Difference between revisions of "2008 AMC 10B Problems"
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==Problem 1== | ==Problem 1== | ||
| + | A basketball player made 5 baskets during a game. Each basket was worth either 2 or 3 points. How many different numbers could represent the total points scored by the player? | ||
| + | <math>\textbf{(A)} 2 \qquad \textbf{(B)} 3 \qquad \textbf{(C)} 4 \qquad \textbf{(D)} 5 \qquad \textbf{(E)} 6</math> | ||
([[2008 AMC 10B Problems/Problem 1|Solution]]) | ([[2008 AMC 10B Problems/Problem 1|Solution]]) | ||
==Problem 2== | ==Problem 2== | ||
| + | A <math>4\times 4</math> block of calendar dates has the numbers <math>1</math> through <math>4</math> in the first row, <math>8</math> though <math>11</math> in the second, <math>15</math> though <math>18</math> in the third, and <math>22</math> through 25<math> in the fourth. The order of the numbers in the second and the fourth rows are reversed. The numbers on each diagonal are added. What will be the positive difference between the diagonal sums? | ||
| + | </math>\textbf{(A)} 2 \qquad \textbf{(B)} 4 \qquad \textbf{(C)} 6 \qquad \textbf{(D)} 8 \qquad \textbf{(E)} 10<math> | ||
([[2008 AMC 10B Problems/Problem 2|Solution]]) | ([[2008 AMC 10B Problems/Problem 2|Solution]]) | ||
==Problem 3== | ==Problem 3== | ||
| + | Assume that </math>x<math> is a [[positive]] [[real number]]. Which is equivalent to </math>\sqrt[3]{x\sqrt{x}}<math>? | ||
| + | </math>\textbf{(A)} x^{1/6} \qquad \textbf{(B)} x^{1/4} \qquad \textbf{(C)} <math>x^{3/8} \qquad \textbf{(D)} x^{1/2} \qquad \textbf{(E)} x</math> | ||
([[2008 AMC 10B Problems/Problem 3|Solution]]) | ([[2008 AMC 10B Problems/Problem 3|Solution]]) | ||
==Problem 4== | ==Problem 4== | ||
| + | A semipro baseball league has teams with 21 players each. League rules state that a player must be paid at least <dollar/>15,000 and that the total of all players' salaries for each team cannot exceed <dollar/>700,000. What is the maximum possible salary, in dollars, for a single player? | ||
| + | <math>\textbf{(A)} 270,000 \qquad \textbf{(B)} 385,000 \qquad \textbf{(C)} 400,000 \qquad \textbf{(D)} 430,000 \qquad \textbf{(E)} 700,000</math> | ||
([[2008 AMC 10B Problems/Problem 4|Solution]]) | ([[2008 AMC 10B Problems/Problem 4|Solution]]) | ||
==Problem 5== | ==Problem 5== | ||
| + | For [[real number]]s <math>a</math> and <math>b</math>, define <math>a\</math> b=(a-b)^2<math>. What is </math>(x-y)^2\<math> (y-x)^2</math>? | ||
| + | <math>\textbf{(A)} 0 \qquad \textbf{(B)} x^2+y^2 \qquad \textbf{(C)} 2x^2 \qquad \textbf{(D)} 2y^2 \qquad \textbf{(E)} 4xy</math> | ||
([[2008 AMC 10B Problems/Problem 5|Solution]]) | ([[2008 AMC 10B Problems/Problem 5|Solution]]) | ||
==Problem 6== | ==Problem 6== | ||
Revision as of 18:42, 28 February 2008
Contents
- 1 Problem 1
- 2 Problem 2
- 3 Problem 4
- 4 Problem 5
- 5 Problem 6
- 6 Problem 7
- 7 Problem 8
- 8 Problem 9
- 9 Problem 10
- 10 Problem 11
- 11 Problem 12
- 12 Problem 13
- 13 Problem 14
- 14 Problem 15
- 15 Problem 16
- 16 Problem 17
- 17 Problem 18
- 18 Problem 19
- 19 Problem 20
- 20 Problem 21
- 21 Problem 22
- 22 Problem 23
- 23 Problem 24
- 24 Problem 25
Problem 1
A basketball player made 5 baskets during a game. Each basket was worth either 2 or 3 points. How many different numbers could represent the total points scored by the player?
(Solution)
Problem 2
A 
block of calendar dates has the numbers 
through 
in the first row, 
though 
in the second, 
though 
in the third, and 
through 25
\textbf{(A)} 2 \qquad \textbf{(B)} 4 \qquad \textbf{(C)} 6 \qquad \textbf{(D)} 8 \qquad \textbf{(E)} 10![$([[2008 AMC 10B Problems/Problem 2|Solution]]) ==Problem 3== Assume that$](http://latex.artofproblemsolving.com/7/e/b/7ebb01864dcb487375217d70bbad1d37531944c6.png)
x![$is a [[positive]] [[real number]]. Which is equivalent to$](http://latex.artofproblemsolving.com/6/4/0/640d3eb88366847a81109b9657d7ebfe35e4a66c.png)
\sqrt[3]{x\sqrt{x}}
\textbf{(A)} x^{1/6} \qquad \textbf{(B)} x^{1/4} \qquad \textbf{(C)} 
(Solution)
Problem 4
A semipro baseball league has teams with 21 players each. League rules state that a player must be paid at least <dollar/>15,000 and that the total of all players' salaries for each team cannot exceed <dollar/>700,000. What is the maximum possible salary, in dollars, for a single player?
(Solution)
Problem 5
For real numbers 
and 
, define 
b=(a-b)^2
(x-y)^2\
?
(Solution)
Problem 6
(Solution)
Problem 7
(Solution)
Problem 8
(Solution)
Problem 9
(Solution)
Problem 10
(Solution)
Problem 11
(Solution)
Problem 12
(Solution)
Problem 13
(Solution)
Problem 14
(Solution)
Problem 15
(Solution)
Problem 16
(Solution)
Problem 17
(Solution)
Problem 18
(Solution)
Problem 19
(Solution)
Problem 20
(Solution)
Problem 21
(Solution)
Problem 22
(Solution)
Problem 23
(Solution)
Problem 24
(Solution)
Problem 25
(Solution)
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