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English Language
WAEC / WASSCE 2025
English Grammar
Solution
It was a cold windy Monday morning just before dawn. A frail old woman who could barely see beyond a few metres ahead of her—an early septuagenarian—braved all odds and stepped out onto the dirty road in the village of Koomla. For her, today's duty had to be done even if it meant further risking her delicate health. "What would I not do for Koku to amount to something in this life that has given me nothing but woes?" Mma Koku thought to herself.
And so, despite the ominous signs from the sky, and wearing just a threadbare sweater over an equally aged wrapper, she forged ahead, daring the draught of air that was threatening to topple her. Luckily, the sand ground was still largely undisturbed owing to the dew, so she didn't have to contend with fending off particles from her often rheumy eyes.
"Come what may" Mma Koku assured herself as her left foot planked into a muddy pothole she hadn't seen in time, "today I shall see the pathfinder, before he leaves for the city." Her destination was still about nine kilometres away. At home, The Pathfinder; a middle-aged university teacher—the very first person to earn the highest postgraduate degree from the village of Koomla—had just roused himself from dreamland. In the dream, a figure in white had told him he owed an obligation to the old woman. She was on her way to give him a parcel for her son studying in the university in the city, about a thousand miles away.
The Pathfinder had come home for a two-day visit and the news had got to Mma Koku, who gladly took all her savings for the last three months, put it in a small envelope and tied up in the edge of her wrapper. The duo were to meet at the junction where the village road led off to the city. "You know, Lord, this is all I have. Please let my son turn out well," the old woman prayed. "No sacrifice is too much for one's child," she heaved, skipping over another muddy pothole, for it had rained the previous day.
By the time Mma Koku got about a mile from The Pathfinder's home, the day was now bright enough for her to see with less strain. However, the sky suddenly became overcast and only seconds later, there was a torrent from the heavens. There was very little that the surprised old woman could do to stave off the watery onslaught, so she trudged on stoically. At the appointed place, The Pathfinder activated his wipers at top speed as he stayed on the lookout for the person he was expecting.
As drenched as Mma Koku came into view, The Pathfinder switched off the ignition and rushed out to meet up with her, guiding her into a nearby shed. After a few minutes of pleasantries, she handed over her widow's mite. "Mma, please wait here till the sky stops weeping," he begged her. "I must run along now."
"Ah, what can beat a mother's love!" Dr Felix Adoka soliloquised pensively, shaking his head as he winked a left turn to an oncoming driver, prepared to confront the elements. "I shall ensure her son gets a teaching job once he is done," he promised himself.
a. Why did Mma Koku leave home on a cold, windy Monday morning?
b. What two difficulties did Mma Koku face on her way to meet The Pathfinder?
c. What may have prompted the villagers to call the man "The Pathfinder"?
d. What two indications are there in the passage that Mma Koku was poor?
e. What was The Pathfinder's attitude toward Mma Koku?
f. What was the expectation of Mma Koku concerning her son?
g. In what age range would you place Mma Koku?
h. "...sky stops weeping..."
What figure of speech is contained in the expression above?
i. "...before he leaves for the city..."
i. What is the grammatical name of the expression above?
ii. What is its function?
j. For the following words, find another word or phrase which means the same and which can replace it as it is used in the passage:
i. delicate
ii. ominous
iii. an obligation
iv. overcast
v. pensively
medium Difficulty
Verified Correct Answer: Option
Grammar & Contextual Explanation
a. She left home to meet "The Pathfinder" (Dr Felix Adoka) at a junction to give him a parcel containing her three months' savings for her son who was studying at a university in the city.
b. The two difficultioes Mma Koku faced on her way to meet The Pathfinder includes:
i. She was a frail, elderly woman with poor eyesight ("rheumy eyes") and delicate health.
ii. She had to navigate muddy potholes from previous rain and was eventually caught in a heavy rainfall that left her drenched.
c. He was the very first person from the village of Koomla to earn the highest postgraduate degree (a PhD).
d. Two indications that Mma Koku was poor include:
i. She was wearing a "threadbare sweater over an equally aged wrapper".
ii. She had to save for three months just to provide the "widow's mite" (a small amount of money) she sent to her son.
e. His attitude was one of respect, empathy and kindness.
f. She expected and prayed that her son would amount to something in this life and turn out well through his university education.
g. She is in her early seventies.
h. The figure of speech used is personification.
i. i. Adverbial clause of time.
ii. It modifies the verb "shall see".
j. i. delicate: frail, fragile, weak
ii. ominous: threatening, menacing, foreboding
iii. an obligation: a duty, a responsibility, a debt
iv. overcast: cloudy, dark, gloomy
v. pensively: thoughtfully, reflectively, deeply in thought
Source: Myschool Past Questions Archive (Record #76614)
English Language
WAEC / WASSCE 2025
English Grammar
Solution
For all well-meaning citizens, the moral decadence in our society nowadays is cause for concern. Some have argued that the root cause of this decadence is poor parenting. Indeed, poor parenting has given rise to most of the criminality that we witness today. We all keep on complaining when in fact parents themselves are largely to blame for the unsavoury situation. In order to improve this situation, parents need to inculcate certain sterling qualities in their children.
There is no doubt that temptations are bound to arise in everyday life. However, if lessons in self-control are instilled in children, they will be able to resist temptations. Children who have self-control are not likely to have problems with the law; moreover, they will be able to avoid health issues and financial stress, as well as other consequences of lack of self-restraint. For example, a child who has been taught to avoid eating junk food will not become obese. Such a child already knows that every action has a consequence.
Today, many people consider themselves better than others and therefore look down on them. They are arrogant, impudent and intolerant; as such they are hardly ever willing to accommodate other people's ideas. A child who has imbibed the virtue of humility will be respectful, take interest in others and be willing to learn from them. Sometimes, humility is misconstrued as a weakness but in reality it is a strength which helps people to recognise their faults and acknowledge their limitation.
Parents should ensure that their children take active part in chores and duties at home. They will therefore know that there is virtue in serving others.
In life, we cannot avoid obstacles and disappointments. A child cannot learn how to walk without occasional falls. Similarly, in life we experience occasional setbacks. For example, a child may fail a test at school. In such a situation, what is needed is encouragement that will boost the child's confidence for future tests. Parents can help the child to work out a strategy for achieving resounding success. Children should be taught the truth in the axiom, "If you fail at first, try, try and try again." This training in resilience helps children to face life's challenges with confidence.
Many adults lack integrity, so when they say "yes" they really mean "no". They can therefore hardly be trusted or relied on and usually fail to take responsibility for their actions or failures. The actions of such adults have grave implications for society. If parents train their children on the need to have integrity, such children will not go about engaging in criminal activities.
Cutting corners in order to get rich quick is the stock-in-trade of many adults, who now engage in all forms of illegal and unwholesome activities to acquire sudden wealth. Indeed, the culture of hand work is fast disappearing. If children are well trained in appreciating the value of hard work, they will grow up into adults who will shun all forms of shady activities aimed at making an overnight fortune.
Obedience to laws is a key quality that will make any society stable and function smoothly. For example, if taxes are paid when due as stipulated by societal laws, money realised will be used to provide the badly needed social amenities and infrastructure. Parents have an important role to play by training their children to obey rules and regulations at home. This training will enable them to become law-abiding adults.
In the light of the foregoing, parents should be good role models in terms of character, comportment, speech and dedication to duty among other things. Only under such circumstances can we build a stable society that benefits all.
In six sentences, one for each, summarise the qualities that the writer advises parents to instill in their children.
medium Difficulty
Verified Correct Answer: Option
Grammar & Contextual Explanation
The following are the qualities the writer advises parents to instil in their children:
Parents should teach their children self-control so they can resist temptations and understand that every action carries a consequence.
It is essential to instil the virtue of humility to enable the children to be respectful and willing to learn from others.
