Difference between revisions of "1996 AHSME Problems"
Talkinaway (talk | contribs) (→Problem 4) |
Talkinaway (talk | contribs) (→Problem 6) |
||
Line 43: | Line 43: | ||
[[1996 AHSME Problems/Problem 5|Solution]] | [[1996 AHSME Problems/Problem 5|Solution]] | ||
− | ==Problem | + | ==Problem== |
If <math> f(x) = x^{(x+1)}(x+2)^{(x+3)} </math>, then <math> f(0)+f(-1)+f(-2)+f(-3) = </math> | If <math> f(x) = x^{(x+1)}(x+2)^{(x+3)} </math>, then <math> f(0)+f(-1)+f(-2)+f(-3) = </math> | ||
Line 50: | Line 50: | ||
[[1996 AHSME Problems/Problem 6|Solution]] | [[1996 AHSME Problems/Problem 6|Solution]] | ||
+ | |||
+ | ==Solution== | ||
+ | |||
+ | Plugging in <math>x=0</math> into the function will give <math>0^1\cdot 2^3</math>. Since <math>0^1 = 0</math>, this gives <math>0</math>. | ||
+ | |||
+ | Plugging in <math>x=-1</math> into the function will give <math>-1^0 \cdot 1^2</math>. Since <math>-1^0 = 1</math> and <math>1^2 = 1</math>, this gives <math>1</math>. | ||
+ | |||
+ | Plugging in <math>x=-2</math> will give a <math>0^1</math> factor as the second term, giving an answer of <math>0</math>. | ||
+ | |||
+ | Plugging in <math>x=-3</math> will give <math>(-3)^{-2}\cdot -1^0</math>. The last term is <math>1</math>, while the first term is <math>\frac{1}{(-3)^2} = \frac{1}{9}</math> | ||
+ | |||
+ | Adding up all four values, the answer is <math>1 + \frac{1}{9} = \frac{10}{9}</math>, and the right answer is <math>\boxed{E}</math>. | ||
==Problem 7== | ==Problem 7== |
Revision as of 20:42, 18 August 2011
Contents
- 1 Problem 1
- 2 Problem 2
- 3 Problem 3
- 4 Problem 4
- 5 Problem 5
- 6 Problem
- 7 Solution
- 8 Problem 7
- 9 Problem 8
- 10 Problem 9
- 11 Problem 10
- 12 Problem 11
- 13 Problem 12
- 14 Problem 13
- 15 Problem 14
- 16 Problem 15
- 17 Problem 16
- 18 Problem 17
- 19 Problem 18
- 20 Problem 19
- 21 Problem 20
- 22 Problem 21
- 23 Problem 22
- 24 Problem 23
- 25 Problem 24
- 26 Problem 25
- 27 Problem 26
- 28 Problem 27
- 29 Problem 28
- 30 Problem 29
- 31 Problem 30
Problem 1
The addition below is incorrect. What is the largest digit that can be changed to make the addition correct?
$\begin{tabular}{r}&\ \texttt{6 4 1}\\ \texttt{8 5 2} &+\texttt{9 7 3}\\ \hline \texttt{2 4 5 6}\end{tabular}$ (Error compiling LaTeX. Unknown error_msg)
Problem 2
Each day Walter gets dollars for doing his chores or
dollars for doing them exceptionally well. After
days of doing his chores daily, Walter has received a total of
dollars. On how many days did Walter do them exceptionally well?
Problem 3
Problem 4
Six numbers from a list of nine integers are and
. The largest possible value of the median of all nine numbers in this list is
$\text{(A)}\ 5\qquad\text{(B)}\6\qquad\text{(C)}\ 7\qquad\text{(D)}\ 8\qquad\text{(E)}\ 9$ (Error compiling LaTeX. Unknown error_msg)
Problem 5
Given that , which of the following is the largest?
Problem
If , then
Solution
Plugging in into the function will give
. Since
, this gives
.
Plugging in into the function will give
. Since
and
, this gives
.
Plugging in will give a
factor as the second term, giving an answer of
.
Plugging in will give
. The last term is
, while the first term is
Adding up all four values, the answer is , and the right answer is
.