What is(20−(2010−201)) + (2010−(201−20))?
(A)−4020(B)−401(C)0(D)40(E)4020Answer (D):Distributing the negative signs gives(20−(2010−201)) + (2010−(201−20))= 20−2010 + 201 + 2010−201 + 20= 40.Difficulty:EasyNCTMStandard:Number and Operations Standard for Grades 9–12:judge the effects ofsuch operations as multiplication, division, and computing powers and roots on the magnitudesof quantities.
2010 AMC 10 B, Problem #1
—
2010 AMC 12 B, Problem #1
—
“
−
(
a
−
b
) =
−
a
+
b
.”
Solution
Tyrone had 63 marbles and Eric had 12 marbles.Tyrone then gave some of his marbles to Eric so thatTyrone ended with twice as many marbles as Eric.How many marbles did Tyrone give to Eric?
2010 AMC 10 B, Problem #2—“Set up a equation to represent the situation.”
Difficulty:
Easy
NCTM
Standard:
Algebra Standard for Grades 9–12:
write equivalent forms of equations,
inequalities, and systems of equations and solve them with fluencymentally or with paper and pencil
in simple cases and using technology in all cases.
A book that is to be recorded onto compact disks
takes 412 minutes to read aloud.
Each disk can
hold up to 56 minutes of reading. Assume that the
smallest possible number of disks is used and that each
disk contains the same length of reading. How many
minutes of reading will each disk contain?
(A)
51
.
5
(B)
52
.
4
(C)
53
.
8
(D)
55
.
2
(E)
56
.
0
2010 AMC 10 B, Problem #3
—
2010 AMC 12 B, Problem #2
—
“Because
412
÷
56
is between 7 and 8, the reading will
need 8 disks.”
Solution
Answer (A):
Because
412
÷
56
is between 7 and 8, the reading will
need 8 disks. Therefore each disk will contain
412
÷
8 = 51
.
5
minutes of
reading.
Difficulty:
Easy
NCTM Standard:
Algebra Standard for Grades 9–12: identify essential quantitative relationships
in a situation and determine the class or classes of functions that might model the relationships.
Suppose
[
a b
]
denotes the average of
a
and
b
, and
{
a b c
}
denotes the average of
a
,
b
, and
c
. What is
{{
0 0 1
}
[0 1] 0
}
?
(A)
1
4
(B)
2
9
(C)
5
18
(D)
1
3
(E)
2
3
2010 AMC 10 B, Problem #4
—
“Note that
{
0 0 1
}
=
1
3
and
[0 1] =
1
2
.”
Solution
Answer (C):
First note that
{
0 0 1
}
=
1
3
and
[0 1] =
1
2
. Therefore
{{
0 0 1
}
[0 1] 0
}
=
{
1
3
1
2
0
}
=
1
3
+
1
2
+ 0
3
=
5
18
.
Difficulty:
Medium-easy
NCTM Standard:
Number and Operations Standard for Grades 9–12: understand meanings of
operations and how they relate to one another.
RectangleABCD, pictured below, shares 50% of itsarea with squareEFGH. SquareEFGHshares 25%of its area with rectangleABCD. What isABAD?ABCDEFGH(A)2(B)4(C)6(D)8(E)162010 AMC 10 B, Problem #5—2010 AMC 12 B, Problem #3—“Half of the area of the rectangle is in the square.”
You've reached the end of your free preview.
Want to read all 25 pages?
- Winter '13
- Kramer
- Platonic solid, United States of America Mathematical Olympiad
