# 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)

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

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

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

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

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

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

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

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

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

**maths:**

**The quadratic formula**

The solutions of ax2+bx+c=0 , where a≠0

x=–b±√(b2–4ac)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+c2–2bc cosA

Area = 12ab sinC

- 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)

- 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

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