JAMB - Mathematics (1987)

1
Convert 241 in base 5 to base 8,
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(B)
107₈
2
Find the least length of a rod which can be cut into exactly equal strips, each of either 40cm or 48cm in length
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(B)
240cm
3
A rectangular lawn has an area of 1815 square yards. if its length is 50 meters, find its width in meters given that 1 metre equals 1.1 yards
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(D)
30.00
4
Reduce each number to two significant figures and then evaluate \(\frac{0.021741 \times 1.2047}{0.023789}\)
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(C)
1.1
5
A train moves from P to Q at an average speed of 90km/h and immediately returns from Q to P through the same route at an average speed of 45km/h. Find the average speed for the entire journey
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(C)
67.50km\h
6
If the length of a square is increased by 20% while while its width is decreased by 20% to form a rectangle, what is the ratio of the area of the rectangle to the area of the square?
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(D)
24 : 25
7
Two brothers invested a total of N5,000.00 on a farm project, the farm yield was sold for N 15,000.00 at the end of the season. If the profit was shared in the ratio 2 : 3, what is the difference in the amount to profit received by the brothers?
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(A)
N2,000.00
8
A man invests a sum of money at 4% per annum simple invest. After 3 years, the principal amounts to N7,000.00. Find the sum invested
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(B)
N6,250.00
9
By selling 20 oranges for N1.35 a trader makes a profit of 8%. What is his percentage gain or loss if he sells the same 20 oranges for N1.10?
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(C)
12%
10
Four boys and ten girls can cut a field in 5 hours if the boys work at \(\frac{5}{4}\) the rate at which the girls work. How many boys will be needed to cut the field in 3 hours?
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(D)
20
11
Evaluate without using tables (0.008) -\(\frac{1}{3}\) x (0.16) - \(\frac{3}{2}\)
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(A)
\(\frac{625}{8}\)
12
Simplify without using tables \(\frac{Log_26 - Log_23}{Log_28 - 2Log_2\frac{1}{2}}\)
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(A)
\(\frac{1}{5}\)
13
Simplify without using tables \(\frac{2\sqrt{14} \times 3\sqrt{21}}{7\sqrt{24} \times 2\sqrt{98}}\)
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(D)
\(\frac{3\sqrt{2}}{28}\)
14
If P = \(\frac{\frac{2}{3}({1 - r^2})}{n^2}\), find n when r = \(\sqrt{\frac{1}{3}}\) and p = 1
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(D)
\(\frac{2}{3}\)
15
If a = u\(^2\) - 3v\(^2\) and b = 2uv + v\(^2\) evaluate (2a - b)(a - b\(^2\)), when u = 1 and v = -1
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(A)
9
16
The formula Q = 1.5 + 0.5n gives the cost Q(in Naira)of feeding n people for a week. Find (in kobo) the extra cost of feeding one additional person
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(D)
50k
17
If P varies inversely as V and V varies directly as R², find the relationship between P and R given that R = 7 when P = 2
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(B)
PR² = 98
18
Make y the subject of the formula Z = x\(^2\) + \(\frac{1}{y^3}\)
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(C)
y = \(\frac{1}{(Z - x^2)^{\frac{1}{3}}}\)
19
Find the values of m which make the following quadratic function a perfect square. x² + 2(m + 1)x + m + 3
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(C)
1, -2
20
Factorize 6^{2x + 1} + 7(6^x) - 5
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(B)
[3(6^x) + 5][2(6^x) - 1]
21
Find the values of y which satisfy the simultaneous equations x + y = 5, x2 - 2y2 = 1
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(C)
-12, +2
22
An (n - 2)² sided figure has n diagonals. Find the number n diagonals for 25-sided figure
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(A)
7
23
Solve the inequality x - 1 > 4(x + 2)
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(B)
x < -3
24
Simplify \(\frac{x^2 - y^2}{2x^2 + xy - y^2}\)
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(C)
\(\frac{x - y}{2x - y}\)
25
The minimum value of y in the equation y = x\(^2\) - 6x + 8 is
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(D)
-1
26
Find the eleventh term of the progression 4, 8, 16.....
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(B)
2¹²
27
Three angles of a nonagon are equal and the sum of six other angles is 1110o. Calculate the size of one of the equal angles
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(D)
50^o
28
Two chords QR and NP of a circle intersect inside the circle at x. If RQP = 37o, RQN = 49o and QPN = 35o, find PRQ
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(D)
59^o
29
The sine, cosine and tangent of 210o are respectively
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(D)
\(\frac{-1}{2}\), \(\frac{\sqrt{-3}}{2}\), \(\frac{\sqrt{3}}{3}\)
30
If tan \(\theta\) = \(\frac{m^2 - n^2}{2mn}\) find sec\(\theta\)
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(B)
\(\frac{m^2 + n^2}{2mn}\)
31
From two points x and y, 8m apart, and in line with a pole, the angles of elevation of the top of the pole are 30ºand 60º respectively. Find the height of the pole assuming that x, y, and the foot of the pole are on the same horizontal plane and x and y are on the same side of the pole.
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(B)
4\(\sqrt{3}\)
32
A room is 12m long, 9m wide and 8m high. Find the cosine of the angle which a diagonal of the room makes with the floor of the room
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(A)
\(\frac{5}{17}\)
33
What is the circumference of latitude 0°S if R is the radius of the earth?
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(B)
2\(\pi\) R cos \(\theta\)
34
The base of a pyramid is a square of side 8cm. If its vertex is directly above the centre, find the height, given that the edge is 4\(\sqrt3\)cm
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(C)
4cm
35
What is the locus of the mid-points of all chords of length 6cm within a circle of radius 5cm and with centre 0
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(B)
The perpendicular bisector of the chords
36
Taking the period of day light on a certain day to be from 5.30a.m to 7.00p.m. Calculate the angle of a pie chart designed to show the periods of the day light and of darkness on that day
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(D)
202^o30' 157^o 30'
37
The goals scored by 40 football teams from three league divisions are recorded below
\(\begin{array}{c|c} \text{Number of goals} & 0 & 1 & 2 & 3 & 4 & 5 & 6 \\ \hline frequency & 4 & 3 & 15 & 16 & 1 & 0 & 1\end{array}\)
What is the total number of goals scored by all the terms?
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(C)
91
38
The numbers 3, 2, 8, 5, 7, 12, 9 and 14 are the marks scored by a group of students in a class test. If P is scored by an group of students in a class test. If P is the mean and Q the median, the P + Q is
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(D)
15
39
Below are the scores of group of students in a music test
\(\begin{array}{c|c}scores & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 \\ \hline \text{No, of students} & 3 & 6 & 10 & 8 & 6 & 5 & 2 & 4 & 12\end{array}\)
If CF(x) is the number of students with scores less than or equal to x, find CF(6)
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(B)
38
40
Find the probability of selecting a figure which is a parallelogram from a square, a rectangle, a rhombus, a kite and a trapezium
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(A)
\(\frac{3}{5}\)
41
An (\(n - 2)^2\) sided figure has n diagonals. Find the number n diagonals for a 25-sided figure
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(A)
7
42
In the diagram, POQ is a diameter, 0 is the centre of the circle and TP is a tangent. Find the value of x
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(A)
30^o
43
In the diagram above, QR // TS, QR : TS = 2.3, Find the ratio of the area of triangle PQR to the area of the trapezium QRST.
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(B)
4:5
44
Three angles of a nonagon are equal and the sum of six other angles is 1110^o. Calculate the size of one of the equal angles.
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(D)
50^o
45
In the figure, find the value of x
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(C)
90^o