2008 - JAMB Mathematics Past Questions and Answers - page 4
31
Find the derivative of \(y=\frac{x^7 - x^5}{x^4}\)
A
x(x2-1)
B
3x(x2-1)
C
3x2-1
D
7x6-5x4
correct option: c
\(y=\frac{x^7 - x^5}{x^4}\\
y = \frac{x^7}{x^4} \div \frac{x^5}{x^4}\\
y = x^3 - x \\
\frac{dy}{dx} = 3x^2 - 1\)
Users' Answers & Comments32
Differentiate sin x - x cos x
A
x cos x
B
x sin x
C
-x cos x
D
-x sin x
correct option: b
sin x - x cos x
dy/dx = cos x - [1.cos x + x -sin x]
= co x - [cos x - x sin x]
= cos x - cos x + x sin x
= x sin x
Users' Answers & Commentsdy/dx = cos x - [1.cos x + x -sin x]
= co x - [cos x - x sin x]
= cos x - cos x + x sin x
= x sin x
33
Find the minimum value of the function y = x(1+x)
A
-1/4
B
-1/2
C
1/4
D
1/2
correct option: a
y = x(1+x)
= x + x2
dy/dx = 1 + 2x
As dy/dy → 0
1 + 2x = 0
2x = -1
X = -1/2
Y = x(1+x)
= -1/2(1 - 1/2) at x = -1/2
= -1/2(1/2)
= -1/4
Users' Answers & Comments= x + x2
dy/dx = 1 + 2x
As dy/dy → 0
1 + 2x = 0
2x = -1
X = -1/2
Y = x(1+x)
= -1/2(1 - 1/2) at x = -1/2
= -1/2(1/2)
= -1/4
34
Evaluate \(\int_1 ^2(6x^2-2x)dx\)
A
16
B
13
C
12
D
11
correct option: d
\(\int_1 ^2(6x^2-2x)dx=[\frac{6x^3}{3}-\frac{2x^2}{2}]_1 ^2\\
= [2x^3 - x^2]_1^2\)
= [2(2)3 - (2)2] – [2(1)3 - (1)2]
= [16-4] – [2-1]
= 12 – 1
= 11
Users' Answers & Comments= [2(2)3 - (2)2] – [2(1)3 - (1)2]
= [16-4] – [2-1]
= 12 – 1
= 11
35
Evaluate \(\int^{\frac{\pi}{2}} _{\frac{-\pi}{2}} cos x dx\)
A
zero
B
1
C
2
D
3
correct option: c
\(\int^{\frac{\pi}{2}} _{\frac{-\pi}{2}} cos x dx = [sinx]^{\frac{\pi}{2}} _{\frac{-\pi}{2}}\\
=sin\frac{\pi}{2} - sin\frac{-\pi}{2}\)
= sin90 – sin-90
= sin90 – sin270
= 1 – (-1)
= 1+1
= 2
Users' Answers & Comments= sin90 – sin-90
= sin90 – sin270
= 1 – (-1)
= 1+1
= 2
36
On a pie chart there s=are six sectors of which four angles are 30o, 45o, 60o, 90o and the remaining two angles are in the ratio 2:1. Find the smallest angles of the remaining two angles
A
15o
B
30o
C
45o
D
60o
correct option: c
30 + 45 + 60 + 90 + 2x + x = 360o
225 + 3x = 360
3x = 360 - 225
3x = 135
x = 45o
Users' Answers & Comments225 + 3x = 360
3x = 360 - 225
3x = 135
x = 45o
37
A
1/4
B
1/3
C
2/3
D
3/4
38
What is the mean of the data t, 2t-1, t-2, 2t-1, 4t and 2t+2?
A
2t
B
2t-1
C
2/3t+1
D
2t-1/3
correct option: d
\(Mean = \frac{t+2t-1+t-2+2t-14t+2t+2}{6}\\
Mean = \frac{12t-2}{6}\\
=\frac{2(6t-1)}{6}\\
=\frac{6t-1}{3}\\
=\frac{6t}{3}- \frac{1}{3}\\
=2t-\frac{1}{3}\)
Users' Answers & Comments39
Find the median of 4, 1, 4, 1, 0, 4, 4, 2 and 0
A
zero
B
1
C
2
D
4
correct option: c
4, 4, 1, 0, 4, 4, 2, 0
Arrange in ascending order:
0, 0, 1, 1, 2, 4, 4, 4, 4
Position of median = N+1 / 2 = 9+1 / 2 = 5th
Median = 2
Users' Answers & CommentsArrange in ascending order:
0, 0, 1, 1, 2, 4, 4, 4, 4
Position of median = N+1 / 2 = 9+1 / 2 = 5th
Median = 2
40
If x > 0, find the range of number x-3, 3x+2,x-1, 4x, 2x-1, x-2, 2x-2, 3x and 3x+1
A
3x+3
B
3x+1
C
2x+5
D
2x+1
correct option: c
x-3, 3x+2,x-1, 4x, 2x-1, x-2, 2x-2, 3x, 3x+1
Range = 3x+2 - (x-3)
= 3x+2 - x - 3
= 2x + 5
Users' Answers & CommentsRange = 3x+2 - (x-3)
= 3x+2 - x - 3
= 2x + 5