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.

1,931.

The square base of a pyramid of side 3cm has height 8cm. If the pyramid is cut into two parts by a plane parallel to the base midway between the base and the vertex, the volumes of the two sections are

A.

(21cm3, 3cm3)

B.

(24cm3, 3cm3)

C.

(24cm3, 21cm3)

D.

(72cm3, 9cm3)

E.

(63cm3, 9cm3)

Correct answer is B

Vol. of the 1st section is side x height

vol. = 3 x 8

= 24cm3

vol. of the second section is 3 x 1 = 3

= 24cm3, 3cm3

1,932.

The area of the curved surface of the cone generated by the sector of a circle radius 6cm and arc length 22cm is (\(\pi\) = \(\frac{22}{7}\))

A.

58 sq.cm

B.

34 sq.cm

C.

132 sq.cm

D.

77 sq.cm

E.

66 sq.cm

Correct answer is E

Given: length of the arc AOB = 22cm ; L = 6cm

Curved surface area of cone = \(\pi\)rl

Length of an arc = \(\frac{\theta}{360}\) x 2 \(\pi\)L

= 22cm

but length of an arc = circumference of the cone = 2\(\pi\)

where r is the radius of the cone circle

2\(\pi\)r = 22, r = \(\frac{22}{2\pi}\)r

= 11 x \(\frac{7}{22}\)

= \(\frac{7}{2}\)

curved surface area = \(\pi\)rl

= \(\frac{22}{7}\) x \(\frac{7}{2}\) x 6

= 66 sq.cm

1,933.

The solution to the simultaneous equations 3x + 5y = 4, 4x + 3y = 5 is

A.

(\(\frac{-13}{11}, \frac{1}{11}\))

B.

(\(\frac{13}{11}, \frac{1}{11}\))

C.

(\(\frac{13}{11}, \frac{-1}{11}\))

D.

(\(\frac{11}{13}, \frac{1}{11}\))

E.

(13, 11)

Correct answer is B

3x + 5y = 4, 4x + 3y = 5

3x + 5y = 4 x 4

4x + 3y = 5 x 3

12x + 20y = 16.....(i)

12x + 9y = 15.......(ii)

subtract eqn.(ii) from eqn.(i)

11y = 1

y = \(\frac{1}{11}\)

12x + 20 x \(\frac{1}{11}\) = 16

12x = \(\frac{156}{11}\)

x = \(\frac{13}{11}\)

= \(\frac{13}{11}, \frac{1}{11}\)

1,934.

A housewife bought 3 kilograms of garri at N13.00 per kg. She deposited N160. 00 for half a cow and bought 24 oranges at 10k each. She came back home with N20.60. She therefore left home with

A.

N220.00

B.

N222.00

C.

N201.40

D.

N202.00

E.

N180.80

Correct answer is B

3 kg of garri at N13.00 per kg = N39.00
half a cow = N160.00
24 oranges at 10k each = N2.40
balance = N20.60
Adding all together = N222.00

1,935.

The solution to the quadratic equation 5 + 3x - 2x2 = 0 is

A.

(\(\frac{5}{2}\), 1)

B.

(5, 3)

C.

-(\(\frac{5}{2}\), -1)

D.

(\(\frac{5}{2}\), -1)

Correct answer is D

5 + 3x - 2x2 = 0, (x + 1)(5 - 2x) (expand to check)

(x + 1)(5 - 2x) = 0

when x = 1 = 0, x = -1

when 5 - 2x = 0, x = \(\frac{5}{2}\) - 1