Positive
Negative
Prime Numbers Part I
Prime Numbers Part II
Factor
Multiples
Reciprocal
Geometry Terminology
Geometry makes up nearly
the questions on the ACT:
geometry questions out of 60 total questions.
The
of an object is the sum of the lengths of its sides.
The area of a rectangle or square is found by multiplying the
by the
.
How many degrees does each of the following have?
TriangleQuadrilateralCircleStraight Line-
Opposite angles are
. Angles next to each other form a line and add up to
degrees.
Number Theory
Division and multiplication are really the
operation. When you multiply or divide two
positive numbers, the result is
. When you multiply or divide two negative
numbers, the result is also
. When you multiply or divide a positive and
negative number, however, the result is
.
A fraction is shorthand for
. When you add fractions, you need to give them a
common
first. When you
them, though, you can go straight across. If you divide fractions, you need to
the second fraction.
makes everything inside of it positive.
Fractions and Decimals
All fractions can be converted into
, and all decimals can be converted into
too.
work math out in your head on the ACT!
You can never have a
fraction with a zero on the bottom is that it is
in the denominator (on the bottom). The technical term for a
.
Exponents and Roots
The
tells you how many times the number needs to be multiplied by
If you're
.
two numbers with exponents together, you can combine them into one if
the number on the bottom (the base) is the
for both, and then add the exponents
together.
If you're
numbers or variables with exponents, you can handle the exponents by
them, as long as the bases are the same.
If you take something to the zero power, it becomes
, no matter what it was before.
If you take something to a negative power, that means take the
Roots are always
.
.
You can multiply and divide roots any time.
The number under the root must be the
to add and subtract.
Solving for X
You'll see two types of solving for x questions on the ACT. One type will give you a
for the variable and have you do the math. The other type will require you to manipulate the equation until you
have
on one side and a
When solving equations, you have to keep the equation
something to
. Every time you do
side of the equation, you must do it to the other. To avoid making careless
mistakes, write down every step.
Summary
What are rational numbers?
How are factors and multiples different?
What is a reciprocal?
on the other side.
What does MADS mean and when do you use it?
What does x0 equal? What does x -3 equal?
What does
What does
equal?
equal?
Comprehensive Drill:
Score-
%
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Better than Algebra
Plugging in Basics
Plug In on any question with
in the answer choices, or questions which
use the phrase "In terms of. . ."
The first thing you'll do is
all the variables in the question with
. Cross out the variables and write the numbers above them. Cross out "in terms
of," too. It's there to
you.
Replace the variables in the answer choices.
Reread the question with your
in the place of the variables, do the
arithmetic and
Finally,
your answer.
each of the answer choices.
Every time you plug in, you must check all
Occasionally, more than
more than one answer matches your target,
those answers again.
answer choices before picking one of them.
answer choice works with the numbers you pick. If you find that
in new numbers, and
On Plugging In questions like this one, use
or
to make the math simpler.
Comprehensive Drill:
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%
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Plugging in Your Own Numbers
in every chance you get.
Plugging In questions are some of the most
questions on the ACT. There are
Plugging In questions on every single ACT.
Plug in numbers that make your life
When plugging in for
. Use small numbers, like
or
.
, what would make good numbers?
Plugging in the Answer Choices
PITA=

Use PITA when the question tells a little story and then asks "

Use PITA if you're looking for

To use PITA, pick an answer choice, and try it in the question. If it works, it's right.

You

PITA is nearly as powerful as regular Plugging In.
that fit an equation in coordinate geometry.
need to try all five answers when using PITA. Only
Start with the
is going to work.
answer choice. If the middle answer is too big, cross off all
answers
than it, too. If it's too small, cross off all answers
Comprehensive Drill:
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."
%
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than it.
Plugging in Geometry
When plugging in on
problems, remember to obey the
of
geometry such as:
Triangles always have
.
Circles always have
.
Parallel lines
meet.
Plug In the Answers anytime you have a geometry question which tells you a silly little
has
and
for all the answer choices.
Comprehensive Drill:
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Geometry
Guesstimating
Whenever you see a
on the test, you can be pretty certain that it
with what is stated in the question.
Your Scantron is a
.
Guesstimating is a lot like
. You have to guesstimate
you start to calculate. It will help you
bad answer choices.
Lines/Angles/Parallels
of the 60 math questions are geometry questions.
On the ACT, you are expected to know the geometry
Two angles that form a line add up to
when the test begins.
.
angles (the ones that are opposite each other when two lines make an X) are equal.
The angles next to each other on vertical angles add up to
A right angle has
.
works very well on angle problems.
.
There are only two types of angles:
and
If two angles look the same, they are the
.
.
Any Big angle plus any Little angle equals
.
Comprehensive Drill:
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Triangles
How many degrees are there in a triangle?
How do you find the perimeter of a triangle?
What's the formula for the area of a triangle?
What's an isosceles triangle?
What's an equilateral triangle?
If ACT doesn't give you a figure, you must
what the problem describes before
beginning to solve the question.
Right Triangles
The lengths of the sides of a right triangle have a fixed relationship called the
.
If the legs of a right triangle are named a and b, and the
opposite the right angle) is named c, then the length of the sides is given by this equation:
The area of a triangle is
.
(the long side
An
triangle has two
sides, and the angles opposite
those sides are equal, too.
In an
triangle, all sides are equal and all angles are equal. The angles are all
.
In a
triangle, the lengths of the sides are given by
.
Comprehensive Drill:
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Quadrilaterals
All quadrilaterals have
sides and have
.
Square
Area = side2.
All four angles are
.
Rectangle
Area = l x w
All four angles equal
.
Parallelogram
Area = b x h
Angles which look the same are the
Any Big angle plus any Little angle equals
.
.
Trapezoid
Area =
The angles can be just about anything, so long as they add up to
.
This is the
common of the quadrilaterals.
Comprehensive Drill:
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Circles
Radius The distance from the center to the edge. Written as
Diameter The length of a line through the
Written as
.
of the circle and from one side to the other.
.
Circumference The
of the circle. The formula for circumference is
.
Area The area of a circle is given by the formula
A
is a line which touches something at only one point. If a line is tangent to
a circle the line makes a
angle with a radius drawn at that same point.
are proportional to the whole circle. For example, if the arc length is
of the
, then the area is also of the whole area.
Coordinate Plane
There are
coordinate geometry questions on every ACT.
The
-axis goes left and right, like the cheerleader making the x.
The
-axis goes up and down, like the cheerleader making the y.
In an ordered pair, like (2,3), the
value comes before the
a coordinate plane and
that doesn't have a figure. It'll raise your score.
The
Formula:
value, just like in the alphabet.
the points for any coordinate geometry question
To find the distance between points, you'll use the
.
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Arithmetic
Averages
An average is also known as a
.
In an average, there are three things to deal with: the
, the number of things, and the
.
Draw a circle with a T in it. You'll always be given
of the three pieces of information that you
need to solve the average. The
sets up the equation you
need to solve to find the missing piece.
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Proportions
You don't frequently see ratios involving many variables, but
If you have two types of things in a question, and they're
there's an excellent chance you're dealing with a proportion question.
proportions are pretty common.
, like miles per hour,
Percent Problems
There aren't usually any percent
questions on the test. The ACT's percent
questions are usually simple percentages.
Percent questions can be tricky because they are usually
problems.
% (percent) means
of means
what is the
is, are, were, was means
Translate: What is 35% of 40?
Comprehensive Drill:
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