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Mathematics
UTME / JAMB 1980
Statistics (Data Representation, Central Tendency & Dispersion)
Solution
The median of the set of numbers 4, 9, 4, 13, 7, 14, 10, 17 is
A
13
B
7
C
\(\frac{19}{2}\)
D
\(\frac{39}{4}\)
E
10
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
Rearranging in increasing order 4, 4, 7, 9, 10, 13, 14, 17, the
median = \(\frac{(9 + 10)}{2}\)
= \(\frac{19}{2}\)
Source: Myschool Past Questions Archive (Record #32611)
Mathematics
UTME / JAMB 1980
Inequalities & Linear Programming
Solution
List all integer values of x satisfying the inequality -1 < 2x - 5 \(\leq\) 5
A
<2, 3, 4, 5
B
3, 4, 5
C
2, 3, 4
D
3, 4
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
\(-1 < 2x - 5 \leq 5\)
\(\implies -1 + 5 < 2x - 5 + 5 \leq 5 + 5\)
\(4 < 2x \leq 10\)
\(\implies 2 < x \leq 5 \)
= 3, 4, 5.
Source: Myschool Past Questions Archive (Record #32612)
Mathematics
UTME / JAMB 1980
Linear, Simultaneous & Quadratic Equations
Solution
Find the roots of the equation 10x2 - 13x - 3 = 0
A
x = \(\frac{3}{5}\) or -\(\frac{1}{2}\)
B
x = \(\frac{3}{10}\) or -1
C
x = \(\frac{3}{10}\) or 1
D
x = \(\frac{1}{5}\) or \(\frac{-3}{2}\)
E
x = -\(\frac{1}{5}\) or \(\frac{3}{2}\)
medium Difficulty
Verified Correct Answer: Option E
Step-by-Step Mathematical Solution
10x2 - 13x - 3 = 0 = 10x2 - 15x + 2x - 3 = 0
5x(2x - 3) + 2x - 3 = 0
= (5x + 1)(2x - 3) = 0
5x + 1 = 0 or 2x - 3 = 0
x = -\(\frac{1}{5}\) or \(\frac{3}{2}\)
Source: Myschool Past Questions Archive (Record #32613)
Mathematics
UTME / JAMB 1980
Mensuration (Areas, Perimeters & Volumes)
Solution
A solid cylinder of radius 3cm has a total surface area of 36\(\pi\)cm2. Find its height
A
2cm
B
3cm
C
4cm
D
5cm
E
6cm
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
Area 2\(\pi\)r2 + 2 \(\pi\)r(r + h)
= 2\(\pi\)r(r + h)
36\(\pi\) = 6\(\pi\)(r + h)
36\(\pi\) = 6\(\pi\)(3 + h)
36\(\pi\) = 18\(\pi\) + 6\(\pi\)h
36\(\pi\) - 18\(\pi\) = 6\(\pi\)h
Divide both side by 6\(\pi\)
h = 3cm
Source: Myschool Past Questions Archive (Record #32614)
Mathematics
UTME / JAMB 1980
Fractions, Decimals, Percentages & Approximations
Solution
The ratio of the areas of similar triangles is necessarily equal to
A
the ratio of the corresponding sides
B
the ratio of the squares of corresponding sides
C
the ratio of the corresponding heights of the triangles
D
half the ratio of the corresponding heights of the triangles
E
the ratio of the corresponding bases to the heights of the triangles
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
The ratio of the areas of two similar triangles is equal to the square of ratio of their corresponding sides.
Source: Myschool Past Questions Archive (Record #32615)
Mathematics
UTME / JAMB 1980
Plane Geometry, Polygons & Circle Theorems
Solution
P and Q are fixed points, and X is a variable point which moves so that angle PXQ = 45º. What is the locus of x?
A
A pair of straight lines parallel to PQ
B
The perpendicular bisector of PQ
C
An arc of a circle passing through P and Q
D
A circle with diameter PQ
E
The bisector of angle PXQ
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
Constant Angle Rule:
In geometry, the locus of points from which a line segment subtends a constant angle is an arc of a circle.
Inscribed Angle Theorem:
This theorem states that angles subtended by the same arc at the circumference of a circle are equal. Consequently, as the point moves along the arc, the subtended angle remains constant.
Source: Myschool Past Questions Archive (Record #32616)
Mathematics
UTME / JAMB 1980
Fractions, Decimals, Percentages & Approximations
Solution
A man and his wife went to buy an article costing N400. The woman had 10% of the cost and the man 40% of the remainder. How much did they have altogether?
