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Mathematics
UTME / JAMB 1987
Plane Geometry, Polygons & Circle Theorems
Solution
Find the probability of selecting a figure which is a parallelogram from a square, a rectangle, a rhombus, a kite and a trapezium
A
\(\frac{3}{5}\)
B
\(\frac{2}{5}\)
C
\(\frac{4}{5}\)
D
\(\frac{1}{5}\)
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
A rectangle, a square and a rhombus are the only parallelogram
∴ Probability of a parallelogram = \(\frac{3}{5}\)
Source: Myschool Past Questions Archive (Record #31993)
Mathematics
UTME / JAMB 1987
Plane Geometry, Polygons & Circle Theorems
Solution
An (\(n - 2)^2\) sided figure has n diagonals. Find the number n diagonals for a 25-sided figure
A
7
B
8
C
9
D
10
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
(n-2)\(^2\) = 25
n - 2 = 5
n = 5 + 2 = 7
Source: Myschool Past Questions Archive (Record #32820)
Mathematics
UTME / JAMB 1987
Plane Geometry, Polygons & Circle Theorems
Diagram
Solution
In the diagram, POQ is a diameter, 0 is the centre of the circle and TP is a tangent. Find the value of x
Attached Figure / Diagram
A
30o
B
40o
C
45o
D
50o
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
From the diagram, POQ is a diameter; o is the centre of the circle and TP is a tangent where RTP = 30o
RTP = RQP = x(at circumference = made by tangent outside the circle) i.e x = 30o
Source: Myschool Past Questions Archive (Record #32822)
Mathematics
UTME / JAMB 1987
Mensuration (Areas, Perimeters & Volumes)
Diagram
Solution
In the diagram above, QR // TS, QR : TS = 2.3, Find the ratio of the area of triangle PQR to the area of the trapezium QRST.
Attached Figure / Diagram
A
4:9
B
4:5
C
1:3
D
2:3
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
h1 = \(\frac{h_1 + h_2}{1.5}\) = \(\frac{h_1}{h_2} = 2\)
\(\frac{A_{\bigtriangleup PQR}}{A_{TP(QRST)}} = \frac{\frac{1}{2} \times 2 \times h_1}{\frac{1}{2} \times h_2 (2 + 3)}\)
\(\frac{2}{5} \times \frac{h_1}{h_2} = \frac{2}{5} \times 2\)
= \(\frac{4}{5}\)
Source: Myschool Past Questions Archive (Record #32824)
Mathematics
UTME / JAMB 1987
Plane Geometry, Polygons & Circle Theorems
Diagram
Solution
Three angles of a nonagon are equal and the sum of six other angles is 1110o. Calculate the size of one of the equal angles.
Attached Figure / Diagram
A
210o
B
150o
C
105o
D
50o
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
Sum of interior angles of any polygon is (2n - 4) right angle; n angles of the nonagon = 9
where 3 are equal and 6 other angles = 1110o
( 2 x 9 - 4)90o = (18 - 4)90o
= 14 x 90o = 1260o
9 angles = 12600, 6 angles = 1110o
Remaining 3 angles = 1260o - 1110o = 150o
size of one of the3 angles \(\frac{150}{3}\) = 50o
Source: Myschool Past Questions Archive (Record #32826)
Mathematics
UTME / JAMB 1987
Plane Geometry, Polygons & Circle Theorems
Diagram
Solution
In the figure, find the value of x
Attached Figure / Diagram
A
110o
B
100o
C
90o
D
80o
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
Z = X = Y = 180o .........(i)
2Z + Y + Y = 190 = 2Z + 2Y = 180
Z + Y = 90o........(ii)
hence x + (z + y) = 180
x + 90o = 180o
x = 180o - 90o
= 90o
Source: Myschool Past Questions Archive (Record #32828)
Mathematics
UTME / JAMB 1987
Plane Geometry, Polygons & Circle Theorems
Diagram
Solution
The figure is an example of the construction of a
Attached Figure / Diagram
A
perpendicular bisector of a given straight line QR
B
perpendicular from a given point to a given line QR
C
perpendicular to a line from a given point P on that line
D
given angle
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
QR is a given line and P is a given point. The construction is the perpendicular from a given point P to a given line QR
Source: Myschool Past Questions Archive (Record #32830)
English Language
UTME / JAMB 1987
Antonyms (Opposite in Meaning)
In the question below choose the option opposite in meaning to the word(s) Underlined:
The house-wife was hard up before the end of each month
A
upset
B
penniless
C
borrowing
D
in no need
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 #5172)
English Language
UTME / JAMB 1987
Antonyms (Opposite in Meaning)
In the question below choose the option opposite in meaning to the word(s) Underlined:
The retired General became a hard- nosed officer after fighting the war
A
tough
B
weak
C
indifferent
D
bed ridden
medium Difficulty
Verified Correct Answer: Option B
Grammar & Contextual Explanation
No expanded working has been attached for this question yet. The verified answer is Option B.
