Question bank AMC12 1954

The square of $5-\sqrt{y^2-25}$ is:

The equation $$
\begin{aligned} \frac{2x^2}{x-1}-\frac{2x+7}{3} &{}+\frac{4-6x}{x-1}\\ &{}+1=0 \end{aligned}
$$ can be transformed by eliminating fractions to the equation $x^2-5x+4=0.$ The roots of the latter equation are $4$ and $1.$ Then the roots of the first equation are:

If $x$ varies as the cube of $y,$ and $y$ varies as the fifth root of $z,$ then $x$ varies as the $n$th power of $z,$ where $n$ is:

If the Highest Common Divisor of $6432$ and $132$ is diminished by $8,$ it will equal:

A regular hexagon is inscribed in a circle of radius $10$ inches. Its area is:

The value of $\left(\dfrac1{16}\right)^{a^0}+\left(\dfrac1{16a}\right)^0$ ${}-64^{-\frac{1}{2}}-(-32)^{-\frac{4}{5}}$ is:

A housewife saved $\$2.50$ in buying a dress on sale. If she spent $\$25$ for the dress, she saved about:

The base of a triangle is twice as long as a side of a square and their areas are the same. Then the ratio of the altitude of the triangle to the side of the square is:

A point $P$ is outside a circle and is $13$ inches from the center. A secant from $P$ cuts the circle at $Q$ and $R$ so that the external segment of the secant $\overline{PQ}$ is $9$ inches and $\overline{QR}$ is $7$ inches. The radius of the circle is:

The sum of the numerical coefficients in the expansion of the binomial $(a+b)^6$ is:

A merchant placed on display some dresses, each with a marked price. He then posted a sign “$\dfrac13$ off on these dresses.” The cost of the dresses was $\dfrac34$ of the price at which he actually sold them. Then the ratio of the cost to the marked price was:

The solution of the equations $$
\begin{aligned} 2x-3y&=7,\\ 4x-6y&=20 \end{aligned}
$$ is:

A quadrilateral is inscribed in a circle. If angles are inscribed in the four arcs cut off by the sides of the quadrilateral, without intersecting the sides between vertices, their sum will be:

When simplified $\sqrt{1+\left(\dfrac{x^4-1}{2x^2}\right)^2}$ equals:

$\log125$ equals:

If $f(x)=5x^2-2x-1,$ then $f(x+h)-f(x)$ equals:

The graph of the function $f(x)=2x^3-7$ goes:

Of the following sets, the one that includes all values of $x$ which will satisfy $2x-3\gt7-x$ is:

If the three points of contact of a circle inscribed in a triangle are joined, the angles of the resulting triangle:

The equation $x^3+6x^2+11x+6=0$ has: