Maths Formulae

For a level edexcel maths

Derivative of a^x

a^xlna

Percentage of data in the IQR

50%

cos2θ in only cos²

2cos²θ – 1

cos2θ in only sin²

1-2sin²θ

cos²θ in cos

1/2 + 1/2 cos2θ

sin²θ in cos

½ - 1/2cos2θ

tan2θ

2tanθ/1-tan²θ

Converting between log bases

log_ab = 1/log_ba

cosine rule

a² = b² + c² -2cbcosA

Area of a triangle

1/2absinc

arc length where angles are rad

θr

Sector area

½ r²θ

Segment area

½ r²(θ – sinθ)

Arithmetic n^th term

a + (n – 1)d

LCM

multiply all the prime factors

HCF

Multiply the common prime factors

the square identity that involves tan

Tan²x + 1 = Sec²x

Sec²x =

Tan²x + 1

Cosec²x =

1 + cot²x

The square identity that doesn’t involve tan

cot^2x + 1 = cosec²x

Parametric Integration

Integral ydx = integral y(dx/dt) dt

Finding a unit vector for a

a/|a|

unit vector a notation

a with a ^

parametric equations of a circle

x = rcost y= rsint

parametric equation of an ellipse

x = atrigt y = b(other trig)t

cartesian equation of an ellipse

x²/a² + y²/b² = 1

Vector AB

B - A

shifting from sin to cos with angles

sinx = cos(90 -x)

shifting from cos to sin with angles

cosx = sin(90-x)

what does each part of the completed square form corresponde to

NEGATIVE of number in bracket is x co ord for TP, outside bracket is y co ord for TP

If there is a coefficient outside the bracket of the completed square form can you still find the turning point and how?

Yes no different

Log_ab =

logb/loga

how to find binomial coefficients from pascals triangle for b^r in (a+b)ⁿ

the (r+1)th term in the (n+1)th row

alternate segment circle theorem

the angle between a tangent and a chord is equal to the angle in the alternate segment

Which is the segment

segment of orange, sector sum of vector

How many 0s after the full stop and before the first figure for a negative standard form of 10^n

n-1

area of rhombus with p and q as the diagonals

pq/2

Area of kite

1/2 (product of “frame"/”cross” beams)

When are two lines perpendicular

product of gradients = -1

area of a trapezium

1/2(a+b)h

derivative of lnx

1/x

integral of 1/x

ln|x| + c

mean of data from a frequency table

∑fx/∑f

what is ∑ from 1 to n

n

when does newton raphson fail

near to points where the gradient is small