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Mathematics
UTME / JAMB 1995
Statistics (Data Representation, Central Tendency & Dispersion)
Solution
\(\begin{array}{c|c} \text{Class Interval} & Frequency & \text{Class boundaries} & Class Mid-point \\ \hline 1.5 - 1.9 & 2 & 1.45 - 1.95 & 1.7\\ 2.0 - 2.4 & 21 & 1.95 - 2.45 & 2.2\\ 2.5 - 2.9 & 4 & 2.45 - 2.95 & 2.7 \\ 3.0 - 2.9 & 15 & 2.95 - 3.45 & 3.2\\ 3.5 - 3.9 & 10 & 3.45 - 3.95 & 3.7\\ 4.0 - 4.4 & 5 & 3.95 - 4.45 & 4.2\\ 4.5 - 4.9 & 3 & 4.45 - 4.95 & 4.7\end{array}\)
The median of the distribution above is
A
4.0
B
3.4
C
3.2
D
3.0
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
Median = \(\frac{a + b}{fm}\) (\(\frac{1}{2} \sum f - CF_b\))
= 2.95 + \(\frac{0.5}{15}\)(2.-7)
= 2.95 + \(\frac{0.5}{15}\) x 13
= 2.95 + 0. 43
= 3.38
= 3.4
Source: Myschool Past Questions Archive (Record #30949)
Mathematics
UTME / JAMB 1995
Permutations, Combinations & Probability
Let p be a probability function on set S, where S = (a1, a2, a3, a4). Find P(a1) if P(a2) = \(\frac{1}{3}\), p(a3) = \(\frac{1}{6}\) and p(a4) = \(\frac{1}{5}\)
A
\(\frac{7}{3}\)
B
\(\frac{2}{3}\)
C
\(\frac{1}{3}\)
D
\(\frac{3}{10}\)
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
No expanded working has been attached for this question yet. The verified answer is Option D.
Source: Myschool Past Questions Archive (Record #30950)
Mathematics
UTME / JAMB 1995
Permutations, Combinations & Probability
Solution
A die has four of it's faces coloured white and the remaining two coloured black. What is the probability that when the die is thrown two consecutive time, the top face will be white in both cases?
A
\(\frac{5}{3}\)
B
\(\frac{1}{9}\)
C
\(\frac{4}{9}\)
D
\(\frac{1}{36}\)
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
\(\begin{array}{c|c} & W & W & W & W & B & B \\ \hline W & WW & WW & WW & WW & WB & WB \\ W & WW & WW & WW & WW & WB & WB\\W & WW & WW & WW & WW & WB & WB\\ W & WW & WW & WW & WW & WB & WB\\ B & BW & BW & BW & BW & BB & BB \\ B & BW & BW & BW & BW & BB & BB\end{array}\)
P(WW) = \(\frac{16}{36}\)
= \(\frac{4}{9}\)
Source: Myschool Past Questions Archive (Record #30951)
Mathematics
UTME / JAMB 1995
Inequalities & Linear Programming
Diagram
Solution
Use the graph of the curve y = f(x)to solve the inequality f(x) \(\leq\) 0
Attached Figure / Diagram
A
-1 \(\geq\) x \(\geq\) 1, x \(\geq\) 2
B
x \(\leq\) -1, 1 \(\geq\) x \(\geq\) 2
C
x \(\geq\) -1, 1 \(\geq\) x \(\geq\) 2
D
x \(\geq\) 2, -1 \(\geq\) x \(\geq\) 1
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
-1 \(\geq\) x \(\geq\) 1, 1 < x \(\geq\) 2
Combining solutions
= x \(\leq\) 1; 1 \(\geq\) x \(\geq\) 2
Source: Myschool Past Questions Archive (Record #33043)
Mathematics
UTME / JAMB 1995
Plane Geometry, Polygons & Circle Theorems
Diagram
Solution
Determine the value of x in the figure
Attached Figure / Diagram
A
134o
B
81o
C
53o
D
46o
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
Within the triangle,
180^\circ - (81^\circ + 53^\circ) = 46^\circ
In a cyclic quadrilateral, the sum of two opposite angles = 180^\circ
\(\therefore\) x = 180^\circ - 46^\circ = 134^\circ
Source: Myschool Past Questions Archive (Record #33044)
Mathematics
UTME / JAMB 1995
Plane Geometry, Polygons & Circle Theorems
Diagram
Solution
PT is a tangent to the circle TYZX. YT = YX and < PTX = 50o. Calculate < TZY
Attached Figure / Diagram
A
50o
B
65o
C
85o
D
130o
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
XTY = 50o = TXY = \(\frac{130^o}{2}\)
= 65o
Source: Myschool Past Questions Archive (Record #33045)
Mathematics
UTME / JAMB 1995
Mensuration (Areas, Perimeters & Volumes)
Diagram
Solution
In the diagram, the base diameter is 14cm while the height is 12cm. Calculate the total surface area if the cylinder has both a base and a top.[\(\pi \frac{22}{7}\)]
Attached Figure / Diagram
A
836cm2
B
308cm2
C
528cm2
D
154cm2
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
Area(S) = 2\(\pi r^2 + 2 \pi rh = 2\pi r(h + r)\)
D = 14cm, 2r = D
r = \(\frac{D}{2}\)
= 7cm
S = 2 x \(\frac{22}{7} \times [7 + 12] = 44 \times 19\)
= 836cm2
Source: Myschool Past Questions Archive (Record #33066)
Mathematics
UTME / JAMB 1995
Trigonometry, Elevation & Bearings
Diagram
Solution
In the diagram, find PQ if the area of triangle PQR is 35cm\(^2\)
Attached Figure / Diagram
A
7cm
B
10cm
C
14cm
D
17cm
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
\(\frac{1}{2}\)(PQ x 10 sin 30) = 35
PQ = \(\frac{35 \times 2}{10 \sin 30}\)
= 14cm
Source: Myschool Past Questions Archive (Record #33067)
Mathematics
UTME / JAMB 1995
Plane Geometry, Polygons & Circle Theorems
Solution
The mean and the range of the set of numbers 1.20, 1.00, 0.90, 1.40, 0.80, 1.20, and 1.10 are m and r, respectively. Find m + r
A
1.11
B
1.65
C
1.85
D
2.45
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
Given:1.20, 1.00, 0.90, 1.40, 0.80, 1.20, 1.10
Sum of the numbers = 1.20 + 1.00 + 0.90 + 1.40 + 0.80 + 1.20 + 1.10
= 7.60
Number of terms = 7
Mean, m = 7.60 \div 7 = 1.0857 (to 4 d.p.)
