1003055401
Level:
A
The number \( x\) is by \( 10\% \) bigger than the number \( y \). It means that:
\( x-y=0.1y \)
\( x = y +10\% \)
\( y=\frac9{10}x \)
\( x - 0.1x = y \)
A
1003054908
Level:
A
A quadrilateral is symmetric across one of its diagonals and can be inscribed in a circle. The measure of one of its interior angles is \( 80^{\circ} \). Determine the measure of its largest interior angle.
\( 100^{\circ} \)
\( 160^{\circ} \)
\( 200^{\circ} \)
\( 120^{\circ} \)
1003021106
Level:
A
Evaluate the following limit.
\[ \lim\limits_{x\rightarrow-3}\frac{x^2+5x+6}{x^3+27} \]
\( -\frac1{27} \)
\( -\frac5{27} \)
\( -\frac19 \)
\( \frac1{27} \)
1003021105
Level:
A
Evaluate the following limit.
\[ \lim\limits_{x\rightarrow1}\frac{x^2+x-2}{1-x^3} \]
\( -1 \)
\( 1 \)
\( 0 \)
\( 3 \)
1003021104
Level:
A
Evaluate the following limit.
\[ \lim\limits_{x\rightarrow-2}\frac{3x^2+3x-6}{2x^2-2x-12} \]
\( \frac9{10} \)
\( -\frac32 \)
\( \frac32 \)
\( 0 \)
1003021103
Level:
A
Evaluate the following limit.
\[ \lim\limits_{x\rightarrow-1}\frac{x^2+x-2}{x^3-1} \]
\( 1 \)
\( 0 \)
\( 2 \)
\( -2 \)
1003044507
Level:
A
How many solutions does the following equation have?
\[ 2^{x+2}+3\cdot3^{x+2}=3^{x+3}+2\cdot2^{x+1} \]
Infinitely many solutions
Exactly one solution
No solutions
Exactly two solutions
1003044506
Level:
A
Which of the given numbers is the product of all the solutions of the following exponential equations?
\begin{align*} 3^x+3^{x+2}&=30\\ 3^{x+1}+3^{x-1}&=\frac{10}9 \end{align*}
\( -1 \)
\( 0 \)
\( 1 \)
\( 2 \)
1003044505
Level:
A
Identify the solution of the equation.
\[ 2^{x-1}-7^{x-3}=2^{x-2}+2^{x-3}\]
\( x=3 \)
The equation has no solution.
\( x=-3 \)
\( x=0 \)
1003044504
Level:
A
How many solutions does the following equation have?
\[ 5^x+5^{x+1}+5^{x+2}+5^{x+3}=156 \]
Exactly one solution
No solutions
Infinitely many solutions
Exactly two solutions