A
N216
B
N200
C
N184
D
N144
E
N100
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
10% of 400 = N40, Remainder = N360
40% of 360 = N144
Altogether they 144 + 40
= N184
Source: Myschool Past Questions Archive (Record #32617)
Mathematics
UTME / JAMB 1980
Indices, Logarithms & Surds
Solution
Simplify \(\frac{log_{10}8}{log_{10}4}\)
A
log102
B
log104
C
\(\frac{3}{2}\)
D
2
E
None of the above
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
\(\frac{log_{10}8}{log_{10}4}\) = \(\frac{log_{10}2^3}{log_{10}2^2}\)
= \(\frac{3 log_{10}2}{2log_{10}2}\)
= \(\frac{3}{2}\)
Source: Myschool Past Questions Archive (Record #32618)
Mathematics
UTME / JAMB 1980
Plane Geometry, Polygons & Circle Theorems
Solution
Make c the subject of formula v = 1 - \(\frac{a}{5}\)(b + \(\frac{3c}{7}\))
A
[\(\frac{7}{3}\) + \(\frac{5}{a}\)(v - 1)] + b
B
[\(\frac{7b}{3}\) + \(\frac{5}{a}\)(v - 1)]
C
\(\frac{-7}{3}\)[b + \(\frac{5}{a}\)(v - 1)]
D
\(\frac{7}{3}\)[b + \(\frac{5v - 1}{a}\)]
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
v = 1 - \(\frac{a}{5}\)(b + \(\frac{3c}{7}\))
V - 1 = - \(\frac{a}{5}\)(b + \(\frac{3c}{7}\))
Multiply both sides by -1
1 - V = \(\frac{a}{5}\)(b + \(\frac{3c}{7}\))
Multiply both sides by \(\frac{5}{\text{a}}\)
\(\frac{a}{5}\)(1 - V) = b + \(\frac{3c}{7}\)
\(\frac{a}{5}\)(1 - V) - b = \(\frac{3c}{7}\)
Multiply both sides by \(\frac{7}{3}\)
\(\frac{7}{3}\)( \(\frac{a}{5}\)(1 - V) - b) = c
- \(\frac{7}{3}\)(\(\frac{a}{5}\)(V - 1) + b)
Source: Myschool Past Questions Archive (Record #32619)
Mathematics
UTME / JAMB 1980
Plane Geometry, Polygons & Circle Theorems
Solution
What factor is common to all the expressions x2 - x, 2x2 + x - 1 and x2 - 1?
A
x
B
x + 1
C
x - 1
D
No common factor
E
(2x - 1)
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
x2 - x = x(x - 1)
= 2x2 + x - 1
= (2x - 1)(x + 10
x2 - 1 = (x + 1)(x - 1)
No factor
Source: Myschool Past Questions Archive (Record #32620)
Mathematics
UTME / JAMB 1980
Plane Geometry, Polygons & Circle Theorems
Solution
Which of the formula below represents the general terms of the following set of numbers(-1, \(\frac{2}{3}\), -\(\frac{1}{2}\), \(\frac{2}{5}\)......) for n = 1, 2, 3, 4.......?
A
\(\frac{2}{n + 1}\)
B
(-1)n + 1 \(\frac{2}{n + 1}\)
C
(-1)n \(\frac{2}{n + 1}\)
D
\(\frac{n}{2n - 1}\)
E
(-1)n\(\frac{n}{2n - 1}\)
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
(-1, \(\frac{2}{3}\), -\(\frac{1}{2}\), \(\frac{2}{5}\)......)
nthterm is (-1)n\(\frac{2}{n + 1}\)
Since (-1)n will always be negative for n = odd
Source: Myschool Past Questions Archive (Record #32621)
Mathematics
UTME / JAMB 1980
Statistics (Data Representation, Central Tendency & Dispersion)
Solution
In a school, there are 35 students in class 2A and 40 in class 2B. The mean score for class 2 in an English Literature examination is 60.0 and that for 2B in the same paper is 52.5. Find, to one place of decimal, the mean for the combined classes
A
2.5
B
56.0
C
56.2
D
56.3
E
6.5
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
Total score for 2A & 2B = 4200
mean score = \(\frac{4200}{40 + 35}\)
= \(\frac{4200}{75}\)
= 56
Source: Myschool Past Questions Archive (Record #32623)
Mathematics
UTME / JAMB 1980
Statistics (Data Representation, Central Tendency & Dispersion)
Solution
A set of data contains a total of 130 items which are divided into six groups for display on a pie chart. If one group contains 26 items, then the sector representing this group on the pie chart contains an angle xo at the centre of the circle where x is
A
36o
B
60o
C
70o
D
72o
E
75o
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
\(\frac{26}{130}\) = \(\frac{x}{360}\)
130x = 26 x 360
= 9360
x = \(\frac{9360}{130}\)
= 72o
Source: Myschool Past Questions Archive (Record #32624)
Mathematics
UTME / JAMB 1980
Fractions, Decimals, Percentages & Approximations
Solution
In triangle FGH, < G = 90º, < H = 60º, while in triangle XYZ, < X = 60º and < Y = 30º. Form XYZ write down the ratio equal to \(\frac{FG}{FH}\)
A
\(\frac{YX}{ZX}\)
B
\(\frac{YX}{YZ}\)
C
\(\frac{ZX}{YZ}\)
D
\(\frac{YZ}{XY}\)
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
The two triangles are similar
\(\frac{FG}{YZ}\) = \(\frac{FH}{XY}\) = \(\frac{GH}{YZ}\) = \(\frac{FG}{FH}\) = \(\frac{YZ}{XZ}\)
Source: Myschool Past Questions Archive (Record #32625)
Mathematics
UTME / JAMB 1980
Plane Geometry, Polygons & Circle Theorems
Solution
A pentagon has four of its angles equal. If the size of the fifth angle is 60o, Find the size of each of the four equal angles.
A
60o
B
108o
C
120o
D
150o
E
None of the above
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
The sum of interior angle of pentagon
(5 sides) = (2n - 4) x 90o
n = 5
(2 x 5 - 4) x 90o = 6 x 90o
= 540o
540o - 60o = 480o \(\div\) 4
= 120o
Source: Myschool Past Questions Archive (Record #32626)