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Mathematics
UTME / JAMB 1982
Statistics (Data Representation, Central Tendency & Dispersion)
Solution
Find the median of the set set of numbers 110, 116, 113, 119, 118, 127, 118, 117, 113
A
117.5
B
118
C
117
D
116
E
113
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
Re-arrange in ascending order: 110, 113, 113, 116, |117|, 118, 119, 127
a= 117
Source: Myschool Past Questions Archive (Record #32493)
Mathematics
UTME / JAMB 1982
Plane Geometry, Polygons & Circle Theorems
Solution
If f(x - 2) = 3\(x^2\) + 4x + 1. Find (1).
A
8
B
40
C
7
D
24
E
32
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
f(x - 2) = 3\(x^2\) + 4x + 1
x - 2 = 1 then x = 3
When x = 3, f(1) = 3(3)2 + 4 x 3 = 1
27 + 12 +1 = 40
Source: Myschool Past Questions Archive (Record #32494)
Mathematics
UTME / JAMB 1982
Mensuration (Areas, Perimeters & Volumes)
Solution
A sector of a circle is bounded by two radii 7cm long and an arc length 6cm. Find the area of the sector.
A
42cm2
B
3cm2
C
21cm2
D
24cm2
E
12cm2
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
Length of arc = \(\frac{\theta}{360}\) x 2\(\pi\)r = 6
\(\theta\) x 2\(\pi\)r = 360 x 6
\(\theta\) = \(\frac{360 \times 6}{2\pi r}\)
Area of the sector = \(\frac{\theta}{360}\) x \(\pi\)r2
\(\frac{360 \times 6}{2\pi r}\) x \(\frac{1}{360}\) x \(\pi\)r2 = r
= 3 x 7
= 21cm2
Source: Myschool Past Questions Archive (Record #32495)
Mathematics
UTME / JAMB 1982
Plane Geometry, Polygons & Circle Theorems
Solution
Given that p:q = \(\frac{1}{3}\):\(\frac{1}{2}\) and q:r = \(\frac{2}{5}\): \(\frac{4}{7}\) find p:r
A
4:105
B
7:15
C
20:21
D
2:35
E
3:20
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
\(p : q = \frac{1}{3} : \frac{1}{2}\)
\(\frac{p}{q} = \frac{2}{3}\)
\(2q = 3p ... (1)\)
\(q : r = \frac{2}{5} : \frac{4}{7}\)
\(\frac{q}{r} = \frac{2}{5} \times \frac{7}{4} = \frac{7}{10}\)
\(10q = 7r ... (2)\)
Eliminating q, we have
(1) : \(2q = 3p \)
\(10q = 15p\)
\(\implies 15p = 7r\)
\(\therefore \frac{p}{r} = \frac{7}{15}\)
\(p : r = 7 : 15\)
Source: Myschool Past Questions Archive (Record #32496)
Mathematics
UTME / JAMB 1982
Trigonometry, Elevation & Bearings
Solution
If sin \(\theta\) = \(\frac{m - n}{m + n}\); Find the value of 1 + tan2\(\theta\)
A
\(\frac{(m^2 + n^2)}{m + n}\)
B
\(\frac{(m^2 + n^2 + 2mn)}{4mn}\)
C
\(\frac{2(m^2 + n^2 + mn)}{m + n}\)
D
\(\frac{(m^2 + n^2 + mn)}{m + n}\)
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
\((m + n)^{2} = (m - n)^{2} + x^{2}\)
\(m^{2} + 2mn + n^{2} = m^{2} - 2mn + n^{2} + x^{2}\)
\(x^{2} = 4mn\)
\(x = \sqrt{4mn} = 2\sqrt{mn}\)
1 + tan2\(\theta\) = sec2\(\theta\)
= \(\frac{1}{cos^2\theta}\)
\(\cos \theta = \frac{2\sqrt{mn}}{(m + n)}\)
\(\frac{1}{\cos \theta} = \frac{(m + n)}{2\sqrt{mn}}\)
\(\sec^{2} \theta = \frac{(m + n)^{2}}{4mn}\)
= \(\frac{(m^2 + n^2 + 2mn)}{4mn}\)
Source: Myschool Past Questions Archive (Record #32497)
Mathematics
UTME / JAMB 1982
Number Bases & Modular Arithmetic
Solution
The currency used in a country is called 'Matimalik'(M) and is of base seven. A lady in that country bought 4 bags of rice at M56 per bag and and 3 tins of milk at M4 per tin. What is the total cost of the item she bought?
A
M2467
B
M2427
C
M2367
D
M3417
E
M3387
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
4 bags of rice - M 56 each
3 tins of milk - M 4 each
\(M 56 \times 4 = M 323\)
\(M 4 \times 3 = M 15\)
\(M (323 + 15) = M 341\)
Source: Myschool Past Questions Archive (Record #32498)
Mathematics
UTME / JAMB 1982
Plane Geometry, Polygons & Circle Theorems
Solution
Solve for x, If \(\frac{\frac{2}{x}}{\frac{1}{p^2} + \frac{1}{q^2}}\) = m
A
\(\frac{4pq}{m(p + q)}\)
B
\(\frac{2p^2q^2}{m(q^2 + p^2)}\)
C
\(\frac{2pq}{m(q^2 + p^2)}\)
D
\(\frac{2p^2q^2}{m(p^2)}\)
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
\(\frac{1}{p^2}\) + \(\frac{1}{q^2}\) = \(\frac{q^2 + p^2}{p^2 + q^2}\)
\(\frac{\frac{2}{x}}{\frac{p^2 + q^2}{p^2 q^2}}\)
m = \(\frac{2p^2q^2}{x(p^2 + q^2)}\)
= 2p2q2 = mx(p2 + q2)
x = \(\frac{2p^2q^2}{m(q^2 + p^2)}\)
Source: Myschool Past Questions Archive (Record #32505)
Mathematics
UTME / JAMB 1982
Fractions, Decimals, Percentages & Approximations
Solution
Express 37.05 x 0.0042 in standard form
A
15.561 x 102
B
1.5561 x 10-4
C
1.556 x 10-1
D
1.5561 x 101
E
1.55 x 101
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
37.05 x 0.0042 in standard form
\(\begin{array}{c|c}No. & log \\\hline 37.05 & 1.5688\\ 0.0042 & 3.6232 \\ \hline & 1.1920\end{array}\)
= 0.1556
= 1.556 x 10-1
Source: Myschool Past Questions Archive (Record #32510)
Mathematics
UTME / JAMB 1982
Algebraic Expressions, Polynomials & Factorisation
Solution
Find the values of x for which the expression \(\frac{(x - 3)(x - 2)}{x^2 + x - 2}\) is undefined?
