Up Your Score (47 page)

(A) 6
x

(B) 42

(C) 3

(D) 11

(E) 17

Answer: (E). Plug in 3 and 4 where
x
and
y
were in the definition.

2.
= 2(
n
²
n
) / (
n
+ 1). What is
?

(A) 70

(B) 64

(C) 32

(D) 35
n

(E) 1

Answer: (A)

Note:
2(
n
²
+
n
) / (
n
+ 1) = 2
n
(
n
+ 1) / (
n
+ 1) = 2
n
.

Take it from here.

3.
L
@
K
=
L
+
. What is
L
@ (
L
@
K
)?

(A)
L
+ 2
K
+

(B) 2
L
+
+ 1

(C)
L

(D)
L
+ 1

(E)

Okay. We know you’re tired of this, so we’ll give it to you:

Answer: (D)

Remember:
Always do the stuff in the parentheses first.

4.

If

what is
x
?

(A) 1½

(B) 3

(C) 4

(D) 5

(E) 8

Answer: (C)

We’re sorry to do this to you, but there are a few additional topics you should probably get familiar with. Don’t worry, they’re nothing you can’t handle. So without further ado, we bring you the section of odds and ends that we like to call Heinous Miscellaneous Math.

Let’s start with some definitions.

In mathematical terms, a
sequence
is a function whose domain is the set of positive integers. There are two kinds of sequences that you’re likely to see—arithmetic and geometric.

In
geometric sequences,
or
exponential growth sequences,
numbers change by a certain ratio, rather than by a certain difference. For example, the set {½, ¼, ⅛,
... } is a geometric sequence, because you can get each number by dividing the one before it by ½. On the other hand, the set {2, 5, 8, 11 ... } is an arithmetic sequence because you get each number by adding 3 to the previous number. The Serpent requires that you know about geometric sequences, so we’ll go into this a little more in-depth.

The formula for a geometric sequence is

a
_n
=
a
₁
r
(
n
–1)

where
a
₁
is the first term,
r
is the ratio of change,
n
is the number of the term you’re trying to get, and a
_n
is the term itself.

Example: Find the eighth term of {½, ¼, ⅛,
...}