Sat math Essentials

4.
e.
To find the total number of different guitars
that are offered, multiply the number of neck
choices by the number of body choices by the
number of color choices: (4)(2)(6) = 48 differ-
ent guitars.
5.
c.
The set of positive factors of 12 is {1, 2, 3, 4, 6,
12}. All of the even numbers (2, 4, 6, and 12) are
multiples of 2. The only positive factors of 12
that are not multiples of 2 are 1 and 3.
6.
b.
Be careful—the question asks you for the num-
ber of values of
f
(3), not 
f
(
x
) = 3. In other words,
how many 
y
values can be generated when 
x
=
3? If the line 
x
= 3 is drawn on the graph, it
passes through only one point. There is only
one value for 
f
(3).
7.
d.
Factor the numerator and denominator of the
fraction:
(
x
2
+ 5
x
) = 
x
(
x
+ 5)
(
x
3
– 25
x
) = 
x
(
x
+ 5)(
x
– 5)
There is an 
x
term and an (
x
+ 5) term in both
the numerator and denominator. Cancel those
terms, leaving the fraction 
x
–
1
5
.
8.
c.
The equation of a parabola with its turning
point 
c
units to the left of the 
y
-axis is written as
y
= (
x
+ 
c
)
2
. The equation of a parabola with its
turning point 
d
units above the 
x
-axis is written
as 
y
= 
x
2
+ 
d
. The vertex of the parabola formed
by the equation 
y
= (
x
+ 1)
2
+ 2 is found one
unit to the left of the 
y
-axis and two units above
the 
x
-axis, at the point (–1,2). Alternatively, test
each answer choice by plugging the 
x
value of
the choice into the equation and solving for 
y
.
Only the coordinates in choice 
c
, (–1, 2), repre-
sent a point on the parabola (
y
= (
x
+ 1)
2
+ 2, 2
= (–1 + 1)
2
+ 2, 2 = 0
2
+ 2, 2 = 2), so it is the only
point of the choices given that could be the ver-
tex of the parabola.