MF26

1. Functions

• Function

  • Test for function - Vertical line test

  • Find range of function by GC

• Inverse function

  • Test for 1-1 function - Horizontal line test

  • Rule, domain, range & graph of inverse function

• Composite function

  • Conditions for composite function to exist

  • Find the range of composite function

• Other concepts

  • Composite functions f⁻¹f and f f⁻¹

  • Self-inverse function

2. Graphs

• Rational functions

• Conics

  • Parabola

  • Circle & ellipse

  • Hyperbola

• Solve equations by graphing in GC

1. Basic properties of vectors in 2D & 3D

• Properties & Formulas: i j k notations, Magnitude of vector, Unit vector, Parallel vectors, Collinearity, Ratio Theorem

2. Scalar product & Vector products

• Scalar product: Formulas, Properties & Angle between 2 vectors

• Vector product: Formulas, Properties & Area of triangle and parallelogram

• Length of projection, Projection vector, Distance from point to vector

3. 3D vector geometry

• Lines

  • Line equations: Vector equation & Cartesian equation

  • Check if point lines on a line & Finding the foot of perpendicular of a point to line

  • Angle between 2 lines & Parallel, intersecting, skew lines

• Planes

  • Plane equations: Parametric form, Scalar-product form & Cartesian equation

  • Plane & origin; XY XZ YZ planes

  • Foot of perpendicular from point to plane

1. Differentiation

• Differentiation techniques

2. Integration techniques

• Integrate algebraic & exponential terms

• Integrate trigonometric terms

• Integrate different forms of algebraic fractions

3. Differential equations (DE)

• Ways to solve first order & second order DE