WAEC Mathematics Past Questions & Answers - Page 93

461.

F x varies inversely as y and y varies directly as Z, what is the relationship between x and z?

A.

x \(\alpha\) z

B.

x \(\alpha \frac{1}{z}\)

C.

x \(\alpha z^2\)

D.

x \(\alpha \frac{1}{z^2}\0

Correct answer is B

x \(\alpha \frac{1}{y}\)

y \(\alpha z\)

the relationship = x \(\alph \frac{1}{z}\)

462.

Make u the subject of formula, E = \(\frac{m}{2g}\)(v2 - u2)

A.

u = \(\sqrt{v^2 - \frac{2Eg}{m}}\)

B.

u = \(\sqrt{\frac{v^2}{m} - \frac{2Eg}{4}}\)

C.

u = \(\sqrt{v- \frac{2Eg}{m}}\)

D.

u = \(\sqrt{\frac{2v^2Eg}{m}}\)

Correct answer is A

E = \(\frac{m}{2g}\)(v2 - u2)

multiply both sides by 2g

2Eg = 2g (\(\frac{M}{2g} (V^2 - U^2)\)

2Eg = m(V2 - U2)

2Eg - mV2 - mU2

mU2 = mV2 - 2Eg

divide both sides by m

\(\frac{mU^2}{m} = \frac{mV^2 - 2Eg}{m}\)

U2 = \(\frac{mV^2 - 2Eg}{m}\)

= \(\frac{mV^2}{m} - \frac{2Eg}{m}\)

U2 = V2 - \(\frac{2Eg}{m}\)

U = \(\sqrt{V^2 - \frac{2Eg}{m}}\)

463.

The coordinates of points P and Q are (4, 3) and (2, -1) respectively. Find the shortest distance between P and Q.

A.

10\(sqrt{2}\)

B.

4\(sqrt{5}\)

C.

5\(sqrt{2}\)

D.

2\(sqrt{5}\)

Correct answer is D

p(4, 3) Q(2 - 1)

distance = \(\sqrt{(x_2 - x_1)^2 + (Y_2 - y_1)^2}\)

= \(\sqrt{(2 - 4)^2 + (-1 - 3)^2}\)

= \(\sqrt{(-2)^2 = (-4)^2}\)

= \(\sqrt{4 + 16}\)

= \(\sqrt{20}\)

= \(\sqrt{4 \times 5}\)

= 2\(\sqrt{5}\)

464.

Find the truth set of the equation x2 = 3(2x + 9)

A.

{x : x = 3, x = 9}

B.

{x : x = -3, x = -9}

C.

{x : x = 3, x = -9}

D.

{x : x = -3, x = 9}

Correct answer is D

x2 = 3(2x + 9)

x2 = 6x + 27

x2 - 6x - 27 = 0

x2 - 9x + 3x - 27 = 0

x(x - 9) + 3(x - 9) = (x + 3)(x - 9) = 0

x + 3 = 0 or x - 9 = 0

x = -3 or x = 9

x = -3, x = 9

465.

If x = {0, 2, 4, 6}, y = {1, 2, 3, 4} and z = {1, 3} are subsets of u = {x:0 \(\geq\) x \(\geq\) 6}, find x \(\cap\) (Y' \(\cup\) Z)

A.

{0, 2, 6}

B.

{1, 3}

C.

{0, 6)

D.

{9}

Correct answer is C

x = {0, 2, 4, 6}; y = {1, 2, 3, 4}; z = {1, 3}

u = {0, 1, 2, 3, 4, 5, 6}

y' = {0, 5, 6}

to find x \(\cap\) (Y' \(\cup\) Z)

first find y' \(\cup\) z = {0, 1, 3, 5, 6}

then x \(\cap\) (Y' \(\cup\) Z) = {0, 6}