Sat math Essentials

Section 2 Answers
1.
e.
An expression is undefined when a denominator
of the expression is equal to zero. When 
x
= –2,
x
2
+ 6
x
+ 8 = (–2)
2
+ 6(–2) + 8 = 4 – 12 + 8 = 0.
2.
e.
Parallel lines have the same slope. The lines 
y
=
6
x
+ 6 and 
y
= 6
x
– 6 both have a slope of 6, so
they are parallel to each other.
3.
c.
Substitute 8 for 
a
:
b
–
8
4
= 
4
8
b
+ 1. Rewrite 1 as 
8
8
and add it to 
4
8
b
, then cross multiply:
b
–
8
4
= 
4
b
8
+ 8
4
b
2
– 8
b
– 32 = 64
b
2
– 2
b
– 8 = 16
b
2
– 2
b
– 24 = 0
(
b
– 6)(
b
+ 4) = 0
b
– 6 = 0,
b
= 6
b
+ 4 = 0,
b
= –4
4.
e.
If the average of five consecutive odd integers is
–21, then the third integer must be –21. The
two larger integers are –19 and –17 and the two
lesser integers are –23 and –25. –25 is the least
of the five integers. Remember, the more a num-
ber is negative, the less is its value.
5.
c.
A square has four right (90-degree) angles. The
diagonals of a square bisect its angles. Diagonal
AC
bisects 
C
, forming two 45-degree angles,
angle 
ACB
and angle 
ACD
. The sine of 45
degrees is equal to 
.
2
2
–
P R A C T I C E T E S T 2
–
2 1 6

---

6.
c.
The volume of a cylinder is equal to 
π
r
2
h
,
where 
r
is the radius of the cylinder and 
h
is
the height. The volume of a cylinder with a
radius of 1 and a height of 1 is 
π
. If the height
is doubled and the radius is halved, then the
volume becomes 
π
(
1
2
)
2
(2)(1) = 
π
(
1
4
)2 = 
1
2
π
.
The volume of the cylinder has become half
as large.
7.
d.
a
1
–1
= = 
a
,
= (
a
b
– 
a
)(
1
a
) = 
a
2
b
– 1
8.
d.
The volume of a cube is equal to 
e
3
, where 
e
is the length of an edge of the cube. The sur-
face area of a cube is equal to 6
e
2
. If the ratio
of the number of cubic units in the volume to
the number of square units in the surface
area is 2:3, then three times the volume is
equal to two times the surface area:
3
e
3
= 2(6
e
2
)
3
e
3
= 12
e
2
3
e
= 12
e
= 4
The edge of the cube is four units and the sur-
face area of the cube is 6(4)
2
= 96 square units.
9.
5
8
The set of whole number factors of 24 is {1, 2, 3,
4, 6, 8, 12, 24}. Of these numbers, four (4, 8,
12, 24) are multiples of four and three (6, 12,
24) are multiples of six. Be sure not to count
12 and 24 twice—there are five numbers out
of the eight factors of 24 that are a multiple of
either four or six. Therefore, the probability
of selecting one of these numbers is 
5
8
.