JAMB - Mathematics (1993)

1
Integrate \(\frac{1 - x}{x^3}\) with respect to x
Atbilde
(C)
\(\frac{1}{x} - \frac{1}{2x^2}\) + k
2
change 71₁₀ to base 8
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(A)
107₈
3
Evaluate \(\frac{3524}{0.05}\) correct to 3 significant figures
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(D)
70, 500
4
If 9\(^{(x - \frac{1}{2})} = 3^{x^2}\) Find the value of x
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(B)
1
5
Solve for y in the equation 10\(^y\) x 5\(^{(2y - 2)}\) x 4\(^{(y - 1)}\) = 1
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(C)
\(\frac{2}{3}\)
6
simplify \(\frac{1}{√3 - 2}\) - \(\frac{1}{√3 + 2}\)
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(D)
-4
7
If 2log₃ y + log₃ x² = 4, then y is
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(D)
\(\pm\) \(\frac{9}{x}\)
8
Solve without using tables log₅(62.5) - log₅(\(\frac{1}{2}\))
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(A)
3
9
If N225.00 yields N27.00 in x years simple interest at the rate of 4% per annum, find x
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(A)
3
10
If \(\sqrt{x^2 + 9}\) = x + 1, solve for x
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(B)
4
11
Make x the subject of the relation \(\frac{1 + ax}{1 - ax}\) = \(\frac{p}{q}\)
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(B)
\(\frac{p - q}{a(p + q)}\)
12
Which of the following is a factor of 15 + 7x - 2x²
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(C)
x - 5
13
Evaluate (x + \(\frac{1}{x}\) + 1)² - (x + \(\frac{1}{x}\) + 1)²
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(D)
4(1 + x)
14
Solve the following simultaneous equation for x. x² + y - 5 = 0, y - 7x + 3 = 0
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(D)
1, -8
15
Solve the following equation (3x - 2)(5x - 4) = (3x - 2)²
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(C)
\(\frac{2}{3}\), 1
16
If the function f is defined by f(x + 2) = 2x\(^2\) + 7x - 5, find f(-1)
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(B)
-8
17
Divide the expression x³ + 7x² - x - 7 by -1 + x²
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(D)
x + 7
18
Simplify \(\frac{1}{p}\) - \(\frac{1}{q}\) \(\div\) \(\frac{p}{q}\) - \(\frac{q}{p}\)
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(B)
\(\frac{-1}{p + q}\)
19
Solve the inequality y2 - 3y > 18
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(B)
y < -3 or y > 6
20
If x is negative, what is the range of values of x within which \(\frac{x + 1}{3}\) > \(\frac{1}{X + 3}\)
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(B)
-4 < x < -3
21
A binary operation \(\ast\) is defined on a set of real numbers by x \(\ast\) y = x^y for all real values of x and y. If x \(\ast\) 2 = x. Find the possible values of x
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(A)
0, 1
22
If k + 1; 2k - 1, 3k + 1 are three consecutive terms of a geometric progression, find the possible values of the common ratio
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(B)
-1, \(\frac{5}{3}\)
23
A man's initial salary is N540.00 a month and increases after each period of six months by N36.00 a month. Find his salary in the eighth month of the third year
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(C)
N720.00
24
A rectangular polygon has 150^o as the size of each interior angle. How many sides has the polygon?
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(A)
12
25
Calculate the length in cm. of the arc of a circle of diameter 8cm which subtends an angle of 22\(\frac{1}{2}\)o at the centre of the circle
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(D)
\(\frac{\pi}{2}\)
26
The three sides of an isosceles triangle are length of lengths (x + 3), (2x + 3), (2x - 3) respectively. Calculate x.
