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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)
Mathematics
UTME / JAMB 1982
Plane Geometry, Polygons & Circle Theorems
Solution
In a regular polygon of n sides, each interior angle is 144o. Find n
A
12
B
11
C
10
D
8
E
6F
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
Formula for an interior angle of a polygon is (2n - 4) x 90
(2n - 4) x 90 = 144n
180n - 360 = 144n
180n - 144n = 360
36n = 360
n = \(\frac{360}{36}\)
= 10
Source: Myschool Past Questions Archive (Record #32532)
Mathematics
UTME / JAMB 1982
Plane Geometry, Polygons & Circle Theorems
Solution
Simplify \(\frac{3}{2x - 1}\) + \(\frac{2 - x}{x - 2}\)
A
\(\frac{2 - x}{(2x - 1)(x - 2)}\)
B
\(\frac{5 - x}{(2x - 1)(x - 2)}\)
C
\(\frac{4 - 2x}{2x - 1}\)
D
\(\frac{6 - 3x}{(2x - 1)(x - 2)}\)
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
\(\frac{3}{2x - 1}\) + \(\frac{2 - x}{x - 2}\)
= \(\frac{3}{2x - 1}\) - \(\frac{x - 2}{x - 2}\)
= \(\frac{3}{2x - 1}\) - 1
= \(\frac{3 - (2x - 1)}{2x - 1}\)
= \(\frac{3 - 2x + 1}{2x - 1}\)
= \(\frac{4 - 2x}{2x - 1}\)
Source: Myschool Past Questions Archive (Record #32533)
Mathematics
UTME / JAMB 1982
Linear, Simultaneous & Quadratic Equations
Solution
The solution to the quadratic equation 5 + 3x - 2x2 = 0 is
A
(\(\frac{5}{2}\), 1)
B
(5, 3)
C
-(\(\frac{5}{2}\), -1)
D
(\(\frac{5}{2}\), -1)
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
5 + 3x - 2x2 = 0, (x + 1)(5 - 2x) (expand to check)
(x + 1)(5 - 2x) = 0
when x = 1 = 0, x = -1
when 5 - 2x = 0, x = \(\frac{5}{2}\) - 1
Source: Myschool Past Questions Archive (Record #32534)
Mathematics
UTME / JAMB 1982
Fractions, Decimals, Percentages & Approximations
Solution
A housewife bought 3 kilograms of garri at N13.00 per kg. She deposited N160. 00 for half a cow and bought 24 oranges at 10k each. She came back home with N20.60. She therefore left home with
A
N220.00
B
N222.00
C
N201.40
D
N202.00
E
N180.80
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
3 kg of garri at N13.00 per kg = N39.00
half a cow = N160.00
24 oranges at 10k each = N2.40
balance = N20.60
Adding all together = N222.00
Source: Myschool Past Questions Archive (Record #32535)
Mathematics
UTME / JAMB 1982
Linear, Simultaneous & Quadratic Equations
Solution
The solution to the simultaneous equations 3x + 5y = 4, 4x + 3y = 5 is
A
(\(\frac{-13}{11}, \frac{1}{11}\))
B
(\(\frac{13}{11}, \frac{1}{11}\))
C
(\(\frac{13}{11}, \frac{-1}{11}\))
D
(\(\frac{11}{13}, \frac{1}{11}\))
E
(13, 11)
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
3x + 5y = 4, 4x + 3y = 5
3x + 5y = 4 x 4
4x + 3y = 5 x 3
12x + 20y = 16.....(i)
12x + 9y = 15.......(ii)
subtract eqn.(ii) from eqn.(i)
11y = 1
y = \(\frac{1}{11}\)
12x + 20 x \(\frac{1}{11}\) = 16
12x = \(\frac{156}{11}\)
x = \(\frac{13}{11}\)
= \(\frac{13}{11}, \frac{1}{11}\)
Source: Myschool Past Questions Archive (Record #32536)
Mathematics
UTME / JAMB 1982
Mensuration (Areas, Perimeters & Volumes)
Solution
The area of the curved surface of the cone generated by the sector of a circle radius 6cm and arc length 22cm is (\(\pi\) = \(\frac{22}{7}\))
A
58 sq.cm
B
34 sq.cm
C
132 sq.cm
D
77 sq.cm
E
66 sq.cm
medium Difficulty
Verified Correct Answer: Option E
Step-by-Step Mathematical Solution
Given: length of the arc AOB = 22cm ; L = 6cm
Curved surface area of cone = \(\pi\)rl
Length of an arc = \(\frac{\theta}{360}\) x 2 \(\pi\)L
= 22cm
but length of an arc = circumference of the cone = 2\(\pi\)
where r is the radius of the cone circle
2\(\pi\)r = 22, r = \(\frac{22}{2\pi}\)r
= 11 x \(\frac{7}{22}\)
= \(\frac{7}{2}\)
curved surface area = \(\pi\)rl
= \(\frac{22}{7}\) x \(\frac{7}{2}\) x 6
= 66 sq.cm
Source: Myschool Past Questions Archive (Record #32537)
