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AP Calculus AB Unit 1B2: Algebraic Limits and Continuity — practice questions — page 3

Explore 73 free Unit 1B2: Algebraic Limits and Continuity 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 1B2: Algebraic Limits and Continuity questions and exercises with answers

Showing questions 61–73 of 73.

The LCM of 6 and 20 is:Read the answer and worked solution →If $3^x = 4^y = 12^z$ with $x,y,z$ nonzero, then $\dfrac{1}{z}$ equalsRead the answer and worked solution →For some integer $m$, every odd integer can be written in the formRead the answer and worked solution →For a quadratic $ax^2 + bx + c$, the sum of its zeroes is:Read the answer and worked solution →The largest number that divides 245 and 1029, leaving remainders 5 and 5 respectively, isRead the answer and worked solution →The smallest positive integer that is divisible by every integer from 1 to 10 isRead the answer and worked solution →If $a = 2^3 \cdot 3^4 \cdot 5^2$ and $b = 2^4 \cdot 3^2 \cdot 7$, then $\dfrac{\text{LCM}(a,b)}{\text{HCF}(a,b)}$ equalsRead the answer and worked solution →The HCF of two consecutive positive integers isRead the answer and worked solution →How many positive integers less than 1000 are divisible by neither 2 nor 5?Read the answer and worked solution →The remainder when $2^{100}$ is divided by 7 isRead the answer and worked solution →Which of the following is an irrational number?Read the answer and worked solution →The product of the HCF and LCM of 6 and 20 is:Read the answer and worked solution →The decimal expansion of $\dfrac{257}{2^3 \cdot 5^4}$ terminates after how many decimal places?Read the answer and worked solution →

Worked practice questions

The LCM of 6 and 20 is:

  1. 26
  2. 120
  3. 2
  4. 60
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Correct answer: D. 60

LCM(6,20) = 2²·3·5 = 60.

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If $3^x = 4^y = 12^z$ with $x,y,z$ nonzero, then $\dfrac{1}{z}$ equals

  1. $\dfrac{1}{x} + \dfrac{1}{y}$
  2. $x + y$
  3. $\dfrac{1}{x} - \dfrac{1}{y}$
  4. $xy$
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Correct answer: A. $\dfrac{1}{x} + \dfrac{1}{y}$

Let $3^x=4^y=12^z=k$. Then $3=k^{1/x}$, $4=k^{1/y}$, $12=k^{1/z}$. Since $12 = 3\cdot4$: $k^{1/z}=k^{1/x}\cdot k^{1/y}=k^{1/x+1/y}$, so $\dfrac1z=\dfrac1x+\dfrac1y$.

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For some integer $m$, every odd integer can be written in the form

  1. $m$
  2. $2m + 1$
  3. $4m$
  4. $2m$
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Correct answer: B. $2m + 1$

Every integer is even ($2m$) or odd ($2m+1$). **So odd integers are exactly those of the form $2m+1$.**

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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 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 Limits