Source: Myschool Past Questions Archive (Record #5173)
English Language
UTME / JAMB 1987
Antonyms (Opposite in Meaning)
In the question below choose the option opposite in meaning to the word(s) Underlined:
The Lions lost the match because their goalkeeper was in a haze most of the time
A
indisposed
B
confused
C
alert
D
sleeping
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 #5174)
English Language
UTME / JAMB 1987
Antonyms (Opposite in Meaning)
In the question below choose the option opposite in meaning to the word(s) Underlined:
Unless we see the evils clearly, contending against them is like fighting the air
A
avoiding
B
strugglling with
C
combating
D
repelling
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 #5175)
English Language
UTME / JAMB 1987
Antonyms (Opposite in Meaning)
In the question below choose the option opposite in meaning to the word(s) Underlined:The explosive growth of world population has not been caused by a sudden increase in human fertility
A
fantastic
B
gradual
C
combustible
D
dangerous
medium Difficulty
Verified Correct Answer: Option B
Grammar & Contextual Explanation
No expanded working has been attached for this question yet. The verified answer is Option B.
Source: Myschool Past Questions Archive (Record #5176)
English Language
UTME / JAMB 1987
Antonyms (Opposite in Meaning)
Solution
In the question below choose the option opposite in meaning to the word(s) Underlined:
It is generally believed that misers are not loved by many
A
spendthrifts
B
spenders
C
hoarders
D
savers
medium Difficulty
Verified Correct Answer: Option A
Grammar & Contextual Explanation
The underlined word "misers" refers to people who hoard money and are reluctant to spend it. The opposite of a miser is someone who spends money excessively, which is best captured by the word "spendthrift".
Source: Myschool Past Questions Archive (Record #5177)
English Language
UTME / JAMB 1987
Antonyms (Opposite in Meaning)
Solution
In the question below choose the option opposite in meaning to the word(s) Underlined:
My brother's primary school foundation was solid and this influenced his secondary education
A
sound
B
sordid
C
shaky
D
weak
medium Difficulty
Verified Correct Answer: Option D
Grammar & Contextual Explanation
The word “solid” in the sentence describes the strength and quality of the academic foundation the brother received in primary school. It implies that his foundation was strong and well-established, which positively influenced his secondary education.
The opposite of “solid” in this context is therefore “weak”, meaning a foundation that is inadequate or not strong enough to support further learning.
Source: Myschool Past Questions Archive (Record #5178)
English Language
UTME / JAMB 1987
Synonyms (Nearest in Meaning)
In the question below choose the option nearest in meaning to the Underlined word(s) or phrase:Ít is very difficult to know who is not entitled to essential commodities these days' observed the mobbed NNSC officials
A
qualified for
B
disqualified from
C
eligible
D
worthy of
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 #5179)