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AP Calculus AB Unit 3B: Implicit Differentiation and Inverse Functions — practice questions — page 4

Explore 97 free Unit 3B: Implicit Differentiation and Inverse Functions questions in AP Calculus AB Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Unit 3B: Implicit Differentiation and Inverse Functions questions and exercises with answers

Showing questions 91–97 of 97.

Solve 3 ≤ 2x - 1 ≤ 7 (a DOUBLE inequality) for real x.Read the answer and worked solution →Probability measures:Read the answer and worked solution →The probability of an IMPOSSIBLE event is:Read the answer and worked solution →If a bag has 6 cards numbered 1 to 6, and 3 of them are purple, the probability of drawing a PURPLE card is:Read the answer and worked solution →The probability of drawing any number from 2 to 10 from a standard deck of 52 cards is:Read the answer and worked solution →If you toss a fair coin and the probability of heads is 1/2, what is the probability of NOT getting heads?Read the answer and worked solution →An event is described as having 'EVEN CHANCE'. Its probability is:Read the answer and worked solution →

Worked practice questions

Solve 3 ≤ 2x - 1 ≤ 7 (a DOUBLE inequality) for real x.

  1. -1 ≤ x ≤ 3
  2. 2 < x < 4
  3. 2 ≤ x ≤ 4
  4. 1 ≤ x ≤ 5
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Correct answer: C. 2 ≤ x ≤ 4

Add 1 throughout: 4 ≤ 2x ≤ 8 → divide by 2 (positive, no sign flip): 2 ≤ x ≤ 4. Solution set [2, 4].

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Probability measures:

  1. Length of an object
  2. Likelihood that an event will occur
  3. Weight of a substance
  4. Temperature
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Correct answer: B. Likelihood that an event will occur

Probability is a measurement of likelihood — how likely an event is to occur. It ranges from 0 (impossible) to 1 (certain). It's analogous to length, mass, or volume, but for uncertain events.

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The probability of an IMPOSSIBLE event is:

  1. 0
  2. 0.5
  3. 1
  4. Negative
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Correct answer: A. 0

An impossible event has probability exactly 0. Example: rolling a 7 on a standard 6-sided die. **Probability scale:** 0 (impossible) → 0.5 (equally likely / even chance) → 1 (certain).

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More Mathematics topics

Unit 3A: Chain Rule and Composite FunctionsUnit 1A3: Function Composition and InversesUnit 1A1: Relations, Functions and GraphsUnit 1A2: Trigonometric Functions & Inverse TrigUnit 2: Differentiation and Fundamental Derivative RulesUnit 6A: Indefinite Integrals & Fundamental TheoremUnit 1B3: Asymptotic Behavior and Infinite LimitsUnit 1B1: Limit Concepts and Graphical Limits