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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
UTME / JAMB 2025
English Grammar
Solution
In the following questions, the word in capital letters has the emphatic stress. Choose the option to which the given word relates.
The doctor examined the patient with a STETHOSCOPE.
A
Did the doctor examine the matron with a stethoscope?
B
Did the nurse examine the patient with a stethoscope?
C
Did the doctor examine the patient with a microscope?
D
Did the doctor cure the patient with a stethoscope?
medium Difficulty
Verified Correct Answer: Option C
Grammar & Contextual Explanation
Since STETHOSCOPE is stressed, the speaker is correcting the instrument used. The question must suggest a different tool, like a microscope.
Source: Official Exam / Past Question Archive
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
UTME / JAMB 2025
Number and Numeration
Diagram
Solution
From the diagram above, find the area of the triangle PQR
Attached Figure / Diagram
A
143cm\(^2\)
B
120cm\(^2\)
C
130cm\(^2\)
D
117cm\(^2\)
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
Area of triangle PQR = \(\frac{1}{2}\) x QR x Pc
Where QR = base of triangle PQR, Pc = height of triangle PQR
Area of triangle PQR = \(\frac{1}{2}\) x 20 x 13 = 10 x 13 = 130cm\(^2\).
Source: Myschool Past Questions Archive (Record #74090)
Mathematics
UTME / JAMB 2025
Number and Numeration
Solution
Given that a * b = \(\frac{a + b}{\text{ab}}\) + (a - b). Find the value of 3 * 2
A
-6
B
\(\frac{11}{6}\)
C
\(\frac{6}{11}\)
D
-1 \(\frac{5}{6}\)
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
Given that a * b = \(\frac{a + b}{\text{ab}}\) + (a - b)
3 * 2 = Given that a * b = \(\frac{3 + 2}{3.2}\) + (3 - 1)
= \(\frac{5}{6}\) + 1 = \(\frac{5}{6}\) + \(\frac{6}{6}\) = \(\frac{11}{6}\)
Source: Myschool Past Questions Archive (Record #74094)
Mathematics
UTME / JAMB 2025
Number and Numeration
Solution
Simplify 125\(^{−\frac{1}{3}}\) \times 49\(^{−\frac{1}{2}}\) \times 10\(^0\)
A
\(\frac{1}{35}\)
B
\(\frac{1}{350}\)
C
350
D
35
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
Given: 125\(^{−\frac{1}{3}}\) \times 49\(^{−\frac{1}{2}}\) \times 10\(^0\)
125\(^{-1/3}\) = (5\(^3\))\(^{-1/3}\) = 5\(^{-1}\) = \(\frac{1}{5}\).
49\(^{-1/2}\) = (7\(^2\))\(^{-1/2}\) = 7\(^{-1}\) = \(\frac{1}{7}\).
10\(^0\) = 1.
Product = \(\frac{1}{5}\) x \(\frac{1}{7}\) x 1 = \(\frac{1}{35}\).
Source: Myschool Past Questions Archive (Record #74095)
Mathematics
UTME / JAMB 2025
Number and Numeration
Solution
Find the coordinates of the midpoint of line PQ given P(-3, 4) and Q(5, 6).
A
(1, 4)
B
(4, 1)
C
(5, 1)
D
(1, 5)
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
Midpoint = [\(\frac{x_1 + x_2}{2}\), \(\frac{y_1 + y_2}{2}\)]
Midpoint = [\(\frac{(-3 + 5)}{2}\), \(\frac{(4 + 6)}{2}\)] = (\(\frac{2}{2}\), (\(\frac{10}{2}\)) = (1, 5).
Source: Myschool Past Questions Archive (Record #74096)
Mathematics
UTME / JAMB 2025
Geometry and Trigonometry
Solution
Given that Cos A = \(\frac{12}{13}\) for 0 \le A \le 90º, find Tan A.
