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Tangent and Normal to Curve

Further Mathematics SS 2 Week WEEK .......... Preview
Lesson Details (Preview)

Week Range: ................... - ...................

Date: ...................

Time: ...................

Duration: 40 minutes minutes

Theme: Calculus: Differentiation and its Applications

Sub-topic: Tangent and Normal to a Curve

Learning Objectives (Preview)

By the end of the lesson, students should be able to:

  1. Define tangent and normal to a curve
  2. Derive the equation of a tangent to a curve at a given point
  3. +2 more objectives in full version
Rationale (Preview)
Understanding tangents and normals is crucial for analyzing the behavior of functions and curves. These concepts are fundamental in further mathematic [Preview only]
Presentation Steps (Preview)
Step / Time Teacher's Activities Student's Activities Learning Points
Step 1: 8 minutes - Introduction and Definition
The teacher will begin by asking students to recall the concept of the gradient of a curve at a poin [Preview only]
Students will recall previous knowledge on gradients and actively listen to the definitions. They wi [Preview only]
Understanding the definitions of tangent and normal and their geometric relationship.
Step 2: 12 minutes - Deriving Equations
The teacher will guide students through the derivation of the equation of the tangent. First, they w [Preview only]
Students will follow the derivation steps, taking notes and participating in discussions, especially [Preview only]
Deriving and understanding the formulas for the equations of tangent and normal.
+2 more steps in full version
Student Note (Preview)
2,169 characters total — showing first 400
## Tangent and Normal to a Curve **What is Tangent and Normal to a Curve?** A tangent is a straight line that touches a curve at exactly one point, while a normal is a straight line perpendicular to the tangent at that point of contact. **Key Points** 1. The gradient of the tangent to a curve $y=f(x)$ at a point $(x_1, y_1)$ is given by $\frac{dy}{dx}$ evaluated at $(x_1, y_1)$. 2. The equation of [Preview only]

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