2004 - JAMB Mathematics Past Questions and Answers - page 2
11
Find the derivatives of (2 + 3x)(1 - x) with respect to x
A
6
B
-3
C
1 - 6x
D
6x - 1
correct option: c
y = (2 + 3x)(i - x)
y = 2 - 2x + 3x - 3x2
y = 2 + x - 3x2
dy/dxb = 1 - 6x
Users' Answers & Commentsy = 2 - 2x + 3x - 3x2
y = 2 + x - 3x2
dy/dxb = 1 - 6x
12
What is the rate of change of the volume v of a hemisphere with respect to its radius r when r = 2?
A
8π
B
16π
C
2π
D
4π
13
Find the derivatives of the function y = 2x2(2x - 1) at the point x = -1
A
18
B
16
C
-4
D
-6
correct option: b
y = 2x2(2x - 1)
y = 4x3 - 2x2
dy/dx = 12x2 - 4x
at x = -1
dy/dx = 12(-1)2 - 4(-1)
= 12 + 4
= 16
Users' Answers & Commentsy = 4x3 - 2x2
dy/dx = 12x2 - 4x
at x = -1
dy/dx = 12(-1)2 - 4(-1)
= 12 + 4
= 16
14
Evaluate \(\int_{1}^{3}(X^2 - 1)dx\)
A
\(\frac{2}{3}\)
B
\(-\frac{2}{3}\)
C
\(-6\frac{2}{3}\)
D
\(6\frac{2}{3}\)
correct option: d
\(\int_{1}^{3}(x^2 - 1)dx=\left[\frac{1}{3}x^2 - x\right] ^{3}_{1}\=(9-3)-(\frac{1}{3}-1)\=6-\left(-\frac{2}{3}\right)\=6+\frac{2}{3}=6\frac{2}{3}\)
Users' Answers & Comments15
Some white balls put in a basket containing twelve red balls and sixteen black balls. If the probability of picking a white balls from the baskets is 3/7, how many white balls were introduced?
A
12
B
21
C
28
D
32
correct option: b
Number of white balls = x
Number of red balls = 12
Number of black balls = 16
Total number of balls = 28 + x
P(white balls) = 3/7
But P(white balls) \(= \frac{x}{28+x}\\ = \frac{3}{7} = \frac{x}{28+x}\\ 3(28 + x) = 7x\\ 84 + 3x = 7x\\ 7x - 3x = 84\\ 4x = 84\\ x = 21\)
Users' Answers & CommentsNumber of red balls = 12
Number of black balls = 16
Total number of balls = 28 + x
P(white balls) = 3/7
But P(white balls) \(= \frac{x}{28+x}\\ = \frac{3}{7} = \frac{x}{28+x}\\ 3(28 + x) = 7x\\ 84 + 3x = 7x\\ 7x - 3x = 84\\ 4x = 84\\ x = 21\)
16
find the mean deviation of 1, 2, 3 and 4
A
2.5
B
2.0
C
1.0
D
1.5
correct option: c
X = 1, 2, 3, 4; ∑X = 10
x = ∑X/n = 10/4 = 2.5
X - x = -1.5, -0.5, 0.5, 1.5
lX - xl = 1.5, 0.5, 0.5, 1.5; ∑lX - xl = 4.0
mean deviation = (∑lX - xl)/n
= 4.0/4
= 1.0
Users' Answers & Commentsx = ∑X/n = 10/4 = 2.5
X - x = -1.5, -0.5, 0.5, 1.5
lX - xl = 1.5, 0.5, 0.5, 1.5; ∑lX - xl = 4.0
mean deviation = (∑lX - xl)/n
= 4.0/4
= 1.0
17
What is the probability of obtaining a 5?
A
1/5
B
1/2
C
1/6
D
1/4
correct option: a
Number of times 5 was obtained = 20
P(obtaining 5) = 20/100
= 1/5
Users' Answers & CommentsP(obtaining 5) = 20/100
= 1/5
18
A
6000 tonnes
B
1500 tonnes
C
1200 tonnes
D
9000 tonnes
correct option: c
Sectorial angle of beans = 360 - (150 + 90 + 60)
= 360 -300
= 60o
if 150o represents 3000 tonnes
1o 3000/150
60o will represents (3000/150) * (60/1)
= 1200 tonnes
Users' Answers & Comments= 360 -300
= 60o
if 150o represents 3000 tonnes
1o 3000/150
60o will represents (3000/150) * (60/1)
= 1200 tonnes
19
In how many ways can2 students be selected from a group of 5 students in a debating competition?
A
25 ways
B
10 ways
C
15 ways
D
20 ways
correct option: b
\(In\hspace{1mm} ^{5}C_{2}\hspace{1mm}ways\hspace{1mm}=\frac{5!}{(5-2)!2!}\=\frac{5!}{3!2!}\=\frac{5\times4\times3!}{3!\times2\times1}\=10\hspace{1mm}ways\)
Users' Answers & Comments20
The mean age of a group of students is 15 years. When the age of a teacher, 45 years old, is added to the age of the students, the mean of their ages becomes 18 years. Find the number of the students in the group
A
9
B
7
C
42
D
15
correct option: a
Let the number of students = x
Total age of the students = 15x
Total age including age of the teacher = 15x + 45
Mean of their ages; (15x + 45)/(x + 1) = 18
= 15x + 45 = 18(x + 1)
= 15x + 45 = 18x + 18
= 18x - 15x = 45 - 18
= 3x = 27
x = 9
Users' Answers & CommentsTotal age of the students = 15x
Total age including age of the teacher = 15x + 45
Mean of their ages; (15x + 45)/(x + 1) = 18
= 15x + 45 = 18(x + 1)
= 15x + 45 = 18x + 18
= 18x - 15x = 45 - 18
= 3x = 27
x = 9