By involving children in household chores, parents can teach them the value of service to others.
Parents should foster resilience in children to help them face life's setbacks and challenges with confidence.
Training children in integrity is necessary to ensure they become trustworthy adults who take responsibility for their actions.
Children must be taught to appreciate hard work and the importance of obeying laws to ensure a stable and functional society.
Source: Myschool Past Questions Archive (Record #76615)
English Language
WAEC / WASSCE 2025
English Grammar
Solution
For all well-meaning citizens, the moral decadence in our society nowadays is cause for concern. Some have argued that the root cause of this decadence is poor parenting. Indeed, poor parenting has given rise to most of the criminality that we witness today. We all keep on complaining when in fact parents themselves are largely to blame for the unsavoury situation. In order to improve this situation, parents need to inculcate certain sterling qualities in their children.
There is no doubt that temptations are bound to arise in everyday life. However, if lessons in self-control are instilled in children, they will be able to resist temptations. Children who have self-control are not likely to have problems with the law; moreover, they will be able to avoid health issues and financial stress, as well as other consequences of lack of self-restraint. For example, a child who has been taught to avoid eating junk food will not become obese. Such a child already knows that every action has a consequence.
Today, many people consider themselves better than others and therefore look down on them. They are arrogant, impudent and intolerant; as such they are hardly ever willing to accommodate other people's ideas. A child who has imbibed the virtue of humility will be respectful, take interest in others and be willing to learn from them. Sometimes, humility is misconstrued as a weakness but in reality it is a strength which helps people to recognise their faults and acknowledge their limitation.
Parents should ensure that their children take active part in chores and duties at home. They will therefore know that there is virtue in serving others.
In life, we cannot avoid obstacles and disappointments. A child cannot learn how to walk without occasional falls. Similarly, in life we experience occasional setbacks. For example, a child may fail a test at school. In such a situation, what is needed is encouragement that will boost the child's confidence for future tests. Parents can help the child to work out a strategy for achieving resounding success. Children should be taught the truth in the axiom, "If you fail at first, try, try and try again." This training in resilience helps children to face life's challenges with confidence.
Many adults lack integrity, so when they say "yes" they really mean "no". They can therefore hardly be trusted or relied on and usually fail to take responsibility for their actions or failures. The actions of such adults have grave implications for society. If parents train their children on the need to have integrity, such children will not go about engaging in criminal activities.
Cutting corners in order to get rich quick is the stock-in-trade of many adults, who now engage in all forms of illegal and unwholesome activities to acquire sudden wealth. Indeed, the culture of hand work is fast disappearing. If children are well trained in appreciating the value of hard work, they will grow up into adults who will shun all forms of shady activities aimed at making an overnight fortune.
Obedience to laws is a key quality that will make any society stable and function smoothly. For example, if taxes are paid when due as stipulated by societal laws, money realised will be used to provide the badly needed social amenities and infrastructure. Parents have an important role to play by training their children to obey rules and regulations at home. This training will enable them to become law-abiding adults.
In the light of the foregoing, parents should be good role models in terms of character, comportment, speech and dedication to duty among other things. Only under such circumstances can we build a stable society that benefits all.
In six sentences, one for each, summarise the qualities that the writer advises parents to instill in their children.
A
value
B
jest
C
flew
D
haste
medium Difficulty
Verified Correct Answer: Option C
Grammar & Contextual Explanation
The following are the qualities the writer advises parents to instil in their children:
Parents should teach their children self-control so they can resist temptations and understand that every action carries a consequence.
It is essential to instil the virtue of humility to enable the children to be respectful and willing to learn from others.
By involving children in household chores, parents can teach them the value of service to others.
Parents should foster resilience in children to help them face life's setbacks and challenges with confidence.
Training children in integrity is necessary to ensure they become trustworthy adults who take responsibility for their actions.
Children must be taught to appreciate hard work and the importance of obeying laws to ensure a stable and functional society.
