JAMB - Mathematics (1983)

1
If M represents the median and D the mode of the measurements 5, 5, 3, 5, 7, 5, 8 and 9, then (M, D) is
Απάντηση
(D)
(5, 5)
2
A construction company is owned by two partners X and Y and it is agreed that their profit will be divided in the ratio 4:5. At the end of the year, Y received N5,000 more than X. What is the total profit of the company for the year?
Απάντηση
(E)
N45, 000
3
Given a regular hexagon, calculate each interior angle of the hexagon
Απάντηση
(C)
120^o
4
If x is jointly proportional to the cube of y and the fourth power of z. In what ratio is x increased or decreased when y is halved and z is doubled?
Απάντηση
(B)
2:1 increase
5
Solve the following equations 4x - 3 = 3x + y = x - y = 3, 3x + y = 2y + 5x - 12
Απάντηση
(A)
x = 5, y = 2
6
In a figure, PQR = 60o, PRS = 90o, RPS = 45o, QR = 8cm. Determine PS
Απάντηση
(B)
4\(\sqrt{6}\)cm
7
Given that cos z = L , whrere z is an acute angle, find an expression for \(\frac{\cot z - \csc z}{\sec z + \tan z}\)
Απάντηση
(D)
\(\frac{L(L - 1)}{1 - L + 1 \sqrt{1 - L^2}}\)
8
If 0.0000152 x 0.00042 = A x 10\(^{B}\), where 1 \(\leq\) A < 10, find A and B
Απάντηση
(B)
A = 6.38, B = -9
9
If (x + 2) and (x - 1) are factors of the expression \(Lx^{3} + 2kx^{2} + 24\), find the values of L and k.
Απάντηση
(A)
1 = -6, k = -9
10
Make T the subject of the equation \(\frac{av}{1 - v}\) = \(\sqrt[3]{\frac{2v + T}{a + 2T}}\)
Απάντηση
(D)
\(\frac{2v(1 - v)^3 - a^4 v^3}{2a^3v^ 3 - (1 - v)^3}\)
11
The value of (0.03)\(^3\) - (0.02)\(^3\) is
Απάντηση
(D)
0.000019
12
y varies partly as the square of x and partly as the inverse of the square root of x.Write down the expression for y if y = 2 when x = 1 and y = 6 when x = 4
Απάντηση
(A)
y = \(\frac{10x^2}{31} + \frac{52}{31\sqrt{x}}\)
13
Simplify \(\frac{x - 7}{x^2 - 9}\) x \(\frac{x^2 - 3x}{x^2 - 49}\)
Απάντηση
(C)
\(\frac{x}{(x + 3)(x + 7)}\)
14
The lengths of the sides of a right angled triangle are (3x + 1)cm, (3x - 1)cm and xcm. Find x
Απάντηση
(D)
12
15
The scores of set of final year students in the first semester examination in a paper are 41, 29, 55, 21, 47, 70, 70, 40, 43, 56, 73, 23, 50, 50. Find the median of the scores.
Απάντηση
(C)
48\(\frac{1}{2}\)
16
Find x if (x\(_4\))\(^2\) = 100100\(_2\)
Απάντηση
(B)
12
17
Simplify log¹⁰ a^{\(\frac{1}{3}\)} + \(\frac{1}{4}\)log₁₀ a - \(\frac{1}{12}\)log₁₀a⁷
Απάντηση
(C)
zero
18
If w varies inversely as V and U varies directly as w³, Find the relationship between u and v given that u = 1, when v = 2
Απάντηση
(A)
u = \(\frac{8}{v^3}\)
19
Solve the simultaneous equations for x in x² + y - 8 = 0, y + 5x - 2 = 0
Απάντηση
(C)
6, -1
20
Find the missing value in the following table \(\begin{array}{c|c} x & -2 & -1 & 0 & 1 & 2 & 3 \\ \hline Y = x^3 - x + 3 & & 3 & 3 & 3 & 9 & 27\end{array}\)
Απάντηση
(A)
-3
21
Find the angle of the sectors representing each item in pie chart of the following data 6, 10, 14, 16, 26
Απάντηση
(D)
30^o, 50^o, 70^o, 80^o, 130^o
22
The scores of 16 students in a Mathematics test are 65, 65, 55, 60, 60, 65, 60, 70, 75, 70, 65, 70, 60, 65, 65, 70. What is the sum of the median and modal scores?
