JAMB - Mathematics (1993)

1
Integrate \(\frac{1 - x}{x^3}\) with respect to x
คำตอบ
(C)
\(\frac{1}{x} - \frac{1}{2x^2}\) + k
2
change 71₁₀ to base 8
คำตอบ
(A)
107₈
3
Evaluate \(\frac{3524}{0.05}\) correct to 3 significant figures
คำตอบ
(D)
70, 500
4
If 9\(^{(x - \frac{1}{2})} = 3^{x^2}\) Find the value of x
คำตอบ
(B)
1
5
Solve for y in the equation 10\(^y\) x 5\(^{(2y - 2)}\) x 4\(^{(y - 1)}\) = 1
คำตอบ
(C)
\(\frac{2}{3}\)
6
simplify \(\frac{1}{√3 - 2}\) - \(\frac{1}{√3 + 2}\)
คำตอบ
(D)
-4
7
If 2log₃ y + log₃ x² = 4, then y is
คำตอบ
(D)
\(\pm\) \(\frac{9}{x}\)
8
Solve without using tables log₅(62.5) - log₅(\(\frac{1}{2}\))
คำตอบ
(A)
3
9
If N225.00 yields N27.00 in x years simple interest at the rate of 4% per annum, find x
คำตอบ
(A)
3
10
If \(\sqrt{x^2 + 9}\) = x + 1, solve for x
คำตอบ
(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
คำตอบ
(C)
x - 5
13
Evaluate (x + \(\frac{1}{x}\) + 1)² - (x + \(\frac{1}{x}\) + 1)²
คำตอบ
(D)
4(1 + x)
14
Solve the following simultaneous equation for x. x² + y - 5 = 0, y - 7x + 3 = 0
คำตอบ
(D)
1, -8
15
Solve the following equation (3x - 2)(5x - 4) = (3x - 2)²
คำตอบ
(C)
\(\frac{2}{3}\), 1
16
If the function f is defined by f(x + 2) = 2x\(^2\) + 7x - 5, find f(-1)
คำตอบ
(B)
-8
17
Divide the expression x³ + 7x² - x - 7 by -1 + x²
คำตอบ
(D)
x + 7
18
Simplify \(\frac{1}{p}\) - \(\frac{1}{q}\) \(\div\) \(\frac{p}{q}\) - \(\frac{q}{p}\)
คำตอบ
(B)
\(\frac{-1}{p + q}\)
19
Solve the inequality y2 - 3y > 18
คำตอบ
(B)
y < -3 or y > 6
20
If x is negative, what is the range of values of x within which \(\frac{x + 1}{3}\) > \(\frac{1}{X + 3}\)
คำตอบ
(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
คำตอบ
(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
คำตอบ
(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
คำตอบ
(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
คำตอบ
(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.
คำตอบ
(D)
6
27
find the radius of a sphere whose surface area is 154cm² (\(\pi = \frac{22}{7}\))
คำตอบ
(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
คำตอบ
(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
คำตอบ
(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
คำตอบ
(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
คำตอบ
(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
คำตอบ
(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
คำตอบ
(A)
\(\frac{2}{11}\)
38
Calculate the standard deviation of the following data: 7, 8, 9, 10, 11, 12, 13.
คำตอบ
(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
คำตอบ
(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?
คำตอบ
(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
คำตอบ
(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.
คำตอบ
(B)
48^o
45
In the diagram, QP//ST:PQR = 34o qrs = 73o and Rs = RT. Find SRT
คำตอบ
(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
คำตอบ
(A)
95^o
47
In the diagram, QPS = SPR, PR = 9cm. PQ = 4cm and QS = 3cm, find SR.
คำตอบ
(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
คำตอบ
(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
คำตอบ
(B)
\(\frac{5}{\sqrt{3} - 1}\)