1003118601
Level:
A
Decide which of the following equations is false.
\( \sqrt5-\sqrt2=\sqrt3 \)
\( \sqrt{15}:\sqrt3=\sqrt5 \)
\( \sqrt5 \cdot \sqrt2 =\sqrt{10} \)
\( \sqrt{\sqrt4}=\sqrt2 \)
A
1103049404
Level:
A
In addition to solving equation \( ax+b=cx+d \) algebraically, you can also solve it graphically. When the lines \( y=ax+b \) and \( y=cx+d \) are graphed, you look for the intersection of these lines. In the pictures below are graphed lines \( y=ax+b \) and \( y=cx+d\). Choose the picture in which the equation \( ax+b=cx+d \) has only one non-negative solution.
1103049403
Level:
A
Choose the picture which represents the graphical solution of the following equation.
\[ 1-\frac{5+2x}3=3 \]
1103049402
Level:
A
Choose the picture which represents the graphical solution of the following equation.
\[ \frac23 x+\frac13=1-\frac32 x \]
1103049401
Level:
A
Choose the equation whose graphical solution is in the picture.
\( \frac12x-3=-\frac52x-5 \)
\( \frac12x-3=-2x-5 \)
\( 2x-3=-\frac52 x-5 \)
\( 2x-3=-2x-5 \)
1003085406
Level:
A
A diagonal of a rectangle has length of \( 30\,\mathrm{cm} \) and the perimeter of the rectangle is \( 84\,\mathrm{cm} \). Find the difference of the length and the width of the rectangle in centimeters.
\( 6 \)
\( 8 \)
\( 9 \)
\( 10 \)
1103085403
Level:
A
Two resistors of unknown resistances \( R_1 \) and \( R_2 \), where \( R_1 < R_2 \) are connected in series (Figure A) and total resistance of the circuit is \( R_S=64\,\Omega \). If the resistors are connected in parallel (Figure B), the total resistance \( R_P=15\,\Omega \). Find \( R_1 \).
\( 24 \)
\( 22 \)
\( 12 \)
\( 15 \)
1003102408
Level:
A
The value of the expression \( \log_{16}\left(\log_216 \right) \) is:
\( \frac12 \)
\( \frac14 \)
\( \frac18 \)
\( 2 \)
1003102406
Level:
A
Find the value of \( z \), if
\( \log_3z=-3 \).
\( z=\frac1{27} \)
\( z=27 \)
\( z=-9 \)
\( z=\frac19 \)
1003102405
Level:
A
If \( \log_x\frac49=-\frac12 \) then \( x \) is equal to:
\( \frac{81}{16} \)
\( \frac{16}{81} \)
\( \frac23 \)
\( -\frac23 \)