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AP Calculus AB Unit 1A3: Function Composition and Inverses — practice questions — page 3

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.

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

Showing questions 61–90 of 95.

Sum of the consecutive odd numbers needed to obtain 5³ = 125 is:Read the answer and worked solution →The smallest natural number by which 392 must be MULTIPLIED to make it a perfect cube is:Read the answer and worked solution →How many digits at MAXIMUM can the cube of a 2-digit number have?Read the answer and worked solution →A cuboid of plasticine has sides 5 cm, 2 cm and 5 cm. The MINIMUM number of such cuboids needed to form a perfect cube (without leftover) is:Read the answer and worked solution →Compute 25³ − 24³ using the pattern (n+1)³ − n³ = 1 + 3·n·(n+1):Read the answer and worked solution →Is 1188 a perfect cube? If not, the smallest natural number by which 1188 must be DIVIDED to make the quotient a perfect cube is:Read the answer and worked solution →A child stacks unit cubes (side 1 cm) to make a larger cube of side 4 cm. The number of unit cubes used is:Read the answer and worked solution →Which of the following statements is TRUE?Read the answer and worked solution →The cube of which number among the following is a 7-digit number?Read the answer and worked solution →Find the smallest perfect cube that is divisible by both 8 and 27.Read the answer and worked solution →A rational number is any number that can be written in the form p/q, where p and q are integers and:Read the answer and worked solution →The multiplicative identity for rational numbers is:Read the answer and worked solution →Find 3/4 − 5/6.Read the answer and worked solution →Find (−4/5) × (3/7) × (15/16) × (−14/9).Read the answer and worked solution →Does the rational number 0 have a multiplicative inverse?Read the answer and worked solution →Which of the following is the WHOLE NUMBER that is closest to 0 but is NOT a natural number?Read the answer and worked solution →Solve for x: x = (4/5)(x + 10)Read the answer and worked solution →Using distributivity, find: (3/5) × [(−7/9) + (4/9)].Read the answer and worked solution →Which of the following is NOT a rational number?Read the answer and worked solution →The additive identity for rational numbers is:Read the answer and worked solution →The additive inverse of 5/8 is:Read the answer and worked solution →Which statement is TRUE for the set of rational numbers?Read the answer and worked solution →The mean of two rational numbers a and b is (a + b)/2. The mean of 1/3 and 1/2 is:Read the answer and worked solution →Simplify using commutativity and distributivity: (2/5) × (−3/7) − (1/14) − (3/7) × (3/5)Read the answer and worked solution →Which property is shown by: (−2/3) + (3/5) = (3/5) + (−2/3)?Read the answer and worked solution →How many rational numbers exist between 1/3 and 1/2?Read the answer and worked solution →Solve for x: (x − 5)/3 = (x − 3)/5Read the answer and worked solution →Using distributivity, the value of (7/5) × (−3/12) + (7/5) × (5/12) is:Read the answer and worked solution →For which rational number a is the statement 'a is its own additive inverse' TRUE?Read the answer and worked solution →Three rational numbers a, b, c are given. Which of the following is ALWAYS true?Read the answer and worked solution →

Worked practice questions

Sum of the consecutive odd numbers needed to obtain 5³ = 125 is:

  1. 21 + 23 + 25 + 27 + 29
  2. 11 + 13 + 15 + 17 + 19
  3. 23 + 25 + 27
  4. 31 + 33 + 35 + 37
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Correct answer: A. 21 + 23 + 25 + 27 + 29

From the chapter's pattern: 1 = 1³ 3+5 = 2³; 7+9+11 = 3³ 13+15+17+19 = 4³; 21+23+25+27+29 = 5³ = 125. Each cube n³ is the sum of n consecutive odd numbers, picking up where the previous block ended.

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The smallest natural number by which 392 must be MULTIPLIED to make it a perfect cube is:

  1. 3
  2. 5
  3. 7
  4. 49
Show answer and solution

Correct answer: C. 7

**Prime factorise:** 392 = 2³ × 7². The prime 7 occurs twice — we need 7³ to have a group of three. **So multiply by 7:** 392 × 7 = 2744 = 14³. The smallest such multiplier is 7.

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How many digits at MAXIMUM can the cube of a 2-digit number have?

  1. 3
  2. 5
  3. 6
  4. 8
Show answer and solution

Correct answer: C. 6

The largest 2-digit number is 99. 99³ = 970299, a 6-digit number. The smallest 2-digit cube is 10³ = 1000 (4 digits). **So cubes of 2-digit numbers have 4, 5, or 6 digits.**

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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