SENAPREP
Cracking the UPSC National Defence Academy (NDA) written examination requires a highly focused preparation timeline. In this comprehensive study guide, our defence education experts analyze the core concepts of NDA trigonometry formulas, heights distances shortcuts, math trig cheat sheet, outline high-yield preparation tips, and provide step-by-step examples.
Part 1: Key Trigonometry Formulas
Trigonometry forms the backbone of Paper 1 Maths (approx. 15-20 questions). Memorize these compound angle formulas:
$$\cos(A \pm B) = \cos A\cos B \mp \sin A\sin B$$
$$\sin 2\theta = 2\sin\theta\cos\theta = \frac{2\tan\theta}{1+\tan^2\theta}$$
$$\cos 2\theta = \cos^2\theta - \sin^2\theta = 2\cos^2\theta - 1 = 1 - 2\sin^2\theta$$
Heights and Distances Quick Ratios
For angles of $30^\circ$, $45^\circ$, and $60^\circ$, the ratios of base to height are:
- At $30^\circ$: Base = $\sqrt{3} \times$ Height
- At $45^\circ$: Base = Height
- At $60^\circ$: Base = $\frac{\text{Height}}{\sqrt{3}}$
Syllabus Breakdown & Marks Allocation
| Subject Segment | Total Questions | Weightage (Marks) | Preparation Priority |
|---|---|---|---|
| Paper 1: Mathematics | 120 Questions | 300 Marks | Critical (Sectional Cutoff) |
| Paper 2: GAT (English) | 50 Questions | 200 Marks | High Yield (4 Marks/Q) |
| Paper 2: GAT (General Knowledge) | 100 Questions | 400 Marks | High Scoring (Science & GS) |
Part 2: Key Revision Strategies for NDA trigonometry formulas, heights distances shortcuts, math trig cheat sheet
Success in this topic requires consistent daily practice. Here are the core routines recommended by top defence educators:
- Build Foundational Concepts: Rely on Class 11 and 12 NCERT books for math/science topics, and read standard grammar texts for English.
- Solve Previous Year Papers (PYQs): Go through at least the last 5-10 years of UPSC question sets to analyze repeat question structures.
- Speed & Time Management: Practice mock tests with a timer to improve your answering speed. You have only 75 seconds per math question in the real exam.
- Track Weak Areas: Bookmark difficult problems and review your mistake history to continuously raise your score.
Part 3: Practical Questions & Solved Examples
Below is a preview of the type of questions asked by the UPSC. Test your current understanding of NDA trigonometry formulas, heights distances shortcuts, math trig cheat sheet and review the step-by-step methods:
Use the interactive test panel below to solve live questions pulled directly from the SenaPrep exam bank.
