waec model questions vol1 2024 mathematics | Essay

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Question 1 View Details
A school organized a quiz competition among its students. The total number of students participating was 240. The students were divided into teams of equal size. If each team consisted of 12 students, calculate the number of teams formed. Additionally, if the school decided to increase the team size to 15 students, determine how many teams would be formed under this new arrangement. Finally, if each team was to compete in 4 rounds and each round required 3 hours, calculate the total time in hours that the quiz competition would take for all teams to complete their rounds.
Question Parts
(a)
Calculate the number of teams formed when each team consists of 12 students.
(b)
Determine how many teams would be formed if the team size was increased to 15 students.
(c)
Calculate the total time in hours for all teams to complete their rounds if each team competes in 4 rounds and each round takes 3 hours.
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Question 2 View Details
A shop sells three types of fruits: apples, oranges, and bananas. The prices per kilogram are ₦200 for apples, ₦150 for oranges, and ₦100 for bananas. If a customer buys 3 kg of apples, 2 kg of oranges, and 5 kg of bananas, calculate the total cost of the fruits. Additionally, if the customer decides to buy an additional 2 kg of apples and 3 kg of oranges, determine the new total cost. Finally, calculate the percentage increase in total cost after the additional purchase.
Question Parts
(a)
Calculate the total cost of the fruits initially purchased.
(b)
Determine the new total cost after the additional purchase.
(c)
Calculate the percentage increase in total cost after the additional purchase.
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Question 3 View Details
A farmer has a rectangular field with a length of 120 meters and a width of 80 meters. The farmer wants to plant two types of crops, A and B, in the field. Crop A requires 2 square meters for each plant, while crop B requires 3 square meters for each plant. The farmer has decided to allocate 60% of the field for crop A and the remaining for crop B. (a) Calculate the total area of the field that will be used for crop A and crop B. (b) Determine how many plants of each type can be planted in their respective areas. (c) If the farmer plans to sell each plant of crop A for ₦150 and each plant of crop B for ₦200, calculate the total potential revenue from selling all the plants.
Question Parts
(a)
Calculate the total area of the field that will be used for crop A and crop B.
(b)
Determine how many plants of each type can be planted in their respective areas.
(c)
Calculate the total potential revenue from selling all the plants.
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Question 4 View Details
In a survey conducted among students about their preferred subjects, the results showed that 60% preferred Mathematics, 40% preferred English, and 20% preferred both subjects. (a) Represent this information in a Venn diagram. (b) Calculate the number of students who preferred only Mathematics, only English, and both subjects if the total number of students surveyed was 200. (c) If 30% of the students who preferred Mathematics also preferred Science, calculate how many students preferred Mathematics and Science.
Question Parts
(a)
Represent this information in a Venn diagram.
(b)
Calculate the number of students who preferred only Mathematics, only English, and both subjects.
(c)
Calculate how many students preferred Mathematics and Science.
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Question 5 View Details
A cylindrical water tank has a radius of 3 meters and a height of 5 meters. The tank is filled with water to a height of 4 meters. A small hole at the bottom of the tank allows water to drain out at a constant rate. The tank is then refilled to its original height. Calculate the following:
Question Parts
(a)
Determine the volume of water currently in the tank when it is filled to a height of 4 meters.
(b)
If the water drains out at a rate of 0.5 cubic meters per hour, how long will it take for the water level to drop from 4 meters to 2 meters?
(c)
After draining, the tank is refilled to its original height. Calculate the total volume of water needed to refill the tank from 2 meters back to 5 meters.
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Question 6 View Details
A company's revenue from selling a product can be modeled by the equation R = 150x - 5x², where R is the revenue in naira and x is the number of units sold. Determine the number of units that need to be sold to maximize revenue. Additionally, calculate the maximum revenue that can be generated.
Question Parts
(a)
Identify the vertex of the quadratic equation and explain how it relates to the maximum revenue.
(b)
Calculate the number of units that must be sold to achieve maximum revenue.
