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UNI Admission Key Formulas

Formulas and rules for mathematics, physics and chemistry used in the admission practice questions. Study material written for practice, not the official exam.

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Quadratic formula for

a x^{2} + b x + c = 0

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Quadratic formula for

a x^{2} + b x + c = 0

x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

Discriminant condition for equal real roots

b^{2} - 4 a c = 0

Sum and product of the roots of

a x^{2} + b x + c = 0

Sum

= - \frac{b}{a}

, product

= \frac{c}{a}

Sum of the first

n

terms of an arithmetic progression

S_{n} = \frac{n}{2} (a_{1} + a_{n})

Sum to infinity of a geometric series (when

∣ r ∣ < 1

)

S = \frac{a}{1 - r}

Remainder theorem

The remainder of

p (x)

divided by

x - c

p (c)

Number of divisors from the prime factorisation

p^{a} q^{b} r^{c}

(a + 1) (b + 1) (c + 1)

Heron's formula for the area of a triangle

s (s - a) (s - b) (s - c)

with

s = \frac{a + b + c}{2}

Sum of the interior angles of an

n

-sided polygon

(n - 2) \times 18 0^{\circ}

Volume of a cone

V = \frac{1}{3} π r^{2} h

, with

h = l^{2} - r^{2}

for slant height

l

Law of cosines

c^{2} = a^{2} + b^{2} - 2 ab cos C

Double-angle formula for cosine

cos 2 θ = 1 - 2 sin^{2} θ = 2 cos^{2} θ - 1

Sine of a sum

sin (A + B) = sin A cos B + cos A sin B

Conversion from degrees to radians

Multiply by

\frac{π}{180}

Equations of uniformly accelerated motion

v = u + a t

s = u t + \frac{1}{2} a t^{2}

v^{2} = u^{2} + 2 a s

Centripetal force on a mass moving in a circle

F = \frac{m v ^{2}}{r}

Heat needed to change the temperature of a substance

Q = m c Δ T

Equivalent resistance of two resistors in parallel

R = \frac{R _{1} R _{2}}{R _{1} + R _{2}}

Coulomb's law

F = \frac{k q _{1} q _{2}}{r ^{2}}

with

k = 9 \times 1 0^{9} N m^{2} / C^{2}

Thin lens equation

\frac{1}{v} + \frac{1}{u} = \frac{1}{f}

(real-is-positive convention)

Moles from mass, and molarity

n = \frac{m}{M}

and

C = \frac{n}{V}

with

V

in litres

Ideal gas equation

P V = n R T

, with

R = 0.082 L atm mo l^{- 1} K^{- 1}

Neutrons in an atom

Mass number minus atomic number,

A - Z

pH and pOH at

2 5^{\circ}

pH + pOH = 14

Le Chatelier's rule for an increase in pressure

The equilibrium shifts towards the side with fewer moles of gas

UNI Admission Exam (Peru) in Peru

In Peru, UNI Admission Exam (Peru) is part of: University admission.

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