As Level Maths

Front 1

The remainder theorem

Back 1

When polynomial f(x) is divided by (ax - b) then the remainder is f(b/a)

Front 2

The sine rule

Back 2

a/SinA = b/SinB = c/SinC

or

SinA/a = SinB/b = SinC/c

Front 3

The cosine rule

Back 3

a² =b² + c² - 2bc CosA

and

CosA = (b² + c² - a²) / (2bc)

Front 4

The area of a triangle

Back 4

1/2 abSinC

Front 5

The multiplication law (logs)

Back 5

LOGaXY = LOGaX + LOGaY

Front 6

The division law (logs)

Back 6

LOGa(X/Y) = LOGaX - LOGaY

Front 7

The power law (logs)

Back 7

LOGa(X)^k = kLOGaX

and

LOGa(1/X) = -LOGaX

Front 8

Change of base rule (logs)

Back 8

LOGaX= LOGbX / LOGbA

Front 9

The mid-point of a line

Back 9

( (X1 + X2) / 2, (Y1 + Y2) / 2 )

Front 10

The length of a line

Back 10

√ (X2 - X1)² + (Y2 - Y1)²

Front 11

Equation of a circle

Back 11

Centre (a, b), radius = r,

(X - a)² + (Y - b)² = r²

Front 12

Pascals Triangle

Back 12

1

1 1

1 2 1

1 3 3 1

1 4 6 4 1

1 5 10 10 5 1

1 6 15 20 15 6 1

Front 13

The binomial expansion

Back 13

(a + bx)^n = nC0 a^n + nC1 a^n-1 bx + nC2 a^n-2 b^2 x^2 + ... nCn b^n x^n

Front 14

Radians into degrees

Back 14

1r = 180d / Pi

Front 15

Length of arc

Back 15

l = rθ

Front 16

Area of a sector

Back 16

A = 1/2 r²

Front 17

Area of a segment

Back 17

A = 1/2 r² (θ - sinθ)

Front 18

Sum to n of a series

Back 18

Sn = a(1-r^n) / (r - 1)

Front 19

Sum to infinity

Back 19

S ∞ = a / (1 - r)

Front 20

sin θ, cos θ, tan θ

Back 20

sin θ = y/r

cos θ = x/r

tan θ = y/x

Front 21

Trig quadrant rule

Back 21

Front 22

Increasing / decreasing functions differentiation

Back 22

f ' (x) > 0 increasing

f ' (x) < 0 decreasing

Front 23

Stationary points

Back 23

f ' (x) = 0

f ''(x) < 0 max point

f ''(x) > 0 min point

Front 24

Trig identities - rule 1

Back 24

tan θ = sin θ / cos θ

Front 25

Trig identities - rule 2

Back 25

sin² θ + cos² θ = 1