JAMB - Mathematics (1986)

1
Evaluate (212)₃ - (121)₃ + (222)₃
პასუხი
(C)
(1020)₃
2
If Musa scored 75 in biology instead of 57, his average mark in four subjects would have been 60. What was his total mark?
პასუხი
(C)
222
3
Divide the L.C.M of 48, 64, and 80 by their H.C.F
პასუხი
(D)
60
4
Find the smallest number by which 252 can be multiplied to obtain a perfect square
პასუხი
(D)
7
5
Find the reciprocal of \(\frac{\frac{2}{3}}{\frac{1}{2} + \frac{1}{3}}\)
პასუხი
(B)
\(\frac{5}{4}\)
6
Three boys shared some oranges. The first received \(\frac{1}{3}\) of the oranges, the second received \(\frac{2}{3}\) of the remainder. If the third boy received the remaining 12 oranges, how many oranges did they share?
პასუხი
(B)
54
7
If P = 18, Q = 21, R = -6 and S = -4, Calculate \(\frac{(P- Q)^3 + S^2}{R^3}\)
პასუხი
(B)
\(\frac{11}{216}\)
8
Simplify \(\frac{0.0324 \times 0.00064}{0.48 \times 0.012}\)
პასუხი
(C)
3.6 x 10^-3
9
Udoh deposited N150.00 in the bank. At the end of 5 years the simple interest on the principal was N55.00. At what rate per annum was the interest paid?
პასუხი
(B)
7\(\frac{1}{3}\)%
10
A number of pencils were shared out among Bisi, Sola and Tunde in the ratio of 2 : 3 : 5 respectively. If Bisi got 5, how many were share out?
პასუხი
(B)
25
11
The ages of Tosan and Isa differ by 6 and the product of their ages is 187. Write their ages in the form (x, y), where x > y.
პასუხი
(C)
(17, 11)
12
In 1984, Ike was 24 yrs old and his father was 45 yrs old. In what year was Ike exactly half his father's age?
პასუხი
(A)
1981
13
Simplify \((\frac{1}{\sqrt{5} + \sqrt{3}} - \frac{1}{\sqrt{5} - \sqrt{3}}) \times \frac{1}{\sqrt{3}}\)
პასუხი
(D)
-1
14
Find n if log\(_{2}\) 4 + log\(_{2}\) 7 - log\(_{2}\) n = 1
პასუხი
(B)
14
15
Simplify \(\frac{9^{\frac{1}{3}} \times 27^{-\frac{1}{2}}}{3^{-\frac{1}{6}} \times 3^{\frac{-2}{3}}}\)
პასუხი
(B)
1
16
If x varies directly as y³ and x = 2 when y = 1, find x when y = 5
პასუხი
(D)
250
17
Factorize completely 8a + 125ax\(^3\)
პასუხი
(B)
a(2 + 5x)(4 - 10x + 25x²)
18
If y = \(\frac{x}{x - 3}\) + \(\frac{x}{x + 4}\) find y when x = -2
პასუხი
(A)
-\(\frac{3}{5}\)
19
Find all real numbers x which satisfy the inequality \(\frac{1}{3}\)(x + 1) - 1 > \(\frac{1}{5}\)(x + 4)
პასუხი
(D)
x > 11
20
Factorize \(x^2 + 2a + ax + 2x\)
პასუხი
(D)
(x + 2)(x + a)
21
Solve the equation 3x\(^2\) + 6x - 2 = 0
პასუხი
(B)
x = -1 \(\pm\) \(\frac{\sqrt{15}}{3}\)
22
Simplify \(\frac{1}{5x + 5}\) + \(\frac{1}{7x+ 7}\)
პასუხი
(D)
\(\frac{12}{35x + 35}\)
23
Factorize (4a + 3)² - (3a - 2)²
პასუხი
(C)
(a + 5)(7a + 1)
24
If \(5^{(x + 2y)} = 5\) and \(4^{(x + 3y)} = 16\), find \(3^{(x + y)}\).
