2010 - JAMB Mathematics Past Questions and Answers - page 3

21
\(\begin{array}{c|c} Marks & 2 & 3 & 4 & 5 & 6 & 7 & 8 \ \hline No. of students & 3 & 1 & 5 & 2 & 4 & 2 & 3\end{array}\)
From the table above, if the pass mark is 5, how many students failed the test?
A
6
B
2
C
9
D
7
correct option: c

From the table, the number of students who failed the test is given as:

3 + 1 + 5 = 9

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22
\(\begin{array}{c|c} Marks & 1 & 2 & 3 & 4 & 5\ \hline Frequency & 2 & 2 & 8 & 4 & 4\end{array}\)
The table above shows the marks obtained in a given test. How many students took the test?
A
16
B
20
C
13
D
15
correct option: b

from the table, the number of students who took the test is 2 + 2 + 8 + 4 + 4 = 20

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23
\(\begin{array}{c|c} Marks & 1 & 2 & 3 & 4 & 5\ \hline Frequency & 2 & 2 & 8 & 4 & 4\end{array}\)
The table above shows the marks obtained in a given test. Find the mean mark.
A
3.1
B
3.0
C
3.3
D
3.2
correct option: c

(\begin{array} & Marks(x) & freq.(f) & fx \1 & 2 & 2 \ 2 & 2 & 4 \ 3 & 8 & 24 \ 4 & 4 & 16\ 5 & 4 & 20 \ \hline & \sum f = 20 & \sum fx = 66\end{array})

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Mean mark ,(\bar{x}) = (\frac{\sum fx}{\sum f})

= (\frac{66}{20})

(\bar{x}) = 3.3

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24
In how many ways can a committee of 2 women and 3 men be chosen from 6 men and 5 women?
A
100
B
200
C
30
D
50
correct option: b

A committee of 2 women and 3 men can be chosen from 6 men and 5 women, in (^{5}C_{2}) x (^{6}C_{3}) ways

= (\frac{5!}{(5 - 2)!2!} \times {\frac{6!}{(6 - 3)!3!}})

= (\frac{5!}{3!2!} \times {\frac{6!}{3 \times 3!}})

= (\frac{5 \times 4 \times 3!}{3! \times 2!} \times {\frac{6 \times 5 \times 4 \times 3!}{3! \times 3!}})

= (\frac{5 \times 4}{1 \times 2} \times {\frac{6 \times 5 \times 4}{1 \times 2 \times 3}})

= 10 x (\frac{6 \times 20}{6})

= 200

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25
If three unbiased coins are tossed, find the probability that they are all heads
A
\(\frac{1}{2}\)
B
\(\frac{1}{3}\)
C
\(\frac{1}{9}\)
D
\(\frac{1}{8}\)
correct option: d

P(H) = (\frac{1}{2}) and P(T) = (\frac{1}{2})

Using the binomial prob. distribution,

(H + T)3 = H3 + 3H2T1 + 3HT2 + T3

Hence the probability that three heads show in a toss of the three coins is H3

= ((\frac{1}{2}))3

= (\frac{1}{8})

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26
Find the standard deviation of 2, 3, 5 and 6
A
√6
B
√10
C
√\(\frac{2}{5}\)
D
√\(\frac{5}{2}\)
correct option: d

(\begin{array}& x & x - \bar{x} & (x - \bar{x})^2 \2 & -2 & 4 \ 3 & -1 & 1 \ 5 & 1 & 1 \ 6 & 2 & 4\ \hline \sum x = 16 & & \sum (x - \bar{x}^2) = 0 \end{array})

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(\bar{x}) = (\frac{\sum x }{N})

= (\frac{16}{4})

= 4

S = (\sqrt{\frac {(x - \bar{x})^2}{N}})

= (\sqrt{\frac {(10)}{4}})

= (\sqrt{\frac {(5)}{2}})

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27
A man bought a second-hand photocopying machine for N34000. He serviced i at a cost N2000 and then sold it at a profit of 15%. What was the selling price?
A
N37550
B
N40400
C
N41400
D
42400
correct option: c

Total cost = N34,000 + N2,000

= N36,000

15% = N115

(\frac{115}{100}) x N36,000

= N41,400

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28
W is directly proportional to U. If W = 5 when U = 3, find U when W = \(\frac{2}{7}\)
A
\(\frac{6}{35}\)
B
\(\frac{10}{21}\)
C
\(\frac{21}{10}\)
D
\(\frac{35}{6}\)
correct option: a

W (\alpha) U

W = ku

u = (\frac{w}{k}); (\frac{2}{7}) x (\frac{3}{5})

= (\frac{6}{35})

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29
Determine the value of x for which (x2 - 1)>0
A
x < -1 or x > 1
B
-1 < x < 1
C
x > 0
D
x < -1
correct option: a

x(x - 1) > 0

x < -1 or x > 1

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30
From the diagram above, find x
A
75o
B
65o
C
55o
D
50o
correct option: b

In the diagram above, < STU = < TRS = 25o

(< between tangent to circle and a circle and a chord through the point of contact = < in the alternate segment)

< RTS = 90o

(< in a semicircle = 90o)

xo + < RTS + < STU = 180o

xo + 90o + 25o = 180o

xo + 115o = 180o

xo = 180o - 115o = 65o

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