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.

201.

Given that r = \( \sqrt \frac{3v}{\pi h} \), make v the subject of the formula

A.

v = 3 \(πr^2\) h

B.

v = \(\frac{πrh}{3}\)

C.

v = \(\frac{πr^2h}{3}\)

D.

v = 3πrh

Correct answer is C

square both sides to remove the big square root

→ r\(^2\) = \(\frac{3v}{πh}\)

cross multiply

3v = r\(^2\) * πh

v = \(\frac{πr^2h}{3}\)

202.

If A = \(\begin{pmatrix} 2 & 1 \\ 2 & 3 \\ 1 & 2 \end{pmatrix}\) and B = \(\begin{pmatrix} 3 & 2 \\ 4 & 2 \end{pmatrix}\). Find AB

A.

\(\begin{pmatrix} 18 & 6 \\ 12 & 10 \\ 10 & 6 \end{pmatrix}\)

B.

\(\begin{pmatrix} 10 & 6 \\ 13 & 10 \\ 12 & 6 \end{pmatrix}\)

C.

\(\begin{pmatrix} 10 & 6 \\ 12 & 10 \\ 11 & 6 \end{pmatrix}\)

D.

\(\begin{pmatrix} 10 & 6 \\ 18 & 10 \\ 11 & 6 \end{pmatrix}\)

Correct answer is D

Given A = \(\begin{pmatrix} 2 & 1 \\ 2 & 3 \\ 1 & 2 \end{pmatrix}\) and B = \(\begin{pmatrix} 3 & 2 \\ 4 & 2 \end{pmatrix}\).

We can multiply these matrices since the number of colums in A = number of rows in B

 

AB = \(\begin{pmatrix} (2*3)+(1*4) & (2*2)+(1*2) \\ (2*3)+(3*4) & (2*2)+(3*2) \\ (1*3)+(2*4) & (1*2)+(2*2) \end{pmatrix}\)

 

AB = \(\begin{pmatrix} (6+4) & (4+2) \\ (6+12) & (4+6) \\ (3+8) & (2+4) \end{pmatrix}\)

 

= \(\begin{pmatrix} 10 & 6 \\ 18 & 10 \\ 11 & 6 \end{pmatrix}\)

 

203.

Integrate (2x+1)\(^3\)

A.

\(\frac{{2x+1}^3}{8}\) + C

B.

\(\frac{{2x+1}^4}{8}\) + C

C.

\(\frac{{2x+1}^4}{4}\) + C

D.

\(\frac{{2x+1}^2}{6}\) + C

Correct answer is B

Recall chain rule: 

u = 2x +1; du = 2dx → dx = \(\frac{du}{2}\)
u\(^3\) = ∫ u\(^3\) \(\frac{du}{2}\) → \(\frac{1}{2}\) ∫ u\(^3\)

=  \(\frac{1*u^4}{2*4}\) 

=  \(\frac{u^4}{8}\) →  \(\frac{{2x+1}^4}{8}\) + C

204.

In how many ways can the letter of ZOOLOGY be arranged?

A.

720

B.

360

C.

840

D.

120

Correct answer is C

Zoology has 7 letters in total, with O repeated thrice

\(\frac{7!}{3!}\) → \(\frac{7*6*5*4*3*2*1}{3*2*1}\)

= 840ways

205.

In the diagram above angle LNM and angle YNZ are represented by g and h respectively. Find ∠MNY

A.

180º - gº - hº

B.

360º - (g-h)º

C.

180º - (g-h)º

D.

360º - gº - hº

Correct answer is A

Using line LZ with angles sum = 180º

: ∠MNY = 180º - (g + h)º or 180º - gº - hº