Scolar

Mathematics

Ten Plus Two (+2) Science · Grade 12

15 units 45 topics 5 credit hours

Advanced calculus, algebra, vectors and mechanics.

UnitChapter & topics
1

Algebra: Permutations, Combinations & Binomial

  • • Counting principles
  • • Binomial theorem
  • • Applications
2

Trigonometry: Inverse Functions & Equations

  • • Inverse circular functions
  • • General solutions
  • • Graphs
3

Conic Sections in Depth

  • • Parabola, ellipse, hyperbola
  • • Tangents and normals
  • • Identifying conics
4

Complex Numbers & Argand Plane

  • • Modulus-argument form
  • • Roots of equations
  • • Locus problems
5

Vector Products

  • • Dot and cross products
  • • Direction cosines
  • • Applications to geometry
6

Statistics: Correlation & Regression

  • • Correlation coefficient
  • • Regression lines
  • • Interpretation
7

Probability Distributions

  • • Random variables
  • • Binomial and normal distributions
  • • Expectation
8

Limits, Continuity & Differentiability

  • • Rigorous limits
  • • Continuity tests
  • • Differentiability conditions
9

Advanced Differentiation & Applications

  • • Implicit differentiation
  • • Mean value ideas
  • • Optimisation problems
10

Integration & Applications

  • • Techniques of integration
  • • Volumes and areas
  • • Numerical integration intro
11

Differential Equations

  • • First order equations
  • • Variable separable
  • • Simple applications
12

Numerical Methods

  • • Bisection method
  • • Newton-Raphson
  • • Trapezoidal and Simpson's rules
13

Linear Programming

  • • Constraints and objective functions
  • • Graphical method
  • • Feasible regions
14

Mechanics: Statics

  • • Resultants and equilibrium
  • • Friction
  • • Centre of gravity
15

Mechanics: Dynamics

  • • Newtonian motion problems
  • • Projectiles on inclines
  • • Impulse-momentum