Question bank AMC12 1959

Each edge of a cube is increased by $50\%.$ The percent of increase of the surface area of the cube is:

Through a point $P$ inside triangle $ABC$ a line is drawn parallel to the base $\overline{AB},$ dividing the triangle into two equal areas. If the altitude to $\overline{AB}$ has length $1,$ then the distance from $P$ to $\overline{AB}$ is:

If the diagonals of a quadrilateral are perpendicular to each other, the figure would always be included under the general classification:

If $78$ is divided into three parts which are proportional to $1,$ $\dfrac13,$ $\dfrac16,$ the middle part is:

The value of $(256)^{0.16}\cdot(256)^{0.09}$ is:

Given the true statement: If a quadrilateral is a square, then it is a rectangle. It follows that, of the converse and the inverse of this true statement:

The sides of a right triangle are $a,$ $a+d,$ and $a+2d,$ with $a$ and $d$ both positive. The ratio of $a$ to $d$ is:

The value of $x^2-6x+13$ can never be less than:

A farmer divides his herd of $n$ cows among his four sons so that one son gets one-half the herd, a second son one-fourth, a third son one-fifth, and the fourth son $7$ cows. Then $n$ is:

In triangle $ABC,$ with $\overline{AB}=\overline{AC}=3.6,$ a point $D$ is taken on $\overline{AB}$ at a distance $1.2$ from $A.$ Point $D$ is joined to point $E$ in the prolongation of $\overline{AC}$ so that triangle $AED$ is equal in area to triangle $ABC.$ Then $\overline{AE}$ equals:

The logarithm of $0.0625$ to the base $2$ is:

By adding the same constant to each of $20,$ $50,$ $100$ a geometric progression results. The common ratio is:

The arithmetic mean (average) of a set of $50$ numbers is $38.$ If two numbers, namely, $45$ and $55,$ are discarded, the mean of the remaining set of numbers is:

Given the set $S$ whose elements are zero and the even integers, positive and negative. Of the five operations applied to any pair of elements: $(1)$ addition, $(2)$ subtraction, $(3)$ multiplication, $(4)$ division, $(5)$ finding the arithmetic mean (average), those operations that yield only elements of $S$ are:

In a right triangle the square of the hypotenuse is equal to twice the product of the legs. One of the acute angles of the triangle is:

The expression $$
\frac{x^2-3x+2}{x^2-5x+6}\div \frac{x^2-5x+4}{x^2-7x+12},
$$ when simplified, is:

If $y=a+\dfrac bx,$ where $a$ and $b$ are constants, and if $y=1$ when $x=-1,$ and $y=5$ when $x=-5,$ then $a+b$ equals:

The arithmetic mean (average) of the first $n$ positive integers is:

With the use of three different weights, namely, $1$ lb., $3$ lb., and $9$ lb., how many objects of different weights can be weighed, if the objects to be weighed and the given weights may be placed in either pan of the scale?

It is given that $x$ varies directly as $y$ and inversely as the square of $z,$ and that $x=10$ when $y=4$ and $z=14.$ Then, when $y=16$ and $z=7,$ $x$ equals: