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
Răspuns
(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?
Răspuns
(E)
N45, 000
3
Given a regular hexagon, calculate each interior angle of the hexagon
Răspuns
(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?
Răspuns
(B)
2:1 increase
5
Solve the following equations 4x - 3 = 3x + y = x - y = 3, 3x + y = 2y + 5x - 12
Răspuns
(A)
x = 5, y = 2
6
In a figure, PQR = 60o, PRS = 90o, RPS = 45o, QR = 8cm. Determine PS
Răspuns
(B)
4\(\sqrt{6}\)cm
7
Given that cos z = L , whrere z is an acute angle, find an expression for \(\frac{\cot z - \csc z}{\sec z + \tan z}\)
Răspuns
(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
Răspuns
(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.
Răspuns
(A)
1 = -6, k = -9
10
Make T the subject of the equation \(\frac{av}{1 - v}\) = \(\sqrt[3]{\frac{2v + T}{a + 2T}}\)
Răspuns
(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
Răspuns
(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
Răspuns
(A)
y = \(\frac{10x^2}{31} + \frac{52}{31\sqrt{x}}\)
13
Simplify \(\frac{x - 7}{x^2 - 9}\) x \(\frac{x^2 - 3x}{x^2 - 49}\)
Răspuns
(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
Răspuns
(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.
Răspuns
(C)
48\(\frac{1}{2}\)
16
Find x if (x\(_4\))\(^2\) = 100100\(_2\)
Răspuns
(B)
12
17
Simplify log¹⁰ a^{\(\frac{1}{3}\)} + \(\frac{1}{4}\)log₁₀ a - \(\frac{1}{12}\)log₁₀a⁷
Răspuns
(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
Răspuns
(A)
u = \(\frac{8}{v^3}\)
19
Solve the simultaneous equations for x in x² + y - 8 = 0, y + 5x - 2 = 0
Răspuns
(C)
6, -1
20
Find the missing value in the following table \(\begin{array}{c|c} x & -2 & -1 & 0 & 1 & 2 & 3 \\ \hline Y = x^3 - x + 3 & & 3 & 3 & 3 & 9 & 27\end{array}\)
Răspuns
(A)
-3
21
Find the angle of the sectors representing each item in pie chart of the following data 6, 10, 14, 16, 26
Răspuns
(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?
Răspuns
(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
Răspuns
(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
Răspuns
(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?
Răspuns
(E)
2
26
If \((\frac{2}{3})^{m} (\frac{3}{4})^{n} = \frac{256}{729}\), find the values of m and n.
Răspuns
(D)
m = 4, n = -2
27
Without using tables find the numerical value of log\(_7\)49 + log\(_7\)(\(\frac{1}{7}\))
Răspuns
(A)
1
28
Factorize completely 81a\(^4\) - 16b\(^4\)
Răspuns
(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
Răspuns
(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?
Răspuns
(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?
Răspuns
(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.
Răspuns
(B)
6.10cm²
33
Simplify \(\sqrt[3]{\frac{27a^{-9}}{8}}\).
Răspuns
(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. \(\pi\) = \(\frac{22}{7}\)
Răspuns
(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
Răspuns
(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
Răspuns
(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?
Răspuns
(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?
Răspuns
(B)
10
39
In the figure, find PRQ
Răspuns
(B)
62\(\frac{1}{2}\)^o
40
Which of the following equations represents the graph?
Răspuns
(D)
y = 1 - 2x - 3x²
41
The figure FGHK is a rhombus. What is the value of angle X?
Răspuns
(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
Răspuns
(E)
10^o 42'
43
If O is the centre of the circle in the figure, find the value of x
Răspuns
(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?
Răspuns
(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?
Răspuns
(B)
19\(\frac{1}{3}\)^o