GCSE formulas and equations

Since the government has decided to change the exam board, resulting in us students being forced to memorise every equation and formula for science and maths, I decided to give my younger readers and myself a head-start by laying out all (i think) of the equations and formulas needed for you in GCSEs.

physics:

W work done (joules) = P power (watts) x t  time (seconds)

Q charge (coulombs) = I  current (amps) x t time (seconds)

W weight (newtons) = m mass (kilograms) x g gravitational field strength (newtons/kilogram)

v wave speed (metres/second) = f frequency (hertz) x L wavelength (metres)

V potential difference (volts) = I current (a) x R resistance (ohms)

W work done (joules or newtonmetres) = F force (newtons) x s distance moved (metres)

p momentum (kilogram metres/second) = m mass (kilograms) x v velocity (metres/second)

E energy (joules or kilowatt hours) = P power (watts or kilowatts) x t time (seconds or hours)

F force (newtons) = k spring constant (newtonmetres) x e extention (metres)

Ek kinetic energy (joules) = 1/2m mass (kilograms) x v squared speed (metres/second)

energy (joules) = charged (coulombs) x V potential difference (voltage)

F force (newtons) = pressure (newtonmetres squared or pascals) x A surface area (m squared)

distance (metres) = v speed (metres/second) x t time (newtons)

power (watts) = I squared current (amps) x resistance (ohms)

mass (kilograms) = D density (kilograms/metre cubed) x volume (metres cubed)

F force (newtons) = mass (kilograms) x acceleration (metres/second squared)

P power (watts) = potential difference (volts) x I current (amps)

M moment of force (newton metres) = force (newtons) x d distance normal to force (metres)

/\v change in velocity (metres/second) = acceleration (metres/second squared) x t time taken (seconds)

 

maths:

The quadratic formula

The solutions of ax2+bx+c=0 , where a0

x=b±(b24ac)2a

Circumference and area of a circle

Where r is the radius and d is the diameter:

Circumference of a circle = 2πr = πd

Area of a circle = πr2

Pythagoras’ theorem

In any right-angled triangle where a , b and c are lengths of the sides and c is the hypotenuse:

a2+b2=c2

Trigonometry formulae

In any right-angled triangle ABC where a , b and c are lengths of the sides andc is the hypotenuse:

sinA=ac , cosA=bc , tanA=ab

In any triangle ABC where a , b and c are lengths of the sides:

sine rule: asinA=bsinB=csinC

cosine rule: a2=b2+c22bc cosA

Area = 12ab sinC

2. Students are expected to know the following formulae or be able to derive them; they will not be given in the exam. Refer to the Subject content section to determine the tier at which these formulae could be used.

Perimeter, area, surface area and volume formulae

Where a and b are the lengths of the parallel sides and h is their perpendicular separation:

Area of a trapezium = 12(a+b)h

Volume of a prism = area of cross section x length

Compound interest

Where P is the principal amount, r is the interest rate over a given period andn is number of times that the interest is compounded:

Total accrued = P(1+r100)n

Probability

Where P(A) is the probability of outcome A and P(B) is the probability of outcome B :

P(A or B)=P(A)+P(B)P(A and B)

P(A and B)=P(A given B)P(B)

3. Students are not expected to memorise the following formulae; they will be given in the exam in the relevant question. Refer to the Subject content section to determine the tier at which these formulae could be used.

Perimeter, area, surface area and volume formulae

Where r is the radius of the sphere or cone, l is the slant height of a cone andh is the perpendicular height of a cone:

Curved surface area of a cone = πrl

Surface area of a sphere = 4πr2

Volume of a sphere = 43πr3

Volume of a cone = 13πr2h

Kinematics formulae

Where a is constant acceleration, u is initial velocity, v is final velocity, s is displacement from the position when t=0 and t is time taken:

v=u+at

s=ut+12at2

v2=u2+2as

For the maths equations and formulas I copied from a reliable source on the internet so let me know in the comments below if there are any i have missed or any that don’t make sense. If you found this useful, please share on twitter and tag me @sianajg

Siana xx