Mathematics
UTME / JAMB 1982
Mensuration (Areas, Perimeters & Volumes)
Solution
The square base of a pyramid of side 3cm has height 8cm. If the pyramid is cut into two parts by a plane parallel to the base midway between the base and the vertex, the volumes of the two sections are
A
(21cm3, 3cm3)
B
(24cm3, 3cm3)
C
(24cm3, 21cm3)
D
(72cm3, 9cm3)
E
(63cm3, 9cm3)
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
Vol. of the 1st section is side x height
vol. = 3 x 8
= 24cm3
vol. of the second section is 3 x 1 = 3
= 24cm3, 3cm3
Source: Myschool Past Questions Archive (Record #32538)
Mathematics
UTME / JAMB 1982
Plane Geometry, Polygons & Circle Theorems
Solution
Simplify f\(^{\frac{1}{2}}\)g\(^2\)h\(^{\frac{1}{3}}\) \(\div\) f\(^{\frac{5}{2}}\)g\(^o\)h\(^{\frac{7}{3}}\)
A
(\(\frac{g}{fh}\))2
B
f2g2h2
C
\(\frac{5}{4}\)goh\(\frac{7}{9}\)
D
\(\frac{g^2}{f^5h^7}\)
E
\(\frac{1}{f^2h^2}\)
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
f\(^{\frac{1}{2}}\)g\(^2\)h\(^{\frac{1}{3}}\) \(\div\) f\(^{\frac{5}{2}}\)g\(^o\)h\(^{\frac{7}{3}}\) = f\(^{\frac{1}{2} - \frac{5}{2}}\) g\(^{2 - 0}\) h\(^{\frac{1}{3} - \frac{7}{3}}\)
= f\(^{-2}\) g\(^2\) h\(^{-2}\)
= \(\frac{g^2}{f^2h^2}\)
= (\(\frac{g}{fh}\))\(^2\)
Source: Myschool Past Questions Archive (Record #32539)
Mathematics
UTME / JAMB 1982
Fractions, Decimals, Percentages & Approximations
Solution
Determine the mean monthly salary of 50 employees of a company from the following frequency distribution.
\(\begin{array}{c|c} \text{Monthly salary} & \text{Frequency}\\\hline N200.00 & 10\\ N325.00 & 5\\N100.00 & 20\\N120.00 & 2\\ N60.00 & 10\\ N80.00 & 3\end{array}\)
A
N215.30
B
N134.10
C
N143.10
D
N80.00
E
N50.30
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
\(\bar{x}\) = \(\frac{fx}{N}\)
= \(\frac{6705}{50}\)
= 1341
= N134.10
Source: Myschool Past Questions Archive (Record #32540)
Mathematics
UTME / JAMB 1982
Plane Geometry, Polygons & Circle Theorems
Solution
If the function y = 5x is graphed, what would be its intercept on the y-axis?
A
5
B
\(\frac{1}{5}\)
C
1
D
2
E
zero
medium Difficulty
Verified Correct Answer: Option E
Step-by-Step Mathematical Solution
y = 5x, when x = 0
y = 0, when x = 1
y = 5
intercept on y axis is 0
Source: Myschool Past Questions Archive (Record #32541)
Mathematics
UTME / JAMB 1982
Plane Geometry, Polygons & Circle Theorems
Solution
A side of a rhombus is 2cm in length. An angle of the rhombus is 60o. What is the length of the diagonal facing this angle?
A
2cm
B
8cm
C
4cm
D
2\(\sqrt{3}\)cm
E
16cm
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
\(\frac{x}{2}\) = sin60o = cos30o
x = 2 sino
= 2 x \(\frac{\sqrt{3}}{2}\)
= \(\sqrt{3}\)
length of the diagonal = 2 x \(\sqrt{2}\)
= 2\(\sqrt{3}\)
Source: Myschool Past Questions Archive (Record #32542)
Mathematics
UTME / JAMB 1982
Variations
Solution
A variable y is inversely proportional to x\(^2\), when y = 10, x = 2. What is y when x = 10?
A
2
B
4
C
100
D
0.4
E
0.1
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
y \(\alpha\) \(\frac{1}{x^2}\)
y = \(\frac{k}{x^2}\)
k = x\(^2\)y
= (2)\(^2\) x 10 = 40
y = \(\frac{40}{x^2}\)
= \(\frac{40}{(10)^2}\)
= \(\frac{40}{100}\) = 0.4
Source: Myschool Past Questions Archive (Record #32543)
Mathematics
UTME / JAMB 1982
Fractions, Decimals, Percentages & Approximations
Solution
Two distinct sectors i the same circle substend 100o and 30o respectively at the centre of the circle. Their corresponding arcs are in ratio
A
10:3
B
1:100
C
3:1
D
5:2
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
The distinct sectors i the same circle substend 100o and 30o respectively at the centre of the circle. Their corresponding arcs are in ratio 100:30 = 10:3
Source: Myschool Past Questions Archive (Record #32544)