Source: Official Exam / Past Question Archive
Mathematics
WAEC / WASSCE 2025
Number and Numeration
Solution
Find (101\(_2\))\(^2\), expressing the answer in base 2.
A
11101
B
10101
C
10010
D
11001
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
(101\(_2\))\(^2\) ⇒ 101\(_2\) = 1\times2\(^2\) + 0 \times 2\(^1\) + 1 \times 2\(^0\) = 1 \times 4 + 0 + 1 (Recall x⁰ = 1) = 4 + 1 = 5
(101\(_2\))\(^2\) = (5\(_{10}\))\(^2\) = 25.
25 in base 2 = 11001
Source: Myschool Past Questions Archive (Record #75796)
Mathematics
WAEC / WASSCE 2025
Number and Numeration
Solution
If three children share ₦10.50 among themselves in the ratio 6:7:8, how much is the largest share?
A
₦3.50
B
₦4.00
C
₦4.50
D
₦3.00
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
Total amount = ₦10.50;
Ratio = 6: 7: 8;
Total ratios = 6 + 7 + 8 = 21
largest share = 8
∴ Largest amount = \(\frac{8}{21}\) \times ₦10.50 = 8 \times ₦0.50 = ₦4.00
Source: Myschool Past Questions Archive (Record #75797)
Mathematics
WAEC / WASSCE 2025
Geometry and Trigonometry
Solution
Express 0.000834 in standard form.
A
8.34 x 10\(^{-4}\)
B
8.34 x 10\(^{-3}\)
C
8.34 x 10\(^4\)
D
8.34 x 10\(^3\)
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
0.000834 = 8.34 x 10\(^{-4}\)
Move the decimal point 4 places to your right.
Source: Myschool Past Questions Archive (Record #75798)
Mathematics
WAEC / WASSCE 2025
Number and Numeration
Solution
Simplify 0.027\(^{-\frac{1}{3}}\)
A
\(\frac{3}{10}\)
B
3\(\frac{1}{3}\)
C
\(\frac{1}{3}\)
D
3
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
0.027\(^{-\frac{1}{3}}\) = (\(\frac{27}{100}\))\(^{-\frac{1}{3}}\)
= (\(\frac{10^3}{3^3}\))\(^{\frac{1}{3}}\) = \(\frac{10}{3}\) = 3\(\frac{1}{3}\)
Source: Myschool Past Questions Archive (Record #75799)
Mathematics
WAEC / WASSCE 2025
Number and Numeration
Solution
Given that log\(_2a\) = log\(_84\), find a.
A
2\(^{\frac{1}{2}}\)
B
2\(^{\frac{2}{3}}\)
C
4\(^{\frac{2}{3}}\)
D
4\(^{\frac{1}{2}}\)
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
log\(_2a\) = log\(_84\)
Let log\(_84\) = y
Then 4 = 8\(^y\)
2\(^2\) = 2\(^{3y}\)
2 = 3y
y = \(\frac{2}{3}\)
log\(_2a\) = log\(_84\) = \(\frac{2}{3}\)
log\(_2a\) = \(\frac{2}{3}\)
a = 2\(^{\frac{2}{3}}\)
(Note: The logarithm was converted to index form.)
Source: Myschool Past Questions Archive (Record #75800)
Mathematics
WAEC / WASSCE 2025
Geometry and Trigonometry
Solution
By selling some crates of soft drinks for ₦600.00, a dealer makes a profit of 50%. How much did the dealer pay for the drinks?
