Roots and Radicals
We just saw that roots express fractional exponents. But it is often easier to work with
roots in a different format. When a number or term is raised to a fractional power, the
expression can be converted into one involving a root in th
1.
Evaluate the expression
x = 2.
(A)
(B)
(C)
(D)
(E)
for the value
4
6
8
2. If a is even and negative, b is negative, and c is even, which of the following
choices could be equal to a
(A) 71
(B) 16
(C) 0
(D) 4
(D) 9
b + c2 + 1?
3. What is the absolute va
1. D
This question tests your
understanding of order of
operations, exponents, and
logarithms.
Well solve it step by step. The
numerator simplies to
The denominator is 5, because 25
= 32. So the answer is 405 = 8.
2. E
The product of two negative
number
Logarithms
Logarithms are closely related to exponents and roots. A logarithm is the power to which you must raise a given
number, called the base, to equal another number. For example, log2 8 = 3 because 23 = 8. In this case, 2 is the base
and 3 is the l
This question is a good example of how its not always simple to isolate a variable. (Dont worry about the logarithm
in this problemwell review these later on in the chapter.) However, as you can see, even the thorniest problems
can be solved systematicall
Scientific Notation
Scientific notation is a convention used to express large numbers. A number written in
scientific notation has two parts:
1 A number between 1 and 10.
2 The power of 10 by which you must multiply the first number in order to get the la
Manipulating Equations
Now that you know how to set up the equation, the next thing to do is to solve for the value that the question asks for.
First and foremost, the most important thing to remember when manipulating equations is to do exactly the same
Writing Equations
For some questions on the Math IC test, youll need to translate the problem from a language youre used toEnglish
into a more useful, albeit less familiar language. Were talking about the language of math, of course, and one of
your major
Math IC Algebra
Strategies
There are several ways to
answer most algebra problems.
You could try to solve a problem
by using standard algebra and
setting up and solving an
equation. Alternatively, you
could try to avoid algebra and
simply plug the answer
To use the picking numbers method, you need to select numbers and plug them into the
answer choices. Youre essentially testing the relationships between the variables in each
given answer and ensuring they remain true. It doesnt matter what specific numbe