Unit 2 AP Precalculus Practice Test 2025

Which of the following functions given below are equivalent?

I. f(x) = (2)^3−x
II. g(x) = 8 · 2^−x
III. h(x) = \frac{8} {2^{x}}

When exposed to sunlight, the number of bacteria in a culture decreases exponentially at the rate of 10% per hour. What is the best approximation for the number of hours required for the initial bacteria to decrease by 50%?

A culture of 3,000 bacteria triples every 40 minutes. If P(t) represents the size of the bacteria population after t minutes, which equation can be used to model the exponential growth of these bacteria?

A radioactive substance has an initial mass of 250 grams, and its mass halves every 5 years. Which equation shows the number of grams, M(t), remaining after t years?

A scientist studying bacteria growth notices interesting behavior with the replication of cells over the course of 24 hours. She records her description of the behavior in hopes of writing a function that can be used to make predictions for future bacteria growth. She observed that for the first 8 hours, the number of bacteria, y, increases at a constant rate of 10 cells per minute. After the initial 8 hours, the number of bacteria varies inversely with time, x, with a proportional constant of 3 for the next 10 hours. Between hour 18 through hour 20, the bacteria decrease at a constant rate of 5 cells per minute. In the last 4 hours, the bacteria double in growth every minute. Which of the following models best fits the scientist’s observations?

Which of the following sequences have the same common ratio or same common difference?

I. −1, 3, −9, 27,. . .
II. −1, 2, 5, 8,. . .
III. a_n = −3(n − 1) + 1
IV. g_n = (−1)ⁿ (3)ⁿ⁺²

Given the sequence whose second term is ae² and fifth term is ae⁵, which of the following equations can represent the kth term of this sequence?

Which of the following represents the graph of the sequence whose terms can be found using the equation a_n = −5 + 3(n − 1)?

In the sequence shown below, a₀ = −7.5 and a_n represents the nth term.

−7.5, −4.3, −1.1, 2.1, 5.3, 8.5, …a_n

Which equation expresses a_n in terms of n?

Which of the following equations would produce sequences with the same terms?

I. g_n = 4 · 2ⁿ
II. g_n = 2²⁺ⁿ
III. g_n = 2⁴ⁿ

Given the two arithmetic sequences whose general term can be found using the following equations:

a_n = k − 2(n − 1)
a_n = 4 − 3(n + 1)

What would be the value of k for the two sequences to have the same third term?

The last term of a geometric sequence is \frac{8} {125} . If the first term is \frac{5} {2} and the sequence has 5 terms, what is the value of the second term?

What is the first term of an arithmetic sequence whose 19th term is 123 and 2nd term is 4?

Which of the following tables of data best fits an exponential regression model?

Which of the following functions given below are equivalent?

I. f(x) = (9)^x/2
II. g(x) = 3^x
III. h(x) = 4.5^x

Which function is the inverse of y = log(x − 5)?

If log3 (x² + 5) = 2, what is the value of x?

If log30 = b, then which of the following expressions is equivalent to (b − 1)²?

What is the domain of the graph of f(x) = c log_b (x − a), where a > 0 and c > 1?

If log N = ½(log a − 2 log b) + log c, what does N equal?

If log a = 2 and log b = 4, which of the following is the numerical value of log \frac{a^{3}} {√b}

A company tracked the sales on their app for the first 14 days after it was released. The data are shown in the table below. The company noticed that the sales slowed over time and wanted to write an equation to model this data to predict future sales. Which of the following regression equations best models the data in the given table?