1991 - JAMB Mathematics Past Questions and Answers - page 2
11
Musa borrows N10.00 at 2% per month simple interest and repays N8.00 after 4 months. How much does he still owe
A
N10.80
B
N10.67
C
N2.80
D
N2.67
correct option: c
I = \(\frac{PRT}{100}\)
= \(\frac{10 \times 2 \times 4}{100}\)
= \(\frac{4}{5}\)
= 0.8
Total amount = N10.80
He pays N8.00
Remainder = 10.80 - 8.00
= N2.80
Users' Answers & Comments= \(\frac{10 \times 2 \times 4}{100}\)
= \(\frac{4}{5}\)
= 0.8
Total amount = N10.80
He pays N8.00
Remainder = 10.80 - 8.00
= N2.80
12
If 3 gallons of spirit containing 20% water are added to 5 gallons of another spirit containing 15% water, what percentage of the mixture is water?
A
2\(\frac{4}{5}\)%
B
16\(\frac{7}{8}\)%
C
18\(\frac{1}{8}\)%
D
18\(\frac{7}{8}\)%
correct option: b
% of water in the mixture
= \(\frac{\text{Total Amount of water}}{\text{Total quantity of spirit}}\) x \(\frac{100}{1}\)
\(\frac{3(\frac{20}{100}) + 5 (\frac{15}{100})}{3 + 5}\) x \(\frac{100}{1}\)
= \(\frac{\frac{6}{10} + \frac{75}{100}}{8}\) x \(\frac{100}{1}\)
= \(\frac{0.6 + 0.75}{8}\) x \(\frac{100}{1}\)
= \(\frac{1.35}{8}\) x \(\frac{100}{1}\)
= \(\frac{33.75}{2}\)
= 16.875
= 16\(\frac{7}{8}\)
Users' Answers & Comments= \(\frac{\text{Total Amount of water}}{\text{Total quantity of spirit}}\) x \(\frac{100}{1}\)
\(\frac{3(\frac{20}{100}) + 5 (\frac{15}{100})}{3 + 5}\) x \(\frac{100}{1}\)
= \(\frac{\frac{6}{10} + \frac{75}{100}}{8}\) x \(\frac{100}{1}\)
= \(\frac{0.6 + 0.75}{8}\) x \(\frac{100}{1}\)
= \(\frac{1.35}{8}\) x \(\frac{100}{1}\)
= \(\frac{33.75}{2}\)
= 16.875
= 16\(\frac{7}{8}\)
13
What is the product of \(\frac{27}{5^1}\)(3)-3 and \(\frac{(1)^{-1}}{5}\)?
A
5
B
3
C
1
D
\(\frac{1}{25}\)
correct option: c
\(\frac{27}{5^1}\)(3)-3 x \(\frac{(1)^{-1}}{5}\) = \(\frac{27}{5}\) x \(\frac{1}{3^3}\) x \(\frac{1}{\frac{1}{5}}\)
= \(\frac{27}{5}\) x \(\frac{1}{27}\) x \(\frac{5}{1}\)
= 1
Users' Answers & Comments= \(\frac{27}{5}\) x \(\frac{1}{27}\) x \(\frac{5}{1}\)
= 1
14
Simplify 2log \(\frac{2}{5}\) - log\(\frac{72}{125}\) + log 9
A
1 - 4 log3
B
-1 + 2 log 3
C
-1 + 5 log2
D
1 - 2log 2
correct option: d
2log \(\frac{2}{5}\) - log\(\frac{72}{125}\) + log 9
[\(\frac{2}{5}\))2 x 9] = log \(\frac{4}{25}\) x \(\frac{9}{1}\) x \(\frac{125}{72}\)
= log \(\frac{72}{125}\)
= log \(\frac{5}{2}\)
= log \(\frac{10}{4}\)
= log 10 - log 4
= log10 10 - log10 22
= 1 - 2 log2
Users' Answers & Comments[\(\frac{2}{5}\))2 x 9] = log \(\frac{4}{25}\) x \(\frac{9}{1}\) x \(\frac{125}{72}\)
= log \(\frac{72}{125}\)
= log \(\frac{5}{2}\)
= log \(\frac{10}{4}\)
= log 10 - log 4
= log10 10 - log10 22
= 1 - 2 log2
15
Simplify \(\frac{1}{1 + \sqrt{5}}\) - \(\frac{1}{1 - \sqrt{5}}\)
A
- \(\frac{1}{2}\sqrt{5}\)
B
\(\frac{1}{2}\sqrt{5}\)
C
-- \(\frac{1}{4}\sqrt{5}\)
D
5
correct option: a
\(\frac{1}{1 + \sqrt{5}}\) - \(\frac{1}{1 - \sqrt{5}}\)
= \(\frac{3 - \sqrt{5} - 3 - \sqrt{5}}{(3 + \sqrt{5}) (3 - \sqrt{5}}\)
= \(\frac{-2\sqrt{5}}{9 - 5}\)
= \(\frac{-2\sqrt{5}}{4}\)
= - \(\frac{1}{2}\sqrt{5}\)
Users' Answers & Comments= \(\frac{3 - \sqrt{5} - 3 - \sqrt{5}}{(3 + \sqrt{5}) (3 - \sqrt{5}}\)
= \(\frac{-2\sqrt{5}}{9 - 5}\)
