1997 - JAMB Mathematics Past Questions and Answers - page 4
31
In a triangle XYZ, if < ZYZ is 60, XY = 3cm and YZ = 4cm, calculate the length of the sides XZ.
A
√23cm
B
√13cm
C
2√5cm
D
2√3cm
correct option: b
(XZ)2 = 32 + 42 - 2 x 3 x 4 cos60o
= 25 - 24\(\frac{1}{2}\)
XZ = √13cm
Users' Answers & Comments= 25 - 24\(\frac{1}{2}\)
XZ = √13cm
32
Differentiate \(\frac{6x^3 - 5x^2 + 1}{3x^2}\) with respect to x
A
\(\frac{2 + 2}{3x^3}\)
B
2 + \(\frac{1}{6x}\)
C
2 - \(\frac{2}{3x^3}\)
D
\(\frac{1}{5}\)
correct option: c
\(\frac{6x^3 - 5x^2 + 1}{3x^2}\)
let y = 3x2
y = \(\frac{6x^3}{3x^2}\) - \(\frac{6x^2}{3x^2}\) + \(\frac{1}{3x^2}\)
Y = 2x - \(\frac{5}{3}\) + \(\frac{1}{3x^2}\)
\(\frac{dy}{dx}\) = 2 + \(\frac{1}{3}\)(-2)x-3
= 2 - \(\frac{2}{3x^3}\)
Users' Answers & Commentslet y = 3x2
y = \(\frac{6x^3}{3x^2}\) - \(\frac{6x^2}{3x^2}\) + \(\frac{1}{3x^2}\)
Y = 2x - \(\frac{5}{3}\) + \(\frac{1}{3x^2}\)
\(\frac{dy}{dx}\) = 2 + \(\frac{1}{3}\)(-2)x-3
= 2 - \(\frac{2}{3x^3}\)
33
\(\frac{d}{dx}\) cos(3x2 - 2x) is equal to
A
-sin(6x - 2)
B
-sin(3x2 - 2x)dx
C
(6x - 2) sin(3x2 - 2x)
D
-(6x - 2)sin(3x2 - 2x)
correct option: d
Users' Answers & Comments34
Integrate \(\frac{1}{x}\) + cos x with respect to x
A
-\(\frac{1}{x^2}\) + sin x + k
B
x + sin x - k
C
x - sin x + k
D
-\(\frac{1}{x^2}\) - sin x + k
correct option: c
Users' Answers & Comments35
If y = x(x4 + x + 1), evaluate ∫\(^{1}_{0}\) ydx
A
\(\frac{11}{12}\)
B
\(\frac{11}{16}\)
C
\(\frac{5}{6}\)
D
zero
correct option: d
Users' Answers & Comments36
\(\begin{array}{c|c} Age & 20 & 25 & 30 & 35 & 40 & 45\\
\hline Number of people & 3 & 5 & 1 & 1 & 2 & 3\end{array}\)
Find the median age of the frequency distribution in the table above.
Find the median age of the frequency distribution in the table above.
A
20
B
25
C
30
D
35
correct option: b
Users' Answers & Comments37
Find the difference between the range and the variance of the following set of numbers 4, 9, 6, 3, 2, 8, 10, 5, 6, 7 where \(\sum d^2\) = 60
A
2
B
3
C
4
D
6
correct option: a
Users' Answers & Comments38
In a basket of fruits, there are 6 grapes, 11 bananas and 13 oranges, if one fruit is chosen at random, what is the probability that the fruit is either a grape or a banana?
A
\(\frac{17}{30}\)
B
\(\frac{11}{30}\)
C
\(\frac{6}{30}\)
D
\(\frac{5}{30}\)
correct option: a
Pgrape or Pbanana = \(\frac{6}{30}\) + \(\frac{11}{30}\)
= \(\frac{17}{30}\)
Users' Answers & Comments= \(\frac{17}{30}\)
39
A number is selected at random between 10 and 20, both numbers inclusive. Find the probability that the number is an even number
A
\(\frac{5}{11}\)
B
\(\frac{1}{2}\)
C
\(\frac{6}{11}\)
D
\(\frac{7}{10}\)
correct option: c
Users' Answers & Comments40
Find the standard derivation of the following data -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5
A
2
B
3
C
\(\sqrt{10}\)
D
\(\sqrt{11}\)
correct option: c
x = \(\frac{\sum x}{N}\)
= \(\frac{0}{11}\)
= 0
\(\begin{array}{c|c} x & (x - x) & (x - x)^2 \\hline -5 & -5 & 25 \ -4 & -4 & 16 \-3 & -3 & 9 \ -2 & -2 & 4 \ -1 & -1 & 1\ 0 & 0 & 0\ 1 & 1 & 1\ 2 & 2 & 4\ 3 & 3 & 9\ 4 & 4 & 16 \5 & 5 & 25\ \hline & & 110\end{array}\)
S.D = \(\sqrt{\frac{\sum(x - x)^2}{\sum f}}\)
= \(\sqrt{\frac{110}{11}}\)
= \(\sqrt{10}\)
Users' Answers & Comments= \(\frac{0}{11}\)
= 0
\(\begin{array}{c|c} x & (x - x) & (x - x)^2 \\hline -5 & -5 & 25 \ -4 & -4 & 16 \-3 & -3 & 9 \ -2 & -2 & 4 \ -1 & -1 & 1\ 0 & 0 & 0\ 1 & 1 & 1\ 2 & 2 & 4\ 3 & 3 & 9\ 4 & 4 & 16 \5 & 5 & 25\ \hline & & 110\end{array}\)
S.D = \(\sqrt{\frac{\sum(x - x)^2}{\sum f}}\)
= \(\sqrt{\frac{110}{11}}\)
= \(\sqrt{10}\)