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Calculus

Each subtopic includes About section, revision page link, 10 preview questions, and practice CTAs.

Limits and Convergence

Subtopic

Limits and Convergence under Calculus for Grade 11 IB.

About Topic & Revision

Preview questions (no answers)

  1. 1.

    Evaluate the limit: lim⁡x→42x−8x−2\lim_{x \to 4} \frac{2x - 8}{\sqrt{x} - 2}.

    A.

    44

    B.

    22

    C.

    88

    D.

    00

  2. 2.

    Find the sum of the series ∑n=1∞2(0.8)n−1\sum_{n=1}^{\infty} 2(0.8)^{n-1}.

    A.

    1010

    B.

    88

    C.

    1.61.6

    D.

    55

  3. 3.

    Calculate: lim⁡x→1x−1x2−1\lim_{x \to 1} \frac{x - 1}{x^2 - 1}.

    A.

    11

    B.

    00

    C.

    1/21/2

    D.

    Undefined

Download the worksheet for Calculus - Limits and Convergence to practice offline. It includes additional chapter-level practice questions.

The Concept of the Derivative (Differentiation from First Principles)

Subtopic

The Concept of the Derivative (Differentiation from First Principles) under Calculus for Grade 11 IB.

About Topic & Revision

Preview questions (no answers)

  1. 1.

    Find f′(x)f'(x) for f(x)=10xf(x) = 10x using the definition of the derivative.

    A.

    lim⁡h→010(x+h)−10xh=10\lim_{h \to 0} \frac{10(x+h) - 10x}{h} = 10

    B.

    lim⁡h→010x+h−10xh=1\lim_{h \to 0} \frac{10x+h - 10x}{h} = 1

    C.

    lim⁡h→010h\lim_{h \to 0} \frac{10}{h}

    D.

    10x10x

  2. 2.

    In the limit lim⁡h→0f(x+h)−f(x)h\lim_{h \to 0} \frac{f(x+h) - f(x)}{h}, if the limit exists, the function ff is said to be _______ at xx.

    A.

    Continuous only

    B.

    Differentiable

    C.

    Integrable

    D.

    Concave

  3. 3.

    Which of the following is equivalent to dydx\frac{dy}{dx} at x=ax=a?

    A.

    f(a)f(a)

    B.

    The y-coordinate of the point

    C.

    The gradient of the curve at x=ax=a

    D.

    The value of hh when it is zero

Download the worksheet for Calculus - The Concept of the Derivative (Differentiation from First Principles) to practice offline. It includes additional chapter-level practice questions.

Rules of Differentiation (Power, Chain, Product, Quotient)

Subtopic

Rules of Differentiation (Power, Chain, Product, Quotient) under Calculus for Grade 11 IB.

About Topic & Revision

Preview questions (no answers)

  1. 1.

    Differentiate y=(10x+2)5y = (10x + 2)^5 using the chain rule.

    A.

    50(10x+2)450(10x + 2)^4

    B.

    5(10x+2)45(10x + 2)^4

    C.

    10(10x+2)410(10x + 2)^4

    D.

    500(10x+2)4500(10x + 2)^4

  2. 2.

    What is the derivative of y=8x3+2x2y = 8x^3 + 2x^2?

    A.

    24x2+4x24x^2 + 4x

    B.

    24x2+424x^2 + 4

    C.

    8x2+2x8x^2 + 2x

    D.

    24x3+4x224x^3 + 4x^2

  3. 3.

    If f(x)=x63f(x) = \frac{x^6}{3}, find f′(x)f'(x).

    A.

    2x52x^5

    B.

    6x56x^5

    C.

    2x62x^6

    D.

    x52\frac{x^5}{2}

Download the worksheet for Calculus - Rules of Differentiation (Power, Chain, Product, Quotient) to practice offline. It includes additional chapter-level practice questions.

Applications of Differentiation (Tangents, Normals, Rates of Change, Optimization)

Subtopic

Applications of Differentiation (Tangents, Normals, Rates of Change, Optimization) under Calculus for Grade 11 IB.

About Topic & Revision

Preview questions (no answers)

  1. 1.

    Find the xx-coordinate of the minimum for f(x)=12x2−4x+1f(x) = \frac{1}{2}x^2 - 4x + 1.

    A.

    2

    B.

    4

    C.

    8

    D.

    0

  2. 2.

    What is the slope of the normal to y=4xy = 4x at the origin?

    A.

    4

    B.

    -4

    C.

    1/4

    D.

    -1/4

  3. 3.

    Find the rate of change of y=x2−xy = x^2 - x at x=3x = 3.

    A.

    3

    B.

    6

    C.

    5

    D.

    2

Download the worksheet for Calculus - Applications of Differentiation (Tangents, Normals, Rates of Change, Optimization) to practice offline. It includes additional chapter-level practice questions.

Introduction to Integration (Anti-differentiation)

Subtopic

Introduction to Integration (Anti-differentiation) under Calculus for Grade 11 IB.

About Topic & Revision

Preview questions (no answers)

  1. 1.

    Find ∫1x8 dx\int \frac{1}{x^8} \, dx.

    A.

    −17x7+C-\frac{1}{7x^7} + C

    B.

    −8x9+C-\frac{8}{x^9} + C

    C.

    19x9+C\frac{1}{9x^9} + C

    D.

    −19x9+C-\frac{1}{9x^9} + C

  2. 2.

    Evaluate ∫(5x4−3x2) dx\int (5x^4 - 3x^2) \, dx.

    A.

    x5−x3+Cx^5 - x^3 + C

    B.

    20x3−6x+C20x^3 - 6x + C

    C.

    5x5−3x3+C5x^5 - 3x^3 + C

    D.

    54x5−x3+C\frac{5}{4}x^5 - x^3 + C

  3. 3.

    What is ∫x4/3 dx\int x^{4/3} \, dx?

    A.

    43x1/3+C\frac{4}{3}x^{1/3} + C

    B.

    37x7/3+C\frac{3}{7}x^{7/3} + C

    C.

    73x7/3+C\frac{7}{3}x^{7/3} + C

    D.

    x7/3+Cx^{7/3} + C

Download the worksheet for Calculus - Introduction to Integration (Anti-differentiation) to practice offline. It includes additional chapter-level practice questions.

Calculus - IB Grade 11 Maths Notes & Revision | Krit.club