2012 - JAMB Mathematics Past Questions and Answers - page 4
31
Evaluate \(\int^2_1(x^2 - 4x)dx\)
A
\(\frac{11}{3}\)
B
\(\frac{3}{11}\)
C
\(-\frac{3}{11}\)
D
\(-\frac{11}{3}\)
correct option: d
\(\int^2_1(x^2 - 4x)dx\)
\((\frac{x^3}{3} - \frac{4x^2}{2})\)
substituting integrate values
\([\frac{8}{3} - \frac{4 \times 4}{2}] - [\frac{1}{2} - 2]\)
= \(-\frac{11}{3}\)
Users' Answers & Comments\((\frac{x^3}{3} - \frac{4x^2}{2})\)
substituting integrate values
\([\frac{8}{3} - \frac{4 \times 4}{2}] - [\frac{1}{2} - 2]\)
= \(-\frac{11}{3}\)
32
Evaluate \(\int^{\frac{\pi}{4}}_0sec^2 \theta d \theta\)
A
1
B
2
C
3
D
4
correct option: a
Users' Answers & Comments33
The mean of seven numbers is 96. If an eighth number is added, the mean becomes 112. Find the eighth number.
A
126
B
180
C
216
D
224
correct option: d
\(\frac{x}{7} = \frac{96}{1}\) ==> \(\frac{672 + x}{8} = 112\)
Therefore x = 224
Users' Answers & CommentsTherefore x = 224
34
Find the median of 2,3,7,3,4,5,8,9,9,4,5,3,4,2,4 and 5
A
9
B
8
C
7
D
4
correct option: d
Arrange all the values in ascending order,
2,2,3,3,3,4,4,4,4,5,5,5,7,8,9,9
Users' Answers & Comments2,2,3,3,3,4,4,4,4,5,5,5,7,8,9,9
35
Find the range of 4,9,6,3,2,8,10 and 11
A
11
B
9
C
8
D
4
36
Find the standard deviation of 2,3,8,10 and 12
A
3.9
B
4.9
C
5.9
D
6.9
correct option: a
\(\begin{array}{c|c} x & (x - \varkappa) & (x - \varkappa)^2 \ \hline 2 & -5 & 25 \ \hline 3 & -4 & 16 \ \hline 8 & 1 & 1 \ \hline 10 & 3 & 9 \ \hline 12 & 5 & 25 \ \hline & & 76
\end{array}\)
S.D = \(\sqrt{\frac{(x - \varkappa)^2}{n}}\)
S.D = \(\sqrt{\frac{76}{5}}\)
S.D = 3.9
Users' Answers & Comments\end{array}\)
S.D = \(\sqrt{\frac{(x - \varkappa)^2}{n}}\)
S.D = \(\sqrt{\frac{76}{5}}\)
S.D = 3.9
37
Evaluate n+1Cn-2 If n =15
A
3630
B
3360
C
1120
D
560
correct option: d
\(\frac{n + 1 (n - 2)}{(n + 1)!}\)
\(\frac{(n + 1) + (n - 2)!(n - 2)!}{(n + 1)!}\)
\(\frac{(n + 1)(n + 1 -1)(n+1-2)(n+1-3)!}{3!(n-2)!}\)
\(\frac{(n + 1)(n)(n-1)(n-2)!}{3!(n-2)!}\)
\(\frac{(n + 1)(n)(n-1)}{3!}\)
Since n = 15
\(\frac{(15 + 1)(15)(15-1)}{3!}\)
\(\frac{16 \times 15 \times 14}{3 \times 2 \times 1}\)
= 560
Users' Answers & Comments\(\frac{(n + 1) + (n - 2)!(n - 2)!}{(n + 1)!}\)
\(\frac{(n + 1)(n + 1 -1)(n+1-2)(n+1-3)!}{3!(n-2)!}\)
\(\frac{(n + 1)(n)(n-1)(n-2)!}{3!(n-2)!}\)
\(\frac{(n + 1)(n)(n-1)}{3!}\)
Since n = 15
\(\frac{(15 + 1)(15)(15-1)}{3!}\)
\(\frac{16 \times 15 \times 14}{3 \times 2 \times 1}\)
= 560
38
In how many ways can the letters of the word TOTALITY be arranged?
A
6720
B
6270
C
6207
D
6027
correct option: a
\(\frac{8!}{3!}\)
\(\frac{8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1}{3 \times 2\times 1}\)
==> 8 x 7 x 6 x 5 x 4 = 6720
Users' Answers & Comments\(\frac{8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1}{3 \times 2\times 1}\)
==> 8 x 7 x 6 x 5 x 4 = 6720
39
The probability that a student passes a physics test is \(\frac{2}{3}\). If he takes three physics tests, what is the probability that he passes two of the tests?
A
\(\frac{2}{27}\)
B
\(\frac{3}{27}\)
C
\(\frac{4}{27}\)
D
\(\frac{5}{3}\)
correct option: c
Pass(P) = \(\frac{2}{3}\), Fail(F) = \(\frac{1}{3}\)
T = P.P.F ==> \(\frac{2}{3} \times \frac{2}{3} \times \frac{1}{3}\) = \(\frac{4}{27}\)
Users' Answers & CommentsT = P.P.F ==> \(\frac{2}{3} \times \frac{2}{3} \times \frac{1}{3}\) = \(\frac{4}{27}\)
40
The probabilities that a man and his wife live for 80 years are \(\frac{2}{3}\) and \(\frac{3}{5}\) respectively. Find the probability that at least one of them will live up to 80 years
A
\(\frac{2}{15}\)
B
\(\frac{3}{15}\)
C
\(\frac{7}{15}\)
D
\(\frac{13}{15}\)
correct option: d
Man lives = \(\frac{2}{3}\) not live = \(\frac{1}{3}\)
Wife lives = \(\frac{3}{5}\) not live = \(\frac{2}{5}\)
\(P(\frac{2}{3} \times \frac{2}{5}) + (\frac{2}{5} \times \frac{1}{3}) + (\frac{2}{3} \times \frac{3}{5})\)
= \(\frac{4}{15} + \frac{3}{15} + \frac{6}{15}\)
= \(\frac{13}{15}\)
Users' Answers & CommentsWife lives = \(\frac{3}{5}\) not live = \(\frac{2}{5}\)
\(P(\frac{2}{3} \times \frac{2}{5}) + (\frac{2}{5} \times \frac{1}{3}) + (\frac{2}{3} \times \frac{3}{5})\)
= \(\frac{4}{15} + \frac{3}{15} + \frac{6}{15}\)
= \(\frac{13}{15}\)