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AP Calculus AB Unit 1B2: Algebraic Limits and Continuity — practice questions — page 2

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 31–60 of 73.

The multiplicative inverse (reciprocal) of −3/7 is:Read the answer and worked solution →Compute (−2/3) × (4/5):Read the answer and worked solution →The sum of three consecutive multiples of 11 is 363. What is the largest of these three multiples?Read the answer and worked solution →Two angles of a triangle are equal, and the third angle is greater than each of them by 30°. What are the three angles of the triangle?Read the answer and worked solution →How many rational numbers are there between any two distinct rationals?Read the answer and worked solution →Which of the following can be written as a rational p/q in lowest terms with q having ONLY 2 as a prime factor?Read the answer and worked solution →Compute (-3/5) × (10/9):Read the answer and worked solution →Which of these is an IRRATIONAL number?Read the answer and worked solution →Find the value of the linear polynomial 5x − 3 at x = −1:Read the answer and worked solution →A polynomial of degree 1 in one variable is called a:Read the answer and worked solution →What is the degree of the polynomial 5y³ + y² + 2y − 1?Read the answer and worked solution →The difference between two positive integers is 63, and they are in the ratio 2:5. The smaller integer is:Read the answer and worked solution →Salil's mother is currently three times Salil's age. After 5 years, their ages will add up to 70 years. What is Salil's CURRENT age?Read the answer and worked solution →Every differentiable function is necessarily:Read the answer and worked solution →The value of $\displaystyle\lim_{x\to 0}\frac{\sin x}{x}$ is:Read the answer and worked solution →The derivative of $x^n$ with respect to $x$ is:Read the answer and worked solution →The derivative of a constant function is:Read the answer and worked solution →The value of $\displaystyle\lim_{x\to 2} x^2$ is:Read the answer and worked solution →The derivative of $\sin x$ with respect to $x$ is:Read the answer and worked solution →By first principles, the derivative of $f$ at $x$ is $\displaystyle\lim_{h\to 0}$ of:Read the answer and worked solution →The derivative of $x^3$ with respect to $x$ is:Read the answer and worked solution →The value of $\displaystyle\lim_{x\to 0}\frac{1-\cos x}{x}$ is:Read the answer and worked solution →The derivative of $\cos x$ with respect to $x$ is:Read the answer and worked solution →The value of $\displaystyle\lim_{x\to 3}\frac{x^2-9}{x-3}$ is:Read the answer and worked solution →For a constant $c$, $\dfrac{d}{dx}\big(c\,f(x)\big)$ equals:Read the answer and worked solution →The value of $\displaystyle\lim_{x\to 0}\frac{\tan x}{x}$ is:Read the answer and worked solution →The square of any odd integer, when divided by 8, leaves remainderRead the answer and worked solution →The general form of a quadratic polynomial is:Read the answer and worked solution →For any integer $n$, the expression $n^2 - 1$ is always divisible by 8 when $n$ isRead the answer and worked solution →The number of prime numbers is:Read the answer and worked solution →

Worked practice questions

The multiplicative inverse (reciprocal) of −3/7 is:

  1. 3/7
  2. −7/3
  3. 7/3
  4. 1
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Correct answer: B. −7/3

For a non-zero rational a, its multiplicative inverse is 1/a so that a × (1/a) = 1. The reciprocal of −3/7 is −7/3, and indeed (−3/7) × (−7/3) = 1.

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Compute (−2/3) × (4/5):

  1. −8/15
  2. 8/15
  3. −6/15
  4. 6/8
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Correct answer: A. −8/15

Multiply numerators and denominators separately: (−2 × 4) / (3 × 5) = −8/15. The negative sign is retained because one factor is negative.

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The sum of three consecutive multiples of 11 is 363. What is the largest of these three multiples?

  1. 121
  2. 132
  3. 143
  4. 154
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Correct answer: B. 132

Let the three consecutive multiples of 11 be 11n, 11(n+1), 11(n+2). Their sum is 11(3n + 3) = 33(n + 1). Setting 33(n+1) = 363 gives n + 1 = 11, so n = 10. The three multiples are 110, 121, 132, and the largest is 132. Distractor 143 belongs to the next set (121+132+143 = 396), and 121 is the middle multiple, not the largest.

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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