პასუხი
(B)
1
25
Simplify \(\frac{1}{x - 2}\) + \(\frac{1}{x + 2}\) + \(\frac{2x}{x^2 - 4}\)
პასუხი
(D)
\(\frac{4x}{x^2 - 4}\)
26
make v the subject of the formula S = \(\sqrt{\frac{6}{v} - \frac{w}{2}}\)
პასუხი
(C)
v = \(\frac{12}{2s^2 + w}\)
27
Find the values of x which satisfy the equation 16^x - 5 x 4^x + 4 = 0
პასუხი
(C)
0 and 1
28
If \(\frac{a}{b}\) = \(\frac{c}{d}\) = k, find the value of \(\frac{3a^2 - ac + c^2}{3b^2 - bd + d^2}\) in terms of k
პასუხი
(D)
k²
29
At what points does the straight line y = 2x + 1 intersect the curve y = \(2x^2\) + 5x - 1?
პასუხი
(A)
(-2, -3) and(\(\frac{1}{2}\), 2)
30
If cos\(\theta\) = \(\frac{a}{b}\), find 1 + tan²\(\theta\)
პასუხი
(A)
\(\frac{b^2}{a^2}\)
31
A regular polygon of n sides has 160^o as the size of each interior angle. Find n
პასუხი
(A)
18
32
A girl walks 45 meters in the direction 050^o from a point Q to a point X. She then walks 24 meters in the direction 140^o from X to a point Y. How far is she then from Q?
პასუხი
(C)
51m
33
An arc of a circle of radius 6cm is 8cm long. Find the area of the sector
პასუხი
(B)
24cm²
34
Find the total surface area of solid cone of radius 2\(\sqrt{3}\)cm and slanting side 4\(\sqrt{3}\)
პასუხი
(D)
36\(\pi \)cm²
35
If U and V are two distinct fixed points and W is a variable points such that UWV is a right angle, what is the locus of W?
პასუხი
(D)
A circle with the line UV as the diameter
36
An open rectangular box externally measures 4m x 3m x 4m. Find the total cost of painting the box externally if it costs N2.00 to paint one square meter
პასუხი
(B)
N112.00
37
Of the nine hundred students admitted in a university in 1979, the following was the distribution by state: Anambrs 185, Imo 135, Kaduna 90, Kwara 110, Ondo 155, Oyo 225. In a pie chart drawn to represent this distribution, The angle subtended at the centre by anambra is
პასუხი
(C)
74^o
38
Find the median of the numbers 89, 141, 130, 161, 120, 131, 131, 100, 108 and 119
პასუხი
(B)
125
39
Find the probability that a number selected at random from 40 to 50 is a prime
პასუხი
(C)
\(\frac{3}{11}\)
40
A man kept 6 black, 5 brown and 7 purple shirts in a drawer. What is the probability of his picking a purple shirt with his eyes closed?
პასუხი
(C)
\(\frac{7}{18}\)
41
The table below gives the scores of a group of students in a Mathematical test.
\(\begin{array}{c|c} Scores & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 \\ \hline Frequency & 2 & 4 & 7 & 14 & 12 & 6 & 4 & 1\end{array}\)
If the mode in m and the number of students who scored 4 or less is s. What is (s, m)?
პასუხი
(A)
(27, 4)
42
In the diagram, PQ and RS are chords of a circle centre O which meet at T outside the circle. If TP = 24cm. TQ = 8cm and TS = 12cm, find TR.
პასუხი
(A)
16cm
43
The figure is a solid with the trapezium PQRS as its uniform cross-section. Find its volume
პასუხი
(C)
816m³
44
PQ and PR are tangents from P to a circle centre O as shown in the figure. If QRP = 34^o, find the angle marked x
პასუხი
(C)
68^o
45
In the figure, \(\bigtriangleup\)PQT is isosceles. PQ = QT, SRQ = 35o, TPQ = 20o and PQR is a straight line.Calculate TSR
პასუხი
(C)
75^o