JAMB - Mathematics (1993)

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