Standard form
a x 10ⁿ, 1 a 10, n Z

Indices
a⁰ = 1
a^m x aⁿ = a^m+n aⁿ x bⁿ = (ab)ⁿ (a^m)ⁿ = a_mn






Identities
(a ± b)² = a² + 2ab + b²
a² - b² = (a + b)(a - b)
a³ ± b³ = (a ± b)(a² ab + b²)

Quadratic Formula


sin θ° = sin (180 - θ)°
cos θ° = -cos (180 - θ)°
tan θ° = -tan (180 - θ)°

Angles in a circle





's in same segment are equal
's in opposite segments are supplementary

at centre = twice at O^ce

in a semi-circle = 90°

exterior of a cyclic quadrilateral = interior opposite (a + b = 180°)

Cosine rule
a² = b² + c² - 2bc cosA


Sine rule


Area of Δ = ½bc sinA

Representing inequalities
Plot inequality as a normal equation (y < x + 1 as y = x + 1)
Shade unwanted region (sub values of s & y, false = unwanted)
> / <: ------ line
/ : line


Matrices

Order: row x column
Square matrices: 1x1, 2x2, 3x3,...
Zero matrices: elements all 0
Row matrices: same # of rows
Column matrices: same # of columns
Equal matrices: same elements, order & arrangement
Identity matrices, I



determinant of A, |A| = ad - bc


A(BC) = (AB)C
AB BA
A^-1A = AA^-1 = I
AI = IA = A




Sets
: is an element of
/ { }: empty/ null set
/ E: universal set
: is a subset of
: is a proper subset of
A': A complement
: intersection
: union
: / of every set
A'+ A = E, n(A') + n(A) = n(E)
A A, but A is not A
s = {1, 2, 3, 4} or s = {x: x is a natural #, 1 x 4}

Finite set: finite # of elements
Infinite set: infinite # of elements
Empty/null set: no elements in the set
Equal set: 2 sets, equal elements
Universal set: set containing all elements
Disjoint sets: 2 sets, = 0

A B = greatest, when A B = / smallest
A B = smallest, when A B = greatest

Emaths2

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