JAMB - Mathematics (1979)

1
The mean of the numbers 1.2, 1.0, 0.9, 1.4, 0.8, 0.8, 1.2 and 1.1 is
Trả lời
(E)
1.05
2
\((1.28 \times 10^{4}) \div (6.4 \times 10^{2})\) equals
Trả lời
(C)
2 x 10¹
3
If the value of \(\pi\) is taken to be \(\frac{22}{7}\), the area of a semi-circle of diameter 42m is
Trả lời
(E)
693m²
4
(3.2)² - (1.8)² equals
Trả lời
(A)
7.0
5
In \(\bigtriangleup\)PQR, PQ = 10cm, QR = 8cm and RP = 6cm, the perpendicular RS is drawn from R to PQ. Find the length of RS
Trả lời
(E)
4.8cm
6
After getting a rise of 15%, a man's new monthly salary is N345. How much per month did he earn before the increase?
Trả lời
(C)
N300
7
In base ten, the number 101101 (base 2) equals
Trả lời
(C)
45
8
The annul profits of a transport business were divided between the partners A and B in the ratio 3 : 5. If B received N3000 more than A, the total profit was
Trả lời
(C)
N12000
9
x is directly proportional to y and inversely proportional to z. If x = 9 when y = 24 and z = 8, what is the value of x when y = 5 and z = 6?
Trả lời
(D)
2\(\frac{1}{2}\)
10
The solution of the equation x² - 2x = 8 is
Trả lời
(B)
x = -2 or 4
11
A trader goes to Ghana for y days with y cedis. For the first x days, he spends X cedis per day. The amount he has to spend per day for the rest of his stay is
Trả lời
(E)
\(\frac{Y - Xx}{y - x}\) cedis
12
Multiply (3x + 5y + 4z) by (2x - 3y + z)
Trả lời
(A)
6x² + xy - 15y² + 4z² + 11xz - 7yz
13
A square of cardboard is taped at the perimeter by a piece of ribbon 20cm long. What is the area of the board?
Trả lời
(C)
25sq.cm
14
Rationalize the denominator of the expression \(\frac{6 + 2\sqrt{5}}{4 - 3\sqrt{6}}\)
Trả lời
(B)
\(\frac{-(24 + 18\sqrt{6} + 8\sqrt{5} + 6\sqrt{30})}{38}\)
15
Simplify \(\frac{5^x \times 25^{x - 1}}{125^{x + 1}}\)
Trả lời
(C)
5^-5
16
A steel ball of radius 1 cm is dropped into a cylinder of radius 2cm and height 4cm. If the cylinder is now filled with water, what is the volume of the water in the cylinder?
Trả lời
(A)
\(\frac{44}{3}\)\(\pi\)cm³
17
Simplify \(\frac{x^2 + y^2 + xy}{x + y}\) - \(\frac{x^2 + y^2}{x - y}\)
Trả lời
(B)
\(\frac{2y^3} {y^2 - x^2}\)
18
A ladder resting on a vertical wall makes an angles whose tangent is 2.4 with the ground. If the distance between the foot of the ladder and the wall is 50cm, What is the length of the ladder?
Trả lời
(E)
1.3m
19
Simplify 2\(\frac{5}{12}\) - 1\(\frac{7}{8}\) x \(\frac{6}{5}\)
Trả lời
(A)
\(\frac{1}{6}\)
20
One of the following statements is wrong. Which is it?
Trả lời
(C)
If two triangles are similar then they are also congurent
21
PQRS is a cyclic quadrilateral with PQ as diameter of the circle. If < PQS = 15^o find < QRS
Trả lời
(D)
105^o
22
Make c the subject of the equation a(b + c) + \(\frac{5}{d}\) - 2 = 0
Trả lời
(B)
c = \(\frac{2d - 5 - abd}{ad}\)
23
Which of the following values of the variable x, (a)x = 0, (b)x = -3, (c)x = 9, satisfy the inequalities 0 < \(\frac{x + 3}{x - 1}\) < 2?
