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

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 61–90 of 96.

The algebraic identity (a + b)² is equal to:Read the answer and worked solution →The identity (a − b)² is equal to:Read the answer and worked solution →Use an identity to compute 102² quickly:Read the answer and worked solution →Compute 98² using an identity:Read the answer and worked solution →Compute 47 × 53 using an identity:Read the answer and worked solution →Factorise: 9x² − 25y²:Read the answer and worked solution →If a + b = 7 and a − b = 3, find a² − b²:Read the answer and worked solution →Find (x − 1/x)² if x + 1/x = 4:Read the answer and worked solution →Is (a + b)² > a² + b² always true for non-zero a, b?Read the answer and worked solution →Expand (2x + 3y)²:Read the answer and worked solution →The probability of an IMPOSSIBLE event 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 →Find the value of x² + y² if x + y = 10 and xy = 21:Read the answer and worked solution →1 - cos²θ equals:Read the answer and worked solution →If sin θ = 3/5 (θ in Q1), find cos θ:Read the answer and worked solution →sin(0°) equals:Read the answer and worked solution →sin²θ + cos²θ equals:Read the answer and worked solution →tan(45°) equals:Read the answer and worked solution →sec θ is defined as:Read the answer and worked solution →sin(A + B) equals:Read the answer and worked solution →Find cos(75°) using cos(A + B):Read the answer and worked solution →sin(2θ) equals:Read the answer and worked solution →sin(60°) cos(30°) + cos(60°) sin(30°) equals:Read the answer and worked solution →For 0 ≤ θ < 2π, solutions of sin θ = 1/2:Read the answer and worked solution →sin(A) + sin(B) equals (sum-to-product):Read the answer and worked solution →In a right triangle, if hypotenuse = 13 and one leg = 5, sin θ for angle θ opposite to that leg:Read the answer and worked solution →tan(A + B) equals:Read the answer and worked solution →sin(180° - θ) equals:Read the answer and worked solution →In triangle ABC with sides a, b, c opposite to angles A, B, C: sine rule states:Read the answer and worked solution →If sin θ + cos θ = 1, then sin θ × cos θ equals:Read the answer and worked solution →

Worked practice questions

The algebraic identity (a + b)² is equal to:

  1. a² + b²
  2. a² − 2ab + b²
  3. a² + 2ab + b²
  4. a² + ab + b²
Show answer and solution

Correct answer: C. a² + 2ab + b²

**By expanding:** (a + b)² = (a + b)(a + b) = a² + ab + ba + b² = a² + 2ab + b². This holds for all real values of a and b.

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The identity (a − b)² is equal to:

  1. a² − b²
  2. a² − 2ab + b²
  3. a² + 2ab + b²
  4. a² + ab − b²
Show answer and solution

Correct answer: B. a² − 2ab + b²

We have (a − b)² = (a − b)(a − b). That is (a − b)² = a² − ab − ba + b². So (a − b)² = a² − 2ab + b². The middle term is negative, distinguishing this from (a + b)².

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Use an identity to compute 102² quickly:

  1. 10404
  2. 10204
  3. 10004
  4. 10404
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Correct answer: A. 10404

102² = (100 + 2)² = 100² + 2·100·2 + 2² = 10000 + 400 + 4 = 10404. The (a+b)² identity makes large squares easy without long multiplication.

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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