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AP Precalculus — Unit 2: Exponential and Logarithmic Functions: 203 practice questions

203 original AP Precalculus questions on Unit 2: Exponential and Logarithmic Functions, each with an explanation and its source. Topics: Exponential Functions, Logarithmic Expressions, Change in Arithmetic and Geometric Sequences, Change in Linear and Exponential Functions, Exponential Function Manipulation, Exponential Function Context and Data Modeling, Competing Function Model Validation, Composition of Functions, Inverse Functions, Inverses of Exponential Functions, Logarithmic Functions, Logarithmic Function Manipulation, Exponential and Logarithmic Equations and Inequalities, Logarithmic Function Context and Data Modeling, Semi-log Plots, 2.5 Exponential Function Context and Data Modeling, 2.6 Competing Function Model Validation, 2.7 Composition of Functions, 2.8 Inverse Functions, 2.9 Logarithmic Expressions, 2.12 Logarithmic Function Manipulation, 2.11 Logarithmic Functions, 2.10 Inverses of Exponential Functions, 2.13 Exponential and Logarithmic Equations and Inequalities, 2.14 Logarithmic Function Context and Data Modeling, 2.15 Semi-log Plots, 2.1 Change in Arithmetic and Geometric Sequences, 2.2 Change in Linear and Exponential Functions, 2.3 Exponential Functions, 2.4 Exponential Function Manipulation. Two free samples are below. Try 5 more free, no sign-up.

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Two Unit 2: Exponential and Logarithmic Functions questions with explanations

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Q1 Exponential Functions

A quantity follows P(t)=3·2ᵗ. What does the model predict about the quantity each time t increases by 1?

  1. It doubles; the initial value at t=0 is 3.
  2. It increases by exactly 2 units; the initial value is 3.
  3. It is halved; the initial value is 2.
  4. It stays constant at 3.
Show the answer and explanation

Answer: A. The base 2 is the multiplicative growth factor for each unit increase in t, so the quantity doubles. P(0)=3·1=3 is the initial value.

Sources: College Board, AP Precalculus Course and Exam Description · College Board AP Central, AP Precalculus

Q2 Logarithmic Expressions

What is log₂(32)?

  1. 4
  2. 5
  3. 16
  4. 64
Show the answer and explanation

Answer: B. A logarithm gives the exponent: log₂(32)=y means 2ʸ=32. Since 2⁵=32, the value is 5.

Sources: College Board, AP Precalculus Course and Exam Description · College Board AP Central, AP Precalculus

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