waec model questions vol1 2022 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. The farmer wants to plant crops that require a minimum area of 3000 square metres to grow effectively. (a) Calculate the area of the plot of land. (b) Determine if the farmer can plant the crops based on the area requirement. (c) If the farmer decides to divide the plot into smaller rectangular sections, with each section having a length of 20 metres, find the number of sections that can be created and the width of each section. (d) If the farmer sells each section for ₦5000, calculate the total revenue generated from selling all sections.
Question Parts
(a)
Calculate the area of the plot of land.
(b)
Determine if the farmer can plant the crops based on the area requirement.
(c)
If the farmer decides to divide the plot into smaller rectangular sections, with each section having a length of 20 metres, find the number of sections that can be created and the width of each section.
(d)
If the farmer sells each section for ₦5000, calculate the total revenue generated from selling all sections.
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Question 2 View Details
A school is organizing a sports day and has a budget of ₦150,000 for various activities. The budget is allocated as follows: 40% for athletics, 30% for games, and the remaining for refreshments. (a) Calculate the amount allocated for athletics. (b) Determine the amount allocated for games. (c) Calculate the amount allocated for refreshments. (d) If the school decides to cut the budget for athletics by 10%, how much will be left for athletics after the cut?
Question Parts
(a)
Calculate the amount allocated for athletics.
(b)
Determine the amount allocated for games.
(c)
Calculate the amount allocated for refreshments.
(d)
If the school decides to cut the budget for athletics by 10%, how much will be left for athletics after the cut?
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Question 3 View Details
A company produces two types of products, A and B. The production of product A requires 2 hours of labor and 3 kg of raw materials, while product B requires 1 hour of labor and 2 kg of raw materials. The company has a total of 40 hours of labor and 60 kg of raw materials available. If the profit from product A is ₦150 per unit and from product B is ₦100 per unit, determine the number of each product the company should produce to maximize profit. Additionally, express the constraints and the objective function mathematically.
Question Parts
(a)
Formulate the objective function and the constraints based on the given information.
(b)
Graph the feasible region defined by the constraints. Clearly label the axes and the lines representing each constraint.
(c)
Determine the optimal solution by evaluating the profit at each vertex of the feasible region.
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Question 4 View Details
In a survey conducted among 300 students, it was found that 180 students like Mathematics, 150 like English, and 90 like both subjects. Using a Venn diagram, determine how many students like only Mathematics, only English, and neither subject.
Question Parts
(a)
Using the data, calculate the number of students who like only Mathematics.
(b)
Calculate the number of students who like only English.
(c)
Determine how many students do not like either subject.
(d)
Draw a Venn diagram representing the survey results.
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Question 5 View Details
A school organized a fundraising event where tickets were sold for ₦150 each. The total amount raised was ₦12,000. Additionally, the school received a donation of ₦3,000 from a local business. After covering the expenses of ₦5,000 for organizing the event, the school plans to use the remaining funds to support a community project. (a) Calculate the total number of tickets sold during the event. (b) Determine the total amount available for the community project after subtracting the expenses from the total funds raised. (c) If the school decides to allocate 60% of the remaining funds to the community project, how much money will be allocated?
Question Parts
(a)
Calculate the total number of tickets sold during the event.
(b)
Determine the total amount available for the community project after subtracting the expenses from the total funds raised.
(c)
If the school decides to allocate 60% of the remaining funds to the community project, how much money will be allocated?
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Question 6 View Details
A car rental company charges a fixed fee of ₦2,000 for renting a car for a day, plus an additional charge of ₦500 for every kilometer driven. A customer rented a car for one day and drove a total of 150 kilometers. (a) Write an expression to represent the total cost of renting the car based on the kilometers driven. (b) Calculate the total cost for the customer using the expression from part (a). (c) If the customer decides to drive 20% more kilometers than they originally planned, how much will the new total cost be?
Question Parts
(a)
Write an expression to represent the total cost of renting the car based on the kilometers driven.
(b)
Calculate the total cost for the customer using the expression from part (a).
(c)
If the customer decides to drive 20% more kilometers than they originally planned, how much will the new total cost be?
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Question 7 View Details
Consider the quadratic equation given by \\((2x^2 - 4x - 6\) = 0.\) Solve for the values of x and determine the nature of the roots. Then, using the roots found, form a new quadratic equation with the same roots but with a leading coefficient of 1. Finally, verify your new equation by substituting the roots back into it.
Question Parts
(a)
Solve the quadratic equation 2x^2 - 4x - 6 = 0 for x.
(b)
Using the roots obtained in part (a), form a new quadratic equation with a leading coefficient of 1.
(c)
Verify your new quadratic equation by substituting the roots back into it.
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Question 8 View Details
Solve the inequality 3(\(x - 2) < 2(x + 1)\). Represent the solution on a number line and describe the solution set in interval notation.
Question Parts
(a)
Solve the inequality 3(x - 2) < 2(x + 1).
(b)
Represent the solution on a number line.
(c)
Describe the solution set in interval notation.
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Question 9 View Details
A student is studying the behavior of a particular arithmetic sequence. The first term is 5, and the common difference is 3. Using this information, answer the following questions:
Question Parts
(a)
Find the 10th term of the sequence. Show your working.
(b)
Determine the sum of the first 20 terms of the sequence. Show all necessary steps.
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Question 10 View Details
A company produces a certain product, and the relationship between the cost (C) in naira and the number of units produced (x) can be modeled by the equation \(C = 200 + 50x\). Additionally, the revenue (R) generated from selling the product is given by \(R = 100x\). Using this information, answer the following questions:
Question Parts
(a)
Determine the break-even point where the cost equals the revenue. Show your working.
(b)
If the company wants to make a profit of at least ₦1,000, what is the minimum number of units that must be produced and sold? Show all necessary steps.
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Question 11 View Details
A company produces two types of products, A and B. The production cost for product A is ₦150 per unit, while product B costs ₦250 per unit. The company has a total budget of ₦5000 for production. Additionally, the company can only produce a maximum of 20 units of product A and 15 units of product B due to resource constraints. (a) Formulate the inequalities that represent the constraints on the production of products A and B. (b) Graph the inequalities on a coordinate plane. Clearly label the feasible region. (c) Determine the maximum number of units of products A and B that the company can produce without exceeding the budget and resource constraints. Show your calculations.
Question Parts
(a)
Formulate the inequalities that represent the constraints on the production of products A and B.
(b)
Graph the inequalities on a coordinate plane. Clearly label the feasible region.
(c)
Determine the maximum number of units of products A and B that the company can produce without exceeding the budget and resource constraints. Show your calculations.
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Question 12 View Details
In a coordinate plane, the points A(2, 3), B(8, 3), and C(5, 7) form a triangle. (a) Calculate the length of each side of the triangle. (b) Determine the area of triangle ABC using the formula for the area of a triangle based on its vertices. (c) If point D is the midpoint of side AB, find the coordinates of point D and determine the distance from point D to point C.
Question Parts
(a)
Calculate the length of each side of the triangle.
(b)
Determine the area of triangle ABC using the formula for the area of a triangle based on its vertices.
(c)
If point D is the midpoint of side AB, find the coordinates of point D and determine the distance from point D to point C.
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Question 13 View Details
A rectangular garden measures 12 meters in length and 8 meters in width. The garden is to be surrounded by a path of uniform width. If the total area of the garden and the path is to be 160 square meters, calculate the width of the path. Additionally, determine the perimeter of the entire area (garden + path).
Question Parts
(a)
Let the width of the path be x meters. Write an equation for the total area of the garden and path in terms of x.
(b)
Solve the equation you formed in part (a) to find the width of the path.
(c)
Using the width of the path found in part (b), calculate the perimeter of the entire area.
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