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)

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