waec model questions vol1 2025 mathematics | Essay

Are you preparing for waec model questions vol1 exams? Reviewing past questions is one of the most effective ways to guarantee a high score. This practice hub features authentic 2025 mathematics (Essay) questions designed to simulate the real exam environment.

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Question 1
A farmer has a rectangular plot of land with a length of 120 meters and a width of 80 meters. He plans to plant crops on this land. Calculate the area of the land and the perimeter of the rectangular plot.
Question Parts
(a)
Calculate the area of the rectangular plot.
(b)
Calculate the perimeter of the rectangular plot.
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Question 2
A quadratic equation is given by the expression x² - 6x + 8 = 0. Find the roots of the equation using the factorization method.
Question Parts
(a)
Factorize the quadratic expression.
(b)
Find the roots of the equation from the factorized form.
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Question 3
A farmer is planning to cultivate a rectangular piece of land that is 120 meters long and 75 meters wide. He wants to build a fence around the entire plot and plant crops in it. Additionally, he plans to leave a pathway of 2 meters wide around the inside perimeter of the fence. Calculate the following:
Question Parts
(a)
Calculate the total perimeter of the rectangular plot.
(b)
Determine the area of the rectangular plot before constructing the pathway.
(c)
Find the area of the land available for planting crops after the pathway has been created.
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Question 4
The graph of a quadratic function is given by the equation y = ax^2 + bx + c, where a, b, and c are constants. Consider the function f(x) = 2x^2 - 8x + 6. Answer the following questions:
Question Parts
(a)
Determine the vertex of the quadratic function.
(b)
Find the x-intercepts of the quadratic function.
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Question 5
A triangular park has sides measuring 40 m, 30 m, and 50 m. Calculate the area of the park. Then, if the park is to be fenced with a decorative fence at a cost of ₦200 per meter, calculate the total cost of the fencing.
Question Parts
(a)
Calculate the area of the triangular park.
(b)
Calculate the total cost of fencing the park.
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Question 6
A cylindrical water tank has a radius of 2.5 m and a height of 3 m. Calculate the volume of the tank. Additionally, if the tank is to be filled with water at a rate of 0.1 m³ per hour, how long will it take to fill the tank completely?
Question Parts
(a)
Calculate the volume of the cylindrical water tank.
(b)
Calculate the time required to fill the tank completely.
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Question 7
In a right triangle, one of the angles is 30 degrees and the length of the opposite side to this angle is 5 cm. Calculate the length of the adjacent side and the hypotenuse of the triangle. Explain your method and show all working.
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Question 8
The heights of a group of students were recorded. The heights in centimeters are: 150, 160, 165, 170, 175, 175, 180. Calculate the mean, median, mode, and range of the heights. Show all your workings.
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Question 9
A bag contains 5 red balls, 3 blue balls, and 2 green balls. If one ball is drawn at random, calculate the following:
Question Parts
(a)
What is the total number of balls in the bag?
(b)
What is the probability of drawing a red ball?
(c)
If a blue ball is drawn, what is the probability of drawing a green ball next, assuming the first ball is not replaced?
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Question 10
In a coordinate plane, point A is at (-3, 4) and point B is at (2, -1). Calculate the following:
Question Parts
(a)
Determine the vector AB.
(b)
Find the magnitude of vector AB.
(c)
What is the direction of vector AB in degrees?
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Question 11
A school has a total of 800 students. The ratio of boys to girls in the school is 3:5. Calculate the number of boys and girls in the school.
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Question 12
Simplify the expression: 4x^2 - 2x + 6x^2 - 5 + 3x - 4.
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Question 13
A company produces two types of products, A and B. The cost to produce product A is ₦150 per unit, and the cost to produce product B is ₦200 per unit. The company has a total production budget of ₦30,000. Additionally, the company can produce at most 150 units of product A and 100 units of product B. Determine the number of units of each product that the company can produce to maximize the use of its budget. Formulate the constraints and solve the linear programming problem.
Question Parts
(a)
Formulate the constraints for the production of products A and B.
(b)
Solve the linear programming problem using the graphical method and identify the optimal solution.
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