Sat math Essentials

independent variables
. The 
y
values 
depend
on the 
x
values, so the 
y
values
are called the 
dependent variables
.
Practice Question
If the function 
f
is defined by 
f
(
x
) 
9
x
3, which of the following is equal to 
f
(4
b
)?
a.
36
b
12
b
b.
36
b
12
c.
36
b
3
d.
4
b
9
3
e.
9
4
b
3
Answer
c.
If
f
(
x
) 
9
x
3, then, for 
f
(4
b
), 4
b
simply replaces 
x
in 9
x
3. Therefore,
f
(4
b
) 
9(4
b
) 
3 
36
b
3.
Qualitative Behavior of Graphs and Functions
For the SAT, you should be able to analyze the graph of a function and interpret, qualitatively, something about
the function itself.
Example
Consider the portion of the graph shown below. Let’s determine how many values there are for 
f
(
x
) 
2.
x
y
–
A L G E B R A R E V I E W
–
9 2

---

When 
f
(
x
) 
2, the 
y
value equals 2. So let’s draw a horizontal line through 
y
2 to see how many times the
line intersects with the function. These points of intersection tell us the 
x
values for 
f
(
x
) 
2. As shown below, there
are 4 such points, so we know there are four values for 
f
(
x
) 
2.
x
y
Fou
r
p
oints
of inte
r
section
at 
y
= 2
–
A L G E B R A R E V I E W
–
9 3

---

---

Vo c a b u l a r y
It is essential in geometry to recognize and understand the terminology used. Before you take the SAT, be sure
you know and understand each geometry term in the following list.
acute angle
an angle that measures less than 90°
acute triangle
a triangle with every angle that measures less than 90°
adjacent angles
two angles that have the same vertex, share one side, and do not overlap
angle
two rays connected by a vertex
arc
a curved section of a circle
area
the number of square units inside a shape 
bisect
divide into two equal parts
central angle
an angle formed by an arc in a circle 
C H A P T E R
Geometry
Review
This chapter reviews key skills and concepts of geometry that you need
to know for the SAT. Throughout the chapter are sample questions in
the style of SAT questions. Each sample SAT question is followed by
an explanation of the correct answer.
7
9 5

---