Trả lời
(B)
(c)
24
On each market day Mrs. Bassey walks to the market from her home at a steady speed. This journey normally takes her 2 hours to complete. She finds, however, that by increasing her usual speed by 1 km/hr she can save 20 minutes. Find her usual speed in km/hr
Trả lời
(C)
5
25
Solve the simultaneous linear equations: 2x + 5y = 11, 7x + 4y = 2
Trả lời
(C)
x = \(\frac{-34}{27}\), y = \(\frac{73}{27}\)
26
If x\(^3\) - 12x - 16 = 0 has x = -2 as a solution then the equation has
Trả lời
(C)
3 roots with two equal and the third different
27
Find the value of (4\(^{\frac{1}{2}}\))\(^6\)
Trả lời
(E)
64
28
Find the value of log\(_{10}\)\(\frac{1}{40}\), given that log10\(_4\) = 0.6021
Trả lời
(C)
-1.6021
29
12 men complete a job in 9 days. How many men working t the same rate would be required to complete the job in 6 days?
Trả lời
(B)
18
30
For the set of numbers 2, 3, 5, 6, 7, 7, 8
Trả lời
(E)
the mean is less than the median
31
Simplify \(\frac{1 - x^2}{x - x^2}\), where x \(\neq\) 0
Trả lời
(C)
\(\frac{1 + x}{x}\)
32
A cylinder of height h and radius r is open at one end. Its surface area is
Trả lời
(C)
2\(\pi\)rh + \(\pi\)r²
33
An arc of circle of radius 2cm subtends an angle of 60º at the centre. Find the area of the sector
Trả lời
(A)
\(\frac{2 \pi}{3}\)cm²
34
What is the greatest straight line distance between two vertices (corners) of a cube whose sides are 2239cm long?
Trả lời
(D)
\(\sqrt{3}\) x 2239cm
35
What is log\(_7{(49^a)}\) - log\(_{10}^{(0.01)}\)?
Trả lời
(D)
2a + 2
36
The size of a quantity first doubles and then increases by a further 16%. After a short time its size decreases by 16%. What is the net increases in size of the quantity?
Trả lời
(C)
200%
37
The following table relates the number of objects f corresponding to a certain size x. What is the average size of an object?
\(\begin{array}{c|c} f & 1 & 2 & 3 & 4 & 5 \\ \hline x & 1 & 2 & 4 & 8 & 16\end{array}\)
Trả lời
(D)
\(\frac{43}{5}\)
38
If y = x\(^2\) - 2x - 3, find the least value of y and the corresponding value of x
Trả lời
(D)
x = 1, y = -4
39
A father is now three times as old as his son. Twelve years ago he was six times as old as his son. How old are the son and the father?
Trả lời
(E)
20 and 60
40
If \(\sqrt{3^{\frac{1}{x}}}\) = \(\sqrt{9}\) then the value of x is:
Trả lời
(E)
\(\frac{1}{2}\)
41
A man is standing in the corridor of a 10-storey building and looking down at a tall tree in front of the building. He sees the top of the tree at angle of depression of 30^o. If the tree is 200m tall and the man's eyes are 300m above the ground, calculate the angle of depression of the foot tree as seen by the man
Trả lời
(B)
60^o
42
In the figure, \(\bigtriangleup\) ABC are in adjacent planes. AB = AC = 5cm, BC = 6cm and o then AE is equal to
Trả lời
(B)
2\(\sqrt{3}\)
43
In this figure, PQRS is a parallelogram, PS = PT and < PST = 55\(^o\). The size of <PQR is
Trả lời
(D)
110^o
44
If O is the centre of the circle, < POS equls
Trả lời
(E)
150^o
45
In the figure, PQ and QR are chords of the circle PQR. QRS is a straight line and PR is equal to RS, < PSR is 20o. What is the size of <POQ.
Trả lời
(C)
80^o
46
In the figure, PQ is parallel to SQ ; QS bisets < PSQ, < PQS is 65^o and < RPS is 20^o. What is the size of < PRS?
Trả lời
(D)
30^o
47
(Numbers indicate the lengths of the sides of the triangles) If the area of \(\bigtriangleup\) PQR is k2sq. units what is the area of the shades portion?
Trả lời
(A)
\(\frac{5}{9}\)k² sq. units
48
In the parallelogram PQRS, PE is perpendicular to QR. Find the area of the parallelogram.
Trả lời
(D)
132cm²
49
PQ is parallel to RS. Calculate the value of x.
Trả lời
(B)
40^o
50
Find x in the diagram below.
Trả lời
(B)
\(\frac{3(\sqrt{3} - 1)}{\sqrt{3} + 1}\)