2000 - JAMB Mathematics Past Questions and Answers - page 4
31
If the mean of the numbers 0, (x+2), (3x+6), and (4x+8) is 4, find their mean deviation.
A
zero
B
2
C
3
D
4
correct option: c
Mean = {0 + (x+2) + (3x+6) + (4x+8)}/4 = 4
=> 0 + (x+2) + (3x+6) + (4x+8) = 16
8x + 16 = 16
x = 0
Now prepare a table showing the deviation of each of 0, (x+2), (3x+6) and (4x+8), adding the deviations will give 12.
Thus M.D = 12/4 = 3
Users' Answers & Comments=> 0 + (x+2) + (3x+6) + (4x+8) = 16
8x + 16 = 16
x = 0
Now prepare a table showing the deviation of each of 0, (x+2), (3x+6) and (4x+8), adding the deviations will give 12.
Thus M.D = 12/4 = 3
32
In how many ways can the word MATHEMATICS be arranged?
A
11!/(9! 2!)
B
11!/(9! 2! 2!)
C
11!/(2! 2! 2!)
D
11!/(2! 2!)
correct option: c
Number of letter in MATHEMATICS = 11
Number of letter M = 2
Number of letter E = 2
Number of letter A = 2
Arrangement = 11!/(2! 2! 2!) ways
Users' Answers & CommentsNumber of letter M = 2
Number of letter E = 2
Number of letter A = 2
Arrangement = 11!/(2! 2! 2!) ways
33
Given that the various faces of a fair dice 1, 2, 3, 4, 5, 6 appeared 30, 43, 54, 40, 41, 32 times respectively in a single toss. Picture the figures as being represented in a simple table with number (X) against frequency (f).
If a pie chart is used to depict the data, the angle corresponding to 4 is?
If a pie chart is used to depict the data, the angle corresponding to 4 is?
A
10°
B
16°
C
40°
D
60°
correct option: d
Angle corresponding to 4 is 40/240 x 360/1 = 60°
Note that total angle in a circle is 360°.
Note also that sum of the frequencies given is 240.
Users' Answers & CommentsNote that total angle in a circle is 360°.
Note also that sum of the frequencies given is 240.
34
If U = {x : x is an integer and 1 \(\leq\) x \(\leq\) 20
E1 = {x : x is a multiple of 3}
E2 = {x : x is a multiple of 4}
and an integer is picked at random from U, find the probability that it is not in E2
E1 = {x : x is a multiple of 3}
E2 = {x : x is a multiple of 4}
and an integer is picked at random from U, find the probability that it is not in E2
A
3/4
B
3/10
C
1/4
D
1/20
correct option: a
U = {1, 2, 3, 4, 5,..., 20}
E1 = {3, 6, 9, 12, 15, 18}
E2 = {4, 8, 12, 16, 20}
P(E1) = 5/20
P(not E1) = 1 - (5/20) = 15/20 = 3/4
Users' Answers & CommentsE1 = {3, 6, 9, 12, 15, 18}
E2 = {4, 8, 12, 16, 20}
P(E1) = 5/20
P(not E1) = 1 - (5/20) = 15/20 = 3/4
35
The variance of x, 2x, 3x, 4x and 5x is
A
x√2
B
2x2
C
x2
D
3x
correct option: b
Hint: prepare a three-columned table, one for (x), another for the (deviation), and the last for the (squared-deviation).
Sum of (x) = 15x, algebraic sum of (deviation) = zero (0)
Sum of (squared-deviation) = 10x2
Variance = ∑(squared-deviation)/n = 10x2/5 = 2x2
Users' Answers & CommentsSum of (x) = 15x, algebraic sum of (deviation) = zero (0)
Sum of (squared-deviation) = 10x2
Variance = ∑(squared-deviation)/n = 10x2/5 = 2x2
36
Find the sum of the range and the mode of the set of numbers 10, 9, 10, 9, 8, 7, 7, 10, 8, 10, 8, 4, 6, 9, 10, 9, 10, 9, 7, 10, 6, 5
A
16
B
14
C
12
D
10
correct option: a
Range = Highest - lowest number => 10-4 = 6
Mode is the number with highest occurrence => Mode = 10
Sum = 6 + 10 = 16
Users' Answers & CommentsMode is the number with highest occurrence => Mode = 10
Sum = 6 + 10 = 16
37
In how many ways can a delegation of 3 be chosen from among 5 men and 3 women, if at least one man and at least one woman must be included?
A
15
B
28
C
30
D
45
correct option: d
No of ways of choosing 1 man, 2 women = 5C1 x 3C2
No of ways of choosing 2 men, 1 woman = 5C2 x 3C1
Summing, => (5C1 x 3C2) + (5C2 x 3C1) = 15 + 30 = 45
Users' Answers & CommentsNo of ways of choosing 2 men, 1 woman = 5C2 x 3C1
Summing, => (5C1 x 3C2) + (5C2 x 3C1) = 15 + 30 = 45
38
A function f(x) passes through the origin and its first derivative is 3x + 2. What is f(x)?
A
y = (3x2/)2 + 2x
B
y = (3x2)/2 + x
C
y = 3x2 + (x/2)
D
y = 3x2 +2x
correct option: a
Hints:
1. Integrate the given first derivative of f(x) at the boundaries, (0,0)
Then solve accordingly to get f(x) = y = (3x2/)2 + 2x
Users' Answers & Comments1. Integrate the given first derivative of f(x) at the boundaries, (0,0)
Then solve accordingly to get f(x) = y = (3x2/)2 + 2x
39
The expression ax2 + bx + c equals 5 at x = 1. If its derivative is 2x + 1, what are the values of a, b, c respectively?
A
1, 3, 1
B
1, 2, 1
C
2, 1, 1
D
1, 1, 3
correct option: d
At x = 1, substituting x = 1 in the equation: ax2 + bx + c = 5;
f(1) => a + b + c = 5 .....(1)
Taking the first derivative of f(x) in the original equation gives dy/dx = 2ax + b = 2x + 1 (given)....(2)
From (2),=> b = 1, and 2ax = 2x, => a = 1.
substituting into (1) 1 + 1 + c = 5, => c = 5 - 2 = 3
Thus a = 1, b = 1 and c = 3
Users' Answers & Commentsf(1) => a + b + c = 5 .....(1)
Taking the first derivative of f(x) in the original equation gives dy/dx = 2ax + b = 2x + 1 (given)....(2)
From (2),=> b = 1, and 2ax = 2x, => a = 1.
substituting into (1) 1 + 1 + c = 5, => c = 5 - 2 = 3
Thus a = 1, b = 1 and c = 3
40
Evaluate 5-3log52 x 22log23
A
8
B
11/8
C
2/5
D
1/8
correct option: b
5-3log52 x 22log23
i Let -3log52 = p => log52-3 = p
∴2-3 = 5p
∴5-3log52 = 5log52-3 = 5p
ii 22log23 = q => log532 = q
∴32 = 2q
∴222log23 = 2q
= 32 = 9
i x ii = 2-3 x 9 = 1/23 x 9
= 1/8 x 9
= 9/8 = 11/8
Users' Answers & Commentsi Let -3log52 = p => log52-3 = p
∴2-3 = 5p
∴5-3log52 = 5log52-3 = 5p
ii 22log23 = q => log532 = q
∴32 = 2q
∴222log23 = 2q
= 32 = 9
i x ii = 2-3 x 9 = 1/23 x 9
= 1/8 x 9
= 9/8 = 11/8