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.

1,826.

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

A.

\(\frac{x^2 + y^2} {(x - y)^2}\)

B.

\(\frac{2y^3} {y^2 - x^2}\)

C.

\(\frac{3x^2 + y^2} {(2x - y)^2}\)

D.

\(\frac{x^2 + y^2} {(x^2 - y)}\)

Correct answer is B

\(\frac{x^2 + y^2 + xy}{x + y}\) - \(\frac{x^2 + y^2}{x -y}\)

= \(\frac{-y^3 - y^3}{x^2 - y^2}\)

= \(\frac{2y^3}{x^2 - y^2}\)

= \(\frac{2y^3}{y^2 - x^2}\)

1,827.

A steel ball of radius 1 cm is dropped into a cylinder of radius 2cm and height 4cm. If the cylinder is now filled with water, what is the volume of the water in the cylinder?

A.

\(\frac{44}{3}\)\(\pi\)cm3

B.

12\(\pi\)cm3

C.

\(\frac{38}{3}\)\(\pi\)cm3

D.

\(\frac{40}{3}\)\(\pi\)cm3

E.

\(\frac{32}{33}\)\(\pi\)cm3

Correct answer is A

Volume of steel ball = \(\frac{4\pi r^2}{3}\)

= \(\frac{4}{3}\) \(\pi\) x 1

= \(\frac{4 \pi}{3}\)cm3

Vol. of cylinder = \(\pi\)r2h

= \(\pi\) x 22 x 3

Vol. of water = 16\(\pi\) - \(\frac{4 \pi}{3}\)

= \(\frac{48 - 4 \pi}{3}\)

= \(\frac{44 \pi}{3}\)cm3

1,828.

Simplify \(\frac{5^x \times 25^{x - 1}}{125^{x + 1}}\)

A.

52x + 1

B.

5x + 1

C.

5-5

D.

52

E.

53

Correct answer is C

\(\frac{5^x \times 25^{x - 1}}{125^{x + 1}}\) = \(\frac{5^x \times 5^{2x - 2}}{5^{3x + 3}}\)

= \(\frac{5^{x + 2x - 2}}{5^{3x + 3}}\)

= \(\frac{5^{3x - 2}}{5^{3x + 3}}\)

= 5\(^{3x - 2 - 3x - 3}\)

= 5\(^{-5}\)

1,829.

Rationalize the denominator of the expression \(\frac{6 + 2\sqrt{5}}{4 - 3\sqrt{6}}\)

A.

\(\frac{12+ 4\sqrt{5 + 7} 5 + 6\sqrt{3}}{39}\)

B.

\(\frac{-(24 + 18\sqrt{6} + 8\sqrt{5} + 6\sqrt{30})}{38}\)

C.

\(\frac{24 + 3\sqrt{6 + 8} 5 + 6\sqrt{30}}{19}\)

D.

\(\frac{-15 + 3\sqrt{5 + 18} 5 + 6\sqrt{30}}{36}\)

E.

\(\frac{-(12 + 4\sqrt{5} +9\sqrt{6} + 3\sqrt{30})}{19}\)

Correct answer is B

Rationalize using the reciprocal of the denominator to multiply through 

(i.e. Multiply both numerator and denominator using \(4 + 3\sqrt{6}\) )

Watch your signs in the course of this.

1,830.

A square of cardboard is taped at the perimeter by a piece of ribbon 20cm long. What is the area of the board?

A.

20sq.cm

B.

100sq.cm

C.

25sq.cm

D.

16sq.cm

E.

36sq.cm

Correct answer is C

Area of a square = 4(5) where S is each sides of the square

Perimeter = 20(given)

4S = 20

S = \(\frac{20}{4}\)

= 5

Area s2 = 52

= 25