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AP Calculus AB Unit 1A1: Relations, Functions and Graphs — practice questions — page 2

Explore 94 free Unit 1A1: Relations, Functions and Graphs 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 1A1: Relations, Functions and Graphs questions and exercises with answers

Showing questions 31–60 of 94.

How many perfect cubes are there from 1 to 1000 (both included)?Read the answer and worked solution →What is the cube of 12?Read the answer and worked solution →Which of the following numbers is NOT a perfect cube?Read the answer and worked solution →The units (one's) digit of (78)³ is:Read the answer and worked solution →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 →arctan(x) is an _____ function (odd/even):Read the answer and worked solution →Maximum value of x² + (arcsin(x))² for x in [-1, 1]:Read the answer and worked solution →Which of the following sets of ordered pairs represents a function?Read the answer and worked solution →For finite sets, $n(A\times B)$ equals:Read the answer and worked solution →A relation $R$ on a set $A$ is reflexive if:Read the answer and worked solution →An equivalence relation is one that is:Read the answer and worked solution →A function $f:A\to B$ is one-one (injective) if:Read the answer and worked solution →A function $f:A\to B$ is onto (surjective) if:Read the answer and worked solution →A bijective function is one that is:Read the answer and worked solution →The function $f:\mathbb{R}\to\mathbb{R}$ given by $f(x) = 2x + 3$ is:Read the answer and worked solution →The function $f:\mathbb{R}\to\mathbb{R}$ given by $f(x) = x^2$ is:Read the answer and worked solution →The number of one-one functions from $\{1,2\}$ to $\{a,b,c\}$ is:Read the answer and worked solution →For functions $f$ and $g$, the composition $(g\circ f)(x)$ means:Read the answer and worked solution →If $f(x) = 2x$ and $g(x) = x + 1$, then $(g\circ f)(x)$ equals:Read the answer and worked solution →A function is invertible if and only if it is:Read the answer and worked solution →The number of bijective functions from a set with $n$ elements onto itself is:Read the answer and worked solution →

Worked practice questions

How many perfect cubes are there from 1 to 1000 (both included)?

  1. 8
  2. 9
  3. 10
  4. 20
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Correct answer: C. 10

The cubes from 1 to 1000 are 1³, 2³, 3³, …, 10³ = 1, 8, 27, 64, 125, 216, 343, 512, 729 and 1000. That is exactly 10 perfect cubes in this range.

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What is the cube of 12?

  1. 144
  2. 1278
  3. 1728
  4. 2178
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Correct answer: C. 1728

12³ = 12 × 12 × 12 = 144 × 12 = 1728. (1728 is also notable as 1 + 1728 = 1729, the Hardy-Ramanujan number.)

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Which of the following numbers is NOT a perfect cube?

  1. 216
  2. 512
  3. 1000
  4. 100
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Correct answer: D. 100

216 = 6³, 512 = 8³, 1000 = 10³ — all perfect cubes. 100 is between 4³ = 64 and 5³ = 125, so it is NOT a perfect cube.

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More Mathematics topics

Unit 3B: Implicit Differentiation and Inverse FunctionsUnit 3A: Chain Rule and Composite FunctionsUnit 1A3: Function Composition and InversesUnit 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