How good are you with figures and formulas? Find out with these Mathematics past questions and answers. This Test is useful for both job aptitude test candidates and students preparing for JAMB, WAEC, NECO or Post UTME.
What value of g will make the expression 4x2 - 18xy + g a perfect square?
9
\(\frac{9y^2}{4}\)
\(81y^2\)
\(\frac{18y^2}{4}\)
Correct answer is D
4x2 - 18xy + g = g \(\to\) (\(\frac{18y}{4}\))2
= \(\frac{18y^2}{4}\)
Make F the subject of the formula t = \(\sqrt{\frac{v}{\frac{1}{f} + \frac{1}{g}}}\)
\(\frac{gv-t^2}{gt^2}\)
\(\frac{gt^2}{gv-t^2}\)
\(\frac{v}{\frac{1}{t^2} - \frac{1}{g}}\)
\(\frac{gv}{t^2 - g}\)
Correct answer is B
t = \(\sqrt{\frac{v}{\frac{1}{f} + \frac{1}{g}}}\)
t2 = \(\frac{v}{\frac{1}{f} + \frac{1}{g}}\)
= \(\frac{vfg}{ftg}\)
\(\frac{1}{f} + \frac{1}{g}\) = \(\frac{v}{t^2}\)
= (g + f)t2 = vfg
gt2 = vfg - ft2
gt2 = f(vg - t2)
f = \(\frac{gt^2}{gv-t^2}\)
Find the minimum value of X2 - 3x + 2 for all real values of x
-\(\frac{1}{4}\)
-\(\frac{1}{2}\)
\(\frac{1}{4}\)
\(\frac{1}{2}\)
Correct answer is A
y = X2 - 3x + 2, \(\frac{dy}{dx}\) = 2x - 3
at turning pt, \(\frac{dy}{dx}\) = 0
∴ 2x - 3 = 0
∴ x = \(\frac{3}{2}\)
\(\frac{d^2y}{dx^2}\) = \(\frac{d}{dx}\)(\(\frac{d}{dx}\))
= 270
∴ ymin = 2\(\frac{3}{2}\) - 3\(\frac{3}{2}\) + 2
= \(\frac{9}{4}\) - \(\frac{9}{2}\) + 2
= -\(\frac{1}{4}\)
x = \(\frac{3}{2}\), y = \(\frac{3}{2}\)
x = \(\frac{1}{2}\), y = \(\frac{3}{2}\)
x = \(\frac{-1}{2}\), y = \(\frac{-3}{2}\)
x = \(\frac{1}{3}\), y = \(\frac{3}{2}\)
Correct answer is B
\(\frac{2}{x} - {\frac{3}{y}}\) = 2.....(1)
\(\frac{4}{x} + {\frac{3}{y}}\) = 10 ... (2)
(1) + (2):
\(\frac{6}{x}\) = 12 \(\to\) x = \(\frac{6}{12}\)
x = \(\frac{1}{2}\)
put x = \(\frac{1}{2}\) in equation (i)
= 4 - \(\frac{3}{y}\) = 2
= 4 - 2
= \(\frac{3}{y}\)
therefore y = \(\frac{3}{2}\)
If the function f(fx) = x3 + 2x2 + qx - 6 is divisible by x + 1, find q
-5
-2
2
5
Correct answer is A
x + 1 = 0, x = -1; f(x) = x3 + 2x2 + qx - 6
0 = -1 + 2 - q - 6
q = -5