(c)
Determine the maximum revenue generated at that number of units sold.
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Question 7 View Details
Consider the quadratic function given by the equation f(x) = ax^2 + bx + c, where a, b, and c are constants. A quadratic function is said to be in standard form when it is expressed as such. Given that the vertex of the parabola represented by this function is at the point (2, -3) and that it opens upwards, find the values of a, b, and c if the function passes through the point (0, 1).
Question Parts
(a)
Express the quadratic function in vertex form and derive the standard form from it.
(b)
Using the point (0, 1), substitute the values of x and f(x) into the standard form to derive a relationship between a, b, and c.
(c)
Using the vertex and the derived relationship from part (b), solve for the values of a, b, and c.
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Question 8 View Details
A company produces two products, A and B. The profit from product A is given by the inequality 3x + 2y > 60, while the profit from product B is represented by the inequality 5x + 4y ≤ 80, where x is the number of product A produced and y is the number of product B produced. Determine the feasible region for the production of both products and find the maximum profit.
Question Parts
(a)
Graph the inequalities on a Cartesian plane and identify the feasible region.
(b)
Identify the corner points of the feasible region and evaluate the profit function at these points.
(c)
Determine the maximum profit and the corresponding values of x and y.
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Question 9 View Details
Consider the arithmetic sequence defined by the first term a_1 = 5 and a common difference d = 3. Determine the 10th term of the sequence and the sum of the first 10 terms. Then, explain how the properties of arithmetic sequences can be applied to solve real-life problems such as calculating total costs or distances.
Question Parts
(a)
Find the 10th term of the sequence.
(b)
Calculate the sum of the first 10 terms of the sequence.
(c)
Explain how the properties of arithmetic sequences can be applied to solve real-life problems such as calculating total costs or distances.
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Question 10 View Details
A company produces two products, A and B, that are related by the equation P_A + 2P_B = 100, where P_A is the production of product A and P_B is the production of product B. If the production of product A is increased by 20 units, derive the new equation and determine how many units of product B can be produced if the total production capacity remains the same. Discuss the implications of this change on resource allocation within the company.
Question Parts
(a)
Derive the new equation after increasing the production of product A by 20 units.
(b)
Determine how many units of product B can be produced with the new equation.
(c)
Discuss the implications of this change on resource allocation within the company.
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Question 11 View Details
A farmer is planning to plant two types of crops on a rectangular piece of land that measures 120 meters in length and 80 meters in width. The farmer decides to allocate two-thirds of the land for maize and the remaining one-third for cassava. Using this information, answer the following:
Question Parts
(a)
Calculate the area of the land allocated for maize.
(b)
If the farmer plans to plant 100 maize seeds per square meter, calculate the total number of maize seeds that will be planted.
(c)
If the farmer can harvest 2 kilograms of maize per seed, calculate the total weight of maize harvested from the area allocated for maize.
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Question 12 View Details
A rectangular plot of land is represented on a coordinate plane with its vertices at points A(1, 2), B(1, 5), C(4, 5), and D(4, 2). Using this information, answer the following:
Question Parts
(a)
Determine the length and width of the rectangular plot.
(b)
Calculate the area of the rectangular plot.
(c)
If the plot is to be fenced and each meter of fencing costs ₦200, calculate the total cost of fencing the rectangular plot.
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Question 13 View Details
A farmer has a rectangular plot of land with a length of 120 meters and a width of 80 meters. The farmer wants to divide this plot into three equal sections for planting different crops. After dividing the land, he plans to construct a fence around the entire area. Additionally, he plans to plant a row of trees along one of the longer sides of the plot, with each tree spaced 4 meters apart. Calculate the following:
Question Parts
(a)
Determine the area of the entire plot of land.
(b)
If the farmer divides the plot into three equal sections, what will be the area of each section?
(c)
Calculate the total length of the fence needed to enclose the entire plot.
(d)
How many trees can the farmer plant along the longer side of the plot, given that each tree is spaced 4 meters apart?
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