1103108903
Level:
A
Which of the given pictures shows the shaded region of the biggest area?
A
1103108902
Level:
A
Which of the given expressions does not describe the area of the region highlighted in yellow? (See the picture.)
$\int\limits_1^3\frac1x\,\mathrm{d}x$
$2\int\limits_1^3\frac1x\,\mathrm{d}x$
$\int\limits_1^4\frac2x\,\mathrm{d}x-\int\limits_3^4\frac2x\,\mathrm{d}x$
$\int\limits_1^3\frac1x\,\mathrm{d}x-\int\limits_1^3-\frac1x\,\mathrm{d}x$
1103108901
Level:
A
Which of the given expressions does not describe the area of the region highlighted in yellow? (See the picture.)
$4\cdot\int\limits_0^{\frac{\pi}4}4\sin x\,\mathrm{d}x$
$4\cdot\int\limits_0^{\pi}\sin x\,\mathrm{d}x$
$8\cdot\int\limits_0^{\pi}\frac{\sin x}2\,\mathrm{d}x$
$\int\limits_0^{\frac{\pi}2}16\cdot\frac{\sin x}2\,\mathrm{d}x$
1003124410
Level:
A
Calculate the area of a plane region bounded by the graphs of the functions $f(x)=-\frac x{\pi}+1$ and $g(x)=-\sin x$, and by the lines $x=\pi$ and $x=0$.
$2+\frac{\pi}2$
$2-\frac{\pi}2$
$-2-\frac{\pi}2$
$\frac{2+\pi}2$
1003124406
Level:
A
Calculate the area of a plane region bounded by the graphs of the functions $f(x)=x^2+2x+2$ and $g(x)=6-x^2$.
$9$
$21$
$15$
$\frac{59}3$
1103124401
Level:
A
Find the area of the region highlighted in red (see the picture).
$1.5\pi$
$2\pi$
$2.5\pi$
$4.5\pi$
Perpendicular Lines
Submitted by ladislav.foltyn on Sat, 03/02/2019 - 17:06Question:
In the table mark pairs of lines that are perpendicular.
\begin{align*} a&\colon\ x-y+6=0\text{, } & b&\colon\ x+3y-2=0\text{ ,} & c&\colon\ y=-\frac12x+5 \\ d&\colon\ y=-\frac32x+2\text{ ,} & e&\colon\ x-2y+6=0\text{ ,}& f&\colon\ x=3+3t;\ y=2t;\ t\in\mathbb{R} \end{align*}
Quadratic functions and vertices of parabolas II
Submitted by ladislav.foltyn on Thu, 02/28/2019 - 15:16Question:
For each quadratic function choose the vertex of the parabola.\\[20pt]
Roots of negative numbers
Submitted by ladislav.foltyn on Sat, 02/09/2019 - 20:02Question:
Calculate the following \( n \)th-roots and mark the correct answers.
1103164710
Level:
A
The graph of \( f \) is given in the figure. Which of the following holds? (\( f' \) is the derivative of the function \( f \).)
\( f'(-1)=0 \), \( f'(2)=-2 \), \( f'(4)=0 \)
\( f'(-1)=0 \), \( f'(2)=-\frac12 \), \( f'(4)=-3 \)
\( f'(-1)=0 \), \( f'(0)=0 \), \( f'(3)=0 \)
\( f'(0)=0 \), \( f'(2)=-1 \), \( f'(4)=0 \)
\( f'(0)=1 \), \( f'(2)=-2 \), \( f'(4)=-3 \)