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(D)
6
27
find the radius of a sphere whose surface area is 154cm² (\(\pi = \frac{22}{7}\))
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(B)
3.50cm
28
Find the area of the sector of a circle with radius 3m, if the angle of the sector is 60^o
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(C)
4.7m²
29
The angle between latitudes 30^oS and 13^oN is
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(C)
43^o
30
If sin \(\theta\) = cos \(\theta\), find \(\theta\) between 0o and 360o
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(A)
45^o, 225^o
31
If two angles of a triangle are 30° each and the longest side is 10cm. Calculate the length of each of the other sides.
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(D)
\(\frac{10\sqrt{3}}{3}\)cm
32
Quantities in the proportions 1, 4, 6, 7 are to be represented in a pie chart. Calculate the angle of the sector with proportion 7
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(D)
140^o
33
The following marks were obtained by twenty students in an examination: 53, 30, 70, 84, 59, 43, 90, 20, 78, 48, 44, 60, 81, 73, 50, 37, 67, 68, 64, 52. Find the numbers of students who scored at least 50 marks
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(D)
14
34
\(\begin{array}{c|c} Weight(s) & 0 -10 & 10 - 20 & 20 - 30 & 40 - 50\\ \hline \text{Number of coconuts} & 10 & 27 & 19 & 6 & 2\end{array}\)
Estimate the mode of the frequency distribution above
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(C)
16.8g
35
The mean of the ages of ten secondary school pupils is 16 but when the age of their teacher is added to it the men becomes 19. Find the age of the teacher
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(D)
49
36
\(\begin{array}{c|c} Class & Frequency\\ \hline 1 - 5 & 2\\6 - 10 & 4\\11 - 15 & 5\\16 - 20 & 2 \\ 21 - 25 & 3\\26 - 30 & 2\\31 - 35 & 1\\36 - 40 & 1 \end{array}\)
Find the median of the observation in the table given
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(D)
14.5
37
A number is selected at random between 20 and 30, both numbers inclusive. Find the probability that the number is a prime
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(A)
\(\frac{2}{11}\)
38
Calculate the standard deviation of the following data: 7, 8, 9, 10, 11, 12, 13.
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(A)
2
39
The chances of three independent events X, Y, Z occurring are \(\frac{1}{2}\), \(\frac{2}{3}\), \(\frac{1}{4}\) respectively. What are the chances of Y and Z only occurring?
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(C)
\(\frac{1}{12}\)
40
The shaded portion in the venn diagram is
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(C)
x \(\cap\) y^o \(\cap\) z
41
The figure represents the graphs of y = x(2 - x) and y = (x - 1)(x - 3). What are the x-coordinates of P, Q and F respectively?
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(D)
1, 2, 3
42
PQRST is a regular pentagon and PQVU is a rectangle with U and V lying on TS and SR respectively as shown in the diagram. Calculate TUP
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(B)
54^o
43
In the diagram, PQRS is a circle with O as centre and PQ||RT. If RTS = 32°. Find PSQ
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(C)
58^o
44
In the diagram, O is the centre of the circle and POQ a diameter. If POR = 96o, find the value of ORQ.
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(B)
48^o
45
In the diagram, QP//ST:PQR = 34o qrs = 73o and Rs = RT. Find SRT
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(B)
102^o
46
In the figure, PT is tangent to the circle at U and QU/RS if TUR = 35º and SRU = 50º find x
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(A)
95^o
47
In the diagram, QPS = SPR, PR = 9cm. PQ = 4cm and QS = 3cm, find SR.
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(A)
6\(\frac{3}{4}\)cm
48
In the figure, the line segment ST is tangent to two circles at S and T. O and Q are the centres of the circles wih OS = 5cm. QT = 2cm and OR = 14cm. Find ST
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(B)
12.9cm
49
In the figure, the area of the square of the square PQRS is 100cm². If the ratio of the area of the square TUYS to the area of the area of the square XQVU is 1 : 16, Find YR
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(C)
8cm
50
From the figure, calculate TH in centimeters
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(B)
\(\frac{5}{\sqrt{3} - 1}\)