IB Class 10 Mathematics – Group 5, Calculus | 4. Tangents and Normals by Abraham | Learn Smarter
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4. Tangents and Normals

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Sections

  • 1

    The Concept Of A Tangent

    This section introduces the concept of a tangent to a curve, defining it as a line that touches the curve at a specific point and has the same slope as the curve at that point.

    Learning Practice

  • 1.1

    What Is A Tangent?

    A tangent is a straight line that just touches a curve at a specific point, sharing the same slope.

    Learning Practice

  • 1.2

    Slope Of The Tangent

    The slope of the tangent line at a point on a curve is defined as the derivative of the function at that point.

    Learning Practice

  • 1.3

    Equation Of The Tangent

    This section explains the concept of a tangent to a curve, its slope, and the equation that represents it.

    Learning Practice

  • 2

    The Concept Of A Normal

    This section introduces the concept of normals in calculus, defining their relationship to tangents at a given point on a curve.

    Learning Practice

  • 2.1

    What Is A Normal?

    The section defines the concept of a normal line to a curve, explaining its relationship with the tangent line at a given point.

    Learning Practice

  • 2.2

    Slope Of The Normal

    This section explores the concept of the slope of the normal to a curve at a specific point, emphasizing its relationship with the slope of the tangent.

    Learning Practice

  • 2.3

    Equation Of The Normal

    In this section, students will learn how to derive the equation of the normal to a curve using differentiation.

    Learning Practice

  • 3

    Finding Tangents And Normals To Curves

    This chapter introduces the concepts of tangents and normals to curves, explaining their geometric interpretations and mathematical applications using differentiation.

    Learning Practice

  • 3.1

    Step-By-Step Process

    This section outlines the systematic approach to finding the equations of tangents and normals to a curve at a given point.

    Learning Practice

  • 4

    Examples

    This section explores the concepts of tangents and normals in calculus, explaining their definitions, equations, and applications with illustrative examples.

    Learning Practice

  • 5

    Special Cases

    This section discusses special cases of tangents, specifically vertical and horizontal tangents, and the conditions under which they occur.

    Learning Practice

  • 6

    Applications Of Tangents And Normals

    The section discusses the concepts of tangents and normals to curves, how to find their equations using differentiation, and their various applications in real-world scenarios.

    Learning Practice

References

10 IB calculus ch4.pdf

Class Notes

Memorization

Revision Tests