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.

3,731.

A binary operation * on the set of rational numbers is defined as \(x \ast y = \frac{x^2 - y^2}{2xy}\). Find \(-5 \ast 3\)

A.

\(\frac{-8}{15}\)

B.

\(\frac{8}{15}\)

C.

\(\frac{17}{15}\)

D.

\(\frac{-17}{15}\)

Correct answer is A

p>\(x \ast y = \frac{x^2 - y^2}{2xy}\\
=\frac{(x+y)(x-y)}{2xy}\\
-5 \ast 3 =\frac{(-5+3)(-5-3)}{2(-5\times3)}\\
=\frac{-2 \times -8}{2(-5\times3)}\\
=\frac{-8}{15}\)

 

3,732.

If p varies inversely as the cube of q and q varies directly as the square of r, what is the relationship between p and r?

A.

p varies directly as r3

B.

p varies inversely as r6

C.

p varies inversely as 6√P

D.

p varies directly as r6

Correct answer is C

P ∝ 1/q3
P = K/q3
q3 = K/P
q = K/p1/3
But q ∝ r2
q = Kr2
K/p1/3 = Kr2
r2 = K/p1/3 x 1/K
r2 = 1/p1/3
r = (1/p1/3)2
r = 1/p1/6
r ∝ 1/p1/6
∴ r varies inversely as 6√P

3,733.

A binary operation \(\oplus\) defined on the set of real number is such that x\(\oplus\)y = xy/6 for all x, y ∈ R. Find the inverse of 20 under this operation when the identity element is 6

A.

1/12

B.

10/3

C.

1/20

D.

9/5

Correct answer is D

x ⊕ y = xy/6 = xe/6 = x
xe = 6x
e = 6
x ⊕ y = xx1/6 where x1 = 20
x x 20/6 = 6
x = 36/20
x = 9/5

3,734.

If the locus of the points which are equidistant from point P and Q meets line PQ at point N, then PN equals

A.

NQ

B.

1/4NQ

C.

2NQ

D.

1/2NQ

Correct answer is A

No explanation has been provided for this answer.

3,735.

PQRSTW is a regular hexagon and QS intersects RT at V. Calculate ∠TVS

A.

120o

B.

90o

C.

30o

D.

60o

Correct answer is D

No explanation has been provided for this answer.