1993 - JAMB Mathematics Past Questions and Answers - page 3

x (\ast) y = x^y

x (\ast) 2 = x²

x (\ast) 2 = x

∴ x² - x = 0

x(x - 1) = 0

x = 0 or 1

Initial salary = N540

increment = N36 (every 6 months)

Period of increment = 2 yrs and 6 months

amount(increment) = N36 x 5 = N180

The man's new salary = N540 = N180

= N720.00

A rectangular polygon has each interior angle to be 150^o

let the polygon has n-sides

therefore, Total interior angle 150 x n = 150n

hence 150n = (2n - 4)90

150n = 180n - 360

360 = (180 - 150)n

30n = 360

n = 12

Diameter = 8cm

∴ Radius = 4cm

Length of arc = (\frac{\theta}{360}) x 2 (\pi)r but Q = 22(\frac{1}{2})

∴ Length (\frac{22\frac{1}{2}}{360}) x 2 x (\pi) x 4

= (\frac{22\frac{1}{2} \times 8\pi}{360})

= (\frac{180}{360})

= (\frac{\pi}{2})

2x + 3 (\neq) 2x - 3 for any value of x

∴ for the (\bigtriangleup) to be isosceles, either

2x - 3 = x + 3 or 2x + 3 = x + 3

solve the two equations we arrive at

x = 6 or x = 0

When x = 6, the sides are 9, 15, 9

When x = 0, the sides are 3, 4, -3 since lengths of a (\bigtriangleup)can never be negative then the value of x = 6

Surface area = 154cm² (area of sphere)

4(\pi)r² = 154

r(\sqrt{\frac{154}{4\pi}})

= 3.50cm

Area of sector

(\frac{\theta}{360}) x (\pi)r², (\theta) = 60^o, r = 3m

= (\frac{60}{360}) x (\frac{12}{7}) x 3 x 3

(\frac{1}{6}) x (\frac{22}{7}) x 9

= (\frac{33}{7})

= 4.7m²

The angle between 2 latitudes one in northern hemisphere and the other in southern hemisphere and the other in southern hemisphere is the sum of their latitudes.

∴ Total angle difference = (30 + 13) = 43^o

sin (\theta) = cos (\theta) 0 (\leq) (\theta) (\leq) 360^o

The acute angle where sin (\theta) = cos (\theta) = 45^o

But at the fourth Quadrant Cos (\theta) = +ve

at the 4th quadrant, value with respect to Q is

(360 - Q) where Q = acute angle

(360 - 45) = 315^o

The two solution are 45^o, 315^o