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.

1,801.

A rectangular picture 6cm by 8cm is enclosed by a frame \(\frac{1}{2}\)cm wide. Calculate the area of the frame

A.

15sq.cm

B.

20sq.cm

C.

13sq.cm

D.

16sq.cm

E.

17sq.cm

Correct answer is A

Area of the rectangular picture = L x B = 8 x 6

= 48 sq.cm.

Area of the whole surface (which is gotten by adding \(\frac{1}{2}\) on every side to the original picture size) is 9 x 7 = 63 sq. cm

area of the frame is 63 - 48

= 15 sq. cm

1,802.

A man is standing in the corridor of a 10-storey building and looking down at a tall tree in front of the building. He sees the top of the tree at angle of depression of 30o. If the tree is 200m tall and the man's eyes are 300m above the ground, calculate the angle of depression of the foot tree as seen by the man

A.

30o

B.

60o

C.

45o

D.

25o

Correct answer is B

Let x rep. the angle of depression of the foot of the tree.

tan 30o = \(\frac{y}{100}\)

y = 100 tan 30o

= 57.8

By Pythagoras, AC2 = 3002 + 582

= 900 + 3354

tan x = \(\frac{opp}{adj}\)

= \(\frac{58}{300}\)

= 0.19

tan x = 0.19

x = tan 0.19

= 60o

1,803.

If \(\sqrt{3^{\frac{1}{x}}}\) = \(\sqrt{9}\) then the value of x is:

A.

\(\frac{3}{4}\)

B.

\(\frac{4}{3}\)

C.

\(\frac{1}{3}\)

D.

\(\frac{2}{3}\)

E.

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

Correct answer is E

\(\sqrt{3^{\frac{1}{x}}}\) = \(\sqrt{9}\)

3\(^{\frac{1}{2x}}\) = \(9^{\frac{1}{2}}\)

3\(^{\frac{1}{2x}}\) = 3\(^{2 \times \frac{1}{2}}\)

3\(\frac{1}{2x}\) = 3\(\frac{2}{2}\) = 3

\(3^{\frac{1}{2x}}\) = \(3^{1}\)

\(\frac{1}{2x}\) = \(\frac{1}{1}\)

x = \(\frac{1}{2}\)

1,804.

A father is now three times as old as his son. Twelve years ago he was six times as old as his son. How old are the son and the father?

A.

20 and 45

B.

100 and 150

C.

45 and 65

D.

35 and 75

E.

20 and 60

Correct answer is E

Son = x, Father = 3x, 12 yrs ago

son = x - 12, father = 3x - 12

3x - 12 = 6(x - 12)

3x - 12 = 6x - 72

3x = 60

x = 20

1,805.

If y = x2 - 2x - 3, Find the least value of y and corresponding value of x

A.

x = 3, y = 3

B.

x = 1, y = -3

C.

x = 4, y = 1

D.

x = 1, y = -4

E.

x = 2, y = -3

Correct answer is D

If the graph of eqn. y = x2 - 2x - 3 is plot and drawn, the lease value of y = -4 while the corresponding value of x = 1

x = 1, y = -4