Find the remainder when \(5x^{3} + 2x^{2} - 7x - 5\) is divided by (x - 2).
-51
-23
29
49
Correct answer is C
Using remainder theorem, the remainder when \(5x^{3} + 2x^{2} - 7x -5\) is divided by (x - 2) = f(2)
\(f(2) = 5(2^{3}) + 2(2^{2}) - 7(2) -5 = 40 + 8 - 14 - 5\)
= 29
Evaluate \(\cos (\frac{\pi}{2} + \frac{\pi}{3})\)
\(\frac{-2}{\sqrt{3}}\)
\(\frac{-\sqrt{3}}{2}\)
\(\frac{\sqrt{3}}{4}\)
\(\frac{4}{\sqrt{3}}\)
Correct answer is B
\(\cos (x + y) = \cos x \cos y - \sin x \sin y\)
\(\cos (\frac{\pi}{2} + \frac{\pi}{3}) = \cos \frac{\pi}{2} \cos \frac{\pi}{3} - \sin \frac{\pi}{2} \sin \frac{\pi}{3}\)
= \((0 \times \frac{1}{2}) - (1 \times \frac{\sqrt{3}}{2})\)
= \(0 - \frac{\sqrt{3}}{2} = -\frac{\sqrt{3}}{2}\)
If \(\log_{9} 3 + 2x = 1\), find x.
\(\frac{-1}{2}\)
\(\frac{-1}{4}\)
\(\frac{1}{4}\)
\(\frac{1}{2}\)
Correct answer is C
\(\log_{9} 3 = \log_{9} (9^{\frac{1}{2}}) = \frac{1}{2}\log_{9} 9 = \frac{1}{2}\)
\(\frac{1}{2} + 2x = 1 \implies 2x = \frac{1}{2}\)
\(x = \frac{1}{4}\)
Express 75° in radians, leaving your answer in terms of \(\pi\).
\(\frac{5\pi}{12}\)
\(\frac{3\pi}{4}\)
\(\frac{5\pi}{6}\)
\(\frac{7\pi}{6}\)
Correct answer is A
\(180° = \pi rads\)
\(1° = \frac{\pi}{180}\)
\(\therefore 75° = \frac{\pi}{180} \times 75 \)
= \(\frac{5\pi}{12}\)
-1
0
1
2
Correct answer is A
\(a * a^{-1} = e = -1\)
\(\therefore a^{-1} = -1\)