Linear & Quadratic Math Challenges for Grade 9

A car rental company charges a flat fee of $30 plus $0.20 per mile driven. Write a linear function to represent the total cost (C) of renting a car for x miles. What is the cost if you drive 150 miles?

• $90

• $75

• $45

• $60

A gardener is planting a rectangular garden that is 3 meters longer than it is wide. If the area of the garden is 54 square meters, write a quadratic equation to find the dimensions of the garden. What are the dimensions?

• Width: 5 meters, Length: 8 meters

• Width: 7 meters, Length: 10 meters

• Width: 6 meters, Length: 9 meters

• Width: 4 meters, Length: 7 meters

A cell phone plan costs $50 per month plus $0.10 for each text message sent. Write a linear function to represent the total cost (C) for sending x text messages. How much will it cost if you send 200 messages?

• $80

• $90

• $60

• $70

The height of a ball thrown into the air can be modeled by the equation h(t) = -16t^2 + 32t + 5, where h is the height in feet and t is the time in seconds. How long will it take for the ball to hit the ground?

• 4.0 seconds

• 2.5 seconds

• 1.5 seconds

• 3.0 seconds

A store is having a sale where the price of a jacket is reduced by $20. If the original price of the jacket is represented by p, write a linear equation for the sale price. If the original price is $80, what is the sale price?

• $70

• $40

• $50

• $60

A rectangular swimming pool is 4 meters longer than it is wide. If the perimeter of the pool is 48 meters, write a quadratic equation to find the dimensions of the pool. What are the dimensions?

• Width: 8 meters, Length: 12 meters

• Width: 10 meters, Length: 14 meters

• Width: 6 meters, Length: 10 meters

• Width: 12 meters, Length: 16 meters

The population of a town is modeled by the function P(t) = 500e^(0.03t), where P is the population and t is the number of years since 2020. What will the population be in 5 years?

• 500

• 581

• 550

• 600

A train travels at a constant speed of 60 miles per hour. Write a linear function to represent the distance (d) traveled after t hours. How far will the train travel in 3 hours?

• 180 miles

• 90 miles

• 240 miles

• 150 miles

A rectangular garden has a length that is 2 meters longer than its width. If the area of the garden is 30 square meters, write a quadratic equation to find the dimensions of the garden. What are the dimensions?

• Width: 5 meters, Length: 7 meters

• Width: 6 meters, Length: 8 meters

• Width: 4 meters, Length: 6 meters

• Width: 3 meters, Length: 5 meters

The height of a projectile is modeled by the equation h(t) = -4.9t^2 + 20t + 1. How long will it take for the projectile to reach its maximum height?

• 2.04 seconds

• 3.0 seconds

• 1.5 seconds

• 2.5 seconds