Question bank AMC12 1956

The value of $x+x(x^x)$ when $x=2$ is:

Mr. Jones sold two pipes at $\$1.20$ each. Based on the cost his profit on one was $20\%$ and his loss on the other was $20\%.$ On the sale of the pipes, he:

The distance light travels in one year is approximately $5{,}870{,}000{,}000{,}000$ miles. The distance light travels in $100$ years is:

A man has $\$10{,}000$ to invest. He invests $\$4{,}000$ at $5\%$ and $\$3{,}500$ at $4\%.$ In order to have a yearly income of $\$500,$ he must invest the remainder at:

A nickel is placed on a table. The number of nickels which can be placed around it, each tangent to it and to two others is:

In a group of cows and chickens, the number of legs was $14$ more than twice the number of heads. The number of cows was:

The roots of the equation $ax^2+bx+c=0$ will be reciprocal if:

If $8\cdot2^x=5^{y+8},$ then, when $y=-8,$ $x=$

Simplify $\left[\sqrt[3]{\sqrt[6]{a^9}}\right]^4\left[\sqrt[6]{\sqrt[3]{a^9}}\right]^4;$ the result is:

A circle of radius $10$ inches has its center at the vertex $C$ of an equilateral triangle $ABC$ and passes through the other two vertices. The side $AC$ extended through $C$ intersects the circle at $D.$ The number of degrees of angle $ADB$ is:

The expression $1-\dfrac1{1+\sqrt3}+\dfrac1{1-\sqrt3}$ equals:

If $x^{-1}-1$ is divided by $x-1$ the quotient is:

Given two positive integers $x$ and $y$ with $x\lt y.$ The percent that $x$ is less than $y$ is:

The points $A,$ $B,$ and $C$ are on a circle $O.$ The tangent line at $A$ and the secant $BC$ intersect at $P,$ $B$ lying between $C$ and $P.$ If $BC=20$ and $PA=10\sqrt3,$ then $PB$ equals:

The root(s) of $\dfrac{15}{x^2-4}-\dfrac2{x-2}=1$ is (are):

The sum of three numbers is $98.$ The ratio of the first to the second is $\dfrac23,$ and the ratio of the second to the third is $\dfrac58.$ The second number is:

The fraction $\dfrac{5x-11}{2x^2+x-6}$ was obtained by adding the two fractions $\dfrac A{x+2}$ and $\dfrac B{2x-3}.$ The values of $A$ and $B$ must be, respectively:

If $10^{2y}=25,$ then $10^{-y}$ equals:

Two candles of the same height are lighted at the same time. The first is consumed in $4$ hours and the second in $3$ hours. Assuming that each candle burns at a constant rate, in how many hours after being lighted was the first candle twice the height of the second?

If $(0.2)^x=2$ and $\log 2=0.3010,$ then the value of $x$ to the nearest tenth is: