Lecture Notes: Differentiation and Integration

Main Topics:

• Differentiation and Integration:
  • Essential formulas for differentiation
  • Challenges in the context of integration
  • O-level formulas: Gradient, Midpoint, Distance

Essential Formulas and Principles

• Gradient equation of a line:
  • Not required at O-level, but now must be memorized.
  • Formula: ( M_2 - M_1 / (1 + M_1 \cdot M_2) )
  • M1 and M2 can be taken in any order, but negatives must be ignored.

Forms of Line Equations

• Forms:
  • Slope-intercept form: ( y = mx + c )
  • Point-slope form: ( y - y_1 = m(x - x_1) )
  • Two-point form: ( (y - y_1) / (y_2 - y_1) = (x - x_1) / (x_2 - x_1) )

Important Issues:

• Form selection:
  • Depends on the data given in the question.
  • Knowledge of gradient and a point is necessary.

Examples and Practice

• Equation of a line examples:
  • Practice with various slopes and points.

Special Shapes and Their Features:

• Types of shapes:
  • Diagonals intersecting at midpoint: Square, Rectangle, Rhombus, Parallelogram
  • Diagonals intersecting at 90 degrees: Square, Rhombus

Other Important Concepts

• Perpendicular bisector:
  • Use of negative reciprocal of gradient
  • Determination of midpoint

Interaction of Lines

• Simultaneous equations:
  • Finding the point of intersection
  • Use of substitution method

Special Questions and Practice

• Point of intersection calculation
  • Linear and quadratic intersections

Class Closing Notes

• Tips to save time:
  • Solve simultaneous equations by making y the subject.
  • The elimination method will not be used in A-Levels.

These notes cover important topics on differentiation and integration, along with information on special shapes and interactions of lines.