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AP Calculus AB Unit 2: Differentiation and Fundamental Derivative Rules — practice questions — page 3

Explore 93 free Unit 2: Differentiation and Fundamental Derivative Rules 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 2: Differentiation and Fundamental Derivative Rules questions and exercises with answers

Showing questions 61–90 of 93.

Catch the derivative toolsRead the answer and worked solution →Pop the shape wordsRead the answer and worked solution →Run the applications gatesRead the answer and worked solution →Slice the calculus wordsRead the answer and worked solution →Slope or bendRead the answer and worked solution →Sort the applicationsRead the answer and worked solution →Type the numberRead the answer and worked solution →Applications bingoRead the answer and worked solution →The list $-1.0, -1.5, -2.0, -2.5, \ldots$ is an AP. What is its common difference?Read the answer and worked solution →If an AP has first term $a=6$ and common difference $d=-3$, which of the following is the correct AP?Read the answer and worked solution →$\sin(180° - \theta)$ equals:Read the answer and worked solution →The present age of a father is twice the present age of his son. Five years ago, the father was three times as old as his son. What is the present age of the son?Read the answer and worked solution →Solve for f: 0.25(4f − 3) = 0.05(10f − 9)Read the answer and worked solution →A pair of linear equations in two variables that has no solution is called:Read the answer and worked solution →A pair of linear equations that has at least one solution is called:Read the answer and worked solution →If the two lines representing a pair of linear equations intersect at one point, the pair has:Read the answer and worked solution →The graph of a linear equation in two variables is always a:Read the answer and worked solution →A dependent pair of linear equations is always:Read the answer and worked solution →For the pair a₁x+b₁y+c₁=0 and a₂x+b₂y+c₂=0, a unique solution exists when:Read the answer and worked solution →Which of the following is an algebraic method to solve a pair of linear equations?Read the answer and worked solution →The solution of a consistent pair of linear equations corresponds graphically to:Read the answer and worked solution →Solving x + y = 5 and x − y = 1 gives:Read the answer and worked solution →If the two lines are parallel and never meet, the pair of equations has:Read the answer and worked solution →The condition $\dfrac{a_1}{a_2}=\dfrac{b_1}{b_2}\neq\dfrac{c_1}{c_2}$ corresponds to lines that are:Read the answer and worked solution →A polynomial of degree 2 is called a:Read the answer and worked solution →If the two lines are coincident (lie on top of each other), the pair has:Read the answer and worked solution →The common difference of the AP 3, 1, −1, −3, … 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 list $-1.0, -1.5, -2.0, -2.5, \ldots$ is an AP. What is its common difference?Read the answer and worked solution →If an AP has first term $a=6$ and common difference $d=-3$, which of the following is the correct AP?Read the answer and worked solution →

Worked practice questions

Catch the derivative tools

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Items
  1. Matches the category
    Yes
    Item
    Related rates
  2. Matches the category
    Yes
    Item
    Linear approx
  3. Matches the category
    Yes
    Item
    Optimization
  4. Matches the category
    Yes
    Item
    Newton method
  5. Matches the category
    No
    Item
    Sonata
  6. Matches the category
    No
    Item
    Pigment
  7. Matches the category
    No
    Item
    Trellis
  8. Matches the category
    No
    Item
    Lantern
Category
Calculus
Instructions
Catch the tools built on derivatives. Let the rest fall.
_Source: OpenStax Calculus Volume 1, Chapter 4, Applications of Derivatives._

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Pop the shape words

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Other terms
  1. Sonata
  2. Pigment
  3. Trellis
  4. Lantern
Matching terms
  1. Concave up
  2. Concave down
  3. Inflection
  4. Extremum
Instructions
Pop the words describing a graph's shape. Leave the rest.
_Source: OpenStax Calculus Volume 1, Chapter 4, Applications of Derivatives._

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Run the applications gates

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Questions
  1. Correct
    First test
    Choices
    1. First test
    2. Second test
    3. Neither
  2. Correct
    Second test
    Choices
    1. First test
    2. Second test
    3. Neither
  3. Correct
    Concave up
    Choices
    1. Concave up
    2. Concave down
    3. Neither
  4. Correct
    Concave down
    Choices
    1. Concave up
    2. Concave down
    3. Neither
  5. Correct
    Newton
    Choices
    1. Newton
    2. L'Hopital
    3. Neither
  6. Correct
    L'Hopital
    Choices
    1. Newton
    2. L'Hopital
    3. Neither
Instructions
Pick the test, then the concavity, then the tool.
_Source: OpenStax Calculus Volume 1, Chapter 4, Applications of Derivatives._

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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 6A: Indefinite Integrals & Fundamental TheoremUnit 1B3: Asymptotic Behavior and Infinite LimitsUnit 1B1: Limit Concepts and Graphical Limits