PSAT Math Multiple-Choice Practice Test 7: Advanced Math

1. Which of the following equations has a vertex of (-5, 2)?

2. In the equation x2 + 24x + c = (x + 9)(x + p), c and p are constants. If the equation is true for all values of x, what is the value of c?

3. The stream of water that shoots out of a public fountain in Central Park takes the form of a parabola. The water shoots from a spout that is 8 feet above the ground and reaches a maximum height of 39.25 feet. If y represents the height of the water and x represents the time (in seconds), which of the following equations could describe the trajectory of the stream of water?

4. An oceanographer is trying to determine the concentration profile of dissolved oxygen in the ocean at depths lower than 10 meters. He determines that the dissolved oxygen concentration is 0.0022 g/L at a depth of 15 meters, and it is 0.00125 g/L at a depth of 20 meters. If C(d) is the concentration of dissolved oxygen at d meters, which of the follow equations best describes the profile below 10 meters?

5. A shipping company pays a driver a fixed fee for each delivery, and deducts a separate fee daily for the use of the company's delivery truck. The driver's net pay in dollars, P, for one day is given by the equation P = 8d - 40, where d is the number of deliveries made in one day. What does the number 40 most likely represent?

6. At a buffet restaurant, students pay $5 per meal and non-students pay $7. The total revenue, R, in dollars, earned per day by the restaurant is given by the equation R = 5s + 7n, where s is the number of student customers and n is the number of non-student customers. Which of the following represents the total number of customers on a given day?

7. T(t) = ΔT(-kt)

The simple cooling of an object can be represented by the equation above, where T is temperature in degrees Celsius, k is a rate constant, and t is time. What might the quantity ΔT represent?


Between 2010 and 2015, researchers tracked populations of Crucian carp in the Ohio River. The graph above displays population sizes as counted by the researchers. According to the line of best fit, what is the approximate average yearly decrease in the number of Crucian carp?

9. A group of students decided to have a car wash to raise funds for the school. The students charged the same rate to wash each car, and they paid for cleaning supplies out of the proceeds. If the net amount, N(c), in dollars, raised from washing c cars is given by the function N(c) = 8c - 0.40c, which of the following can be deduced from the function?


Two employees at a certain company were asked to gauge their energy levels on a scale of 1 to 10 after eating lunch at noon. The results were averaged and plotted as illustrated in the above figure. Which of the following statements is most consistent with the given data?

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