Start learning →

AP Calculus AB Unit 1A3: Function Composition and Inverses — practice questions — page 4

Explore 95 free Unit 1A3: Function Composition and Inverses questions in AP Calculus AB Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

Practise Unit 1A3: Function Composition and Inverses with Quill →

Unit 1A3: Function Composition and Inverses questions and exercises with answers

Showing questions 91–95 of 95.

Which of the following is NOT a perfect square?Read the answer and worked solution →Which of the following is a perfect square?Read the answer and worked solution →The sum 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 equals:Read the answer and worked solution →Using prime factorisation, √324 equals:Read the answer and worked solution →How many PERFECT SQUARES lie strictly between 100 and 200?Read the answer and worked solution →

Worked practice questions

Which of the following is NOT a perfect square?

  1. 49
  2. 81
  3. 121
  4. 132
Show answer and solution

Correct answer: D. 132

49 = 7², 81 = 9², 121 = 11². Now 11² = 121 and 12² = 144, so there is no natural number n with n² = 132. Therefore 132 is not a perfect square.

Open this question →

Which of the following is a perfect square?

  1. 50
  2. 81
  3. 160
  4. 250
Show answer and solution

Correct answer: B. 81

81 = 9 × 9 = 9², a perfect square. None of the others can be written as the square of a natural number (50 ≈ 7.07², 160 ≈ 12.65², 250 ≈ 15.81²).

Open this question →

The sum 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 equals:

  1. 64
  2. 72
  3. 81
  4. 100
Show answer and solution

Correct answer: C. 81

The sum of the first n odd natural numbers is n². Here we have the first 9 odd numbers (1 through 17) so the sum is 9² = 81. This is also the basis of the 'repeated subtraction' method for finding √81.

Open this question →

How to practise

  1. Choose a Unit 1A3: Function Composition and Inverses 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 1A3: Function Composition and Inverses practice for AP Calculus AB. Read explanations as you go. No signup form needed to start.

Practise Unit 1A3: Function Composition and Inverses →

More Mathematics topics

Unit 3B: Implicit Differentiation and Inverse FunctionsUnit 3A: Chain Rule and Composite FunctionsUnit 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