| 2121 |
AMC 12 1983 A Q5 |
Triangle \(ABC\) has a right angle at \(C\). If \(... |
1500.00 |
| 2122 |
AMC 12 1983 A Q6 |
When \[x^5, \quad x+\frac{1}{x}\quad \text{and}\qu... |
1500.00 |
| 2123 |
AMC 12 1983 A Q7 |
Alice sells an item at \(\$10\) less than the list... |
1500.00 |
| 2124 |
AMC 12 1983 A Q8 |
Let \(f(x) = \frac{x+1}{x-1}\). Then for \(x^2 \ne... |
1500.00 |
| 2125 |
AMC 12 1983 A Q9 |
In a certain population the ratio of the number of... |
1500.00 |
| 2126 |
AMC 12 1983 A Q11 |
Simplify \(\sin (x-y) \cos y + \cos (x-y) \sin y\)... |
1500.00 |
| 2127 |
AMC 12 1983 A Q12 |
If \(\log_7 \Big(\log_3 (\log_2 x) \Big) = 0\), th... |
1500.00 |
| 2128 |
AMC 12 1983 A Q13 |
If \(xy = a, xz =b,\) and \(yz = c\), and none of ... |
1500.00 |
| 2129 |
AMC 12 1983 A Q15 |
Three balls marked 1,2, and 3, are placed in an ur... |
1500.00 |
| 2130 |
AMC 12 1983 A Q16 |
Let \[x = .123456789101112\ldots998999,\]where the... |
1500.00 |
| 2131 |
AMC 12 1983 A Q17 |
The diagram to the right shows several numbers in ... |
1500.00 |
| 2132 |
AMC 12 1983 A Q18 |
Let \(f\) be a polynomial function such that, for ... |
1500.00 |
| 2133 |
AMC 12 1983 A Q19 |
Point \(D\) is on side \(CB\) of triangle \(ABC\).... |
1500.00 |
| 2134 |
AMC 12 1983 A Q20 |
If \(\tan{\alpha}\) and \(\tan{\beta}\) are the ro... |
1500.00 |
| 2135 |
AMC 12 1983 A Q22 |
Consider the two functions \[f(x) = x^2+2bx+1\quad... |
1500.00 |
| 2136 |
AMC 12 1983 A Q25 |
If \(60^a = 3\) and \(60^b = 5\), then \(12^{[(1-a... |
1500.00 |
| 2137 |
AMC 12 1983 A Q27 |
A large sphere is on a horizontal field on a sunny... |
1500.00 |
| 2138 |
AMC 12 1983 A Q28 |
Triangle \(\triangle ABC\) in the figure has area ... |
1500.00 |
| 2139 |
AMC 12 1983 A Q29 |
A point \(P\) lies in the same plane as a given sq... |
1500.00 |
| 2140 |
AMC 12 1983 A Q30 |
Distinct points \(A\) and \(B\) are on a semicircl... |
1500.00 |