IAR Math Modeling and Application 2 — Questions and Answers
Question 1: A phone plan charges $20 per month plus $0.10 per text. Which equation models the monthly cost C for t texts?
- C = 20 + 0.10t (Correct answer)
- C = 20t + 0.10
- C = 0.10 + 20t
- C = 20 - 0.10t
Correct answer: C = 20 + 0.10t
The fixed $20 is constant and $0.10 multiplies the number of texts t.
Question 2: A car travels at a steady 55 miles per hour. How far does it go in 3.5 hours?
- 192.5 miles (Correct answer)
- 157.5 miles
- 165 miles
- 180 miles
Correct answer: 192.5 miles
Distance equals rate times time, so 55 x 3.5 = 192.5 miles.
Question 3: A recipe for 4 servings uses 3 cups of flour. How much flour is needed for 10 servings?
- 7.5 cups (Correct answer)
- 6 cups
- 8 cups
- 5 cups
Correct answer: 7.5 cups
Set up the proportion 3/4 = x/10, giving x = 7.5 cups.
Question 4: A pool fills at 12 gallons per minute and already holds 50 gallons. Which models total gallons G after m minutes?
- G = 50 + 12m (Correct answer)
- G = 12 + 50m
- G = 50m + 12
- G = 62m
Correct answer: G = 50 + 12m
The starting 50 gallons is constant and 12 gallons are added each minute.
Question 5: A store marks up an item costing $40 by 25%. What is the selling price?
- $50 (Correct answer)
- $45
- $65
- $48
Correct answer: $50
A 25% markup adds $10 to the $40 cost, giving $50.
Question 6: A function gives the height of a ball as h = -16t^2 + 32t. At what time does the ball return to the ground?
- t = 2 seconds (Correct answer)
- t = 1 second
- t = 4 seconds
- t = 16 seconds
Correct answer: t = 2 seconds
Setting h = 0 gives t(−16t + 32) = 0, so t = 0 or t = 2 seconds.
Question 7: A worker earns $15 per hour plus a $50 bonus. If she earned $215, how many hours did she work?
- 11 hours (Correct answer)
- 14 hours
- 10 hours
- 12 hours
Correct answer: 11 hours
Solving 15h + 50 = 215 gives 15h = 165, so h = 11 hours.
IAR Math Modeling and Application 2
A phone plan charges $20 per month plus $0.10 per text.
Which equation models the monthly cost C for t texts?