JAMB - Mathematics (1993)

1
Integrate \(\frac{1 - x}{x^3}\) with respect to x
პასუხი
(C)
\(\frac{1}{x} - \frac{1}{2x^2}\) + k
2
change 71₁₀ to base 8
პასუხი
(A)
107₈
3
Evaluate \(\frac{3524}{0.05}\) correct to 3 significant figures
პასუხი
(D)
70, 500
4
If 9\(^{(x - \frac{1}{2})} = 3^{x^2}\) Find the value of x
პასუხი
(B)
1
5
Solve for y in the equation 10\(^y\) x 5\(^{(2y - 2)}\) x 4\(^{(y - 1)}\) = 1
პასუხი
(C)
\(\frac{2}{3}\)
6
simplify \(\frac{1}{√3 - 2}\) - \(\frac{1}{√3 + 2}\)
პასუხი
(D)
-4
7
If 2log₃ y + log₃ x² = 4, then y is
პასუხი
(D)
\(\pm\) \(\frac{9}{x}\)
8
Solve without using tables log₅(62.5) - log₅(\(\frac{1}{2}\))
პასუხი
(A)
3
9
If N225.00 yields N27.00 in x years simple interest at the rate of 4% per annum, find x
პასუხი
(A)
3
10
If \(\sqrt{x^2 + 9}\) = x + 1, solve for x
პასუხი
(B)
4
11
Make x the subject of the relation \(\frac{1 + ax}{1 - ax}\) = \(\frac{p}{q}\)
პასუხი
(B)
\(\frac{p - q}{a(p + q)}\)
12
Which of the following is a factor of 15 + 7x - 2x²
პასუხი
(C)
x - 5
13
Evaluate (x + \(\frac{1}{x}\) + 1)² - (x + \(\frac{1}{x}\) + 1)²
პასუხი
(D)
4(1 + x)
14
Solve the following simultaneous equation for x. x² + y - 5 = 0, y - 7x + 3 = 0
პასუხი
(D)
1, -8
15
Solve the following equation (3x - 2)(5x - 4) = (3x - 2)²
პასუხი
(C)
\(\frac{2}{3}\), 1
16
If the function f is defined by f(x + 2) = 2x\(^2\) + 7x - 5, find f(-1)
პასუხი
(B)
-8
17
Divide the expression x³ + 7x² - x - 7 by -1 + x²
პასუხი
(D)
x + 7
18
Simplify \(\frac{1}{p}\) - \(\frac{1}{q}\) \(\div\) \(\frac{p}{q}\) - \(\frac{q}{p}\)
პასუხი
(B)
\(\frac{-1}{p + q}\)
19
Solve the inequality y2 - 3y > 18
პასუხი
(B)
y < -3 or y > 6
20
If x is negative, what is the range of values of x within which \(\frac{x + 1}{3}\) > \(\frac{1}{X + 3}\)
პასუხი
(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
პასუხი
(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
პასუხი
(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
პასუხი
(C)
N720.00
24
A rectangular polygon has 150^o as the size of each interior angle. How many sides has the polygon?
პასუხი
(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
პასუხი
(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.
პასუხი
(D)
6
27
find the radius of a sphere whose surface area is 154cm² (\(\pi = \frac{22}{7}\))
პასუხი
(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
პასუხი
(C)
4.7m²
29
The angle between latitudes 30^oS and 13^oN is
პასუხი
(C)
43^o
30
If sin \(\theta\) = cos \(\theta\), find \(\theta\) between 0o and 360o
პასუხი
(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.
პასუხი
(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
პასუხი
(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
პასუხი
(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
პასუხი
(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
პასუხი
(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
პასუხი
(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
პასუხი
(A)
\(\frac{2}{11}\)
38
Calculate the standard deviation of the following data: 7, 8, 9, 10, 11, 12, 13.
პასუხი
(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?
პასუხი
(C)
\(\frac{1}{12}\)
40
The shaded portion in the venn diagram is
პასუხი
(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?
პასუხი
(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
პასუხი
(B)
54^o
43
In the diagram, PQRS is a circle with O as centre and PQ||RT. If RTS = 32°. Find PSQ
პასუხი
(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.
პასუხი
(B)
48^o
45
In the diagram, QP//ST:PQR = 34o qrs = 73o and Rs = RT. Find SRT
პასუხი
(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
პასუხი
(A)
95^o
47
In the diagram, QPS = SPR, PR = 9cm. PQ = 4cm and QS = 3cm, find SR.
პასუხი
(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
პასუხი
(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
პასუხი
(C)
8cm
50
From the figure, calculate TH in centimeters
პასუხი
(B)
\(\frac{5}{\sqrt{3} - 1}\)