CEnT-S formulas you have to memorise

CEnT-S provides no formula sheet, no periodic table and no calculator. You are given pen and paper, and that is all. Anything a question genuinely cannot expect you to recall, such as the relative atomic mass of sulfur, is printed in the question itself. Everything on this page is not.

Mathematics

Algebra

x = (−b ± √(b² − 4ac)) / 2a

Quadratic formula — use this whenever factoring isn't immediate.

Δ = b² − 4ac

Discriminant. Δ > 0 → two real roots, Δ = 0 → one root, Δ < 0 → no real roots.

Sum of roots = −b/a | Product of roots = c/a

Often faster than solving — check whether the question asks for x₁ + x₂ or x₁x₂ rather than x₁ and x₂ individually.

Analytic geometry

d = √((x₂ − x₁)² + (y₂ − y₁)²)

Distance between two points.

M = ((x₁ + x₂)/2 , (y₁ + y₂)/2)

Midpoint.

m = (y₂ − y₁) / (x₂ − x₁)

Gradient of the line through two points.

(x − h)² + (y − k)² = r²

Circle with centre (h, k) and radius r.

m₁ × m₂ = −1

Condition for two lines to be perpendicular.

Exponentials and logarithms

log(ab) = log a + log b

log(a/b) = log a − log b

log(aⁿ) = n log a

log_b a = log a / log b

Change of base — useful when the answer must be in a specific base.

Combinatorics

P(n, r) = n! / (n − r)!

Permutations — order matters.

C(n, r) = n! / (r! × (n − r)!)

Combinations — order does not matter.

P(A and B) = P(A) × P(B)

For independent events.

Areas and volumes

Circle: area = πr² | circumference = 2πr

Sphere: V = (4/3)πr³ | A = 4πr²

Cylinder: V = πr²h

Cone: V = (1/3)πr²h

Chemistry

n = m / M

Amount in moles = mass ÷ molar mass.

c = n / V

Concentration in mol dm⁻³, with V in dm³ (litres). Divide cm³ by 1000 first.

c₁V₁ = c₂V₂

Dilution equation.

pH = −log₁₀[H⁺] | pOH = −log₁₀[OH⁻]

pH + pOH = 14

At 25 °C.

pV = nRT

Ideal gas equation.

pᵢ = xᵢ × p_total

Partial pressure: mole fraction × total pressure.

ΔG = ΔH − TΔS

Spontaneous when ΔG < 0. Watch units: ΔH is usually in kJ, ΔS in J K⁻¹ — convert one before combining.

Physics

Take g = 10 m s⁻² unless a question states otherwise.

Kinematics — uniform acceleration

v = u + at

s = ut + ½at²

v² = u² + 2as

Dynamics and energy

F = ma

W = mg

Weight.

W = Fs

Work done.

Eₖ = ½mv²

Kinetic energy.

Eₚ = mgh

Gravitational potential energy.

P = W / t

Power.

Fluids and thermodynamics

ρ = m / V

Density.

p = F / A

Pressure.

p = ρgh

Pressure at depth h in a fluid.

Q = mcΔT (temperature change)

c is the specific heat capacity.

Q = mL (change of state)

L is the specific latent heat.

Electromagnetism

V = IR

Ohm's law.

P = VI

Electrical power.

R = R₁ + R₂

Resistors in series.

1/R = 1/R₁ + 1/R₂

Resistors in parallel.

Constants you will be given

Relative atomic masses appear in the question when a calculation needs them, so there is nothing to memorise there. The same applies to the gas constant and to any value a question could not fairly assume. What is not given is the relationship between quantities, which is what this page covers.

Practice with pen and paper

Every question here is solvable in two minutes, exactly as on the day.

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Also on this topic

CEnT-S overview

Exam format, scoring, allowed materials, dates and fees.

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CEnT-S syllabus

Every topic, section by section — what's covered and what isn't.

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