1990 - JAMB Mathematics Past Questions and Answers - page 3

Let his assistant work for x days

∴ his master worked (x + 10) day. Amount received by master = 40(x + 10),

amount got by his assistance = 10x

Total amount collected = N2000.00

∴ 40(x + 10) + 10x = 2000

= 40x + 400 + 10x

= 2000

50x + 400 = 2000

50x = 2000 - 400

50x = 1600

x = \(\frac{1600}{50}\)

x = 32 days

\(\frac{x}{x + y}\) + \(\frac{y}{x - y}\) - \(\frac{x^2}{x^2 - y^2}\)

\(\frac{x}{x + y}\) + \(\frac{y}{x - y}\) - \(\frac{x^2}{(x + y)(x - y}\)

= \(\frac{x(x - y) + y(x + y) - x^2}{(x + y)(x - y}\)

= \(\frac{x^2 + xy + xy + y^2 - x^2}{(x + y)(x - y}\)

= \(\frac{y^2}{(x + y)(x - y)}\)

= \(\frac{y^2}{(x^2 - y^2)}\)

Given that x² + y² + z² = 194, calculate z if x = 7 and \(\sqrt{y}\) = 3

x = 7

∴ x² = 49

\(\sqrt{y}\) = 3

∴ y² = 81 = x² + y² + z² = 194

49 + 81 + z² = 194

130 + z² = 194

z² = 194 - 130

= 64

z = \(\sqrt{64}\)

= 8

3 + 6 + 12 + .....18thy term

1st term = 3, common ratio \(\frac{6}{3}\) = 2

n = 18, sum og GP is given by Sn = a\(\frac{(r^n - 1)}{r - 1}\)

s¹⁸ = 3\(\frac{(2^{18} - 1)}{2 - 1}\)

= 3(2¹⁷ - 1)

x + x + 1

\(\frac{dy}{dx}\) = 2x + 1

At the turning point, \(\frac{dy}{dx}\) = 0

2x + 1 = 0

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

\(\frac{d^2y}{dx^2}\) = 2 > 0(min Pt)

= \(\frac{1}{4}\) + \(\frac{1}{2}\)

= 1

Length of Arc AB = \(\frac{\theta}{360}\) 2\(\pi\)r

= \(\frac{48}{360}\) x 2\(\frac{22}{7}\) x \(\frac{21}{2}\)

= \(\frac{4 \times 22 \times \times 3}{30}\) \(\frac{88}{10}\) = 8.8cm

Perimeter = 8.8 + 2r

= 8.8 + 2(10.5)

= 8.8 + 21

= 29.8cm

For a regular polygon of n sides

n = \(\frac{360}{\text{Exterior angle}}\)

Exterior < = 180^o - 140^o

= 40^o

n = \(\frac{360}{40}\)

= 9 sides

Cos \(\theta\) = \(\frac{12}{13}\)

x² + 12² = 13²

x² = 169- 144 = 25

x = 25

= 5

Hence, tan\(\theta\) = \(\frac{5}{12}\) and cos\(\theta\) = \(\frac{12}{13}\)

If cos²\(\theta\) = 1 + \(\frac{1}{tan^2\theta}\)

= 1 + \(\frac{1}{\frac{(5)^2}{12}}\)

= 1 + \(\frac{1}{\frac{25}{144}}\)

= 1 + \(\frac{144}{25}\)

= \(\frac{25 + 144}{25}\)

= \(\frac{169}{25}\)