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.
If -8, m, n, 19 are in arithmetic progression, find (m, n)
1, 10
2, 10
3, 13
4, 16
Correct answer is A
-8, m, n, 19 = m + 8
= 19 - n
m + n = 11
i.e. 1, 10
\(\frac{x}{y}\)
\(\frac{y}{x}\)
(\(\frac{x}{y}\))\(\frac{1}{n - 2}\)
(\(\frac{y}{x}\))\(\frac{1}{n - 2}\)
Correct answer is D
Sum of nth term of a G.P = Sn = \(\frac{ar^n - 1}{r - 1}\)
sum of the first two terms = \(\frac{ar^2 - 1}{r - 1}\)
x = a(r + 1)
sum of the last two terms = Sn - Sn - 2
= \(\frac{ar^n - 1}{r - 1}\) - \(\frac{(ar^{n - 1})}{r - 1}\)
= \(\frac{a(r^n - 1 - r^{n - 2} + 1)}{r - 1}\) (r2 - 1)
∴ \(\frac{ar^{n - 2}(r + 1)(r - 1)}{1}\)= arn - 2(r + 1) = y
= a(r + 1)r^n - 2
y = xrn - 2
= yrn - 2
\(\frac{y}{x}\) = r = (\(\frac{y}{x}\))\(\frac{1}{n - 2}\)
Simplify \(\frac{x(x + 1)^{\frac{1}{2}} - (x + 1)^{\frac{1}{2}}}{(x + 1)^{\frac{1}{2}}}\)
\(\frac{-1}{x + 1}\)
\(\frac{1}{x + 1}\)
\(\frac{1}{x}\)
\(\frac{1}{x - 1}\)
Correct answer is A
\(\frac{x}{(x + 1)}\) - \(\frac{\sqrt{(x + 1)}}{\sqrt(x + 1)}\)
= \(\frac{x}{x + 1}\) - 1
\(\frac{x - x - 1}{x + 1}\) = \(\frac{-1}{x + 1}\)
Express \(\frac{1}{x + 1}\) - \(\frac{1}{x - 2}\) as a single algebraic fraction
\(\frac{-3}{(x + 1)(2 - x)}\)
\(\frac{3}{(x + 1)(2 - x)}\)
\(\frac{-1}{(x + 1)}\)
\(\frac{1}{(x + 1)(x - 2)}\)
Correct answer is A
\(\frac{1}{x + 1}\) - \(\frac{1}{x - 2}\) = \(\frac{x - 2 - x - 1}{(x + 1)(x - 2)}\)
= \(\frac{-3}{(x + 1)(2 - x)}\)
r > \(\frac{abc}{bc + ac + ab}\)
r < abc
r > \(\frac{1}{a}\) + \(\frac{1}{b}\) + \(\frac{1}{c}\)
\(\frac{1}{abc}\)
Correct answer is A
\(\frac{r}{a}\) + \(\frac{r}{b}\) + \(\frac{r}{c}\) > 1 = \(\frac{bcr + acr + abr}{abc}\) > 1
r(bc + ac + ba > abc) = r > \(\frac{abc}{bc + ac + ab}\)