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Mathematics
Scientific notation
1.6x106 x 2x105 = 3.2x1011 spac[1.6x106]/[2x105] = 8spac 1.6x106 + 2x105 = 1.8x106

Change the subject of an algebraic equation
For example: If A = BxC then C = A/B and so B = A/C

Solve algebraic equations of the form: ax2 + bx + c = 0
Roots of the equation = [-b (b2 - 4ac)1/2]/2a

Logarithms
log (ab) = log a + log bsp log (a/b) = log a - log bsp log (xn) = n log xsp ln(ekx)=kx

Binomial theorem ( for small x)
(1 + xn) = 1 + nx (1 + x-n) = 1 - nx

Areas and volumes
Area of a circle = pr2sp Circumference of a circle = 2pr sp Surface area of a sphere = 4pr2sp
Volume of a sphere = 4/3 pr3
Surface area of a cylinder = 2pr2 + 2prLsp Volume of a cylinder = pr2L
Surface area of rectangular block with sides a, b and c = 2ab + 4acsp
Surface area of cube with sides a = 2a2 + 4a2 = 6a2
Volume of rectangular block with sides a, b and c = abcsp Volume of cube with sides a = a3

Sines, cosines and tangents
sin A = opposite side/hypotenusesp cos A = adjacent side/hypotenusesp
tan A = opposite side/adjacent side
sin A = cos(90 - A)sp cos A = sin(90 - A)

Expansions of sin(A B) and cos(A B)
sin(A + B) = sinAcosB + cosAsinBspaces sin(A - B) = sinAcosB - cosAsinB
cos(A + B) = cosAcosB - sinAsinBspaces cos(A - B) = cosAcos B + sinAsinB

Identities:
sin2A + cos2A = 1spaces sin 2A = 2 sin A cos Aspaces cos 2A = 1 - 2 sin2 A

When q tends to zero:
sin q tends to qC
cos q tends to 1
tan q tends to qC
If qC is the angle expressed in radians.
 
 
 
© Keith Gibbs 2009