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AP Calculus AB Unit 3A: Chain Rule and Composite Functions — practice questions — page 2

Explore 96 free Unit 3A: Chain Rule and Composite 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 3A: Chain Rule and Composite Functions questions and exercises with answers

Showing questions 31–60 of 96.

A student differentiates e^x. The result is:Read the answer and worked solution →The inverse of the natural exponential function has its own name. It is the:Read the answer and worked solution →A calculus course opens by going back to secant lines and one other kind of line. That other kind is:Read the answer and worked solution →Average speed over a whole trip differs from speed at one instant. That second quantity is:Read the answer and worked solution →Catch the derivative rulesRead the answer and worked solution →Pop the calculus wordsRead the answer and worked solution →Run the derivative gatesRead the answer and worked solution →Slice the calculus wordsRead the answer and worked solution →Basic or advancedRead the answer and worked solution →Sort the calculus wordsRead the answer and worked solution →Type the numberRead the answer and worked solution →Derivatives bingoRead the answer and worked solution →$\cos 2\theta$ equals:Read the answer and worked solution →What is the maximum number of real roots a quadratic equation can have?Read the answer and worked solution →Which of the following is NOT a quadratic equation after simplification?Read the answer and worked solution →If the discriminant of a quadratic equation is negative, what can be concluded about its roots?Read the answer and worked solution →$\sin(A + B) = $Read the answer and worked solution →If $\alpha$ is a root of the quadratic equation $ax^2+bx+c=0$ with $a\neq 0$, then which statement must be true?Read the answer and worked solution →If $\sin\theta + \cos\theta = 1$, then $\sin\theta \cdot \cos\theta$ equals:Read the answer and worked solution →$\cos 3\theta$ equals:Read the answer and worked solution →$\sin^2\theta + \cos^2\theta$ equals:Read the answer and worked solution →Which equation appears cubic at first glance but actually simplifies to a quadratic equation?Read the answer and worked solution →For the quadratic equation $ax^2+bx+c=0$, what is the discriminant?Read the answer and worked solution →Find the roots of $2x^2-5x+3=0$ by factorisation.Read the answer and worked solution →Probability measures: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 →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 →The identity (a + b)(a − b) equals:Read the answer and worked solution →Which of the following gives a LINEAR equation when set equal to zero?Read the answer and worked solution →

Worked practice questions

A student differentiates e^x. The result is:

  1. e^x itself
  2. e^x plus 1
  3. x times e^x
  4. e^x minus 1
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Correct answer: A. e^x itself

1. This function is unusual. 2. Differentiating changes nothing. 3. It is e^x itself. _Source: OpenStax Calculus Volume 1, Chapter 3, Derivatives._

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The inverse of the natural exponential function has its own name. It is the:

  1. Secant function
  2. Natural logarithm
  3. Sine function
  4. Power function
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Correct answer: B. Natural logarithm

1. The two undo each other. 2. Its short form is ln. 3. It is the natural logarithm. _Source: OpenStax Calculus Volume 1, Chapter 3, Derivatives._

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A calculus course opens by going back to secant lines and one other kind of line. That other kind is:

  1. Parallel lines
  2. Vertical lines
  3. Tangent lines
  4. Contour lines
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Correct answer: C. Tangent lines

1. A secant cuts the curve twice. 2. The other touches at one point. 3. They are tangent lines. _Source: OpenStax Calculus Volume 1, Chapter 3, Derivatives._

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More Mathematics topics

Unit 3B: Implicit Differentiation and Inverse 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