= \(\frac{-2\sqrt{5}}{4}\)
= - \(\frac{1}{2}\sqrt{5}\)
16
Rationalize \(\frac{2\sqrt{3} + 3 \sqrt{2}}{3\sqrt{2} - 2 \sqrt{3}}\)
A
5 - 2\(\sqrt{6}\)
B
5 + 2\(\sqrt{6}\)
C
5\(\sqrt{6}\)
D
5
correct option: b
\(\frac{2\sqrt{3} + 3 \sqrt{2}}{3\sqrt{2} - 2 \sqrt{3}}\)
= \(\frac{2\sqrt{3} + 3 \sqrt{2}}{3\sqrt{2} - 2 \sqrt{3}}\) x \(\frac{3\sqrt{2} + 2 \sqrt{3}}{3\sqrt{2} - 2 \sqrt{3}}\)
\(\frac{4(3) + 9(2) + 2(6) \sqrt{6}}{9(2) - 4(3)}\)
\(\frac{12 + 18 + 12\sqrt{6}}{1`8 - 12}\)
= \(\frac{30 + 12\sqrt{6}}{6}\)
= 5 + 2\(\sqrt{6}\)
Users' Answers & Comments= \(\frac{2\sqrt{3} + 3 \sqrt{2}}{3\sqrt{2} - 2 \sqrt{3}}\) x \(\frac{3\sqrt{2} + 2 \sqrt{3}}{3\sqrt{2} - 2 \sqrt{3}}\)
\(\frac{4(3) + 9(2) + 2(6) \sqrt{6}}{9(2) - 4(3)}\)
\(\frac{12 + 18 + 12\sqrt{6}}{1`8 - 12}\)
= \(\frac{30 + 12\sqrt{6}}{6}\)
= 5 + 2\(\sqrt{6}\)
17
Multiply (x2 - 3x + 1) by (x - a)
A
x3 - (3 + a) x2 + (1 + 3a)x - a
B
x3 - (3 - a)x2 + 3ax - a
C
x3 - (3 - a)x2 - (1 = 3a) - a
D
x3 + (3 - a)x2 + (1 + 3a) - a
correct option: a
(x2 - 3x + 1)(x - a) = x3 - 3x2 + x - ax2 + 3ax - a
= x3 - (3 + a) x2 + (1 + 3a)x - a
Users' Answers & Comments= x3 - (3 + a) x2 + (1 + 3a)x - a
18
Evaluate \(\frac{xy^2 - x^2y}{x^2 - xy^1}\) When x = -2 and y = 2
A
3
B
-\(\frac{3}{5}\)
C
\(\frac{3}{5}\)
D
-3
correct option: d
\(\frac{xy^2 - x^2y}{x^2 - xy^1}\)
= \(\frac{(-2)(3)^2 - (-2)^2(3)}{(-2)^2 - (-2)(3)}\)
= -30
= -3
Users' Answers & Comments= \(\frac{(-2)(3)^2 - (-2)^2(3)}{(-2)^2 - (-2)(3)}\)
= -30
= -3
19
A car travels from calabar to Enugu, a distance of P km with an average speed of U km per hour and continues to benin, a distance of Q km, with an average speed of Wkm per hour. Find its average speed from Calabar to Benin
A
\(\frac{(p + q)}{pw + qu}\)
B
\(\frac{uw(p + q)}{pw + qu}\)
C
\(\frac{uw(p + q)}{pw}\)
D
\(\frac{uw}{pw + qu}\)
correct option: b
Average speed = \(\frac{\text{total Distance}}{\text{Total Time}\)
from Calabar to Enugu in time t1, hence
t1 = \(\frac{P}{U}\) also from Enugu to Benin
t2 \(\frac{q}{w}\)
Av. speed = \(\frac{p + q}{t_1 + t_2}
= \(\frac{p + q}{\frac{p}{u} + \frac{q}{w}\)
= p + q x \(\frac{uw}{pw + qu}\)
= \(\frac{uw(p + q)}{pw + qu}\)
Users' Answers & Commentsfrom Calabar to Enugu in time t1, hence
t1 = \(\frac{P}{U}\) also from Enugu to Benin
t2 \(\frac{q}{w}\)
Av. speed = \(\frac{p + q}{t_1 + t_2}
= \(\frac{p + q}{\frac{p}{u} + \frac{q}{w}\)
= p + q x \(\frac{uw}{pw + qu}\)
= \(\frac{uw(p + q)}{pw + qu}\)
20
If w varies inversely as \(\frac{ur}{u + r}\) and is equal to 8 when
u = 2 and r = 6, find a relationship between u, v, w.
u = 2 and r = 6, find a relationship between u, v, w.
A
urw = 16(u + v)
B
16ur = 3w(u + v)
C
urw = 12(u + v)
D
12urw = u + v
correct option: c
W \(\alpha\) \(\frac{\frac{1}{uv}}{u + v}\)
∴ w = \(\frac{\frac{k}{uv}}{u + v}\)
= \(\frac{k(u + v)}{uv}\)
w = \(\frac{k(u + v)}{uv}\)
w = 8, u = 2 and v = 6
8 = \(\frac{k(2 + 6)}{2(6)}\)
= \(\frac{k(8)}{12}\)
k = 12
Users' Answers & Comments∴ w = \(\frac{\frac{k}{uv}}{u + v}\)
= \(\frac{k(u + v)}{uv}\)
w = \(\frac{k(u + v)}{uv}\)
w = 8, u = 2 and v = 6
8 = \(\frac{k(2 + 6)}{2(6)}\)
= \(\frac{k(8)}{12}\)
k = 12