9000091203
Level:
A
Consider the circle \(x^{2} - 2x + y^{2} - 6y + 8 = 0\).
Find the radius of the circle.
\(\sqrt{2}\)
\(2\)
\(3\)
\(4\)
A
9000085609
Level:
A
Given the number \(45\: 875\),
round this number to nearest thousands, nearest hundreds and subtract the results.
\(100\)
\(200\)
\(1\: 000\)
\(0\)
9000085603
Level:
A
Find the sum of the three numbers obtained by rounding the number
\(5\: 316\) to the
nearest tens, hundreds and thousands.
\(15\: 620\)
\(15\: 610\)
\(15\: 560\)
\(15\: 580\)
9000085610
Level:
A
Given the number \(82\: 361\),
round this number to nearest thousands, nearest hundreds and subtract the results.
\(400\)
\(300\)
\(200\)
\(100\)
9000086709
Level:
A
Identify the equation which arises from the following equation using an optimal
substitution.
\[
6\cos ^{2}x +\sin x - 5 = 0
\]
\(6t^{2} - t = 1\)
\(6t^{2} + t - 5 = 0\)
\(6t = 5\)
Equation is not convenient for a substitution.
9000086603
Level:
A
Determine the truth values of propositions \(a\) and \(b\) if you know that the compound proposition
\[
\neg a \wedge b
\]
is true.
The statement \(a\)
is false, \(b\)
is true.
Both statements are true.
The statement \(a\)
is true, \(b\)
is false.
Both statements are false.
9000086710
Level:
A
Identify the equation which arises from the following equation using an optimal
substitution.
\[
2\mathop{\mathrm{tg}}\nolimits x + 3\mathop{\mathrm{cotg}}\nolimits x = 5
\]
\(2t^{2} - 5t = -3\)
\(2t^{2} + 3t - 5 = 0\)
\(2t = \frac{3}
{5}\)
\(2t + 3t = 5\)
9000088804
Level:
A
Simplify the following expression.
\[
\frac{2s - 8rs}
{16r^{2} - 1}
\]
\(- \frac{2s}
{4r+1}\)
\(\frac{2s}
{4r+1}\)
\(\frac{2s}
{4r-1}\)
\(\frac{2s}
{1-4r}\)
9000088805
Level:
A
Simplify the following expression.
\[
\frac{a^{4} - 1}
{1 - a^{2}}
\]
\(- a^{2} - 1\)
\(a^{2} + 1\)
\(a^{2} - 1\)
\(1 - a^{2}\)
9000088803
Level:
A
Evaluate the following expression at \(x = \frac{1}
{2}\).
\[
1 - \frac{x - 2}
{2x + 1}
\]
\(\frac{7}
{4}\)
\(\frac{1}
{4}\)
\(\frac{5}
{4}\)
\(\frac{3}
{4}\)