A
₦400.00
B
₦1200.00
C
₦900.00
D
₦450.00
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
To find the cost price
Selling price = ₦600; Profit = 50%
Multiply the selling price by 100 and add 100% to the profit
new selling price = 600 x 100 = 60,000, new profit = 150%
Cost price = = \(\frac{60,000}{150}\) = ₦400
Source: Myschool Past Questions Archive (Record #75802)
Mathematics
WAEC / WASSCE 2025
Algebra
Solution
Find the nth term U\(_n\) of the A.P. 11, 4, -3, …
A
U\(_n\) = 19 - 7n
B
U\(_n\) = 19 + 7n
C
U\(_n\) = 18 - 7n
D
U\(_n\) = 18 + 7n
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
U\(_n\) = a + (n – 1)d ;
where a = 11 ; d = –7
U\(_n\) = 11 + (n – 1)(–7) = 11 – 7n + 7 = 18 – 7n
Source: Myschool Past Questions Archive (Record #75803)
Mathematics
WAEC / WASSCE 2025
Number and Numeration
Solution
If R = {2, 4, 6, 7} and S = {1, 2, 4, 8} then R ∪ S equals
A
{1, 2, 4, 6, 7, 8}
B
{1, 2, 4, 7, 8}
C
{1, 4, 7, 8}
D
{2, 6, 7}
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
R = {2, 4, 6, 7}, S = {1, 2, 4, 8}
R ∪ S ⇒ element in R and S together without replacement.
∴ R ∪ S = {1, 2, 4, 6, 7, 8}
Source: Myschool Past Questions Archive (Record #75804)
Mathematics
WAEC / WASSCE 2025
Number and Numeration
Solution
If \(\frac{16}{9}\), x, 1, y are in geometric progression (G.P.). Find the product of x and y.
A
\(\frac{16}{9}\)
B
\(\frac{3}{4}\)
C
1
D
\(\frac{4}{3}\)
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
Using common ratios
\(\frac{\text{x}}{\frac{16}{9}}\) = \(\frac{1}{\text{x}}\)
x\(^2\) = \(\frac{16}{9}\)
x = \(\frac{4}{3}\)
If x = \(\frac{4}{3}\)
Then, the common ratio = \(\frac{3}{4}\)
y = ar\(^3\) = \(\frac{16}{9}\) x (\(\frac{3}{4}\))\(^3\)
y = \(\frac{16}{9}\) x \(\frac{27}{64}\) = \(\frac{3}{4}\)
Therefore, the product of x and y = \(\frac{4}{3}\) x \(\frac{3}{4}\) = 1
Source: Myschool Past Questions Archive (Record #75807)
Mathematics
WAEC / WASSCE 2025
Number and Numeration
Diagram
Solution
In the diagram above, the shaded portion is
Attached Figure / Diagram
A
(P ∪ Q)\(^1\) ∩ R
B
P\(^1\) ∩ Q ∩ R
C
P\(^1\) ∩ R
D
Q\(^1\) ∩ R
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
Shaded is the portion that does not fall in the field of P ⇒ P\(^1\);
It is the area in R. Area common to P\(^1\), and R is denoted as P\(^1\) ∩ R.
Source: Myschool Past Questions Archive (Record #75808)
Mathematics
WAEC / WASSCE 2025
Number and Numeration
Solution
Find the values of x for which the expression is undefined: \(\frac{6x - 1}{x^2 + 4x - 5}\)
A
+5 or -1
B
-5 or +1
C
-5 or -1
D
+4 or +1
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
A fraction is undefined when its denominator is zero, i.e.
\(\frac{6x - 1}{x^2 + 4x - 5}\) is undefined when x\(^2\) + 4x - 5 = 0
x\(^2\) + 4x - 5 = 0
= x\(^2\) + 5x - x - 5 = 0
x\(^2\) + 5x - x - 5 = 0
= x(x + 5) - 1(x + 5) = 0
(x - 1)(x + 5) = 0
x = 1 0r -5
Source: Myschool Past Questions Archive (Record #75810)
Mathematics
WAEC / WASSCE 2025
Algebra
Solution
Solve the inequality \(\frac{1}{3}\)(2x - 1) < 5
A
x < -5
B
x < 8
C
x < -6
D
x < 7
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
\(\frac{1}{3}\)(2x - 1) < 5
Multiply through by 3
2x - 1 < 5 x 3
2x - 1 < 15
2x < 15 + 1 = 16
2x < 16
x < \(\frac{16}{2}\) < 8
Source: Myschool Past Questions Archive (Record #75811)