1993 - JAMB Mathematics Past Questions & Answers - page 1

1
Integrate \(\frac{1 - x}{x^3}\) with respect to x
A
\(\frac{x - x^2}{x^4}\) + k
B
\(\frac{4}{x^4} - \frac{3 + k}{x^3}\)
C
\(\frac{1}{x} - \frac{1}{2x^2}\) + k
D
\(\frac{1}{3x^2} - \frac{1}{2x}\) + k
CORRECT OPTION: c
\(\int \frac{1 - x}{x^3}\)

= \(\int^{1}_{x^3} - \int^{x}_{x^3}\)

= x-3 dx - x-2dx

= \(\frac{1}{2x^2} + \frac{1}{x}\)
2
change 7110 to base 8
A
1078
B
1068
C
718
D
178
CORRECT OPTION: a
\(\begin{array}{c|c} 8 & 71 \ 8 & 8 \text{rem} 7\ 8 & 1 \text{rem} 0\end{array}\)

= 1078
3
Evaluate \(\frac{3524}{0.05}\) correct to 3 significant figures
A
705
B
70,000
C
70, 480
D
70, 500
CORRECT OPTION: d
\(\frac{3524}{0.05}\) = 70480

\(\approx\) 70500(3 s.g)
4
If 9(x - \(\frac{1}{2}\)) 3x2
A
\(\frac{1}{2}\)
B
1
C
2
D
3
CORRECT OPTION: b
9(x - \(\frac{1}{2}\)) 3x2 = 32(x - \(\frac{1}{2}\)) = 3x2
∴ 2(x - \(\frac{1}{2}\)) = x2

2x - 1 = x2

hence x2 - 2x + 1 = 0

(x - 1)(x - 1) = 0

x = 1
5
Solve for y in the equation 101 x 5(2x - 2) x 4(y - 1) = 1
A
\(\frac{3}{4}\)
B
\(\frac{5}{4}\)
C
\(\frac{2}{3}\)
D
5
CORRECT OPTION: c
10y x 5(2y - 2) x 4(y - 1) = 1

but 10y - (5 x 2)y = 5y x 2y

= (Law of indices)

5y x 2y x 5(2y - 2) x 4(y - 1)
6
simplify \(\frac{1}{√3 - 2}\) - \(\frac{1}{√3 + 2}\)
A
3
B
\(\frac{2}{3}\)
C
7
D
-4
CORRECT OPTION: d
\(\frac{1}{√3 - 2}\) - \(\frac{1}{√3 + 2}\)

L.C.M = (3- 2) (3 + 2)

∴ \(\frac{1}{\sqrt{3 - 2}}\) - \(\frac{1}{\sqrt{3 - 2}}\) = \(\frac{\sqrt{3 + 2} - \sqrt{3 - 2}}{\sqrt{3 - 2} + \sqrt{3 - 2}}\)


\(\frac{√3 + 2 - √3 + 2}{3 - 2√3 + 2√3 - 4}\) = \(\frac{4}{3 - 2}\)

= \(\frac{4}{-1}\)

= -4
7
If 2log3 y + log3 x2 = 4, then y is
A
4 - log3
B
\(\frac{4}{log_3 x}\)
C
\(\frac{4}{x}\)
D
\(\pm\) \(\frac{9}{x}\)
CORRECT OPTION: d
2log3y + log3x2 = 4

log3y2 + log3x2 = 4

∴ log3 (x2y2) = log381(correct all to base 4)

x2y2 = 81

∴ xy = \(\pm\)9

∴ y = \(\pm\)\(\frac{9}{x}\)
8
Solve without using tables log5(62.5) - log5(\(\frac{1}{2}\))
A
3
B
4
C
5
D
8
CORRECT OPTION: a
log5(62.5) - log5(\(\frac{1}{2}\))

= log5\(\frac{(62.5)}{\frac{1}{2}}\) - log5(2 x 62.5)

= log5(125)

= log553 - 3log55

= 3
9
If N225.00 yields N27.00 in x years simple interest at the rate of 4% per annum, find x
A
3
B
4
C
12
D
17
CORRECT OPTION: a
Principal = N255.00, Interest = 27.00

year = x Rate: 4%

∴ 1 = \(\frac{PRT}{100}\)

27 = \(\frac{225 \times 4 \times T}{100}\)

2700 = 900T

T = 3 years
10
If \(\sqrt{x^2 + 9}\) = x + 1, solve for x
A
5
B
4
C
3
D
2
CORRECT OPTION: b
\(\sqrt{x^2 + 9}\) = x + 1

x2 + 9 = (x + 1)2 + 1

0 = x2 + 2x + 1 - x2 - 9

= 2x - 8 = 0

2(x - 4) = 0

x = 4
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