1999 - JAMB Mathematics Past Questions and Answers - page 3
21
Find the tangent to the acute angle between the lines 2x+y = 3 and 3x-2y = 5.
A
-7/4
B
7/8
C
7/4
D
7/2
correct option: c
Users' Answers & Comments22
From a point P, the bearings of two points Q and R are N670W and N230E respectively. If the bearing of R from Q is N680E and PQ = 150m, calculate PR
A
120m
B
140m
C
150m
D
160m
correct option: c
Users' Answers & Comments23
Find the equation of the locus of a point P(x,y) such that PV = PW, where V = (1,1) and W = (3,5)
A
2x + 2y = 9
B
2x + 3y = 8
C
2x + y = 9
D
x + 2y = 8
correct option: d
The locus of a point P(x,y) such that PV = PW where V = (1,1) and W = (3,5). This means that the point P moves so that its distance from V and W are equidistance.
PV = PW
\(\sqrt{(x-1)^{2} + (y-1)^{2}} = \sqrt{(x-3)^{2}
+ (y-5)^{2}}\).
Squaring both sides of the equation,
(x-1)2 + (y-1)2 = (x-3)2 + (y-5)2.
x2-2x+1+y2-2y+1 = x2-6x+9+y2-10y+25
Collecting like terms and solving, x + 2y = 8.
Users' Answers & CommentsPV = PW
\(\sqrt{(x-1)^{2} + (y-1)^{2}} = \sqrt{(x-3)^{2}
+ (y-5)^{2}}\).
Squaring both sides of the equation,
(x-1)2 + (y-1)2 = (x-3)2 + (y-5)2.
x2-2x+1+y2-2y+1 = x2-6x+9+y2-10y+25
Collecting like terms and solving, x + 2y = 8.
24
Find the area bounded by the curve y = x(2-x). The x-axis, x = 0 and x = 2.
A
4 sq units
B
2 sq units
C
\(\frac{4}{3}sq\hspace{1 mm}units\)
D
\(\frac{1}{3}sq\hspace{1 mm}units\)
correct option: c
\(y = x(2-x) \Rightarrow y= 2x - x^{2};
\int^{2}_{0}(2x-x^{2} = (x^{2}-\frac{x{3}}{3})^{2}\\ solving further gives (4 - \frac{1}{3} * 8) - (0) = \frac{4}{3} sq\hspace{1 mm}unit\)
Users' Answers & Comments\int^{2}_{0}(2x-x^{2} = (x^{2}-\frac{x{3}}{3})^{2}\\ solving further gives (4 - \frac{1}{3} * 8) - (0) = \frac{4}{3} sq\hspace{1 mm}unit\)
25
Evaluate: \(\int^{z}_{0}(sin x - cos x) dx \hspace{1mm}
Where\hspace{1mm}letter\hspace{1mm}z = \frac{\pi}{4}. (\pi = pi)\)
Where\hspace{1mm}letter\hspace{1mm}z = \frac{\pi}{4}. (\pi = pi)\)
A
\(\sqrt{2 +1}\)
B
\(\sqrt{2 }-1\)
C
\(-\sqrt{2 }-1\)
D
\(1-\sqrt{2}\)
correct option: b
Users' Answers & Comments26
Find the volume of solid generated when the area enclosed by y = 0, y = 2x, and x = 3 is rotated about the x-axis.
A
81 π cubic units
B
36 π cubic units
C
18 π cubic units
D
9 π cubic units
correct option: b
\(y = 2x \ V = \int\pi^{2}dy \ but\hspace{1mm}y = 2x \ V = \int\pi4x^{2}dx\ V = \frac{4(3)^{3}\pi}{3}-\frac{4(3)^{3}\pi}{3}\V=\frac{4*27\pi}{3} = 36\pi \hspace{1mm}cubic\hspace{1mm}units\)
Users' Answers & Comments27
What is the derivative of t2 sin (3t - 5) with respect to t?
A
6t cos (3t - 5)
B
2t sin (3t - 5) - 3t2 cos (3t - 5)
C
2t sin (3t - 5) + 3t2 cos (3t - 5)
D
2t sin (3t - 5) + t2 cos 3t
correct option: c
t2 sin (3t - 5) = 2t sin ( 3t - 5) + t2 x 3 cos (3t - 5) = 2t sin (3t - 5) + 3t2 cos (3t - 5).
Detailed answer below was provided by Ifechuks, a female prospective student of Okopoly.
Users' Answers & CommentsDetailed answer below was provided by Ifechuks, a female prospective student of Okopoly.
28
Evaluate \(\int^{1}_{-2}(x-1)^{2}dx\)
A
\(\frac{-10}{3}\)
B
7
C
9
D
11
correct option: c
Users' Answers & Comments29
Find the value of x for which the function y = x3 - x has a minimum value.
A
\(-\sqrt{3}\)
B
\(-\sqrt{\frac{3}{3}}\)
C
\(\sqrt{\frac{3}{3}}\)
D
\(\sqrt{3}\)
correct option: c
Users' Answers & Comments30
If the minimum value of y = 1 + hx - 3x2 is 13, find h.
A
13
B
12
C
11
D
10
correct option: b
Users' Answers & Comments