0
Physics
Motion
\( v = u + at \)
\( s = ut + \frac{1}{2}at^2 \)
\( v^2 = u^2 + 2as \)
Newton’s Laws
\( F = ma \)
\( \sum F = 0 \) (1st Law)
Circular Motion
\( a_c = \frac{v^2}{r} \)
\( T = \frac{2\pi r}{v} \)
Forces & Dynamics
\( W = Fd\cos\theta \)
Friction
\( f = \mu N \)
Centripetal Force
\( F_c = \frac{mv^2}{r} \)
Energy
\( KE = \frac{1}{2}mv^2 \)
\( PE = mgh \)
\( W = \Delta KE \)
Thermodynamics
\( Q = mc\Delta T \)
\( PV = nRT \)
Waves
\( v = f\lambda \)
\( \lambda_n = \frac{2L}{n} \)
Electricity
Ohm’s Law: \( V = IR \)
\( V = \epsilon - Ir \)
\( C = \frac{Q}{V} \)
Magnetism
Lorentz Force: \( F = q(E + vB) \)
Ampere's Law: \( \oint B \cdot dl = \mu_0 I \)
Modern Physics
\( E = mc^2 \)
Photoelectric: \( E = hf - \phi \)
Chemistry
Gas Laws
\( PV = nRT \)
\( P_1V_1 = P_2V_2 \)
Moles and Stoichiometry
\( n = \frac{m}{M} \)
\( C = \frac{n}{V} \)
Reaction Rates
\( \text{Rate} = k[A]^m[B]^n \)
pH, Ka, Kb
\( \text{pH} = -\log[H^+] \)
\( K_w = K_a K_b \)
Electrochemistry
\( E = E^\circ - \frac{0.0591}{n} \log Q \)
Biology
Respiration
\( C_6H_{12}O_6 + 6O_2 \rightarrow 6CO_2 + 6H_2O + ATP \)
Photosynthesis
\( 6CO_2 + 6H_2O \rightarrow C_6H_{12}O_6 + 6O_2 \)
Enzyme Kinetics
\( v = \frac{V_{max}[S]}{K_m + [S]} \)
Genetic Ratios
Monohybrid: \( 3:1 \), Dihybrid: \( 9:3:3:1 \)
Math
Algebra
Quadratic: \( ax^2 + bx + c = 0 \)
Discriminant: \( D = b^2 - 4ac \)
Calculus
Derivative: \( f'(x) = \lim_{h\to 0} \frac{f(x+h)-f(x)}{h} \)
Integral: \( \int f(x)\,dx \)
Trigonometry
\( \sin^2 x + \cos^2 x = 1 \)
\( \tan x = \frac{\sin x}{\cos x} \)
Geometry
Pythagorean: \( a^2 + b^2 = c^2 \)
Circle: \( A = \pi r^2 \)
Probability & Statistics
\( P(A \cap B) = P(A)P(B|A) \)
Mean: \( \mu = \frac{1}{n} \sum x_i \)