JAMB - Mathematics (2000)

1
Let P = {1, 2, u, v, w, x}; Q = {2, 3, u, v, w, 5, 6, y} and R = {2, 3, 4, v, x, y}.

Determine (P-Q) ∩ R
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(C)
{x}
2
If the population of a town was 240,000 in January 1998 and it increased by 2% each year, what would be the population of the town in January, 2000?
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(B)
249,696
3
If \(\frac{(2\sqrt{3}-\sqrt{2})}{(\sqrt{3}+2\sqrt{2})} = m +n\sqrt{6}\), find the values of m and n respectively.
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(B)
-2, 1
4
In a youth club with 94 members, 60 like modern music, and 50 like traditional music. The number of members who like both traditional and modern music is three times those who do not like any type of music. How many members like only one type of music?
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(C)
62
5
Evaluate \(\frac{(2.813 \times 10^{-3} \times 1.063)}{(5.637 \times 10^{-2})}\) reducing each number to two significant figures and leaving your answer in two significant figures.
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(B)
0.055
6
A man wishes to keep his money in a savings deposit at 25% compound interest so that after three years he can buy a car for N150,000. How much does he need to deposit?
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(D)
N76,800.00
7
If 314\(_{10}\) - 256\(_7\) = 340\(_x\), find x.
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(A)
7
8
Simplify \(\frac{3(2^{n+1}) - 4(2^{n-1})}{2^{n+1} - 2^n}\)
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(C)
4
9
If \(P344_{6} - 23P2_{6} = 2PP2_{6}\), find the value of the digit P.
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(D)
5
10
A binary operation * is defined by a * b = a\(^b\). If a * 2 = 2 - a, find the possible values of a.
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(D)
1, -2
11
The 3rd term of an A.P is 4x - 2y and the 9th term is 10x - 8y. Find the common difference.
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(C)
x - y
12
Find the inverse of p under the binary operation * defined by p*q = p + q - pq, where p and q are real numbers and zero is the identity
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(C)
p/(p-1)
13
Evaluate (\(\frac{1}{2} - \frac{1}{4} + \frac{1}{8} - \frac{1}{16} + ...) -1\)
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(C)
-2/3
14
if (x - 1), (x + 1) and (x - 2) are factors of the polynomial ax\(^3\) + bx\(^2\) + cx - 1, find a, b, c in that order.
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(A)
-1/2, 1., 1/2
15
A trader realizes 10x - x\(^2\) naira profit from the sale of x bags on corn. How many bags will give him the desired profit?
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(B)
5
16
Solve the inequality 2 - x > x\(^2\).
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(D)
-2 < x < 1
17
If α and β are the roots of the equation 3x\(^2\) + 5x - 2 = 0, find the value of 1/α + 1/β
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(D)
5/2
18
A frustrum of pyramid with square base has its upper and lower sections as squares of sizes 2m and 5m respectively and the distance between them 6m. Find the height of the pyramid from which the frustrum was obtained.
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(D)
10.0 m
19
P is a point on one side of the straight line UV and P moves in the same direction as UV. If the straight line ST is on the locus of P and angle VUS = 50°, find angle UST.
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(B)
130°
20
An equilateral triangle of side √3cm is inscribed in a circle. Find the radius of the circle.
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(C)
1 cm
21
3y = 4x - 1 and Ky = x + 3 are equations of two straight lines. If the two lines are perpendicular to each other, find K.
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(A)
-\(\frac{4}{3}\)
22
if P and Q are fixed points and X is a point which moves so that XP = XQ, the locus of X is
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(D)
the perpendicular bisector of PQ
23
In a regular polygon, each interior angle doubles its corresponding exterior angle. Find the number of sides of the polygon.
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(B)
6
24
A predator moves in a circle of radius √2 centre (0,0), while a prey moves along the line y = x. If 0 \(\leq\) x \(\leq\) 2, at which point(s) will they meet?
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(A)
(1,1) only
25
Find the value of \(\int^{\pi}_{0}\frac{cos^{2}\theta-1}{sin^{2}\theta}d\theta\)
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(D)
-π
26
If y = 2xcos2x - sin2x, find \(\frac{dy}{dx}\) when x = \(\frac{π}{4}\)
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(B)
-π
27
A bowl is designed by revolving completely the area enclosed by y = x2 - 1, y = 3 and x ≥ 0 around the y-axis. What is the volume of this bowl?
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(B)
15π/2 cubic units
28
If the volume of a hemisphere is increasing at a steady rate of 18π m\(^{3}\) s\(^{-1}\), at what rate is its radius changing when its is 6m?
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(C)
0.25 m/s
29
X and Y are two events. The probability of X or Y is 0.7 and that of X is 0.4. If X and Y are independent, find the probability of Y.
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(A)
0.30
30
If the mean of the numbers 0, (x+2), (3x+6), and (4x+8) is 4, find their mean deviation.
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(C)
3
31
In how many ways can the word MATHEMATICS be arranged?
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(C)
11!/(2! 2! 2!)
32
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?
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(D)
60°
33
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
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(A)
3/4
34
The variance of x, 2x, 3x, 4x and 5x is
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(B)
2x²
35
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
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(A)
16
36
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?
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(D)
45
37
A function f(x) passes through the origin and its first derivative is 3x + 2. What is f(x)?
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(A)
y = \(\frac{3x^2}{2}\) + 2x
38
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?
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(D)
1, 1, 3
39
Evaluate 5^-3log₅2 x 2^2log₂3
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(B)
1¹/₈
40
In the diagram above, if ∠RPS = 50^o, ∠RPQ = 30^o and PQ = QR, find the value of ∠PRS.
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(B)
70^o
41
In the diagram, EFGH is a circle centre O. FH is a diameter and GE is a chord which meets FH at right angle at the point N. If NH = 8cm and EG = 24cm, calculate FH
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(B)
26cm
42
If the diagram is the graph of y = x\(^2\), the shaded area is
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(B)
\(\frac{128}{3}\) square units
43
The cumulative frequency curve represents the ages of ages of students in a school. What age group do 70% of the students belongs?
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(A)
17.5 - 20.5
44
Audu bought an article for N50,000 and sold it to Femi at a loss of x%. Femi later sold the article to Oche at a profit of 40%. If Femi made a profit of N10,000, find the value of x.
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(B)
50
45
A ship sails a distance of 50km in the direction S50ºE and then sails in the distance of 50km in the direction N40ºE. Find the bearing of the ship from its original position.
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(A)
S90\(^0\)E