9000086705
Level:
A
Identify the optimal substitution which simplifies the following equation as much as
possible.
\[
2\cos (3x + 33^{\circ }) = -\sqrt{2}
\]
\(3x + 33^{\circ } = t\)
\(\sin 3x = t\)
\(3x = t\)
\(3x + 33^{\circ } = -\sqrt{2}\)
A
9000085601
Level:
A
Evaluate the following numbers and round to the nearest tens.
\[
10^{2} + 11^{2} + 12^{2} + 13^{2} + 14^{2}
\]
\(730\)
\(720\)
\(740\)
\(750\)
9000086706
Level:
A
Identify the equation which arises from the following equation using an optimal
substitution.
\[
2\cos ^{2}x - 7\cos x + 3 = 0
\]
\(2t^{2} - 7t + 3 = 0\)
\(2t^{2} = \frac{3}
{7}\)
\(\cos t = 0\)
\(7\cos t = 3\)
9000081405
Level:
A
Find the inequality which describes the set graphed in the picture.
\(|2 - x| < 1;\ x\in \mathbb{R}\)
\(|2 + x| > 1;\ x\in \mathbb{R}\)
\(|2 + x| < 1;\ x\in \mathbb{R}\)
\(|2 - x| > 1;\ x\in \mathbb{R}\)
\(|1 - x| < 2;\ x\in \mathbb{R}\)
9000083701
Level:
A
Find all the values of \(x\in \mathbb{R}\)
for which the given expression equals zero.
\[
\frac{x^{2} - 16}
{2x - 8}
\]
\(x = -4\)
\(x = 4\)
\(x =\pm 4\)
\(x = 0\)
9000083702
Level:
A
Find all the values of \(x\in \mathbb{R}\)
for which the given expression equals zero.
\[
\frac{x^{2} + 6x + 9}
{x^{2} - 9}
\]
The expression never equals zero.
\(x =\pm 3\)
\(x = 3\)
\(x = -3\)
9000083703
Level:
A
Find all the values of \(x\in \mathbb{R}\)
for which the given expression equals zero.
\[
\frac{x^{3} - x}
{x - 1}
\]
\(x = -1,\ x = 0\)
\(x = 0\)
\(x = 1\)
\(x = -1,\ x = 0,\ x = 1\)
9000083704
Level:
A
Find all the values of \(x\in \mathbb{R}\)
for which the given expression equals zero.
\[
\frac{x^{2} - 4x + 4}
{x(x - 2)}
\]
The expression never equals zero.
\(x = 0\)
\(x = 2\)
\(x = -2,\ x = 0\)
9000083705
Level:
A
Find all the values of \(x\in \mathbb{R}\)
for which the given expression equals zero.
\[
\frac{2x(x + 2)(x - 3)}
{x^{2} - 4}
\]
\(x = 0,\ x = 3\)
\(x = -2,\ x = 0,\ x = 3\)
\(x = 0\)
\(x =\pm 2\)
9000083706
Level:
A
Find all the values of \(x\in \mathbb{R}\)
for which the given expression equals zero.
\[
\frac{4x^{2} - 36}
{4x^{2} + 24x + 36}
\]
\(x = 3\)
\(x = 4\)
\(x = -3,\ x = 3\)
The expression never equals zero.