


Tackling Math and Supermath
Head Items
Math Head items are pretty simple, but it’s easy to fall
into traps if you’re not careful when solving these items. The goal
is to protect yourself against traps by following our fourstep
method. Supermath Head items are a bit more complicated, but you
can use the same step method to solve these items. The only major
difference between the two is that steps 2 and 3 are more intensive
for Supermath Head items and may contain several different concepts
and formulas.
Follow these four steps every time you approach a Math
Head or Supermath Head item:
Step 1: Determine what the item is really asking you
to solve.
Step 2: Determine which formulas and concepts to use.
Step 3: Do the math by writing out every step.
Step 4: Plug it in.
Math Head and Supermath Head Items
in Slow Motion
Now let’s work out each step in slow motion. We’ll start
out with a basic Math Head item:

Step 1: Determine what the item is really asking you to
solve.
Carefully analyze the item. In this case, the ultimate
goal is to find the value of x. Also notice that
all the answers involve exponents.
Step 2: Determine which formulas and concepts to use.
To calculate the value of x, you first
need to simplify the equation by getting rid of the parentheses
and exponents so you can arrive at the answer. To simplify the equation,
you need to follow PEMDAS on the left side of the equation.
Step 3: Do the math by writing out every step.
Make sure you take the time to write out your steps. If
you try doing the math in your head, you run the risk of making
a careless mistake. Furthermore, writing out your work reinforces
the concepts you’ve already learned. The more explicit you make
these concepts, the easier it will be to remember them.
First, solve the parentheses:
Now do the exponents:
Be very careful with signs changes depending
on the odd or even exponent.
Then do the multiplication:
There is no division, so do the addition:
Now do a little algebra and divide both sides by 5:
Step 4: Plug it in.
Congratulations. You solved for x.
Before giving your humble acceptance speech, look down at the answer
choices. There’s no 35, so there’s one more step to go. Simplify
each answer choice to see which one gives you 35.
Choice A:
Choice B:
Voilà! Answer B is correct.
Guided Practice
Try solving this Math Head item on your own:

Step 1: Determine what the item is really asking you to
solve.
What is the stem asking you for? What concepts apply?
Step 2: Determine which formulas and concepts to use.
What steps do you have to follow? How can you simplify
the equations?
Step 3: Do the math by writing out every step.
Be careful when you bring the numbers to the same base,
and be attentive when you change the exponents.
Step 4: Plug it in.
Is the answer that you found in the form the item requires?
If so, choose the correct answer. If not, what are you going to
do about it?
Guided practice: Explanation
Step 1: Determine what the item is really asking you to
solve.
The stem tells you that you have to figure out the
value of . However, your real goal is to find
the value of x. The item revolves around that unknown
variable. Once you know x, you’ll be able to find .
Step 2: Determine which formulas and concepts to use.
Think back to what you learned about exponents and
roots in the previous section. To solve for x in
the first equation, you want to simplify the numbers so that you
have the same bases on either side of the equation. Once the bases
are the same on both sides, the exponents will be equal. After
you find the value of x, you can plug it into .
To make it easier to find the answer, you might have to change into
exponential form.
Step 3: Do the math by writing out every step.
To solve , you need to bring
both expressions to the same base. In this case, convert both bases
to 5:
Now you can solve for x:
Once you find x, plug it into the second
expression:
Step 4: Plug it in.
Now you have the answer, 4. But the stem doesn’t have
a plain old 4 as an answer choice. Typical. Take a close look at
the choices. Answer choice A works out to the value
you need.
Independent Practice
Here’s a tougher Supermath Head item for you to solve
on your own. Once you’ve completed your work, look at the following
page to see how we solved it.

Independent Practice: Explanation
Step 1: Determine what the item is really asking you to
solve.
There are no answer choices here, so this is a gridin.
The stem asks you to find out when will
be greater than . You need to find
a number whose value increases when the exponent decreases.
Step 2: Determine which formulas and concepts to use.
How do you solve such an item? Think back to what you’ve
learned about fractions. When fractions are multiplied by themselves,
their value decreases. So a fraction raised to a higher power is
less than a fraction raised to a lower power. Of course, we are
talking about only positive numbers here because you can’t grid
in a negative number.
Step 3: Do the math by writing out every step.
Because the stem asks for one possible value
of x, you know there’s going to be more than one
correct answer. Plug in an easy fraction, such
as , and check it:
That works.
Step 4: Plug it in.
There is more than one correct answer to this gridin
item, but works just fine. Make sure the answer
is a decimal or a proper fraction.