Highest value = 1.40
Lowest value = 0.80
Range, r = 1.40 − 0.80 = 0.60
m + r = 1.0857 + 0.60 = 1.6857 closest to 1.65.
Source: Myschool Past Questions Archive (Record #33068)
English Language
UTME / JAMB 1995
Concord (Subject-Verb Agreement)
Select the option that best explains the information conveyed in the sentence.
Most of the time, their presence is a menace?
A
Their presence isw always meaningful
B
Their presence is seldom a bother
C
Their presence is ussually of great concern
D
Their presence is frequently a threat
medium Difficulty
Verified Correct Answer: Option D
Grammar & Contextual Explanation
No expanded working has been attached for this question yet. The verified answer is Option D.
Source: Myschool Past Questions Archive (Record #10584)
English Language
UTME / JAMB 1995
Concord (Subject-Verb Agreement)
Solution
Select the option that best explains the information conveyed in the sentence.
My son, who is in the U.S.A., is studying Engineering.
A
My only son in the U.S.A is studying Engineering
B
One of my sons is in the U.S.A studying Engineering
C
My sons are in the U.S.A but only one is studying Engineering
D
My only son is in the U.S.A studying Engineering
medium Difficulty
Verified Correct Answer: Option B
Grammar & Contextual Explanation
The phrase "My son, who is in the U.S.A, is studying Engineering" contains a non-restrictive (or non-defining) relative clause ("who is in the U.S.A"). This means:
The sentence assumes that the speaker has more than one son (otherwise, the phrase would use "My only son").
The comma before "who" indicates that the information about being in the U.S.A is additional, rather than essential.
Therefore, it suggests that one of the speaker's sons is in the U.S.A and studying Engineering.
Source: Myschool Past Questions Archive (Record #10587)
English Language
UTME / JAMB 1995
Concord (Subject-Verb Agreement)
Solution
Select the option that best explains the information conveyed in the sentence.
The mills of God grind slowly, but they grind exceedingly small
A
God has a mill where every material in life is thoroughly ground
B
God may seem slow in action, but he adequately rewards every bit of injustice
C
The world is like a food factory where God take his time in grinding all raw materials properly
D
Even though God is never in a hurry, He achieves al things
medium Difficulty
Verified Correct Answer: Option B
Grammar & Contextual Explanation
The proverbial expression of the mills of God grinding slowly refers to the notion of slow but certain divine retribution. Which means that no matter how long it takes, he who needs to be punished will be punished. God watches all, and the day of reckoning will come. the prover is attributed to
Source: Myschool Past Questions Archive (Record #10592)
English Language
UTME / JAMB 1995
Concord (Subject-Verb Agreement)
Select the option that best explains the information conveyed in the sentence.
I was one of those who actively believe in his development programmes?
A
I was part of those who renounced the programmes
B
I was the originator of the programmes
C
I was one of the people who embraced the programmes
D
I was one of the great number who developed his programmes actively
medium Difficulty
Verified Correct Answer: Option C
Grammar & Contextual Explanation
No expanded working has been attached for this question yet. The verified answer is Option C.
Source: Myschool Past Questions Archive (Record #10593)
English Language
UTME / JAMB 1995
Concord (Subject-Verb Agreement)
Solution
Select the option that best explains the information conveyed in the sentence.
People are not interested in who rules?
A
People who rules are not interested in the rule
B
The rulers are not indifferent about the people
C
People are indifferent about the rulers
D
People are ruled by the people they are interest in
medium Difficulty
Verified Correct Answer: Option C
Grammar & Contextual Explanation
e not
Source: Myschool Past Questions Archive (Record #10595)
English Language
UTME / JAMB 1995
Antonyms (Opposite in Meaning)
Choose the most appropriate option opposite in meaning to the underlined word.
Good student can easily identify spurious arguments?
A
genuine
B
interesting
C
false
D
illogical
medium Difficulty
Verified Correct Answer: Option A
Grammar & Contextual Explanation
No expanded working has been attached for this question yet. The verified answer is Option A.
Source: Myschool Past Questions Archive (Record #10598)