2019 - JAMB Mathematics Past Questions and Answers - page 5

3x + y = 21 ---- (i)

xy = 30 --------- (ii)

From (ii), \(y = \frac{30}{x}\).

Substitute the value of y in (i):

3x + \(\frac{30}{x}\) = 21

\(\implies\) 3x\(^2\) + 30 = 21x

3x\(^2\) - 21x + 30 = 0

3x\(^2\) - 15x - 6x + 30 = 0

3x(x - 5) - 6(x - 5) = 0

(3x - 6)(x - 5) = 0

3x - 6 = 0 \(\implies\) x = 2.

x - 5 = 0 \(\implies\) x = 5.

when x = 2, y = \(\frac{30}{2}\) = 15;

when x = 5, y = \(\frac{30}{5}\) = 6.

\(\tan \theta = \frac{9}{20} = 0.45\)

\(\theta = \tan^{-1} (0.45) \)

= 24.23°

\(\therefore\) The bearing of Y from X = 180° - 24.23°

= 155.77°

= 156° approximately

\(P = (\frac{Q(R - T)}{15})^{\frac{1}{3}}\)

\(P^3 = \frac{Q(R - T)}{15}\)

\(Q(R - T) = 15P^3\)

\(R - T = \frac{15P^3}{Q}\)

\(T = R - \frac{15P^3}{Q}\)

< BAC = \(\frac{130}{2}\) (angle subtended at the centre)

< BAC = 65°

Also, x = 26° (theorem)

y = 65° - 26° = 39°

< AOC = 180° - (39° + 39°)

= 102°

Given that each interior angle = 140°, 

each exterior angle = 180° - 140° = 40°

Number of sides of the polygon = \(\frac{360°}{40°}\) = 9 

Sum of the angles in the polygon = 140° x 9

= 1260°

The cost price of the car = N 1,250.00

The selling price of the car = N 1,085.00

Loss is the difference in the buying and selling price = N (1250 - 1085)

= N 165.00

% loss = \(\frac{165}{1250} \times 100%\)

= 13.2% loss

\(V = \frac{\pi h}{3} (R^2 + Rr + r^2)\)

\(V = \frac{\pi R^2 h}{3} + \frac{\pi Rr h}{3} + \frac{\pi r^2 h}{3}\)

\(\frac{\mathrm d V}{\mathrm d R} = \frac{2 \pi R h}{3} + \frac{\pi r h}{3}\)

= \(\frac{\pi}{3} (2R + r)\)

\((0.0439 \div 3.62)\)

= 0.01213

\(\approxeq\) 0.012

= \(\frac{12}{1000}\)

\(25^{1 - x} \times 5^{x + 2} \div (\frac{1}{125})^{x} = 625^{-1}\)

\((5^2)^{(1 - x)} \times 5^{(x + 2)} \div (5^{-3})^x = (5^4)^{-1}\)

\(5^{2 - 2x} \times 5^{x + 2} \div 5^{-3x} = 5^{-4}\)

\(5^{(2 - 2x) + (x + 2) - (-3x)} = 5^{-4}\)

By equating the bases, we have

\(2 - 2x + x + 2 + 3x = -4\)

\(4 + 2x = -4 \implies 2x = -4 - 4\)

\(2x = -8\)

\(x = -4\)