AP Precalculus Problems and Solutions (Part - 1)

Problem 1 :

The function h is given by h(x) = 8 ⋅ 2^x. For which of the following values of x, h(x) = 256?

A)  x = 2

B)  x = 5

C)  x = 8

D)  x = 16

Solution :

Problem 2 :

The function h is given by h(x) = log₃ x. Which of the following is equivalent to the expression

2 ⋅ h(w) + h(p),

where w and p are values in the domain of h?

A) log₃ (wp)²

B) (log₃ w)² ⋅ (log₃ p)

C) log₃ (w²p)

D) log₃ (2wp)

Solution :

Problem 3 :

Let x and y be positive constants. Which of the following is equivalent to 2ln x - 2 ln y ?

Solution :

Problem 4 :

The function f is given by f(x) = 2log₅ x. Which of the following describes f?

A) is an increasing function that increases at an increasing rate.

B) is an increasing function that increases at a decreasing rate.

C) is a decreasing function that decreases at an increasing rate.

D) is a decreasing function that decreases at a decreasing rate.

Solution :

Problem 5 :

The Richter scale is a numerical scale that uses base 10 logarithms for measuring an earthquake’s magnitude. The larger the number, the more intense the earthquake. As intensities increase multiplicatively by a factor of 10, the Richter scale increases additively by 1. Consider two earthquakes that occurred in the year 2022. An earthquake in Indonesia had a magnitude of 5.1, and an earthquake in Mexico had a magnitude of 2.5. Approximately how many times more intense was the Indonesia earthquake than the Mexico earthquake?

A)  2.6

B)  26

C)  100

D)  400

Solution :

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