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National 5 Formulae and Equations

28 flashcards covering key National 5 Mathematics and Physics formulae and relationships. Original study material for practice.

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N5 Maths: quadratic formula

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N5 Maths: quadratic formula

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

for

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

N5 Maths: discriminant

b^{2} - 4 a c

: positive gives two real roots, zero gives equal roots, negative gives no real roots.

N5 Maths: gradient

m = \frac{y _{2} - y _{1}}{x _{2} - x _{1}}

N5 Maths: equation of a straight line

y = m x + c

, or

y - b = m (x - a)

through the point

(a, b)

N5 Maths: sine rule

\frac{a}{sin A} = \frac{b}{sin B} = \frac{c}{sin C}

N5 Maths: cosine rule (side)

a^{2} = b^{2} + c^{2} - 2 b c cos A

N5 Maths: cosine rule (angle)

cos A = \frac{b ^{2} + c ^{2} - a ^{2}}{2 b c}

N5 Maths: area of a triangle

A = \frac{1}{2} ab sin C

N5 Maths: trigonometric identities

sin^{2} x + cos^{2} x = 1

and

tan x = \frac{sin x}{cos x}

N5 Maths: arc length and sector area

Arc

= \frac{θ}{360} \times 2 π r

; sector area

= \frac{θ}{360} \times π r^{2}

N5 Maths: volume of a cone

V = \frac{1}{3} π r^{2} h

N5 Maths: volume of a sphere

V = \frac{4}{3} π r^{3}

N5 Maths: sample standard deviation

s = \frac{\sum ( x - x ˉ ) ^{2}}{n - 1}

N5 Maths: magnitude of a vector

∣ u ∣ = x^{2} + y^{2}

in 2D, and

x^{2} + y^{2} + z^{2}

in 3D.

N5 Physics: speed, distance, time

d = v t

N5 Physics: acceleration

a = \frac{v - u}{t}

N5 Physics: Newton's second law

F = ma

N5 Physics: weight

W = m g

with

g = 9.8

N/kg on Earth.

N5 Physics: work done

E_{w} = F d

N5 Physics: gravitational potential energy

E_{p} = m g h

N5 Physics: kinetic energy

E_{k} = \frac{1}{2} m v^{2}

N5 Physics: Ohm's law

V = I R

N5 Physics: electrical power

P = I V = I^{2} R = \frac{V ^{2}}{R}

N5 Physics: charge

Q = I t

N5 Physics: heat energy

E_{h} = c m Δ T

for temperature change;

E_{h} = m l

for a change of state.

N5 Physics: wave speed

v = f λ

and

T = \frac{1}{f}

N5 Physics: equivalent dose

H = D w_{R}

where

D = \frac{E}{m}

N5 Chemistry: calorimetry

E_{h} = c m Δ T

with

c = 4.18

kJ/kg/°C for water.

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