1998 - JAMB Mathematics Past Questions & Answers - page 5

41
Given that log4(Y - 1) + log4(\(\frac{1}{2}\)x) = 1 and log2(y + 1) + log2x = 2, solve for x and y respectively
A
2, 3
B
3, 2
C
-2, -3
D
-3, -2
CORRECT OPTION: c
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
42
Find the value of k if \(\frac{k}{\sqrt{3} + \sqrt{2}}\) = k\(\sqrt{3 - 2}\)
A
3
B
2
C
\(\sqrt{3}\)
D
\(\sqrt 2\)
CORRECT OPTION: d
\(\frac{k}{\sqrt{3} + \sqrt{2}}\) = 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 = \(\frac{2}{\sqrt{2}}\)

= \(\sqrt{2}\)
43
A market woman sells oil in cylindrical tins 10cm deep and 6cm in diameter at N15.00 each. If she bought a full cylindrical jug 18cm deep and 10cm in diameter for N50.00, how much did she make by selling all the oil?
A
N62.50
B
N35.00
C
N31.00
D
N25.00
CORRECT OPTION: d
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
44
A man is paid r naira per hour for normal work and double rate for overtime. if he does a 35-hour week which includes q hours of overtime, what is his weekly earning in naira?
A
r(35 + q)
B
q(35r - q)
C
q(35 + r)
D
r(35 + 2q)
CORRECT OPTION: d
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)
45
When the expression pm2 + qm + 1 is divided by (m - 1), it has a remainder is 4, Find p and q respectively
A
2, -1
B
-1, 2
C
3, -2
D
-2, 3
CORRECT OPTION: b
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
46
Factorize r2 - r(2p + q) + 2pq
A
(r - 2q)(2r - p)
B
(r - p)(r + p0
C
(r - q)(r - 2p)
D
(2r - q)(r + p)
CORRECT OPTION: c
r2 - r(2p + q) + 2pq = r2 - 2pr -qr + 2pq

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

= (r - q)(r - 2p)
47
Solve for the equation \(\sqrt{x}\) - \(\sqrt{(x - 2)}\) - 1 = 0
A
\(\frac{3}{2}\)
B
\(\frac{2}{3}\)
C
\(\frac{4}{9}\)
D
\(\frac{9}{4}\)
CORRECT OPTION: d
\(\sqrt{x}\) - \(\sqrt{(x - 2)}\) - 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 = \(\frac{9}{4}\)
48
Make \(\frac{a}{x}\) the subject of formula \(\frac{x + 1}{x - a}\)
A
\(\frac{m - 1}{m + 1}\)
B
\(\frac{m + 1}{1 - m}\)
C
\(\frac{m - 1}{1 + m}\)
D
\(\frac{m + 1}{m - 1}\)
CORRECT OPTION: a
\(\frac{x + a}{x - a}\) = m

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

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