9000085601
Level:
A
Evaluate the following numbers and round to the nearest tens.
\[
10^{2} + 11^{2} + 12^{2} + 13^{2} + 14^{2}
\]
\(730\)
\(720\)
\(740\)
\(750\)
A
9000086706
Level:
A
Identify the equation which arises from the following equation using an optimal
substitution.
\[
2\cos ^{2}x - 7\cos x + 3 = 0
\]
\(2t^{2} - 7t + 3 = 0\)
\(2t^{2} = \frac{3}
{7}\)
\(\cos t = 0\)
\(7\cos t = 3\)
9000085607
Level:
A
Given numbers \(8\: 175\)
and \(3\: 926\),
find the difference between the sum of these numbers rounded to the nearest tens and the sum of these numbers rounded to the nearest hundreds.
\(10\)
\(20\)
\(100\)
\(0\)
9000086707
Level:
A
Identify the equation which arises from the following equation using an optimal
substitution.
\[
\mathop{\mathrm{tg}}\nolimits ^{2}y - 2\mathop{\mathrm{tg}}\nolimits y = 3
\]
\(t^{2} - 2t - 3 = 0\)
\(\mathop{\mathrm{tg}}\nolimits t = \frac{3}
{2}\)
\(t^{2} = \frac{3}
{2}\)
\(\mathop{\mathrm{tg}}\nolimits t = 3\)
9000085608
Level:
A
Given numbers \(456\: 138\)
and \(321\: 814\),
find the difference between the sum of these numbers rounded to the nearest tens and the sum of these numbers rounded to the nearest hundreds.
\(50\)
\(100\)
\(1\: 000\)
\(0\)
9000086708
Level:
A
Identify the equation which arises from the following equation using an optimal
substitution.
\[
\mathop{\mathrm{tg}}\nolimits ^{2}v -\mathop{\mathrm{cotg}}\nolimits ^{-1}v = 2
\]
\(t^{2} - t - 2 = 0\)
Equation is not convenient for a substitution.
\(t^{2} + t = 0\)
\(\mathop{\mathrm{tg}}\nolimits t = 2\)
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.