WAEC Mathematics Past Questions & Answers - Page 77

381.

Find the value of p if \(\frac{1}{4}\)p + 3q = 10 and 2p - q = 7

A.

4

B.

3

C.

-3

D.

-4

Correct answer is A

\(\frac{1}{4}\)p + 3p = 10...(1)

2p - \(\frac{1}{3}\)q = 7...(2)

Multiply equation (2) by 3 to clear fraction

3 x 2p - 3 x \(\frac{1}{3}\)q = 3 x 7

6p - q = 21

6p - 21 = q....(3)

substituting 6p - 21 for q in (1)

\(\frac{1}{4}\)p + 3(6p - 21) = 10...(4)

Multiply equation (4) by 4 to clear fraction

4 x \(\frac{1}{4}\)p + 4 x 3(6p - 21) = 4 x 10

p + 12(6p - 21) = 40

p + 72p - 252

73p = 292

p = \(\frac{292}{73}\)

= 4

382.

Describe the shaded portion in the diagram

A.

P' \(\cap\) Q \(\cap\) R'

B.

(P' \(\cap\) R)' \(\cap\) R

C.

P' \(\cap\) Q \(\cap\) R

D.

(P \(\cap\) Q)' \(\cap\) R

Correct answer is A

No explanation has been provided for this answer.

383.

A trader bought 100 oranges at 5 for N40.00 and 20 for N120.00. Find the profit or loss percent

A.

20% profit

B.

20% loss

C.

25% profit

D.

25% loss

Correct answer is D

Cost price CP of the 100 oranges = \(\frac{100}{5}\) x N40.00

selling price SP of the 100 oranges = \(\frac{100}{20}\) x N120

= N600.00

so, profit or loss per cent

= \(\frac{SP - CP}{CP}\) x 100%

= \(\frac{600 - 800}{800}\) x 100%

= \(\frac{-200}{800}\) x 100%

Hence, loss per cent = 25%

384.

The rate of consumption of petrol by a vehicle varies directly as the square of the distance covered. If 4 litres of petrol is consumed on a distance of 15km. how far would the vehicle go on 9 litres of petrol?

A.

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

B.

30km

C.

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

D.

45km

Correct answer is A

R \(\alpha\) D2

R = D2K

R = 4 Litres when D = 15cm

thus; 4 = 152k

4 = 225k

k = \(\frac{4}{225}\)

This gives R = \(\frac{4D^2}{225}\)

Where R = 9litres

equation gives

9 = \(\frac{4D^2}{225}\)

9 x 225 = 4d2

D2 = \(\frac{9 \times 225}{4}\)

D = \(\sqrt{9 \times 225}{4}\)

= \(\frac{3 \times 15}{2}\)

= 22\(\frac{1}{2}\)km

385.

A farmer uses \(\frac{2}{5}\) of his land to grow cassava, \(\frac{1}{3}\) of the remaining for yam and the rest for maize. Find the part of the land used for maize

A.

\(\frac{2}{15}\)

B.

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

C.

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

D.

\(\frac{4}{5}\)

Correct answer is B

Let x represent the entire farmland

then, \(\frac{2}{5}\)x + \(\frac{1}{3}\)[x - \(\frac{2}{3}x\)] + M = x

Where M represents the part of the farmland used for growing maize, continuing

\(\frac{2}{5}\)x + \(\frac{1}{3}\)x [1 - \(\frac{2}{3}x\)] + M = x

\(\frac{2}{5}x + \frac{1}{3}\)x [\(\frac{3}{5}\)] + M = x

\(\frac{2}{5}\)x + \(\frac{1x}{5}\) + M = x

\(\frac{3x}{5} + M = x\)

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

= x[1 - \(\frac{3}{5}\)]

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

Hence the part of the land used for growing maize is

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