Start learning →

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

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.

Practise Unit 3B: Implicit Differentiation and Inverse Functions with Quill →

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

Showing questions 1–30 of 97.

If z = cos(π/7) + i sin(π/7), then z⁷ equals:Read the answer and worked solution →For complex z, |z + i| = |z - i| describes:Read the answer and worked solution →|z|² = z × z̄. If |z|² = 4 and Re(z) = 1, then Im(z):Read the answer and worked solution →Find principal argument of -1 - i:Read the answer and worked solution →For roots of unity ω^n = 1: which is the SMALLEST n such that 1 + ω + ω² + ... + ω^(n-1) = 0?Read the answer and worked solution →Solve: z² + z + 1 = 0:Read the answer and worked solution →If z1, z2, z3 are vertices of an equilateral triangle, then:Read the answer and worked solution →Find (3 + 4i)/(1 + 2i):Read the answer and worked solution →The value of $i^2$ is:Read the answer and worked solution →If sin θ = 12/13 (acute θ in Q1), find tan(θ/2):Read the answer and worked solution →Find sin(15°):Read the answer and worked solution →cos(A + B) equals:Read the answer and worked solution →cos(90°) equals:Read the answer and worked solution →If tan θ = 1/2 (acute), find sin 2θ:Read the answer and worked solution →Minimum value of sin²θ + cos⁴θ:Read the answer and worked solution →The imaginary unit i is defined as:Read the answer and worked solution →For z = 3 + 4i, find |z|:Read the answer and worked solution →The conjugate of z = a + ib is:Read the answer and worked solution →i² + i³ equals:Read the answer and worked solution →In polar form z = r(cos θ + i sin θ), r is called the ___ and θ is the ___:Read the answer and worked solution →For z = a + ib, Re(z) and Im(z) are:Read the answer and worked solution →Compute (2 + i)(3 - 2i):Read the answer and worked solution →Find (1 + i)²:Read the answer and worked solution →Solve z² + 1 = 0:Read the answer and worked solution →Modulus of z1 z2 where z1 and z2 are complex:Read the answer and worked solution →Argument of z1 z2:Read the answer and worked solution →For z = 1 + i, find arg(z):Read the answer and worked solution →Find z̄ × z (where z = a + ib):Read the answer and worked solution →Convert i to polar form:Read the answer and worked solution →DeMoivre's theorem: (cos θ + i sin θ)ⁿ equals:Read the answer and worked solution →

Worked practice questions

If z = cos(π/7) + i sin(π/7), then z⁷ equals:

  1. i
  2. -1
  3. 1
  4. -i
Show answer and solution

Correct answer: B. -1

By DeMoivre: z⁷ = (cos π/7 + i sin π/7)⁷ = cos(π) + i sin(π) = -1 + 0i = -1.

Open this question →

For complex z, |z + i| = |z - i| describes:

  1. A circle
  2. The real axis
  3. The imaginary axis
  4. Origin only
Show answer and solution

Correct answer: B. The real axis

Equidistant from i (= (0, 1)) and -i (= (0, -1)) means z lies on the perpendicular bisector — the real axis (y = 0).

Open this question →

|z|² = z × z̄. If |z|² = 4 and Re(z) = 1, then Im(z):

  1. ±√3
  2. √3
  3. 2
  4. ±2
Show answer and solution

Correct answer: A. ±√3

|z|² = a² + b² = 4. With a = 1: b² = 3, so b = ±√3.

Open this question →

How to practise

  1. Choose a Unit 3B: Implicit Differentiation and Inverse Functions question and try to work out your answer.
  2. Open the question to check the correct answer and read its worked solution.
  3. Continue in the app for bite-sized lessons, explanations and review with Quill. You can start without creating an account.

Put it into practice

Continue with Unit 3B: Implicit Differentiation and Inverse Functions practice for AP Calculus AB. Read explanations as you go. No signup form needed to start.

Practise Unit 3B: Implicit Differentiation and Inverse Functions →

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