KCET cheat sheet

Projectile range R = u²sin2θ/g; maximum range occurs at θ = 45° and complementary angles give equal ranges.

For uniform circular motion, centripetal acceleration a = v²/r = ω²r and is directed toward the center; speed stays constant.

Work-energy theorem: net work equals change in kinetic energy, W_net = ΔKE = ½mv² − ½mu².

Momentum is conserved in every collision; kinetic energy is conserved only in elastic collisions.

Ohm's law V = IR holds for ohmic conductors at constant temperature; resistivity ρ = RA/L depends on material, not shape.

Lens/mirror formula 1/f = 1/v − 1/u (lens) or 1/f = 1/v + 1/u (mirror); power of a lens P = 1/f in diopters with f in meters.

Photoelectric equation: hν = φ + KE_max, where φ is the work function; below threshold frequency no emission occurs regardless of intensity.

Half-life relation: N = N₀(1/2)^(t/T), and activity A = λN with decay constant λ = 0.693/T.

Number of moles n = mass/molar mass; at STP one mole of ideal gas occupies 22.4 L.

Ideal gas law PV = nRT with R = 0.0821 L·atm/(mol·K) or 8.314 J/(mol·K); use Kelvin always.

pH = −log[H⁺]; for a strong monobasic acid pH = −log C, and pH + pOH = 14 at 25 °C.

Le Chatelier's principle: adding reactant shifts equilibrium forward; increasing pressure shifts toward fewer gas moles; a catalyst changes rate only.

Hund's rule and Aufbau order (1s 2s 2p 3s 3p 4s 3d) determine ground-state electron configurations; 4s fills before 3d.

SN1 proceeds via carbocation intermediate (racemization, favored by polar protic solvent and tertiary carbon); SN2 is one-step with inversion.

Bond order = (bonding electrons − antibonding electrons)/2; higher bond order means shorter, stronger bond.

Oxidizing agent is reduced; reducing agent is oxidized - assign oxidation numbers to track electron transfer.

Derivative rules: d/dx(xⁿ) = nxⁿ⁻¹, d/dx(sin x) = cos x, product rule (uv)' = u'v + uv', quotient and chain rules apply composition.

For a local extremum, f'(x) = 0; classify by sign change of f' or by f''(x) > 0 (minimum) and f''(x) < 0 (maximum).

Integration by parts: ∫u dv = uv − ∫v du; choose u by the LIATE order (log, inverse trig, algebraic, trig, exponential).

Straight line: slope m = (y₂ − y₁)/(x₂ − x₁); point-slope y − y₁ = m(x − x₁); perpendicular slopes satisfy m₁m₂ = −1.

Conic sections: circle x² + y² = r²; parabola y² = 4ax with focus (a, 0); ellipse x²/a² + y²/b² = 1 with e = √(1 − b²/a²).

Probability: P(A∪B) = P(A) + P(B) − P(A∩B); conditional P(A|B) = P(A∩B)/P(B); Bayes' theorem reverses conditioning.

Sum formulas: Σn = n(n+1)/2, Σn² = n(n+1)(2n+1)/6; binomial term T_(r+1) = ⁿC_r a^(n−r) b^r.

Limits: L'Hôpital's rule applies to 0/0 or ∞/∞ forms; lim(x→0) sin x/x = 1 and lim(x→0)(1+x)^(1/x) = e.

Photosynthesis light reaction splits water at photosystem II, releasing O₂ and producing ATP and NADPH; the Calvin cycle fixes CO₂ via RuBisCO.

Cellular respiration: glycolysis (cytosol, net 2 ATP) → Krebs cycle (mitochondrial matrix) → oxidative phosphorylation on the inner membrane (~34 ATP).

Mendelian ratios: monohybrid F₂ phenotypic ratio 3:1, dihybrid 9:3:3:1; test cross with a homozygous recessive reveals genotype.

DNA replication is semiconservative; adenine pairs with thymine (2 H-bonds) and guanine with cytosine (3 H-bonds).

Transcription makes mRNA from the template strand; translation reads codons 5'→3' on mRNA and builds protein N-terminus to C-terminus.

Blood flow: right atrium → right ventricle → pulmonary artery → lungs → left atrium → left ventricle → aorta; arteries carry blood away from the heart.

Nephron order: Bowman's capsule → proximal tubule → loop of Henle → distal tubule → collecting duct; most reabsorption occurs in the proximal tubule.

Resting membrane potential is maintained by the Na⁺/K⁺ ATPase (3 Na⁺ out, 2 K⁺ in); an action potential depolarizes via Na⁺ influx.

