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