A
1, -2
B
-1, 2
C
2, 3
D
-1. -2
E
-2, -3
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
to find the values of x for which the expression is undefined, let x\(^2\) + x - 2 = 0
By factorizing, we have (x + 2)(x - 1) = 0
when x + 2 = 0, when x - 1 = 0, x = -2 or x = 1
The two values are -2 and 1
Source: Myschool Past Questions Archive (Record #32513)
Mathematics
UTME / JAMB 1982
Trigonometry, Elevation & Bearings
Solution
A stone Q is tied to a point P vertically above Q by an inelastic string of length 2 meters. How high does the stone rise when the string is inclined at an angle 60o to the vertical?
A
It does not rise
B
2\(\sqrt{3}\) meters
C
3 meters
D
1 meters
E
3
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
Cos 60o = \(\frac{PD}{2}\)
Cos 60o x 2 = 0.5 x 2
= 1m
Source: Myschool Past Questions Archive (Record #32517)
Mathematics
UTME / JAMB 1982
Plane Geometry, Polygons & Circle Theorems
Solution
Express 130 kilometers per second in meters per hour
A
7.8 x 10-5
B
4.68 x 106
C
7,800,000
D
4.68 x 108
E
7.80 x 105
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
1km = 1000m
60sec. = 1 mins
60 mins. = 1 hr
130000m per sec = 130000 x 3600
= 468000000m/hr
= 468 x 108 m/hr
Source: Myschool Past Questions Archive (Record #32520)
Mathematics
UTME / JAMB 1982
Variations
Solution
The quantity y is partly constant and partly varies inversely as the square of x. With P and Q as constants, a possible relationship between x and y is
A
y = Q + \(\frac{P}{x^2}\)
B
y = Q + px
C
y = \(\frac{PQ}{x^2}\)
D
y = Q - \(\frac{P}{x^2}\)
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
Given the above statement,
\(y = Q + \frac{P}{x^{2}}\)
Source: Myschool Past Questions Archive (Record #32524)
Mathematics
UTME / JAMB 1982
Plane Geometry, Polygons & Circle Theorems
Solution
If \(\frac{3e + f}{3f - e}\) = \(\frac{2}{5}\), find the value of \(\frac{e + 3f}{f - 3e}\)
A
\(\frac{5}{2}\)
B
1
C
\(\frac{26}{7}\)
D
\(\frac{1}{3}\)
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
\(\frac{3e + f}{3f - e}\) = \(\frac{2}{5}\)
= 3e + f
= 2 x 1
\(\frac{-e + 3f}{3e - f}\) = \(\frac{5 \times 3}{2}\)
= \(\frac{3e + 9f = 15}{10f = 17}\)
f = \(\frac{17}{10}\)
Sub. for equ. (1)
3e + \(\frac{17}{10}\) = 2
3e = 2 - \(\frac{17}{10}\)
\(\frac{3}{10}\)
e = \(\frac{3}{10}\) x \(\frac{1}{3}\)
= \(\frac{1}{10}\)
= e + 3f = \(\frac{1}{10}\) + \(\frac{3 \times}{10}\) = \(\frac{52}{10}\)
f - 3e = \(\frac{17}{10}\) - 3 x \(\frac{1}{10}\)
= \(\frac{14}{10}\)
= \(\frac{52}{10}\) x \(\frac{10}{14}\)
= \(\frac{26}{7}\)
Source: Myschool Past Questions Archive (Record #32529)
Mathematics
UTME / JAMB 1982
Statistics (Data Representation, Central Tendency & Dispersion)
Solution
A world congress of mathematicians were held in Nice in 1970 with 800 people participating. There were 300 from Europe, 200 from America, 150 from Asia, 45 from Africa and 105 from Australia. Representing the above on a pie chart, the angle of the sector representing the participants from Asia is?
A
150o
B
67\(\frac{1}{2}\)o
C
67o
D
135o
E
68o
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
Representing from Asia is 150
\(\frac{150}{800}\) x 360
= \(\frac{135}{2}\)
= 67\(\frac{1}{2}\)o
Source: Myschool Past Questions Archive (Record #32530)
Mathematics
UTME / JAMB 1982
Fractions, Decimals, Percentages & Approximations
Solution
The diameter of a metal rod is measured as 23.40 cm to four significant figures. What is the maximum error in the measurement?
A
0.05cm
B
0.5cm
C
0.045cm
D
0.005cm
E
0.004cm
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
Maximum error in measurement to 2 decimal places
Maximum error = \(\frac{1}{2}\) x 0.001
= 0.005
Source: Myschool Past Questions Archive (Record #32531)