2009 - JAMB Mathematics Past Questions and Answers - page 9
81
What value of x will make the function x(4 - x) a maximum?
A
4
B
3
C
2
D
1
correct option: c
x(4 - x)
4x - x2
\(\frac{dy}{dx}\) = 4 - 2x
\(\frac{dy}{dx}\) = 0
2x = 4
x = \(\frac{4}{2}\)
= 2
Users' Answers & Comments4x - x2
\(\frac{dy}{dx}\) = 4 - 2x
\(\frac{dy}{dx}\) = 0
2x = 4
x = \(\frac{4}{2}\)
= 2
82
The distance travelled by a particle from a fixed point is given as s = (t3 - t2 - t + 5)cm. Find the minimum distance that the particle can cover from the fixed point.
A
2.3 cm
B
4.0cm
C
5.2
D
g
correct option: b
S = (t3 - t2 - t + 5)cm
\(\frac{ds}{dt}\) = 3t2 - 2t - 1
= (3t + 1)(t - 1)
t = -\(\frac{1}{3}\) or t = 1
Substitute value of t
s = (13 - 12 - 1 + 5)cm
= 4.0 cm
Users' Answers & Comments\(\frac{ds}{dt}\) = 3t2 - 2t - 1
= (3t + 1)(t - 1)
t = -\(\frac{1}{3}\) or t = 1
Substitute value of t
s = (13 - 12 - 1 + 5)cm
= 4.0 cm
83
Evaluate \(\int\) sec2\(\theta\) d \(\theta\)
A
sec\(\theta\) tan\(\theta\) + k
B
tan\(\theta\) + k
C
2 sec\(\theta\) + k
D
sec\(\theta\) + k
84
\(\begin{array}{c|c} No. of days & 1 & 2 & 3 & 4 & 5 & 6\ \hline No. of students & 20 & 2x & 60 & 40 & x & 50 \end{array}\)
The distribution above shows the number of days a group of 260 students were absent from school in a particular term. How many students were absent for at least four days in the term
The distribution above shows the number of days a group of 260 students were absent from school in a particular term. How many students were absent for at least four days in the term
A
180
B
120
C
110
D
40
correct option: a
3x + 170 = 260
3x = 260 - 170
3x = 90 \(\to\) x = 30
therefore, 20 + 2x + 60 + 40
= 180
Users' Answers & Comments3x = 260 - 170
3x = 90 \(\to\) x = 30
therefore, 20 + 2x + 60 + 40
= 180
85
5, 8, 6 and k occurs with frequencies 3, 2, 4 and 1 respectively and have a mean of 5.7. Find the value of k
A
4
B
3
C
2
D
1
correct option: c
\(\begin{array}{c|c} x & f & fx\ \hline 5 & 3 & 15\ 8 & 2 & 16 \ 6 & 4 & 24\ k & 1 & k\ & \sum f & \sum fx = 55 + k\end{array}\)
mean \(\bar{x}\) = \(\frac{55 + k}{10}\)
= 5.7
k = 2
Users' Answers & Commentsmean \(\bar{x}\) = \(\frac{55 + k}{10}\)
= 5.7
k = 2
86
What is the mean deviation of x, 2x, x + 1 and 3x, if their mean is 2?
A
0.5
B
1.0
C
1.5
D
2.0
correct option: d
deviation x - \(\bar{x}\)
x - 2 + 2x - 2 + (x + 1) - 2 + 3x - 2 = 0
x - 2 + 2x - 2 -2x - 2 + 3x - 2 = 0
= 4x - 8
4x = 8
x = \(\frac{8}{4}\)
= 2
Users' Answers & Commentsx - 2 + 2x - 2 + (x + 1) - 2 + 3x - 2 = 0
x - 2 + 2x - 2 -2x - 2 + 3x - 2 = 0
= 4x - 8
4x = 8
x = \(\frac{8}{4}\)
= 2
87
in how many ways can 9 people be seated if 3 chairs 3 chairs are available
A
720
B
504
C
336
D
210
correct option: b
\(\frac{n!}{n - r!}\) = \(\frac{9!}{9 - 3!}\)
= \(\frac{9!}{6!}\)
= 9 x 8 x 7
= 502
Users' Answers & Comments= \(\frac{9!}{6!}\)
= 9 x 8 x 7
= 502
88
In how many ways can a delegation of 3 be chosen from 5 men and 3 women, if at least 1 man and 1 woman must be included?
A
15
B
28
C
30
D
45
correct option: b
\(\frac{\begin{pmatrix} 8 \ 3 \end{pmatrix}}{\begin{pmatrix} 4 \ 1 \end{pmatrix}\begin{pmatrix} 4\ 1\end{pmatrix}}\)(Two boys and a girl) OR \(\frac{\begin{pmatrix} 8 \ 3 \end{pmatrix}}{\begin{pmatrix} 4 \ 1 \end{pmatrix}\begin{pmatrix} 4\ 1\end{pmatrix}}\)(Two girls and a boy in the committee)
\(\frac{336}{24}\) or \(\frac{336}{24}\)
14 + 14
= 28
Users' Answers & Comments\(\frac{336}{24}\) or \(\frac{336}{24}\)
14 + 14
= 28
89
The probability of a student passing any examination is \(\frac{2}{3}\). If the student takes three examinations, what is the probability that he will not pass any of them?
A
\(\frac{2}{3}\)
B
\(\frac{4}{9}\)
C
\(\frac{8}{27}\)
D
\(\frac{1}{27}\)
correct option: d
p(pass) = \(\frac{2}{3}\)
p(fail) = \(\frac{1}{3}\)
p(pass at 5 marks) = \(\frac{1}{3}\) x \(\frac{1}{3}\) x \(\frac{1}{3}\)
= \(\frac{1}{27}\)
Users' Answers & Commentsp(fail) = \(\frac{1}{3}\)
p(pass at 5 marks) = \(\frac{1}{3}\) x \(\frac{1}{3}\) x \(\frac{1}{3}\)
= \(\frac{1}{27}\)
90
\(\begin{array}{c|c} Marks & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9\ \hline No. of students & 3 & 4 & 1 & 0 & 4 & 5 & 2 & 1\end{array}\)
The table above shows the distribution of marks of students in a test. Find the probability of passing the test if the pass mark is 5.
The table above shows the distribution of marks of students in a test. Find the probability of passing the test if the pass mark is 5.
A
\(\frac{3}{5}\)
B
\(\frac{2}{5}\)
C
\(\frac{7}{20}\)
D
\(\frac{1}{5}\)