Question bank AMC12 1950

If $64$ is divided into three parts proportional to $2,$ $4,$ and $6,$ the smallest part is:

Let $R=gS-4.$ When $S=8,$ $R=16.$ When $S=10,$ $R$ is equal to:

The sum of the roots of the equation $4x^2+5-8x=0$ is equal to:

Reduced to lowest terms, $$
\frac{a^2-b^2}{ab}-\frac{ab-b^2}{ab-a^2}
$$ is equal to:

If five geometric means are inserted between $8$ and $5832,$ the fifth term in the geometric series is:

The values of $y$ which will satisfy the equations

$$
\begin{aligned} 2x^2+6x+5y+1&=0,\\ 2x+y+3&=0 \end{aligned}
$$

may be found by solving:

If the digit $1$ is placed after a two digit number whose tens’ digit is $t,$ and units’ digit is $u,$ the new number is:

If the radius of a circle is increased $100\%,$ the area is increased:

The area of the largest triangle that can be inscribed in a semicircle whose radius is $r$ is:

After rationalizing the numerator of $\dfrac{\sqrt3-\sqrt2}{\sqrt3},$ the denominator in simplest form is:

If in the formula $C=\dfrac{en}{R+nr},$ $n$ is increased while $e,$ $R,$ and $r$ are kept constant, then $C:$

As the number of sides of a polygon increases from $3$ to $n,$ the sum of the exterior angles formed by extending each side in succession:

The roots of $(x^2-3x+2)(x)(x-4)=0$ are:

For the simultaneous equations

$$
\begin{aligned} 2x-3y&=8,\\ 6y-4x&=9, \end{aligned}
$$

The real factors of $x^2+4$ are:

The number of terms in the expansion of $\big[(a+3b)^2(a-3b)^2\big]^2$ when simplified is:

The formula which expresses the relationship between $x$ and $y$ as shown in the accompanying table is:

$$
\begin{array}{|c|c|c|c|c|c|} \hline x&0&1&2&3&4\\ \hline y&100&90&70&40&0\\ \hline \end{array}
$$

Of the following

$(1)\quad a(x-y)=ax-ay$

$(2)\quad a^{x-y}=a^x-a^y$

$(3)\quad \log(x-y)=\log x-\log y$

$(4)\quad \dfrac{\log x}{\log y}=\log x-\log y$

$(5)\quad a(xy)=ax\times ay$

If $m$ men can do a job in $d$ days, then $m+r$ men can do the job in:

When $x^{13}+1$ is divided by $x-1,$ the remainder is: