JAMB - Mathematics (1993)

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