2010009801
Level:
A
How many solutions does the equation \( \sin^2x = 0.75 \) have for \( 0\leq x\leq 2\pi \)?
\( 4 \) solutions
\( 1 \) solution
\( 2 \) solutions
\( 3 \) solutions
A
2010009707
Level:
A
Find the factored form of the equation.
\[ x^4-81=0 \]
\( \left(x^2+9\right)\left(x-3\right)\left(x+3\right)=0 \)
\( \left(x-3\right)^2\left(x+3\right)^2=0 \)
\( \left(x-3\right)^4=0 \)
\( \left(x+9\right)\left(x-3\right)\left(x+3\right)=0 \)
2010009706
Level:
A
Find the sum of all the natural roots of the next equation. Multiple roots, if any, count only once.
\[ \left(x^3+8\right)\left(x^2-1\right)=0 \]
\( 1\)
\( -1\)
\( 3\)
\( 0\)
2010009705
Level:
A
Find the sum of all the natural roots of the next equation. Multiple roots, if any, count only once.
\[ \left(x^2+1\right)\left(x^2-16 \right)=0 \]
\( 4\)
\( 3\)
\( 5\)
\( 0\)
2010009704
Level:
A
Find the sum of all real solutions of the following equation.
\[
\left (2 - x\right )\left (x^{2} - 9\right ) = 0
\]
\( 2\)
\( 0\)
\( 5\)
\( 3\)
2010009703
Level:
A
In the following list identify a true statement on the function
\(f\).
\[
f(x) = (x + 3)(x -1)(x - 2)
\]
\(f(x) > 0 \iff x\in (-3;1)\cup (2;\infty)\)
\(f(x) > 0 \iff x\in (-2;-1)\cup (3;\infty)\)
\(f(x) > 0 \iff x\in (-\infty ;-3)\cup (1;2)\)
\(f(x) < 0 \iff x\in (-3;1)\cup (2;\infty)\)
2010009702
Level:
A
Assuming \(x\in \mathbb{N}\),
find the solution set of the following equation.
\[
3 x^{3} - 2x^{2} = 0
\]
\(\emptyset \)
\(\left \{0\right \}\)
\(\left \{\frac23\right \}\)
\(\left \{0;\frac23\right \}\)
2010009701
Level:
A
Assuming \(x\in \mathbb{N}\),
find the solution set of the following equation.
\[
x^{3} - 8x^{2} + 16x = 0
\]
\(\left \{4\right \}\)
\(\emptyset \)
\(\left \{0;4\right \}\)
\(\left \{-4;4\right \}\)
2000009408
Level:
A
Choose a false statement.
\( 2^4\cdot 4^2 > 2^3\cdot 4^3\)
\(3^8=9^4\)
\( \sqrt{3} + \sqrt{6} > \sqrt{3+6}\)
\(\sqrt{2}\cdot \sqrt{2} = \sqrt{2+2}\)
2000009407
Level:
A
For \(x \in \mathbb{R}\), \(x \neq 0\), simplify the expression \( \frac{x^{-3}x^4}{(x^{-2})^3}\).
\(x^7\)
\(x^2\)
\(1\)
\(x^{-5}\)