DU Ka Unit (Science Unit) cheat sheet

Newton's second law: F = ma; net force in newtons equals mass in kilograms times acceleration in m/s².

Kinematics: v = u + at, s = ut + ½at², v² = u² + 2as; valid only for constant acceleration.

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

Momentum is conserved in all collisions; kinetic energy is conserved only in elastic collisions.

Ohm's law: V = IR; power dissipated P = VI = I²R = V²/R.

Lens/mirror equation: 1/f = 1/v + 1/u, with magnification m = v/u; sign conventions must be applied consistently.

Wave relation: speed = frequency × wavelength (v = fλ); frequency is fixed by the source when a wave changes medium.

Ideal gas law: PV = nRT with R ≈ 8.314 J/(mol·K); temperature must be in kelvin.

Mole concept: number of moles n = mass / molar mass; one mole contains 6.022 × 10²³ particles.

Molarity M = moles of solute / litres of solution; dilution obeys M₁V₁ = M₂V₂.

pH = −log₁₀[H⁺]; pH + pOH = 14 at 25 °C, and neutral pH is 7.

Oxidation is loss of electrons, reduction is gain; in a redox reaction total electrons lost equal electrons gained.

Ideal gas at STP (273.15 K, 1 bar): one mole occupies about 22.7 L (22.4 L at 1 atm).

Empirical formula gives the simplest atom ratio; molecular formula = empirical formula × integer n.

Le Chatelier's principle: raising pressure shifts equilibrium toward the side with fewer gas moles.

Bond polarity follows electronegativity difference; a molecule is polar only if bond dipoles do not cancel by symmetry.

Quadratic roots: for ax² + bx + c = 0, x = [−b ± √(b² − 4ac)] / 2a; discriminant b² − 4ac decides root nature.

Sum and product of roots: α + β = −b/a and αβ = c/a.

Arithmetic progression: nth term a + (n−1)d; sum = n/2 × [2a + (n−1)d].

Geometric progression: nth term ar^(n−1); sum of n terms = a(rⁿ − 1)/(r − 1) for r ≠ 1.

Differentiation: d/dx(xⁿ) = nx^(n−1), d/dx(sin x) = cos x, d/dx(eˣ) = eˣ, d/dx(ln x) = 1/x.

Integration reverses differentiation; ∫xⁿ dx = x^(n+1)/(n+1) + C for n ≠ −1.

Trigonometric identity: sin²θ + cos²θ = 1; also 1 + tan²θ = sec²θ.

Probability of an event lies between 0 and 1; P(A ∪ B) = P(A) + P(B) − P(A ∩ B).

Photosynthesis overall: 6CO₂ + 6H₂O + light energy → C₆H₁₂O₆ + 6O₂, occurring in chloroplasts.

Cellular respiration: C₆H₁₂O₆ + 6O₂ → 6CO₂ + 6H₂O + energy (ATP); glycolysis happens in the cytoplasm.

DNA base pairing: adenine pairs with thymine, guanine with cytosine; in RNA, uracil replaces thymine.

Mendel's law of segregation: two alleles of a gene separate during gamete formation, one per gamete.

Mitosis produces two genetically identical diploid cells; meiosis produces four haploid gametes.

Blood groups follow ABO alleles: A and B are codominant, O is recessive; O negative is the universal donor.

Enzymes are biological catalysts that lower activation energy and are not consumed in the reaction.

Human normal karyotype is 46 chromosomes (23 pairs), including one pair of sex chromosomes.

Average speed for equal distances at speeds a and b is the harmonic mean 2ab/(a + b), not (a + b)/2.

Percentage change = (new − old)/old × 100; successive changes of x% and y% give net change x + y + xy/100.

Work rate adds: if A finishes in a days and B in b days, together they take ab/(a + b) days.

Simple interest = PRT/100; compound amount = P(1 + R/100)^T.

In a series, check differences first, then ratios, then alternating or square/cube patterns.

Syllogism rule: a conclusion follows only if it is true in every possible arrangement of the premises.

Clock angle = |30H − 5.5M| degrees, where H is the hour and M the minute.

Odd-one-out and analogy items are solved by naming the exact relation (part-whole, cause-effect, synonym) before comparing options.