1998 - JAMB Mathematics Past Questions and Answers - page 5

log₄(y - 1) + log₄((\frac{1}{2})x) = 1

log₄(y - 1)((\frac{1}{2})x) (\to) (y - 1)((\frac{1}{2})x) = 4 ........(1)

log₂(y + 1) + log₂x = 2

log₂(y + 1)x = 2 (\to) (y + 1)x = 2₂ = 4.....(ii)

From equation (ii) x = (\frac{4}{y + 1})........(iii)

put equation (iii) in (i) = y (y - 1)[(\frac{1}{2}(\frac{4}{y - 1}))] = 4

= 2y - 2

= 4y + 4

2y = -6

y = -3

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

= (\frac{4}{-2})

X = 2

therefore x = -2, y = -3

(\frac{k}{\sqrt{3} + \sqrt{2}}) = k(\sqrt{3 - 2})

(\frac{k}{\sqrt{3} + \sqrt{2}}) x (\frac{\sqrt{3} - \sqrt{2}}{\sqrt{3} - \sqrt{2}})

= k(\sqrt{3 - 2})

= k((\sqrt{3} - \sqrt{2}))

= k(\sqrt{3 - 2})

= k(\sqrt{3}) - k(\sqrt{2})

= k(\sqrt{3 - 2})

k2 = (\sqrt{2})

k = (\frac{2}{\sqrt{2}})

= (\sqrt{2})

V(\pi)r²h = (\pi)(3)²(10) = 90(\pi)cm³

V = (\pi)(5)² x 18 = 450(\pi)cm³

No of volume = (\frac{450\pi}{90\pi})

= 5

selling price = 5 x N15 = N75

profit = N75 - N50 = N25.00

The cost of normal work = 35r

The cost of overtime = q x 2r = 2qr

The man's total weekly earning = 35r + 2qr

= r(35 + 2q)

pm² + qm + 1 = (m - 1) Q(x) + 2

p(1)² + q(1) + 1 = 2

p + q + 1 = 2

p + q = 1.....(i)

pm² + qm + 1 = (m - 1)Q(x) + 4

p(-1)² + q(-1) + 1 = 4

p - q + 1 = 4

p - q = 3....(ii)

p + q = 1, p - q = -3

2p = -2, p = -1

-1 + q = 1

q = 2

r² - r(2p + q) + 2pq = r² - 2pr -qr + 2pq

= r(r - 2p) - q(r - 2p)

= (r - q)(r - 2p)

(\sqrt{x}) - (\sqrt{(x - 2)}) - 1 = 0

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

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

= x - 2 (\sqrt{x(x - 2)}) + x -2 = 1

= (2x - 3)² = [2 (\sqrt{x(x - 4)})]²

= 4x² - 12x + 9

= 4(x² - 2x)

= 4x² - 12x + 9

= 4x² - 8x

4x = 9

x = (\frac{9}{4})

(\frac{x + a}{x - a}) = m

x + a = mx - ma

a + ma = mx - x

a(m + 1) = x(m - 1)

(\frac{a}{x}) = (\frac{m - 1}{m + a})