2006 - JAMB Mathematics Past Questions & Answers - page 1

1
The table above shows the scores of a group of students in a physics test. If the mode is m and the number of students who scored 4 or more is n, what is (n, m)?
A
(33, 4)
B
(22, 4)
C
(33, 12)
D
(12, 4)
CORRECT OPTION: a
2
A final examination requires that a student answer any 4 out of 6 questions. In how many ways can this be done?
A
15
B
20
C
30
D
45
CORRECT OPTION: a
The question will be answered in
\(^5C_4 = \frac{6!}{(6-4)!4!}\=\frac{6!}{2!4!}\=\frac{6\times5\times4!}{2\times1\times4!}\=15\hspace{1mm}ways\)
3
If the mean of five consecutive integers is 30, find the largest of the numbers
A
28
B
30
C
32
D
34
CORRECT OPTION: c
Let the consecutive numbers be a, a+1, a+2, a+3, a+4
Mean = \(\frac{(a+a+1+a+2+a+3+a+4)}{5}\\ 30 = \frac{5a+10}{5}\\ 30 \times 5 = 5a + 10\\ 5a = 150 - 10\\ 5a = 140\\ a = 28 \\ ∴ a + 4 = 28 + 4\\ = 32\)
4
A bag contains 5 black, 4 white and x red marbles. If the probability of picking a red marble is 2/3, find the value of x
A
8
B
10
C
4
D
6
CORRECT OPTION: d
Black = 5
White = 4
Red = x
Total = 9+x
P(red) = 2/3
x / (9+x) = 2/5
5x = 2(9+x)
5x = 18+2x
5x-2 = 18
3x = 18
x = 6
5
Find the variance of 2x, 2x-1 and 2x+1
A
2/3
B
2
C
√(2/3)
D
1
CORRECT OPTION: a
\(\sum x = 6x\\ \sum(x-\bar{x})^2 = 2\\ \bar{x} = \frac{\sum x}{n}\\ = \frac{6x}{3}\\ = 2x\\ Variance = \frac{\sum(x-\bar{x})^2}{n}\\ = \frac{2}{3}\)
6
The table above shows the distribution of recharge cards of four major GSM operators. What is the probability that a recharge card selected at random will be GTN or Qtel?
A
3/20
B
1/4
C
2/5
D
3/4
CORRECT OPTION: c
P(GTN) = 5/20
P(Qtel) = 3/20
∴P(GTN or Qtel) = (5/20) + (3/20)
= 8/20
= 2/5
7
The pie chart above shows the expenditure of a family whose income is N30,000. If the expenditure on food is twice that on housing and that on school fees is twice that on transport, how much does the family spend on food?
A
N 28 000
B
N 25 500
C
N15 000
D
N 12 500
CORRECT OPTION: d
Expenditure on housing = x
Expenditure on food = 2x
Expenditure on school fees = 90o
Expenditure on transport = 45o
x + 2x + 90 + 45 = 360o
3x + 135 = 360o
3x = 360 - 135
3x = 225
x = 225/3 = 75o
∴∠ for food = 2x = 2 * 75
= 150
360o = N30,000
1o = ?
1o = 30,000/360
150o = (30000/360) * (150/1)
= N12500
8
For what of n is n+1C3 = 4(nC3)?
A
6
B
5
C
4
D
3
CORRECT OPTION: d
\(^{n+1}C_3 = 4(^nC_3)\\frac{(n+1)!}{(n+1-3)!3!} = 4\left(\frac{n!}{(n-3)!3!}\right)\\frac{(n+1)n!}{(n-2)(n-3)!}=4\left(\frac{n!}{n-3!}\right)\=\frac{n+1}{n-2}=\frac{4}{1}\n+1 = 4(n-2)\n+1 = 4n-8\-3n = -9\\frac{-9}{-3}\n=3\)
9
The gradient of a curve is 2x + 7 and the curve passes through point (2, 0). find the equation of the curve.
A
y = x2 + 7x + 9
B
y = x2 + 7x - 18
C
y = x2 + 7x + 18
D
y = x2 + 14x + 11
CORRECT OPTION: b
dy/dx = 2x + 7
y = ∫2x + 7
y = x2 + 7x + C at (2,0)
0 = 22 + 7(2) + C
0 = 4 + 14 + C
0 = 18 + C
C = -18
∴ The equation is y = x2 + 7x - 18
10
Differentiate (x2 - 1/x)2 with respect to x
A
4x2 - 4x - 2/x
B
4x2 - 2 + 2/x3
C
4x2 - 2 - 2/x3
D
4x2 - 3x + 2/x
CORRECT OPTION: c
y = (x2 - 1/x)2
y = (x2 - 1/x)(x2 - 1/x)
y = x4 - x - x + 1/x2
y = x4 - 2x + 1/x2
y= x4 - 2x + x-2
dy/dx = 4x2 - 2 - 2x-3
= 4x2 - 2 - 2/x3
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