Projectile range R = u²sin2θ/g; maximum range occurs at θ = 45° and complementary angles give equal ranges.

For uniform circular motion, centripetal acceleration a = v²/r = ω²r and is directed toward the center; speed stays constant.

Work-energy theorem: net work equals change in kinetic energy, W_net = ΔKE = ½mv² − ½mu².

Momentum is conserved in every collision; kinetic energy is conserved only in elastic collisions.

Ohm's law V = IR holds for ohmic conductors at constant temperature; resistivity ρ = RA/L depends on material, not shape.

Lens/mirror formula 1/f = 1/v − 1/u (lens) or 1/f = 1/v + 1/u (mirror); power of a lens P = 1/f in diopters with f in meters.

Photoelectric equation: hν = φ + KE_max, where φ is the work function; below threshold frequency no emission occurs regardless of intensity.

Half-life relation: N = N₀(1/2)^(t/T), and activity A = λN with decay constant λ = 0.693/T.

Number of moles n = mass/molar mass; at STP one mole of ideal gas occupies 22.4 L.

Ideal gas law PV = nRT with R = 0.0821 L·atm/(mol·K) or 8.314 J/(mol·K); use Kelvin always.

pH = −log[H⁺]; for a strong monobasic acid pH = −log C, and pH + pOH = 14 at 25 °C.

Le Chatelier's principle: adding reactant shifts equilibrium forward; increasing pressure shifts toward fewer gas moles; a catalyst changes rate only.

Hund's rule and Aufbau order (1s 2s 2p 3s 3p 4s 3d) determine ground-state electron configurations; 4s fills before 3d.

SN1 proceeds via carbocation intermediate (racemization, favored by polar protic solvent and tertiary carbon); SN2 is one-step with inversion.

Bond order = (bonding electrons − antibonding electrons)/2; higher bond order means shorter, stronger bond.

Oxidizing agent is reduced; reducing agent is oxidized - assign oxidation numbers to track electron transfer.

Derivative rules: d/dx(xⁿ) = nxⁿ⁻¹, d/dx(sin x) = cos x, product rule (uv)' = u'v + uv', quotient and chain rules apply composition.

For a local extremum, f'(x) = 0; classify by sign change of f' or by f''(x) > 0 (minimum) and f''(x) < 0 (maximum).

Integration by parts: ∫u dv = uv − ∫v du; choose u by the LIATE order (log, inverse trig, algebraic, trig, exponential).

Straight line: slope m = (y₂ − y₁)/(x₂ − x₁); point-slope y − y₁ = m(x − x₁); perpendicular slopes satisfy m₁m₂ = −1.

Conic sections: circle x² + y² = r²; parabola y² = 4ax with focus (a, 0); ellipse x²/a² + y²/b² = 1 with e = √(1 − b²/a²).

Probability: P(A∪B) = P(A) + P(B) − P(A∩B); conditional P(A|B) = P(A∩B)/P(B); Bayes' theorem reverses conditioning.

Sum formulas: Σn = n(n+1)/2, Σn² = n(n+1)(2n+1)/6; binomial term T_(r+1) = ⁿC_r a^(n−r) b^r.

Limits: L'Hôpital's rule applies to 0/0 or ∞/∞ forms; lim(x→0) sin x/x = 1 and lim(x→0)(1+x)^(1/x) = e.

Photosynthesis light reaction splits water at photosystem II, releasing O₂ and producing ATP and NADPH; the Calvin cycle fixes CO₂ via RuBisCO.

Cellular respiration: glycolysis (cytosol, net 2 ATP) → Krebs cycle (mitochondrial matrix) → oxidative phosphorylation on the inner membrane (~34 ATP).

Mendelian ratios: monohybrid F₂ phenotypic ratio 3:1, dihybrid 9:3:3:1; test cross with a homozygous recessive reveals genotype.

DNA replication is semiconservative; adenine pairs with thymine (2 H-bonds) and guanine with cytosine (3 H-bonds).

Transcription makes mRNA from the template strand; translation reads codons 5'→3' on mRNA and builds protein N-terminus to C-terminus.

Blood flow: right atrium → right ventricle → pulmonary artery → lungs → left atrium → left ventricle → aorta; arteries carry blood away from the heart.

Nephron order: Bowman's capsule → proximal tubule → loop of Henle → distal tubule → collecting duct; most reabsorption occurs in the proximal tubule.

Resting membrane potential is maintained by the Na⁺/K⁺ ATPase (3 Na⁺ out, 2 K⁺ in); an action potential depolarizes via Na⁺ influx.