Gd 12 Math

📅 Term 1: Mapping, Functions, Variations & Advanced Algebra

Unit 1: Functions, Mappings, & Inverse Functions  

• Types of Mapping: Define injective (one-to-one), surjective (onto), and bijective mappings.

• Functions: Determine the domain and range of real-valued functions. Solve composite functions, f(g(x)), and find inverse functions, f⁻¹(x).  

Unit 2: Variations & Binary Operations  

• Variations: Solve complex equations involving joint and partial variations.

• Binary Operations: Evaluate closure, commutativity, associativity, and distributivity under a given operation. Find identity elements and inverse elements.  

Unit 3: Advanced Coordinate Geometry 

• Parallel & Perpendicular Lines: Use the gradients m₁ = m₂ and m₁ ⋅ m₂ = -1 to find equations of related straight lines.

• Midpoint & Division of Line Segments: Calculate coordinates of points dividing a line internally or externally in a given ratio.  

Unit 4: Integral Calculus  

• Integration Rules: Integrate basic algebraic functions using the power rule reversal  

• Definite Integrals: Evaluate definite integrals between given limits to compute the area bounded by a curve and the x-axis.

📅 Term 2: High-Intensity Revision 

Unit 5: Master Review of High-Yield Topics (3 Weeks)

• Geometry & Trigonometry: Rapid drills on the 8 Circle Theorems, 3-point Bearings, and the Sine/Cosine rules.

• Algebraic Proofs: Re-mastering quadratic equations, 3-variable simultaneous equations, and multi-set Venn diagrams.

• Sequences & Progressions: Speed-solving Word problems combining Arithmetic (A.P.) and Geometric (G.P.) progressions.

Unit 6: Speed & Accuracy Drills (MCQ Questions) (2 Weeks)

• Multiple-Choice Tactics: Practice elimination techniques for the 50 objective questions.

• Time Management: Train to solve each objective question in under 1 minute and 40 seconds.

• Logarithmic Tables: Refresh four-figure table skills for quick multiplication, division, and roots.

Unit 7: Structural Essay Mastery (Paper 2) (3 Weeks)

• Part A (Compulsory Short Answers): Perfecting step-by-step mathematical layout to secure maximum "Method Marks" (M-marks) and "Accuracy Marks" (A-marks). 

• Part B (Long Electives): Strategies for selecting the easiest 5 out of 8 long-form questions (focusing on high-scoring questions like Statistics, Graphs, and Mensuration).

📅 Term 3: Final Examination