Basic maths JEE class 11

Natural numbers,Positive integers starting from 1

Whole numbers,All natural numbers including 0

Integers,All positive and negative whole numbers including 0

Rational numbers,Numbers that can be expressed as p/q where q ≠ 0

Irrational numbers,Numbers that cannot be expressed as p/q

Real numbers,All rational and irrational numbers

Set,A well-defined collection of distinct objects

Subset,A set A is a subset of set B if every element of A is in B

Power set,Set of all subsets of a set

Universal set,The set that contains all elements under consideration

Empty set,A set with no elements

Union of sets,Set containing all elements of both sets

Intersection of sets,Set containing only common elements of both sets

Complement of a set,All elements in universal set not in the set

Difference of sets,Elements in one set but not in the other

Cardinality,Number of elements in a set

Ordered pair,(a, b) where a ≠ b; position matters

Relation,Subset of Cartesian product of two sets

Function,A relation where each input has one output

Domain,Set of all input values of a function

Range,Set of all output values of a function

One-one function,Each element of domain maps to unique element in codomain

Onto function,Every element of codomain is mapped by at least one element of domain

Bijective function,Function that is both one-one and onto

Composite function,Function formed by combining two functions

Inverse function,A function that reverses the effect of the original function

Trigonometric ratios,sin, cos, tan, cosec, sec, cot

sin²θ + cos²θ,1

1 + tan²θ,sec²θ

1 + cot²θ,cosec²θ

sin(90° – θ),cosθ

cos(90° – θ),sinθ

Graphs of sinθ and cosθ,Wave-like, periodic with period 2π

Angle in radians,π radians = 180°

π radians,180°

1 radian,180°/π degrees

log(ab),log a + log b

log(a/b),log a – log b

log(a^n),n log a

log 1,0

log base a of a,1

i,√–1

i²,–1

(1 + i)(1 – i),2

Complex number form,a + bi where a and b are real numbers

Quadratic equation,ax² + bx + c = 0

Discriminant,D = b² – 4ac

Roots of quadratic,(-b ± √D)/2a

Condition for real roots,D ≥ 0

Point in coordinate plane,(x, y)

Distance formula,√[(x₂ – x₁)² + (y₂ – y₁)²]

Midpoint formula,((x₁ + x₂)/2, (y₁ + y₂)/2)

Slope of line,m = (y₂ – y₁)/(x₂ – x₁)