2011_10A_Worksheets.pdf - A cell phone plan costs 20...

A cell phone plan costs 20 dollars each month, plus 5 cents per
text message sent, plus 10 cents for each minute used over 30
hours. In January Michelle sent 100 text messages and talked
for 30 . 5 hours. How much did she have to pay?
(A) $24 . 00 (B) $24 . 50 (C) $25 . 50 (D) $28 . 00
(E) $30 . 00
2011 AMC 10A, Problem #1—
2011 AMC 12A, Problem #1—
“How many minutes of excess chatting are there, and what do
they cost?”
Difficulty: Easy
CCSS-M: N-Q.1. Use units as a way to understand problems and to guide the solution of multi-step
problems; choose and interpret units consistently in formulas.
1

A small bottle of shampoo can hold 35 milliliters of shampoo,
whereas a large bottle can hold 500 milliliters of shampoo.
Jasmine wants to buy the minimum number of small bottles
necessary to completely fill a large bottle. How many bottles
must she buy?
2011 AMC 10A, Problem #2—
2011 AMC 12A, Problem #3—
“The quantity 35 goes into 500 how many times?”
needs to buy is 15.
Difficulty: Easy
CCSS-M: N-Q.3. Choose a level of accuracy appropriate to limitations on measurement when reporting
quantities.
2

Suppose [ a b ] denotes the average of a and b , and { a b c }
denotes the average of a , b , and c . What is {{ 1 1 0 } [0 1] 0 } ?
(A)
2
9
(B)
5
18
(C)
1
3
(D)
7
18
(E)
2
Answer (D): First note that { 1 1 0 } =
2
3
and [0 1] =
2
. Therefore
{{ 1 1 0 } [0 1] 0 } = {
2
3
1
2
0 } =
2
3
+
1
2
+ 0
3
=
7
18
.
Difficulty: Medium Easy
CCSS-M: A-SSE.1. Interpret expressions that represent a quantity in terms of its context. Interpret
complicated expressions by viewing one or more of their parts as a single entity.
3
2011 AMC 10A, Problem #3—
“Pay attention to the order of substitutions.”
Solution
1
3

Let X and Y be the following sums of arithmetic sequences:
X = 10 + 12 + 14 + · · · + 100 ,
Y = 12 + 14 + 16 + · · · + 102 .
What is the value of Y - X ?
2011 AMC 10A, Problem #4—
“What are the elements in Y but not in X , and vice versa?”
Difficulty: Medium
CCSS-M: A-SSE.2. Use the structure of an expression to identify ways to rewrite it.
4