Mathematics questions and answers

Mathematics Questions and Answers

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.

2,176.

PQRS is a rhombus. If PR\(^2\) + QS\(^2\) = kPQ\(^2\), determine k.

A.

1

B.

2

C.

3

D.

4

Correct answer is D

PR\(^2\) + QS\(^2\) = kPQ\(^2\)

SQ\(^2\) = SR\(^2\) + RQ\(^2\)

PR\(^2\) + SQ\(^2\) = PQ\(^2\) + SR\(^2\) + 2RQ\(^2\)

= 2PQ\(^2\) + 2RQ\(^2\)

= 4PQ\(^2\)

∴ K = 4

2,177.

A regular polygon of (2k + 1) sides has 140° as the size of each interior angle. Find k

A.

4

B.

4\(\frac{1}{2}\)

C.

8

D.

8\(\frac{1}{2}\)

Correct answer is A

A regular has all sides and all angles equal. If each interior angle is 140° each exterior angle must be

180° - 140° = 40°

The number of sides must be \(\frac{360^o}{40^o}\) = 9 sides

hence 2k + 1 = 9

2k = 9 - 1

8 = 2k

k = \(\frac{8}{2}\)

= 4

2,178.

If -8, m, n, 19 are in arithmetic progression, find (m, n)

A.

1, 10

B.

2, 10

C.

3, 13

D.

4, 16

Correct answer is A

-8, m, n, 19 = m + 8

= 19 - n

m + n = 11

i.e. 1, 10

2,179.

The sum of the first two terms of a geometric progression is x and sum of the last terms is y. If there are n terms in all, then the common ratio is

A.

\(\frac{x}{y}\)

B.

\(\frac{y}{x}\)

C.

(\(\frac{x}{y}\))\(\frac{1}{n - 2}\)

D.

(\(\frac{y}{x}\))\(\frac{1}{n - 2}\)

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 = (\(\frac{y}{x}\))\(\frac{1}{n - 2}\)

2,180.

Simplify \(\frac{x(x + 1)^{\frac{1}{2}} - (x + 1)^{\frac{1}{2}}}{(x + 1)^{\frac{1}{2}}}\)

A.

\(\frac{-1}{x + 1}\)

B.

\(\frac{1}{x + 1}\)

C.

\(\frac{1}{x}\)

D.

\(\frac{1}{x - 1}\)

Correct answer is A

\(\frac{x}{(x + 1)}\) - \(\frac{\sqrt{(x + 1)}}{\sqrt(x + 1)}\)

= \(\frac{x}{x + 1}\) - 1

\(\frac{x - x - 1}{x + 1}\) = \(\frac{-1}{x + 1}\)