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AP Intermediate 2nd Year Continuity, Differentiability & Derivatives — practice questions — page 2

Explore 165 free Continuity, Differentiability & Derivatives questions in AP Intermediate 2nd Year Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Continuity, Differentiability & Derivatives questions and exercises with answers

Showing questions 31–60 of 165.

Which test is being described?Read the answer and worked solution →Assertion and reason: rates of changeRead the answer and worked solution →Spot the odd oneRead the answer and worked solution →Complete the second derivative testRead the answer and worked solution →True or false: scope of this chapterRead the answer and worked solution →Complete the definition of continuityRead the answer and worked solution →True or false: continuity and differentiabilityRead the answer and worked solution →Which way does the implication run?Read the answer and worked solution →Tap every operation that preserves continuityRead the answer and worked solution →Combining continuous functionsRead the answer and worked solution →Assertion and reasonRead the answer and worked solution →Two are true, one is notRead the answer and worked solution →Three of these are wrong. Find the one that holds.Read the answer and worked solution →Complete the chain rule ideaRead the answer and worked solution →Flip and pair: rule with what it handlesRead the answer and worked solution →Spot the one that does not belongRead the answer and worked solution →Order the test for continuity at a pointRead the answer and worked solution →True or false: reading the definitionsRead the answer and worked solution →Where continuity can failRead the answer and worked solution →Which property is stronger?Read the answer and worked solution →True or false: combining functionsRead the answer and worked solution →Flip and pair: condition with what followsRead the answer and worked solution →Spot the odd one outRead the answer and worked solution →Assertion and reason: continuityRead the answer and worked solution →Tap every requirement for continuity at a pointRead the answer and worked solution →Two true, one falseRead the answer and worked solution →Complete the one-way implicationRead the answer and worked solution →A function whose graph can be drawn without lifting the pen is:Read the answer and worked solution →If f is not continuous at c, then c is called a point of:Read the answer and worked solution →If a function is differentiable at a point, it is also:Read the answer and worked solution →

Worked practice questions

Which test is being described?

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Items
  1. Item
    Checks the sign of f ′ either side of c
    Category
    First derivative test
  2. Item
    Can identify a point of inflexion
    Category
    First derivative test
  3. Item
    Needs only f ′ to exist near c
    Category
    First derivative test
  4. Item
    Uses the sign of f ″(c)
    Category
    Second derivative test
  5. Item
    Needs f to be twice differentiable at c
    Category
    Second derivative test
  6. Item
    Fails outright when f ″(c) = 0
    Category
    Second derivative test
Categories
  1. Item
    First derivative test
  2. Item
    Second derivative test
Both tests answer the same question by different evidence. Source: syllabus Maths Part I, Ch 6 Application of Derivatives.

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Assertion and reason: rates of change

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Questions
  1. Reason
    The chain rule lets the parameter t cancel between the two rates.
    Verdict
    Both are true; the reason explains the assertion.
    Assertion
    dy/dx can be found from dy/dt and dx/dt.
  2. Reason
    dx/dt appears in the denominator.
    Verdict
    Both are true; the reason explains the assertion.
    Assertion
    The related-rates formula needs dx/dt ≠ 0.
  3. Reason
    A derivative is defined as a limit.
    Verdict
    Both are true; the reason does not explain the assertion.
    Assertion
    f ′(x₀) is the rate of change at a single point.
The chain rule carries a condition, and it is the condition being tested. Source: syllabus Maths Part I, Ch 6 Application of Derivatives.

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Spot the odd one

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Questions
  1. Items
    1. Increasing
    2. Decreasing
    3. Constant
    4. Continuous
    Odd item
    Continuous
  2. Items
    1. Absolute maximum
    2. Local maximum
    3. Local minimum
    Odd item
    Absolute maximum
  3. Items
    1. f ′(c) = 0
    2. f(c) < 0
    3. f ″(c) < 0
    Odd item
    f(c) < 0
Grouped by which decision each belongs to. Source: syllabus Maths Part I, Ch 6 Application of Derivatives.

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