1 point

1. The line ${ax5y+c=0}$ and the line $AB$, where $A[2,\,1]$, $B[3,\,1]$, are identical if and only if 






2 points

2. An equation of the ellipse with the axes parallel to the coordinate axes and tangent to both coordinate axes at the points ${M[4,\,0]}$, ${N[0,\,3]}$ is 






1 point

3. The term $a_4$ of the sequence $(a_n)_{n=1}^{\infty}$, that is given by the recurrent formula ${a_{n+1}=(n+1)a_n5}$ and by the term ${a_1=0}$, is 






1 point

4. If ${\cos2\alpha=1}$, then 






2 points

5. In the cube $ABCDEFGH$ with the side $a$ denote $L$ as a midpoint of side $EH$. The volume of pyramid $BCDL$ is 






1 point

6. Find the set of all solutions of the inequality ${\dfrac1{2x+3}<1}$ with the unknown ${x\in\R}$. 






1 point

7. The algebraic form of the complex number ${z=(1+2\i)[\cos(\frac14\pi)\i\sin(\frac14\pi)]}$ is 






1 point

8. The expression ${\left(\dfrac{2x^24x+2}{x^2+1}:\dfrac{6x6}{x^41}\right):\dfrac{x+1}3}$ equals to 






1 point

9. The set of all solutions of the equation ${\cos^2x+3\sin x+3=0}$ in the interval $\langle \pi,\,2\pi)$ is 






1 point

10. If ${\log_2y=2\frac12\log_2(2x+1)\log_2(x+3)}$, then the number $y$ equals to 






1 point

11. The graph of the function ${f(x)=\sqrt{\dfrac{x+3}{x^2+5x+6}}}$ is 






1 point

12. The maximal domain of the function ${f(x)=\log^{1}x}$ is 






2 points

13. The set of all solutions of the inequality ${\left\dfrac{{5}}{x+2}\right<\left\dfrac{10}{x1}\right}$ with the unknown ${x\in\R}$ is 






2 points

14. The area ratio of a regular hexagon and the circle inscribed in the hexagon is 






2 points

15. The equation ${x^2+x+m^2+4m5=0}$ (with the unknown $x$) has one root equal to zero, if and only if 





