WAEC Mathematics Past Questions & Answers - Page 110

546.

If x + 0.4y = 3 and y = \(\frac{1}{2}\)x, find the value of (x + y)

A.

1\(\frac{1}{4}\)

B.

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

C.

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

D.

5

Correct answer is C

x + 0.4y = 3...(i)

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

x = 2y

x - 2y = 0....(ii)

solve simultaneously; x + 0.4y

= 3 - x - 2y = 0

2.4 = 3

y = \(\frac{3 \times 10}{2.4 \times 10} \)

= \(\frac{30}{24} = \frac{5}{4}\)

x - 2(\(\frac{5}{4}\)) = 0

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

x = \(\frac{5}{2}\)

x + y = \(\frac{5}{2} + \frac{5}{4}\)

\(\frac{10 + 5}{4} = \frac{15}{4}\)

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

547.

Which of these statements about y = 8\(\sqrt{m}\) is correct?

A.

log y = log 8 x log \(\sqrt{m}\)

B.

log y = 3 log 2 x \(\frac{1}{2}\) log m

C.

log y = 3 log 2 - \(\frac{1}{2}\) log m

D.

log y = 3 log 2 + \(\frac{1}{2}\) log m

Correct answer is D

y = 8\(\sqrt{m}\); log y = log 8\(\sqrt{m}\)

log y = log 8 + log \(\sqrt{m}\)

log y = log 23 + log m\(\frac{1}{2}\)

log y = 3 log 3 + \(\frac{1}{2}\) log m

548.

A bag contains 4 red and 6 black balls of the same size. If the balls are shuffled briskly and two balls are drawn one after the other without replacement, find the probability of picking balls of different colours

A.

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

B.

\(\frac{13}{25}\)

C.

\(\frac{11}{15}\)

D.

\(\frac{13}{15}\)

Correct answer is A

Prob(RB + BR) = Total balls = 4 + 6 = 10

= prob(\(\frac{4}{10} \times \frac{6}{9}\)) + prob(\(\frac{6}{10} \times \frac{4}{9}) = \frac{24}{90} + \frac{24}{90}\)

= \(\frac{48}{90} = \frac{16}{30} = \frac{8}{15}\)

549.

Given that the mean of the scores 15, 21, 17, 26, 18 and 29 is 21, calculate the standard deviation of the scores

A.

\(\sqrt{10}\)

B.

4

C.

5

D.

\(\sqrt{30}\)

Correct answer is C

\(\begin{array}{c|c} x & x - x & (x - \bar{x})^2\\ \hline 15 & -6 & 36\\21 & 0 & 0\\17 & -4 & 16\\ 26 & 5 & 25 \\ 18 & -3 &9 \\ 29 & 8 & 64 \end{array}\)

\(E(x - \bar{x})^2\) = 150

N = 6

S.D = \(\sqrt{\frac{(x - x)^2}{N}}\)

S.D = \(\sqrt{\frac{150}{6}}\) = 5

550.

A kite flies on a taut string of length 50m inclined at tan angle 54o to the horizontal ground. The height of the kite above the ground is

A.

50 tan 30o

B.

50 sin 54o

C.

50 tan 54o

D.

50 sin 36o

Correct answer is B

No explanation has been provided for this answer.