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26 cardsUnified Tertiary Matriculation Examination

UTME JAMB Science and Mathematics Core

Essential formulas, physics laws, chemical reactions, and mathematical relations for JAMB.

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Equations of Uniform Linear Motion
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1
Equations of Uniform Linear Motion
1. v = u + at
2. s = ut + 0.5 a t²
3. v² = u² + 2as
4. s = 0.5 (u + v) t
2
Newton's Second Law of Motion
Resultant force equals the rate of change of momentum: F = ma (for constant mass) or F = Δp / Δt.
3
Law of Conservation of Linear Momentum
In a closed system with no external forces, total initial momentum equals total final momentum: m1 u1 + m2 u2 = m1 v1 + m2 v2.
4
Hooke's Law and Elastic Potential Energy
F = k e (within elastic limit). Elastic potential energy stored: E = 0.5 F e = 0.5 k e².
5
Archimedes' Principle
Upthrust on an object fully or partially submerged in a fluid equals the weight of fluid displaced: U = ρ_fluid × V_submerged × g.
6
Ideal Gas Equation and Gas Laws
PV = nRT. Combined gas law: (P1 V1) / T1 = (P2 V2) / T2 (where temperature T must be in Kelvin).
7
Specific Heat Capacity vs Latent Heat
Temperature change: Q = m c ΔT. Phase change (at constant temperature): Q = m L (fusion or vaporization).
8
Snell's Law of Refraction
n1 sin i = n2 sin r. For light entering a medium from air (n1 = 1): n = sin i / sin r = c / v = 1 / sin c (critical angle).
9
Coulomb's Law of Electrostatics
F = (k |q1 q2|) / r², where k = 1 / (4πε0) ≈ 9.0 × 10⁹ N·m²/C².
10
Capacitors in Series vs Parallel
Series: 1/C = 1/C1 + 1/C2 + ... (charges are equal, voltages add).
Parallel: C = C1 + C2 + ... (voltages are equal, charges add).
11
Ohm's Law and Electrical Power
V = I R. Electrical power: P = I V = I² R = V² / R. Electrical energy: E = P t.
12
Magnetic Force on Moving Charge and Conductor
Moving charge: F = q v B sin θ.
Current-carrying wire: F = B I L sin θ.
13
Faraday's Law of Electromagnetic Induction
Induced electromotive force is directly proportional to rate of change of magnetic flux linkage: ε = -N (ΔΦ / Δt).
14
Transformer Turns and Voltage Ratio
Vs / Vp = Ns / Np = Ip / Is (for 100% efficient transformer). Efficiency = (Vs Is) / (Vp Ip) × 100%.
15
Einstein's Photoelectric Equation
hf = W0 + K_max = h f0 + 0.5 m v_max² = h f0 + e Vs (where Vs is stopping potential and W0 is work function).
16
Radioactive Decay Law and Half-Life
N(t) = N0 (1/2)^(t / T_half). Decay constant relation: λ = (ln 2) / T_half ≈ 0.693 / T_half.
17
Aufbau Principle, Hund's Rule, and Pauli Exclusion
Aufbau: electrons fill lowest energy orbitals first. Hund's rule: orbitals of equal energy occupy singly with parallel spins before pairing. Pauli: no two electrons have identical 4 quantum numbers.
18
Mole Concept and Avogadro's Number
Moles n = mass / molar mass = N / NA = volume of gas at STP / 22.4 dm³ (where NA ≈ 6.02 × 10²³ mol⁻¹).
19
pH Scale and Water Autoionization
pH = -log10[H⁺], pOH = -log10[OH⁻]. At 25°C: Kw = [H⁺][OH⁻] = 1.0 × 10⁻¹⁴, so pH + pOH = 14.
20
Le Chatelier's Principle
If a chemical system at dynamic equilibrium experiences a change in concentration, temperature, or pressure, the equilibrium shifts in the direction that counteracts the applied change.
21
Faraday's First Law of Electrolysis
m = Z I t = (M I t) / (z F), where F = 96,500 C/mol, z = valency (electrons transferred), and M = molar mass.
22
Standard Cell Potential Formula
E°cell = E°cathode - E°anode. A positive E°cell (greater than 0) indicates a thermodynamically spontaneous redox reaction under standard conditions.
23
General Formulas of Aliphatic Hydrocarbons
Alkanes (saturated): CnH2n+2.
Alkenes (mono-unsaturated): CnH2n.
Alkynes (triple bond): CnH2n-2.
24
Markovnikov's Addition Rule
In electrophilic addition of hydrogen halides (HX) to unsymmetrical alkenes, the hydrogen atom attaches to the carbon atom with the greater number of hydrogen substituents.
25
Quadratic Formula and Discriminant Roots
For ax² + bx + c = 0: x = [-b ± √(b² - 4ac)] / (2a).
Discriminant Δ = b² - 4ac: if Δ > 0 two real distinct roots; Δ = 0 equal roots; Δ < 0 complex/imaginary roots.
26
Arithmetic vs Geometric Progressions
AP: nth term Tn = a + (n - 1)d; Sum Sn = 0.5 n [2a + (n - 1)d].
GP: nth term Tn = a r^(n - 1); Sum Sn = a(r^n - 1) / (r - 1); Sum to infinity S_inf = a / (1 - r) for |r| < 1.

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