If f(x - 4) = x2 + 2x + 3, Find, f(2)
6
11
27
51
Correct answer is D
f(x - 4) = x2 + 2x + 3
To find f(2) = f(x - 4)
= f(2)
x - 4 = 2
x = 6
f(2) = 62 + 2(6) + 3
= 36 + 12 + 3
= 51
If a = 2, b = -2 and c = -\(\frac{1}{2}\), evaluate (ab2 - bc2)(a2c - abc)
2
-28
-30
-34
Correct answer is D
(ab2 - bc2)(a2c - abc)
[2(2)2 - (- 2x\(\frac{1}{2}\))] [22(-\(\frac{1}{2}\)) - 2(-2)(-\(\frac{1}{2}\))]
[8 = \(\frac{1}{2}\)][-2 - 2] = \(\frac{17}{2}\) x 42
= -34
Simplify (\(\frac{1}{x^{-1}} + \frac{1}{y^{-1}}\))-1
\(\frac{x}{y}\)
xy
\(\frac{x}{y}\)
(xy)-1
Correct answer is C
Simplify (\(\frac{1}{x^{-1}} + \frac{1}{y^{-1}}\))-1 = (\(\frac{1}{x^{-1}} + \frac{1}{y^{-1}}\))-1
= (x + y)-1 = \(\frac{(x)}{y}\)
= \(\frac{x}{y}\)
Simplify 3 log69 + log612 + log664 - log672
5
7776
log631
(7776)6
Correct answer is A
3 log69 + log612 + log664 - log672
= log693 + log612 + log664 - log672
log6729 + log612 + log664 - log672
log6(729 x 12 x 64) = log6776
= log665 = 5 log66 = 5
N.B: log66 = 1
Simplify \(\sqrt{27}\) + \(\frac{3}{\sqrt{3}}\)
4\(\sqrt{3}\)
\(\frac{4}{\sqrt{3}}\)
3\(\sqrt{3}\)
\(\frac{\sqrt{3}}{4}\)
Correct answer is A
\(\sqrt{27}\) + \(\frac{3}{\sqrt{3}}\)
= \(\sqrt{9 \times 3}\) + \(\frac{3 \times {\sqrt{3}}}{{\sqrt{3}} \times {\sqrt{3}}}\)
= 3\(\sqrt{3}\) + \(\sqrt{3}\)
= 4\(\sqrt{3}\)