# Mathematical Modeling for Precalculus Chapter Exam

Choose your answers to the questions and click 'Next' to see the next set of questions. You can skip questions if you would like and come back to them later with the yellow "Go To First Skipped Question" button. When you have completed the practice exam, a green submit button will appear. Click it to see your results. Good luck!

### Page 1

#### Question 1 1. On a certain credit card, customers earn a percentage of their purchases back as rewards. The percentage earned is directly proportional to the average balance on the card. With an average balance of $2,000, the reward percentage is 1.5%. What is the percentage with an average balance of $2,500?

####
Question 2
2.
What is the best equation for the following scenario?

A mountain climber starts at the bottom of a mountain and climbs at a rate of 20 feet per hour. What equation represents his rate of climbing?

####
Question 3
3.
Find the minimum value of the parabola using the following equation:

f(x)=1/4(x+4)^2 +3

####
Question 4
4.
Which scenario is the best fit for the linear equation?

y=200x +1200

#### Question 5 5. Elizabeth found a picture frame on sale. She wants to know if her poster will fit inside the frame, but she left the poster at home. In the image, the blue rectangle represents the frame (perimeter = 43) and the purple rectangle represents the poster. Find x and determine if the poster will fit in the frame.

### Page 2

#### Question 6 6. The y-coordinate of the vertex of a parabola that opens up is called the _____.

#### Question 7 7. A plant grows at a rate inversely proportional to the temperature outside. At 45 degrees, it grows 2 inches per day. How many inches will it grow per day at 50 degrees?

#### Question 8 8. Supply function is defined as _____.

#### Question 9 9. The y-coordinate of the vertex of a parabola that opens down is called the _____.

#### Question 10 10. The speed of a horse is inversely proportional to the size of the jockey. When the jockey weighs 95 pounds, the horse can run at 40 miles per hour. When the jockey weighs 100 pounds, how many miles per hour will the horse be able to run?

### Page 3

#### Question 11 11. All of the sides of the square are the same length. Use this information to solve for y.

#### Question 12 12. Jonathan enjoys gardening. The east side of his house is 45 units in length. He can put 30 flowers along the length of the east side of his house. Each flower is 1.5 units in length. Assuming that the west side of his house is the same length as the east side, how many flowers can he put along wall B?

####
Question 13
13.
Find the market equilibrium point (x, y) of the following functions:

Supply: y = -0.05x +3.7

Demand: y = 0.02x + 2.3

####
Question 14
14.
What is the correct equation for the following scenario?

Alex wants to figure out how much money she will make at the end of the week. She is making $12.50 an hour plus a $20 bonus.

####
Question 15
15.
Find the breakeven point of the following functions:

C(x) = 5x - 7

R(x) = 2x

### Page 4

#### Question 16 16. What type of graph is this?

####
Question 17
17.
Find the maximum value of the parabola using the following equation:

f(x)=-x^2+4x+3

#### Question 18 18. In a certain car factory, the price per car varies inversely with the number of cars made. If the factory makes 250 cars, the price per car is $15,000. How many cars will the factory have to make to drive the price per car down to $10,000?

#### Question 19 19. The distance Catelyn travels is directly proportional to the time she spends on the road. If Catelyn spends 5 hours on the road, she travels 30 miles. How far will she go if she only spends 3 hours on the road?

#### Question 20 20. If the market price of a product is above the equilibrium price, the quantity supplied is _____ the quantity demanded.

### Page 5

#### Question 21 21. The length and steepness of a line that shows the rate of change between two values is called the _____.

####
Question 22
22.
Find the breakeven point of the following functions:

C(x) = 2x + 1

R(x) = 3x

#### Question 23 23. Which Law states that the quantity demanded will increase as the price of the product decreases?

####
Question 24
24.
Which scenario best fits the linear equation?

y=-2x + 5

####
Question 25
25.
Find the market equilibrium point for the following equations:

Supply: .10x + 5

Demand: -.15x + 10

### Page 6

#### Question 26 26. In marketing, the _____ represents the point where products neither make a profit nor incur a loss.

####
Question 27
27.
Find the breakeven point of the following functions:

C(x)= 4x +4

R(x) = 6x

#### Question 28 28. The _____ is the linear function which represents the seller's cost of a product.

#### Question 29 29. Solve for x using the image as a reference. The perimeter of the triangle is 36 units.

#### Question 30 30. Savanna needs to pick up gift bags for a party. She wants gift bags of different shapes, but they must be the same perimeter. She found a bag that is a pink rectangle with a perimeter of 16. Which of the following shapes have the same perimeter as the pink rectangle?

#### Mathematical Modeling for Precalculus Chapter Exam Instructions

Choose your answers to the questions and click 'Next' to see the next set of questions. You can skip questions if you would like and come back to them later with the yellow "Go To First Skipped Question" button. When you have completed the practice exam, a green submit button will appear. Click it to see your results. Good luck!