NEET Mathematics | American School

Core Mathematical Concepts for NEET Physics

Concept	Key Subtopics	Physics Applications	Example NEET-Style Problem	Importance
Algebra	Quadratic equations (roots via formula, discriminant); inequalities (linear/quadratic); logarithms (properties, solving equations); binomial expansion (for approximations).	Solving for time/range in projectile motion; error propagation; logarithmic scales in graphs.	Find time of flight for a projectile: solve $t = \frac{2u \sin \theta}{g}$ $t$ $=$ $g$ $2$ $u$ $sin$ $θ$ $$ or quadratic $gt^2 - 2u \sin \theta t = 0$ $g$ $t$ $2$ $-$ $2$ $u$ $sin$ $θt$ $=$ $0$ .	Medium (10-15% of Physics)
Trigonometry	Basic ratios (sin, cos, tan); identities (Pythagorean, sum/difference); inverse functions; heights/distances (sine/cosine rule).	Resolving vectors (components); angles in optics (refraction); waves (phase difference).	Resolve force F at angle θ: $F_x = F \cos \theta$ $F$ $x$ $$ $=$ $F$ $cos$ $θ$ , $F_y = F \sin \theta$ $F$ $y$ $$ $=$ $F$ $sin$ $θ$ .	High (15-20%) – Frequent in Mechanics & Optics
Coordinate Geometry	Distance/section formulas; straight lines (slope, equation); circles (general equation).	Position-time graphs; electric field mapping; 2D motion trajectories.	Find distance between two points in a velocity graph for displacement.	Medium (10%) – Key for Kinematics
Calculus (Differential)	Limits (basic evaluation); differentiation (first/second order, chain/product/quotient rules); implicit differentiation; maxima/minima (first derivative test).	Instantaneous velocity ( $v = \frac{ds}{dt}$ $v$ $=$ $dt$ $ds$ $$ ); acceleration; SHM ( $a = -\omega^2 x$ $a$ $=$ $-$ $ω$ $2$ $x$ ); error analysis.	Differentiate $s = ut + \frac{1}{2}at^2$ $s$ $=$ $ut$ $+$ $2$ $1$ $$ $at$ $2$ to get $v = u + at$ $v$ $=$ $u$ $+$ $at$ .	High (20%) – Essential for Dynamics & Thermodynamics
Calculus (Integral)	Indefinite/definite integrals; integration by substitution/parts; area under curves.	Work done ( $W = \int F \, dx$ $W$ $=$ $\int$ $F$ $dx$ ); velocity from acceleration; charge from current.	Integrate power $P = VI$ $P$ $=$ $V$ $I$ over time for energy.	High (15-20%) – Used in Work-Energy & Electrostatics
Vectors	Addition/subtraction (parallelogram/triangle law); scalar/dot product (work); vector/cross product (torque); unit vectors.	Force/momentum resolution; relative velocity; magnetic force ( $\vec{F} = q(\vec{v} \times \vec{B})$ $F$ $=$ $q$ $($ $v$ $\times$ $B$ $)$ .	Dot product for angle between forces: $\vec{A} \cdot \vec{B} = AB \cos \theta$ $A$ $\cdot$ $B$ $=$ $A$ $B$ $cos$ $θ$ .	High (15-20%) – Core for Mechanics & Magnetism
3D Geometry	Direction cosines/ratios; lines/planes (parametric equations, angle between); shortest distance.	Torque in 3D ( $\vec{\tau} = \vec{r} \times \vec{F}$ $τ$ $=$ $r$ $\times$ $F$ ); orbital paths in gravitation.	Angle between two vectors in space for dipole moment.	Low-Medium (5-10%) – Advanced Mechanics
Statistics & Probability	Mean/median/mode; standard deviation; basic probability (events, conditional).	Error in measurements (absolute/relative); uncertainty in experiments.	Calculate percentage error in g from pendulum: $\Delta g / g \times 100\%$ $Δ$ $g$ $/$ $g$ $\times$ $100%$ .	Low (5%) –