Απάντηση
(B)
130
23
The letters of the word MATRICULATION are cut and put into a box. One letter is drawn at random from the box. Find the probability of drawing a vowel
Απάντηση
(C)
\(\frac{6}{13}\)
24
Correct each of the numbers 59.81798 and 0.0746829 to three significant figures and multiply them, giving your answer to three significant figures
Απάντηση
(C)
4.47
25
If a rod of length 250cm is measured as 255cm long in error, what is the percentage error in the measurement?
Απάντηση
(E)
2
26
If \((\frac{2}{3})^{m} (\frac{3}{4})^{n} = \frac{256}{729}\), find the values of m and n.
Απάντηση
(D)
m = 4, n = -2
27
Without using tables find the numerical value of log\(_7\)49 + log\(_7\)(\(\frac{1}{7}\))
Απάντηση
(A)
1
28
Factorize completely 81a\(^4\) - 16b\(^4\)
Απάντηση
(C)
(3a - 2b)(3a + 2b)(9a² + 4b²)
29
One interior angle of a convex hexagon is 170^o and each of the remaining interior angles is equal to x^o. Find x
Απάντηση
(B)
110^o
30
A ship H leaves a port P and sails 30 km due south. Then it sails 60km due west. What is the bearing of H from P?
Απάντηση
(B)
243^o 26'
31
In a sample survey of a University Community, the following table shows the percentage distribution of the number of members per house hold
\(\begin{array}{c|c} \text{No. of members per household} & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & \text{Total} \\ \hline \text{No. of households} & 3 & 12 & 15 & 28 & 21 & 10 & 7 & 4 & 100\end{array}\)

What is the median?
Απάντηση
(A)
4
32
On a square paper of length 2.524375cm is inscribed square diagram of length 0.524375cm. Find the area of the paper not covered by the diagram. correct to 3 significant figures.
Απάντηση
(B)
6.10cm²
33
Simplify \(\sqrt[3]{\frac{27a^{-9}}{8}}\).
Απάντηση
(B)
\(\frac{3}{2a^3}\)
34
PQR is the diagram of a semicircle RSP with centre at Q and radius of length 3.5cm. If QPT = 60o. Find the perimeter of the figure PTRS. \(\pi\) = \(\frac{22}{7}\)
Απάντηση
(A)
25cm
35
In a triangle PQT, QR = \(\sqrt{3}cm\), PR = 3cm, PQ = \(2\sqrt{3}\)cm and PQR = 30o. Find angles P and R
Απάντηση
(A)
P = 60^o and R = 90^o
36
Find the mean of the following 24.57, 25.63, 24.32, 26.01, 25.77
Απάντηση
(C)
25.26
37
A man drove for 4 hours at a certain speed, he then doubled his speed and drove for another 3 hours. Although he covered 600 kilometers. At what speed did he drive for the last 3 hours?
Απάντηση
(A)
120km/hr
38
In a class of 60 pupils, the statistical distribution of the numbers of pupils offering Biology, History, French, Geography and Additional mathematics is as shown in the pie chart. How many pupils offer Additional Mathematics?
Απάντηση
(B)
10
39
In the figure, find PRQ
Απάντηση
(B)
62\(\frac{1}{2}\)^o
40
Which of the following equations represents the graph?
Απάντηση
(D)
y = 1 - 2x - 3x²
41
The figure FGHK is a rhombus. What is the value of angle X?
Απάντηση
(D)
120^o
42
PQRS is a desk of dimensions 2m x 0.8 which is inclined at 30^o to the horizontal. Find the inclination of the diagonal PR to the horizontal
Απάντηση
(E)
10^o 42'
43
If O is the centre of the circle in the figure, find the value of x
Απάντηση
(C)
100
44
PQRS isa cyclic quadrilateral which PQ = PS. PT is a tangent to the circle and PQ makes an angle of 50o with the tangent as shown in the figure. What is the size of QRS?
Απάντηση
(E)
80^o
45
The farm yield of four crops on a piece of land in Ondo are represented on the pie chart. what is the angle of the sector occupies by Okro in the chart?
Απάντηση
(B)
19\(\frac{1}{3}\)^o