A
\(\frac{5}{12}\)
B
\(\frac{12}{13}\)
C
\(\frac{5}{13}\)
D
\(\frac{13}{12}\)
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
Sin A = \(\sqrt{(1 - (\frac{12}{13})^2)}\) = \(\sqrt{(1 - \frac{144}{169}}\))
= \(\sqrt{(\frac{25}{169})}\) = \(\frac{5}{13}\).
Tan A = (\(\frac{5}{13}\)) \(\div\) (\(\frac{12}{13}\)) = \(\frac{5}{12}\).
Source: Myschool Past Questions Archive (Record #74097)
Mathematics
UTME / JAMB 2025
Statistics and Probability
Solution
The mean of the numbers 0, x + 2, 3x + 6, and 4x + 8 is 4, find the value of x.
A
\(\frac{2}{5}\)
B
\(\frac{2}{9}\)
C
0
D
4
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
Mean = \(\frac{(0 + x + 2 + 3x + 6 + 4x + 8)}{4}\) = 4.
Simplify numerator: 8x + 16.
So \(\frac{(8x + 16)}{4}\) = 4.
8x + 16 = 16.
8x = 0.
x = 0.
Source: Myschool Past Questions Archive (Record #74154)
Mathematics
UTME / JAMB 2025
Number and Numeration
Solution
Obtain the equation of a straight line passing through (3, 15) whose slope = 3\(\frac{1}{5}\).
A
5y + 16x + 27 = 0
B
5y - 16x + 27 = 0
C
5y - 16x - 27 = 0
D
5y + 16x - 27 = 0
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
Convert the mixed number slope to an improper fraction: 3 \(\frac{1}{5} = \frac{16}{5}\)
Use the point-slope form with the given point (3,15)
y - 15 = \(\frac{16}{5}\)(x - 3)
Multiply both sides by 5 to clear the fraction: 5(y−15) = 16(x−3)
5y − 75 = 16x − 48
Rearrange terms to standard form: 5y − 16x − 75 + 48 = 0
5y − 16x − 27 = 0
Source: Myschool Past Questions Archive (Record #74155)
Mathematics
UTME / JAMB 2025
Number and Numeration
Solution
Simplify (\(\frac{3}{4} \div 2\frac{1}{4}\)) of 1 \(\frac{7}{11}\) (3 \(\frac{2}{3}\) - \(\frac{15}{6}\))
A
\(\frac{7}{11}\).
B
\(\frac{11}{7}\).
C
\(\frac{5}{11}\).
D
\(\frac{11}{5}\).
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
Given (\(\frac{3}{4} \div 2\frac{1}{4}\)) of 1 \(\frac{7}{11}\) (3 \(\frac{2}{3}\) - \(\frac{15}{6}\))
1. Simplify the division in the first parentheses: \(\frac{3}{4} \div 2 \frac{1}{4} = \frac{3}{4} \div \frac{9}{4} = \frac{3}{4} \times \frac{4}{9} = \frac{3}{9} = \frac{1}{3}\).
2. Convert the mixed number: \(1 \frac{7}{11} = \frac{18}{11}\).
3. Simplify the subtraction in the second parentheses: \(3 \frac{2}{3} - \frac{15}{6} = \frac{11}{3} - \frac{5}{2} = \frac{22}{6} - \frac{15}{6} = \frac{7}{6}\).
4. The "of" indicates multiplication, so multiply the results: \(\frac{1}{3} \times \frac{18}{11} \times \frac{7}{6} = \frac{126}{198} = \frac{7}{11}\).
Source: Myschool Past Questions Archive (Record #74157)
Mathematics
UTME / JAMB 2025
Statistics and Probability
Solution
In a basket of fruits, there are 6 grapes, 11 bananas, and 13 oranges. If one fruit is chosen at random, what is the probability that the fruit is either a grape or a banana?
