1991 - JAMB Mathematics Past Questions and Answers - page 1

PQM = 110^o(Ext. < of a cyclic quad)

MPQ = 180^o - (110 + 55)

= 180^o - 165^o

= 15^o

ADB = 180^o - 152^o = 28^o

28^o + y + 30^o = 180^o

y = 180^o - 58^o

= 122^o

Since PQRS is quadrilateral 2y + 2x = QPS = 360^o

i.e. 2(y + x) + QPS = 360^o

QPS = 360^o - 2(y + x)

But x + y + 68^o = 180^o

x + y = 180^o - 68^o = 180^o

x + y = 180^o - 68^o

= 112^o

QPS = 360^o - 2(112^o)

360^o - 224^o = 136^o

3 - \(\frac{1}{3}\) - (\(\frac{5}{4}\) x \(\frac{2}{3}\)) + 1\(\frac{2}{5}\)

= \(\frac{10}{3}\) - \(\frac{5}{6}\) + \(\frac{7}{5}\)

= \(\frac{100 - 25 + 42}{30}\)

= \(\frac{117}{30}\)

= 3.9

\(\approx\) 4

\(\begin{array}{c|c} 7056 \ \text{- 4577} \\hline 2257 \end{array}\)
By trial and error method

Let the base to 8

i.e. Let n = 8 and it is easily verified that the subtraction holds.

The subtraction does not hold when other values of n are tried

n = 8

(\(\frac{1}{0.05}\) + \(\frac{1}{5.005}\)) - (0.05 x 2.05)

(\(\frac{1}{0.05}\) x 5.005) - (0.05 x 2.05)


\(\frac{500.5}{0.05}\) - 1025

100.1 - 0.1025

= 99.9975

99.998 to 3 sig. fiq.

\(\frac{62}{3}\) = 20.6666.....

= 20.7 to 3 sig. fig.

P produces 20,000 bags

P reduces production by 5%

i.e. reduction = \(\frac{5}{100}\) x \(\frac{20000}{1}\)

= 1000

Q produces 15000 bags

Q increases production by 5%

i.e. increase = \(\frac{5}{100}\) x \(\frac{15000}{1}\)

= 750

Effective loss by the two = 1000 - 750

= 250 bags