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.
At what value of x is the function x\(^2\) + x + 1 minimum?
-1
\(-\frac{1}{2}\)
\(\frac{1}{2}\)
1
Correct answer is B
x\(^2\) + x + 1
\(\frac{dy}{dx}\) = 2x + 1
At the turning point, \(\frac{dy}{dx}\) = 0
2x + 1 = 0
x = -\(\frac{1}{2}\)
Find the sum of the first 18 terms of the progression 3, 6, 12......
3(217 - 1)
3(218 - 1)
3(218 + 1)
3(217 - 1)
Correct answer is B
3 + 6 + 12 + .....18thy term
1st term = 3, common ratio \(\frac{6}{3}\) = 2
n = 18, sum of GP is given by Sn = a\(\frac{(r^n - 1)}{r - 1}\)
s18 = 3\(\frac{(2^{18} - 1)}{2 - 1}\)
= 3(2^18 - 1)
Find the sum of the first twenty terms of the progression log a, log a2, log a3.....
log a20
log a21
log a200
log a210
Correct answer is D
No explanation has been provided for this answer.
Given that x2 + y2 + z2 = 194, calculate z if x = 7 and \(\sqrt{y}\) = 3
\(\sqrt{10}\)
8
12.2
13.4
Correct answer is B
Given that x2 + y2 + z2 = 194, calculate z if x = 7 and \(\sqrt{y}\) = 3
x = 7
∴ x2 = 49
\(\sqrt{y}\) = 3
∴ y2 = 81 = x2 + y2 + z2 = 194
49 + 81 + z2 = 194
130 + z2 = 194
z2 = 194 - 130
= 64
z = \(\sqrt{64}\)
= 8
Simplify \(\frac{x}{x + y}\) + \(\frac{y}{x - y}\) - \(\frac{x^2}{x^2 - y^2}\)
\(\frac{x}{x^2 - y^2}\)
\(\frac{y^2}{x^2 - y^2}\)
\(\frac{x^2}{x^2 - y^2}\)
\(\frac{y}{x^2 - y^2}\)
Correct answer is B
\(\frac{x}{x + y}\) + \(\frac{y}{x - y}\) - \(\frac{x^2}{x^2 - y^2}\)
\(\frac{x}{x + y}\) + \(\frac{y}{x - y}\) - \(\frac{x^2}{(x + y)(x - y}\)
= \(\frac{x(x - y) + y(x + y) - x^2}{(x + y)(x - y}\)
= \(\frac{x^2 + xy + xy + y^2 - x^2}{(x + y)(x - y}\)
= \(\frac{y^2}{(x + y)(x - y)}\)
= \(\frac{y^2}{(x^2 - y^2)}\)