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Mathematics
WAEC / WASSCE 1991
Statistics (Data Representation, Central Tendency & Dispersion)
Solution
The table below shows the distribution of the waiting times for some customers in a certain petrol station.
Waiting time (in mins)
No of customers
1.5 - 1.9
3
2.0 - 2.4
10
2.5 - 2.9
18
3.0 - 3.4
10
3.5 - 3.9
7
4.0 - 4.4
2
(a) Write down the class boundaries of the distribution.
(b) Construct a cumulative frequency curve for the data;
(c) Using your graph, estimate: (i) the interquartile range of the distribution ; (ii) the proportion of customers who could have waited for more than 3 minutes.
medium Difficulty
Verified Correct Answer: Option
Step-by-Step Mathematical Solution
Waiting time (in mins)
Class boundaries
No of customers
Cum Freq
1.5 - 1.9
1.45 - 1.95
3
3
2.0 - 2.4
1.95 - 2.45
10
13
2.5 - 2.9
2.45 - 2.95
18
31
3.0 - 3.4
2.95 - 3.45
10
41
3.5 - 3.9
3.45 - 3.95
7
48
4.0 - 4.4
3.95 - 4.45
2
50
(b)
(c) Interquartile range of the distribution = \(Q_{3} - Q_{1}\)
\(Q_{3} = \frac{3 \times 51}{4} = 38.25\)
\(Q_{1} = \frac{1 \times 51}{4} = 12.75\)
From the graph, \(Q_{3} = 3.25 ; Q_{1} = 2.45\)
\(\therefore \text{The interquartile range of the distribution } = 3.25 - 2.45 = 0.80\)
(ii) Proportion of customers who must have waited for more than 3 minutes = \(\frac{16}{50} = \frac{8}{25}\)
Source: Myschool Past Questions Archive (Record #54626)
Mathematics
WAEC / WASSCE 1991
Plane Geometry, Polygons & Circle Theorems
Solution
(a) Using a ruler and a pair of compasses only, construct a parallelogram PQRS with diagonals |PR| = 9cm and |QS| = 6cm, intersecting at K and < QKR = 60^\circ.
(b) Construct a rectangle PABS which is equal in area to PQRS in (a) above and on the same side of PS as PQRS. Measure |PA|.
medium Difficulty
Verified Correct Answer: Option
Step-by-Step Mathematical Solution
(a) & (b)
Source: Myschool Past Questions Archive (Record #54627)
Mathematics
WAEC / WASSCE 1991
Trigonometry, Elevation & Bearings
Solution
From a horizontal distance of 8.5 km, a pilot observes that the angles of depression of the top and the base of a control tower are 30^\circ and 33^\circ respectively. Calculate, correct to three significant figures :
(a) the shortest distance between the pilot and the base of the control tower;
(b) the height of the control tower.
medium Difficulty
Verified Correct Answer: Option
Step-by-Step Mathematical Solution
Let T and B be the top and base of the control tower respectively; P, the point of pilot's observation and PS, the line of observation.
(a) Shortest distance is |PB|.
\(\therefore \cos 33^\circ = \frac{8.5}{PB}\)
\(PB = \frac{8.5}{\cos 33} = \frac{8.5}{0.8387}\)
\(|PB| = 10.135km \approxeq 10.1km\)
(b) Height of the control tower = |SB| - |ST|
\(\therefore \tan 33^\circ = \frac{|SB|}{8.5 km} \implies |SB| = 8.5 \tan 33^\circ\)
\(|SB| = 5.52 km\)
\(\tan 30^\circ = \frac{|ST|}{8.5 km} \implies |ST| = 8.5 \tan 30^\circ\)
\(|ST| = 4.907 km\)
\(\therefore\) The height of the tower = 5.52 km - 4.907 km = 0.613 km.
Source: Myschool Past Questions Archive (Record #54628)
English Language
UTME / JAMB 1991
Antonyms (Opposite in Meaning)
In the question below choose the option opposite in meaning to the word underlined:
I am happy to inform you that your boys are conscientious
A
industrious
B
carefree
C
careful
D
corrupt
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 #6455)
English Language
UTME / JAMB 1991
Antonyms (Opposite in Meaning)
In the question below choose the option opposite in meaning to the word underlined:
My father is a very prosperous businessman
A
ungrateful
B
unscrupulous
C
unskilful
D
unsuccessful
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 #6456)
English Language
UTME / JAMB 1991
Antonyms (Opposite in Meaning)
Solution
In the question below choose the option opposite in meaning to the word underlined:
The hostess greeted her guests in a very relaxed manner.
