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Mathematical Modelling Sample Questions

Question 1: The dimension of a bedroom was . Calculate the number of square tiles of dimension required to cover the floor of the bedroom?

Answer: 36 nos.

Explanation: We need to calculate the area of the room and the area of the tile to solve the problem.


Question 2: A bus travels 280 miles by consuming 7 gallons of gas. How many gallons of gas would be needed to drive 120 miles?

Answer: 3 gallons

Explanation: We need to establish a relationship between distance traveled and gas consumed.


Question 3: A manufacturer is earning a profit of $1500 by making 50 units of product. Find the profit earned by the manufacturer, if he scales up the production to 175 units.

Answer: $5250

Explanation: The profit earned and the product manufactured is directly related to each other. Write a relationship between these quantities.


Question 4: The boat has 14 mph speed in still water. Find the time required to cover a distance of 88 miles, when the boat is going downstream. Assume the speed of the water in the river as 2 mph.

Answer: 5.5 hours

Explanation: When going downstream, we need to add the speed of the boat and the speed of the river, to get the net speed.


Question 5: How much space would be inside cardboard with dimensions ?

Answer: 1536 cubic inches

Explanation: Space inside the cardboard would be the volume of the cardboard.


Question 6: The volume of a pyramid with an 11-inch height is 550 cubic inches. Find the base area of the pyramid.

Answer: 150 square inches

Explanation: Rewrite the volume of the pyramid equation to find the base area.


Question 7: Rearrange the following equation to find the acceleration (a)


Explanation: Rewrite the formula to highlight the acceleration.


Question 8: The fixed cost of renting a car for a day is $45, and the charge per mile is $0.11/mile. Write a mathematical equation that models the cost.

Answer: .

Explanation: Let the variable , represents the distance covered by the car in miles.


Question 9: Use mathematical modeling to find the set of two numbers. Where one number exceeds the second number by 16. And, the second number is thrice more than the first number.

Answer: The first number is 4. And, the second number is 12.

Explanation: Let the variable , represents the first number. And represents the second number.


Question 10: The fixed monthly cost of a telecom company A is $30 and a rate of 0.3/min talk time. Another company B has a fixed cost of $40 and a rate of 0.25/min. Which company has a cheaper price for using 400 mins?

Answer: Company B has a cheaper price for using 400 mins.

Explanation: Let the variable , represents the number of minutes used.

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