A
\(\frac{17}{30}\)
B
\(\frac{11}{30}\)
C
\(\frac{6}{30}\)
D
\(\frac{5}{30}\)
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
Total fruits = 6 + 11 + 13 = 30
Favorable (grape or banana) = 6 + 11 = 17
Probability = \(\frac{17}{30}\)
Source: Myschool Past Questions Archive (Record #74158)
Mathematics
UTME / JAMB 2025
Number and Numeration
Solution
The second and fifth terms of a G.P are 1 and \(\frac{1}{8}\) respectively. Find the common ratio
A
\(\frac{1}{4}\)
B
\(\frac{1}{5}\)
C
\(\frac{1}{2}\)
D
\(\frac{1}{3}\)
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
Let the first term be \( a \), and the common ratio be \( r \). Given:
- Second term: \( ar = 1 \)
- Fifth term: \( ar^4 = \frac{1}{8} \)
From the first equation, we have: \(a = \frac{1}{r}\)
Substituting into the second equation:
\(\frac{1}{r} r^4 = \frac{1}{8}\)
\(r^3 = \frac{1}{8}\)
Taking the cube root gives:
\(r = \frac{1}{2}\)
Thus, the common ratio is \(\frac{1}{2}\)
Source: Myschool Past Questions Archive (Record #74169)
Mathematics
UTME / JAMB 2025
Number and Numeration
Solution
If A = \(\frac{\theta}{360}\)\(\pi r^2\), make \(\theta\) the subject of the formula
A
\(\theta\) =\(\frac{360}{π A}\)
B
\(\theta\) =\(\frac{360A}{π \theta}\)
C
\(\theta\) =\(\frac{360 A}{\pi r^2}\)
D
\(\theta\) = \(\frac{360 r^2}{\pi A}\)
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
Given:
\(A = \frac{\theta}{360} \pi r^2 \)
To make \(\theta\) the subject, isolate \(\theta\).
Multiply both sides by 360:
\(360A = \theta \pi r^2 \)
Divide both sides by \(\pi r^2\):
\( \theta = \frac{360A}{\pi r^2} \)
The rearranged formula is: \( \theta = \frac{360A}{\pi r^2} \)
Source: Myschool Past Questions Archive (Record #74174)
Mathematics
UTME / JAMB 2025
Algebra
Solution
What is the minimum value of y = 2 - 4x - 2x\(^2\)
A
4
B
5
C
3
D
2
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
The function is \( y = -2x^2 - 4x + 2 \).
This is a quadratic function with a negative leading coefficient (\( a = -2 < 0 \)), so the parabola opens downwards and has a maximum value (not a minimum). The minimum value would be \( -\infty \) as \( x \to \pm \infty \).
Method 1: Vertex formula
For \( y = ax^2 + bx + c \), the vertex occurs at \( x = -\frac{b}{2a} \).
Here, \( a = -2 \), \( b = -4 \), \( c = 2 \).
\( x = -\frac{-4}{2(-2)} = \frac{4}{-4} = -1 \)
Substitute \( x = -1 \):
\( y = -2(-1)^2 - 4(-1) + 2 = -2(1) + 4 + 2 = -2 + 4 + 2 = 4 \)
Method 2: Completing the square
\( y = -2x^2 - 4x + 2 = -2(x^2 + 2x) + 2 \)
Complete the square inside: \( x^2 + 2x = (x + 1)^2 - 1 \)
\( y = -2[(x + 1)^2 - 1] + 2 = -2(x + 1)^2 + 2 + 2 = -2(x + 1)^2 + 4 \)
The maximum value is 4 (when \( x = -1 \)), and \( y \leq 4 \).
Method 3: Calculus (derivative)
\( \frac{dy}{dx} = -4x - 4 \)
Set to zero: \( -4x - 4 = 0 \) → \( x = -1 \)
Second derivative \( \frac{d^2y}{dx^2} = -4 < 0 \), confirming a maximum.
\( y(-1) = 4 \)
Conclusion:
The function has "no minimum value" (it decreases without bound).
The "maximum value" is 4.
Source: Myschool Past Questions Archive (Record #74175)