A
energetic
B
athletic
C
stiff
D
perplexed
medium Difficulty
Verified Correct Answer: Option C
Grammar & Contextual Explanation
Relaxed describes a manner that is calm and at ease. The opposite of this is “stiff,” which suggests being formal, rigid or uncomfortable in behaviour.
Source: Myschool Past Questions Archive (Record #6457)
English Language
UTME / JAMB 1991
Antonyms (Opposite in Meaning)
In the question below choose the option opposite in meaning to the word underlined:
Ayo takes his studies rather lightly
A
humorously
B
tediously
C
carefully
D
seriously
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 #6458)
English Language
UTME / JAMB 1991
Antonyms (Opposite in Meaning)
In the question below choose the option opposite in meaning to the word underlined:
The doctor was very gentle with his patients in the examining room
A
harsh
B
rude
C
rough
D
unkind
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 #6459)
English Language
UTME / JAMB 1991
Synonyms (Nearest in Meaning)
Solution
In the question below choose the option nearest in meaning to the word or phrase underlined:
There is no love lost between Hassan and Hassana
A
dislike each other
B
are head over heals in love
C
will love each other
D
are still good friends
medium Difficulty
Verified Correct Answer: Option A
Grammar & Contextual Explanation
No love lost between two people means that they are not friends, they dislike each other intensely.
Source: Myschool Past Questions Archive (Record #6460)
English Language
UTME / JAMB 1991
Synonyms (Nearest in Meaning)
In the question below choose the option nearest in meaning to the word or phrase underlined:
Whether the villages head should identify himself with the activities of religious demonstrations has remained a burning question
A
a subject of discord
B
a perennial issue
C
a matter of serious controversy
D
a sensitive matter
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 #6461)
English Language
UTME / JAMB 1991
Synonyms (Nearest in Meaning)
In the question below choose the option nearest in meaning to the word or phrase underlined:
I would rather not attend the party
A
detest attending
B
do not have the enthusiasm to attend
C
must not attend
D
have a choice to attend or not to
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 #6462)
English Language
UTME / JAMB 1991
Concord (Subject-Verb Agreement)
In the question below choose the option nearest meaning to the word or phrase underlined:
If Garba had listen to advice, he would not have had to be rushed to the hospital
A
deliberately desired to be rushed
B
was in a position to have prevented the need to be rushed
C
was rushed against his wish
D
was given a cheque, but preferred to go
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 #6463)
English Language
UTME / JAMB 1991
Synonyms (Nearest in Meaning)
Solution
In the question below choose the option nearest in meaning to the word or phrase underlined:
Aduke: Ngozi, let's visit the market.
Ngozi: if you insist, Ngozi
A
is very willing to accompany Aduke
B
must accompany Aduke
C
is not keen on going with Aduke
D
is pretending not to be interested in going with Aduke
medium Difficulty
Verified Correct Answer: Option C
Grammar & Contextual Explanation
Meaning/Usage: To agree after the other person demands it. Explanation: "Insist" means to demand something and that they will not accept refusal. It became common to say this phrase by itself when the other person insisted on something. "We will stay longer if you insist.". "We can go another night if you insist.".
Source: Myschool Past Questions Archive (Record #6464)
English Language
UTME / JAMB 1991
Synonyms (Nearest in Meaning)
In the question below choose the option nearest in meaning to the word or phrase in underlined:
The new leader hands out an olive branch
A
sues for peace
B
gives out branches of the olive tree
C
challenges his opponents to a fight
D
blesses his congregation
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 #6465)
English Language
UTME / JAMB 1991
Synonyms (Nearest in Meaning)
Solution
In the question below choose the option nearest in meaning to the word or phrase in italics:
When you go to a foreign country to study, you will discover that life is not a bed of roses
A
as pleasant as one thought
B
a bed with roses
C
an unmitigated disapointment
D
as expected
medium Difficulty
Verified Correct Answer: Option A
Grammar & Contextual Explanation
The idiom “not a bed of roses” means not easy, not completely pleasant, or full of difficulties. So the sentence:
“Life is not a bed of roses” → life will not be as pleasant or easy as one might imagine, which corresponds to option A: as pleasant as one thought.
Source: Myschool Past Questions Archive (Record #6466)