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Calculus

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

Differentiation of Polynomials

Subtopic

Differentiation of Polynomials under Calculus for Grade 12 IGCSE.

About Topic & Revision

Preview questions (no answers)

  1. 1.

    Differentiate f(x)=x44+x33+x22f(x) = \frac{x^4}{4} + \frac{x^3}{3} + \frac{x^2}{2} with respect to xx.

    A.

    x3+x2+xx^3 + x^2 + x

    B.

    x34+x23+x2\frac{x^3}{4} + \frac{x^2}{3} + \frac{x}{2}

    C.

    4x3+3x2+2x4x^3 + 3x^2 + 2x

    D.

    x4+x3+x2x^4 + x^3 + x^2

  2. 2.

    Find dydx\frac{dy}{dx} for y=11x3+1y = 11x^3 + 1.

    A.

    33x2+133x^2 + 1

    B.

    11x211x^2

    C.

    33x233x^2

    D.

    33x333x^3

  3. 3.

    What is the derivative of f(x)=2x4āˆ’4x3+6x2f(x) = 2x^4 - 4x^3 + 6x^2?

    A.

    8x3āˆ’12x2+12x8x^3 - 12x^2 + 12x

    B.

    8x4āˆ’12x3+12x28x^4 - 12x^3 + 12x^2

    C.

    2x3āˆ’4x2+6x2x^3 - 4x^2 + 6x

    D.

    8x3āˆ’4x2+6x8x^3 - 4x^2 + 6x

Download the worksheet for Calculus - Differentiation of Polynomials to practice offline. It includes additional chapter-level practice questions.

Tangents and Normals

Subtopic

Tangents and Normals under Calculus for Grade 12 IGCSE.

About Topic & Revision

Preview questions (no answers)

  1. 1.

    What is the gradient of the tangent to y=4xāˆ’12x2y = 4x - \frac{1}{2}x^2 at x=2x = 2?

    A.

    0

    B.

    2

    C.

    4

    D.

    6

  2. 2.

    Find the xx-coordinate on the curve y=x3āˆ’3x2y = x^3 - 3x^2 where the tangent is horizontal (excluding x=0x=0).

    A.

    x=1x = 1

    B.

    x=2x = 2

    C.

    x=3x = 3

    D.

    x=āˆ’1x = -1

  3. 3.

    What is the gradient of the tangent to y=x2āˆ’xy = x^2 - x at the origin?

    A.

    0

    B.

    1

    C.

    -1

    D.

    2

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

Stationary Points (Max/Min)

Subtopic

Stationary Points (Max/Min) under Calculus for Grade 12 IGCSE.

About Topic & Revision

Preview questions (no answers)

  1. 1.

    For the curve y=13x3āˆ’4xy = \frac{1}{3}x^3 - 4x, find the positive value of xx where the gradient is zero.

    A.

    x=4x = 4

    B.

    x=1x = 1

    C.

    x=2x = 2

    D.

    x=2x = \sqrt{2}

  2. 2.

    Find the yy-coordinate of the stationary point of the function f(x)=x2+6x+2f(x) = x^2 + 6x + 2.

    A.

    y=āˆ’7y = -7

    B.

    y=2y = 2

    C.

    y=11y = 11

    D.

    y=āˆ’3y = -3

  3. 3.

    What is the nature of the stationary point of the function f(x)=10āˆ’x2f(x) = 10 - x^2?

    A.

    Maximum

    B.

    Minimum

    C.

    Point of Inflection

    D.

    The function has no stationary point

Download the worksheet for Calculus - Stationary Points (Max/Min) to practice offline. It includes additional chapter-level practice questions.

Basic Integration and Area Under a Curve

Subtopic

Basic Integration and Area Under a Curve under Calculus for Grade 12 IGCSE.

About Topic & Revision

Preview questions (no answers)

  1. 1.

    Find the integral: āˆ«(x2/4)ā€‰dx\int (x^2/4) \, dx.

    A.

    x312+C\frac{x^3}{12} + C

    B.

    x34+C\frac{x^3}{4} + C

    C.

    x33+C\frac{x^3}{3} + C

    D.

    x2+C\frac{x}{2} + C

  2. 2.

    Find āˆ«243x2ā€‰dx\int_{2}^{4} 3x^2 \, dx.

    A.

    24

    B.

    56

    C.

    64

    D.

    48

  3. 3.

    Evaluate āˆ«(2x+3)ā€‰dx\int (2x + 3) \, dx.

    A.

    x2+3x+Cx^2 + 3x + C

    B.

    2x2+3x+C2x^2 + 3x + C

    C.

    2+C2 + C

    D.

    x2+Cx^2 + C

Download the worksheet for Calculus - Basic Integration and Area Under a Curve to practice offline. It includes additional chapter-level practice questions.

Kinematics (Displacement, Velocity, Acceleration)

Subtopic

Kinematics (Displacement, Velocity, Acceleration) under Calculus for Grade 12 IGCSE.

About Topic & Revision

Preview questions (no answers)

  1. 1.

    The displacement of a particle is s=t2+4ts = t^2 + 4t. Find the average velocity of the particle between t=0t = 0 and t=2t = 2 seconds.

    A.

    4 m/s

    B.

    8 m/s

    C.

    6 m/s

    D.

    12 m/s

  2. 2.

    An object decelerates at a constant rate a=āˆ’2a = -2 m/sĀ². If its initial velocity is 1010 m/s, how long does it take to stop?

    A.

    10 seconds

    B.

    5 seconds

    C.

    2 seconds

    D.

    20 seconds

  3. 3.

    A particle's velocity is v=4t+3v = 4t + 3. If the initial displacement is 00, what is the displacement at t=2t = 2 seconds?

    A.

    11 m

    B.

    8 m

    C.

    10 m

    D.

    14 m

Download the worksheet for Calculus - Kinematics (Displacement, Velocity, Acceleration) to practice offline. It includes additional chapter-level practice questions.

Calculus - IGCSE Grade 12 Maths Notes & Revision | Krit.club