Pretest

\begin{block}
\page{Required pretest}
\margin{Do not forget to hit submit buttom your choices within 45 minutes after the beginning of the test. Only your first submission will be accepted. \\ \\
<iframe src="https://spreadsheets.google.com/embeddedform?key=0Ap0ZFygKIY9FcFVLX28xcUVzMUFTaW9uNnMwMjlZUVE" width="300" height="2369" frameborder="0" marginheight="0" marginwidth="0">Loading...</iframe>
}
\begin{questions}
Have a sheet of paper and a pen. After solving each problem mark your choice on the margin to the left. 
Note: the form on the margin may be not aligned with the problems. Please pay attention to the number of the problem - maximize the browser.
\question Based on this graph of $y=ax^2+bx+c$,
\begin{pspicture}(-1,-1)(3.5,4.2)
\psset{unit=.33}
\psaxes[ticks=none]{->}(0,0)(-1,-1)(3.5,4.2)
\psset{algebraic=true, plotpoints=100}
\psplot[linecolor=red]{-1}{4.2}{.5*(x-1)^2-1}
\end{pspicture}
we can conclude that 
\begin{choices}
\choice $b^2 - 4 a c > 0$
\choice $b^2 - 4 a c < 0$
\choice  $a < 0$
\choice  $b^2 - 4 a c =0$
\choice  $a = 0$
\end{choices}

\question The number $\pi^3 -4 \pi$ is 
\begin{choices}
\choice $\pi^2$
\choice $-\pi$
\choice $\pi(\pi-2)(\pi+2)$ 
\choice $\pi^{-1}$
\choice $\pi^{3}$. 
\end{choices}

\question The expression $\frac{a^2-2ab}{a}$ can be simplied to
\begin{choices}
\choice $a-2b$
\choice $a- 2ab$
\choice  $a^2-2b$
\choice $a^2-a- 2ab-a$
\choice $a+ 2ab$
\end{choices}

\question An equation of the line passing through: $(3,3)$ and $(3,4)$ is
\begin{choices}
\choice  $x=3$
\choice  $y=3$
\choice $y = 4x -3$
\choice $3$
\choice such an equation does not exist.
\end{choices}

\question
Let $f(x) = \sqrt{x}+2x^3$ and $g(x) = \sin^2 x$. (Note that $\sin^n x = (\sin x)^n$.
Then the composition $f(g(x))$ is 
\begin{choices}
\choice $\left ( \sqrt{x}+2x^3 \right ) \cdot \sin^2 x$
\choice $|\sin x|+2 \sin^6 x$
\choice $|\sin x|-2 \sin^6 x$
\choice  $\left ( \sqrt{x}+2x^3 \right ) / \sin^2 x$
\choice none of the above choices.
\end{choices}

\question Let $f(x) = \frac{1}{2}x^2$. The fraction $\frac{f(a+h)-f(a)}{h}$ is
\begin{choices}
\choice $\frac{\frac{1}{2}x^2(a+h) - \frac{1}{2}x^2(h)}{h}$
\choice $a + \tfrac{1}{2}h$
\choice $a$
\choice $2 x$
\choice $2 a$.
\end{choices}

\question The largest possible domain of the function $f(x) = \sqrt{\frac{x-1}{x+2}}$ is the set
\begin{choices}
\choice  all $x$ except $x=-2$
\choice $x < -2$ or $x \ge 1$ 
\choice  only positive $x$.
\choice only negative $x$
\choice $x >2$.
\end{choices}

\question The solution of the inequality $(x-3)(x^2-3x +2) > 0$ is
\begin{choices}
\choice $1 < x < 2 $ or $x > 3$
\choice $x > 3$
\choice all real $x$
\choice $x < 1$ or $x >3 $
\choice $x < 3$. 
\end{choices}

\question In the triangle whose sides are $3$, $4$, and $5$, $\alpha$ is the angle between the sides of lengths $3$ and $5$. What is the value of
 $\cos^2 \alpha + \sin^2 \alpha$?
\begin{choices}
\choice $0.8$
\choice  $1$
\choice $0.75$
\choice  $1.66666666\dots$
\choice $4$.
\end{choices}

\question The intersection of the lines $y - 2 = 3 (x -3)$ and $y=-x+3$
is the point
\begin{choices}
\choice $(\tfrac{5}{2},\frac{1}{2})$
\choice $(-2,-3)$
\choice  The lines do not intersect
\choice $(3,2)$
\choice $(2,3)$.
\end{choices}

\end{questions}

\end{block}