waec model questions vol1 2025 mathematics | Essay

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Question 1 View Details
A farmer has a rectangular plot of land with a length of 80 metres and a width of 50 metres. He wants to create a path of uniform width around the plot. The total area of the path and the plot combined should be 5000 square metres. Calculate the width of the path and determine the area of the path alone.
Question Parts
(a)
Let the width of the path be x metres. Write an equation that represents the total area of the plot and the path combined.
(b)
Solve the equation from part (a) to find the value of x.
(c)
Using the value of x obtained in part (b), calculate the area of the path alone.
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Question 2 View Details
A shop sells a pair of shoes for ₦8,000. During a sale, the shop offers a discount of 15%. Calculate the selling price after the discount and determine the total amount saved by the customer.
Question Parts
(a)
Calculate the amount of discount given on the shoes.
(b)
Determine the selling price of the shoes after applying the discount.
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Question 3 View Details
Consider the expression involving indices and logarithms. Simplify the expression: \(2^(3x) * 4^\)\((2x-1) / 8\\()^(x+1)\). Then, express your answer in the form a * \(b^x\), where a and b are constants. Finally, determine the value of x if the expression equals 64.
Question Parts
(a)
Simplify the expression 2^(3x) * 4^(2x-1) / 8^(x+1) and express it in the form a * b^x.
(b)
Determine the value of x if the simplified expression equals 64.
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Question 4 View Details
In a survey of students' favorite fruits, the results are as follows: 30 students like apples, 25 like bananas, 20 like oranges, and 15 like both apples and bananas. Represent this information using a Venn diagram. Calculate the number of students who like only apples, only bananas, and only oranges. Also, determine how many students do not like any of the fruits.
Question Parts
(a)
Draw a Venn diagram to represent the survey results of students' favorite fruits.
(b)
Calculate the number of students who like only apples, only bananas, and only oranges.
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Question 5 View Details
A small company produces two types of products: A and B. The company has a budget of ₦500,000 for production costs. The cost to produce one unit of product A is ₦10,000, while the cost to produce one unit of product B is ₦15,000. The company aims to produce at least 30 units of product A and at least 20 units of product B. Additionally, the company wants to maximize its total production output. (a) Formulate a system of inequalities to represent the constraints of this problem. (b) Determine the feasible region for the production of products A and B using a graphical method. (c) Identify the coordinates of the vertices of the feasible region. (d) Calculate the maximum number of units of products A and B that can be produced while adhering to the budget and minimum production requirements. Show all your workings.
Question Parts
(a)
Formulate a system of inequalities to represent the constraints of this problem.
(b)
Determine the feasible region for the production of products A and B using a graphical method.
(c)
Identify the coordinates of the vertices of the feasible region.
(d)
Calculate the maximum number of units of products A and B that can be produced while adhering to the budget and minimum production requirements. Show all your workings.
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Question 6 View Details
A school is organizing a sports day event and expects to have three types of races: 100m dash, 200m dash, and 400m dash. The number of participants in the 100m dash is 50% of the total participants, while the number of participants in the 200m dash is 30% of the total participants. The remaining participants will participate in the 400m dash. If the total number of participants is 200, (a) Calculate the number of participants in each race. (b) If each participant pays a registration fee of ₦500, determine the total amount collected from the registration fees. (c) The school plans to use 40% of the total registration fees collected for prizes. Calculate the amount allocated for prizes.
Question Parts
(a)
Calculate the number of participants in each race.
(b)
If each participant pays a registration fee of ₦500, determine the total amount collected from the registration fees.
(c)
The school plans to use 40% of the total registration fees collected for prizes. Calculate the amount allocated for prizes.
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Question 7 View Details
Solve the following quadratic equation and analyze the nature of its roots: 2x² - \(4x + 2 = 0\).
Question Parts
(a)
Using the quadratic formula, find the values of x.
(b)
Determine the nature of the roots of the quadratic equation.
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Question 8 View Details
Consider the inequality \(3x - 5 < 2x + 1\). Solve for x and represent the solution on a number line.
Question Parts
(a)
Solve the inequality for x.
(b)
Draw a number line to represent the solution of the inequality.
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Question 9 View Details
A sequence is defined by the formula \(a_n = 3n\\()^2 - 2n + 1\) for \(n = 1\), 2, 3, ... Calculate the following:
Question Parts
(a)
Find the first five terms of the sequence.
(b)
Determine the sum of the first ten terms of the sequence.
(c)
If a_n represents the nth term of the sequence, find the value of n for which a_n = 73.
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Question 10 View Details
A company manufactures two types of gadgets, A and B. The production of gadget A requires 2 hours of labor and 3 units of raw materials, while gadget B requires 1 hour of labor and 4 units of raw materials. If the company has a total of 100 hours of labor and 120 units of raw materials available, formulate and solve the equations to determine how many of each type of gadget can be produced.
Question Parts
(a)
Formulate the system of inequalities representing the constraints on the production of gadgets A and B.
(b)
Using the inequalities from part (a), determine the maximum number of gadgets A and B that can be produced.
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Question 11 View Details
The graph of a quadratic function is represented by the equation \(y = ax\\()^2 + bx + c\), where a, b, and c are constants. The function intersects the x-axis at points P and Q, and the y-axis at point R. Given that the coordinates of P and Q are (2, 0) and (-3, 0) respectively, and the value of c is 6, answer the following questions:
Question Parts
(a)
Determine the values of a and b in the quadratic equation.
(b)
Sketch the graph of the quadratic function based on the values obtained in part (a). Clearly label the points of intersection with the axes.
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Question 12 View Details
In a coordinate plane, the points A(1, 2), B(4, 6), and C(-2, 3) form a triangle. Answer the following questions:
Question Parts
(a)
Calculate the lengths of the sides of triangle ABC.
(b)
Determine the area of triangle ABC using the coordinates of the vertices.
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Question 13 View Details
A triangular plot of land has sides measuring 15 m, 20 m, and 25 m. The owner wants to build a fence around the plot and plant grass inside it. Calculate the following:
Question Parts
(a)
Determine the area of the triangular plot using Heron's formula. Show all your workings.
(b)
If the cost of fencing the plot is ₦200 per meter, calculate the total cost of fencing the entire plot.
(c)
Assuming the owner wants to plant grass at a cost of ₦50 per square meter, calculate the total cost of planting grass over the entire area of the triangular plot.
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