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

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 1–30 of 73.

Given that $\operatorname{HCF}(306,657)=9$, what is $\operatorname{LCM}(306,657)$?Read the answer and worked solution →For any two positive integers $a$ and $b$, which identity is always true?Read the answer and worked solution →For the numbers 6, 72 and 120, which pair gives the HCF and LCM respectively?Read the answer and worked solution →The prime factorizations of 96 and 404 are $96=2^5\times 3$ and $404=2^2\times 101$. What is their LCM?Read the answer and worked solution →If $6=2\times 3$ and $20=2^2\times 5$, then their HCF and LCM respectively areRead the answer and worked solution →If $\alpha,\beta,\gamma$ are the zeroes of the cubic polynomial $ax^3+bx^2+cx+d$, then $\alpha\beta\gamma$ is equal toRead the answer and worked solution →The zeroes of the quadratic polynomial $x^2+7x+10$ areRead the answer and worked solution →The zero of the linear polynomial $ax+b$ with $a\neq 0$ isRead the answer and worked solution →Let $r$ be a non-zero rational number and $x$ be an irrational number. Which of the following must be irrational?Read the answer and worked solution →For the polynomial $p(x)=x^2-3x-4$, what is the value of $p(-1)$?Read the answer and worked solution →A quadratic polynomial has sum of zeroes $-3$ and product of zeroes $2$. Which of the following is one such polynomial?Read the answer and worked solution →If $\alpha$ and $\beta$ are the zeroes of the quadratic polynomial $ax^2+bx+c$ with $a\neq 0$, then $\alpha+\beta$ equalsRead the answer and worked solution →A square matrix $A$ is called **idempotent** if:Read the answer and worked solution →Which of the following rational numbers has a terminating decimal expansion?Read the answer and worked solution →Which of the following fractions will have a non-terminating recurring decimal expansion?Read the answer and worked solution →Which statement is always true about the sum of a rational number and an irrational number?Read the answer and worked solution →For any two positive integers $a$ and $b$, which relation is always true?Read the answer and worked solution →If the prime factorisations of two numbers are $2^3\times 3^2\times 5$ and $2^2\times 3\times 5^2$, then their HCF isRead the answer and worked solution →The trace of the matrix $A = \begin{bmatrix} 1 & 2 & -1 \\ 0 & 5 & 3 \\ 4 & -2 & 7 \end{bmatrix}$ is:Read the answer and worked solution →Which non-parametric vector condition represents the line through points with position vectors $\bar a$ and $\bar b$?Read the answer and worked solution →If a line passes through points with position vectors $\bar a$ and $\bar b$, then its vector equation isRead the answer and worked solution →Which non-parametric vector equation represents the line passing through the point with position vector $\bar a$ and parallel to $\bar b$?Read the answer and worked solution →The vector equation of the line passing through the point with position vector $\bar a$ and parallel to the vector $\bar b$ isRead the answer and worked solution →If $p$ is a prime number and $p$ divides $a^2$, then which statement must be true?Read the answer and worked solution →Which of the following best describes the set of real numbers?Read the answer and worked solution →For which rational number a is the statement 'a is its own multiplicative inverse' TRUE?Read the answer and worked solution →Find (−5/6) ÷ (2/3).Read the answer and worked solution →Which property is used to write a × (b + c) = ab + ac for any three rational numbers a, b, c?Read the answer and worked solution →A rational number lying between 1/4 and 1/2 is:Read the answer and worked solution →Rational numbers are NOT closed under:Read the answer and worked solution →

Worked practice questions

Given that $\operatorname{HCF}(306,657)=9$, what is $\operatorname{LCM}(306,657)$?

  1. $22338$
  2. $204$
  3. $21318$
  4. $19998$
Show answer and solution

Correct answer: A. $22338$

Use $\operatorname{HCF}(a,b)\times \operatorname{LCM}(a,b)=a\times b$. Thus, $$ \operatorname{LCM}(306,657)=\frac{306\times 657}{9}. $$ Now $306\div 9=34$, so the LCM is $34\times 657=22338$.

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For any two positive integers $a$ and $b$, which identity is always true?

  1. $\operatorname{HCF}(a,b)+\operatorname{LCM}(a,b)=a+b$
  2. $\operatorname{HCF}(a,b)\times \operatorname{LCM}(a,b)=a\times b$
  3. $\operatorname{HCF}(a,b)=a\times b$
  4. $\operatorname{LCM}(a,b)=a+b$
Show answer and solution

Correct answer: B. $\operatorname{HCF}(a,b)\times \operatorname{LCM}(a,b)=a\times b$

For any two positive integers, the product of their HCF and LCM equals the product of the numbers themselves. This relation is frequently used to find one when the other is known.

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For the numbers 6, 72 and 120, which pair gives the HCF and LCM respectively?

  1. $6$ and $360$
  2. $12$ and $720$
  3. $6$ and $720$
  4. $3$ and $360$
Show answer and solution

Correct answer: A. $6$ and $360$

Their prime factorizations are $6=2\times 3$, $72=2^3\times 3^2$, and $120=2^3\times 3\times 5$. The HCF uses the smallest common powers of common primes: $2^1\times 3^1=6$. The LCM uses the greatest powers of all primes involved: $2^3\times 3^2\times 5=360$.

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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