Maths Formulas for Class 12 PDF State Board

For some Maths can be fun and for some, it can be a nightmare. Maths Formulas are difficult to memorize and we have curated a list of Maths Formulas for Class 12 PDF State Board just for you. You can use this as a go-to sheet whenever you want to prepare Class 12 Maths Formulas. Students can get Formulas on Algebra, Calculus, and Geometry that can be useful in your preparation and help you do your homework.

Here in this article Maths Formulas for Class 12 PDF State Board, we have listed basic Maths formulas so that you can learn the fundamentals of Maths. Our unique way of solving Maths Problems will make you learn how the equation came into existence instead of memorizing it. Solve all the important problems and questions in Maths with the Best Maths Formulas for Class 12.

Maths Formulas for Class 12 PDF State Board

Feel free to directly use the best Maths formulas during your homework or exam preparation. You need to know the list of Class 12 formulas as they will not just be useful in your academic books but also in your day-to-day lives.

Remember the Maths Formulas in a smart way by making use of our list. You can practice Questions and Answers based on these Class 12 Maths Formulas. Students can get basic Maths formulas Free PDF Download for Class 12. Candidates can use the handy learning aid Maths Formulas PDF to have in-depth knowledge on the subject as per the latest CBSE Syllabus.

CBSE Class 12 Maths Formulas according to the Chapters are prepared by subject experts and you can rely on them during your preparation. Click on the topic you wish to prepare from the list of formulas prevailing.

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12th Maths Formulas List

Areas

Square			: length of side
Rectangle			: width : height
Triangle			: base : height
Rhombus			: large diagonal : small diagonal
Trapezoid			: large side : small side : height
Regular polygon			: perimeter : apothem
Circle			: radius : perimeter
Cone (lateral surface)			: radius : slant height
Sphere (surface area)			: radius

Volumes

Cube	$V = s^{3}$	$s$ : side
Parallelepiped	$V = l \times w \times h$	$l$ : length $w$ : width $h$ : height
Regular prism	$V = b \times h$	$b$ : base $h$ : height
Cylinder	$V = π r^{2} \times h$	$r$ : radius $h$ : height
Cone (or pyramid)	$V = \frac{1}{3} b \times h$	$b$ : base $h$ : height
Sphere	$V = \frac{4}{3} π r^{3}$	$r$ : radius

Functions and Equations

Directly Proportional	$y = k x$ $k = \frac{y}{x}$	$k$ : Constant of Proportionality
Inversely Proportional	$y = \frac{k}{x}$ $k = y x$	$k$ : Constant of Proportionality
$a x^{2} + b x + c = 0$	Quadratic formula	$x = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}$
	Concavity	Concave up: $a > 0$
	Concavity	Concave down: $a < 0$
	Discriminant	$Δ = b^{2} - 4 a c$
	Vertex of the parabola	$V (\frac{- b}{2 a}, \frac{- Δ}{4 a})$
$y = a {(x - h)}^{2} + k$	Concavity	Concave up: $a > 0$
	Concavity	Concave down: $a < 0$
	Vertex of the parabola	$V (h, k)$
Zero-product property	$A \times B = 0 \Leftrightarrow A = 0 \lor B = 0$	ex : $(x + 2) \times (x - 1) = 0 \Leftrightarrow$ $x + 2 = 0 \lor x - 1 = 0 \Leftrightarrow x = - 2 \lor x = 1$
Difference of two squares	$(a - b) (a + b) = a^{2} - b^{2}$	ex : $(x - 2) (x + 2) = x^{2} - 2^{2} = x^{2} - 4$
Perfect square trinomial	${(a + b)}^{2} = a^{2} + 2 a b + b^{2}$	ex : ${(2 x + 3)}^{2} = {(2 x)}^{2} + 2 \cdot 2 x \cdot 3 + 3^{2} =$ $4 x^{2} + 12 x + 9$
Binomial theorem	${(x + y)}^{n} = \sum_{k = 0}^{n}^{n} C_{k} x^{n - k} y^{k}$

Probability and Sets

Commutative	$A \cup B = B \cup A$	$A \cap B = B \cap A$
Associative	$A \cup (B \cup C) = A \cup (B \cup C)$	$A \cap (B \cap C) = A \cap (B \cap C)$
Neutral element	$A \cup \emptyset = A$	$A \cap E = A$
Absorbing element	$A \cup E = E$	$A \cap \emptyset = \emptyset$
Distributive	$A \cup (B \cap C) = (A \cup B) \cap (A \cup C)$	$A \cap (B \cup C) = (A \cap B) \cup (A \cap C)$
De Morgan’s laws	$\bar{A \cap B} = \bar{A} \cup \bar{B}$	$\bar{A \cup B} = \bar{A} \cap \bar{B}$
Laplace laws	$P (A) = \frac{Number of ways it can happen}{Total number of outcomes}$
Complement of an Event	$P (\bar{A}) = 1 - P (A)$
Union of Events	$P (A \cup B) = P (A) + P (B) - P (A \cap B)$
Conditional Probability	$P (A ∣ B) = \frac{P (A \cap B)}{P (B)}$
Independent Events	$P (A ∣ B) = P (A)$	$P (A \cap B) = P (A) \times P (B)$
Permutation	$P_{n} = n! = n \times (n - 1) \times ... \times 2 \times 1$	ex : $P_{4} = 4! = 4 \times 3 \times 2 \times 1 = 24$
Permutations without repetition	$^{n} A_{p} = \frac{n!}{(n - p)!}$	ex : $^{6} A_{2} = \frac{6!}{(6 - 2)!} = 30$
Permutations with repetition	$^{n} A_{p}^{'} = n^{p}$	ex : $^{5} A_{3}^{'} = 5^{3} = 125$
Combination	$^{n} C_{p} = \frac{^{n} A_{p}}{p!} = \frac{n!}{(n - p)! \times p!}$	ex : $^{5} C_{4} = \frac{^{5} A_{4}}{4!} = 5$
Probability Distribution	Average value	$μ = x_{1} p_{1} + x_{2} p_{2} + ... + x_{k} p_{k}$
Probability Distribution	Standard deviation	$σ = \sqrt{\sum_{i = 1}^{k} p_{i} {(x_{i} - μ)}^{2}}$
Binomial distribution	$P (X = k) =^{n} C_{k} . p^{k} . {(1 - p)}^{n - k}$	ex : $B (10; 0, 6)$ $P (X = 3) =^{10} C_{3} \times 0, 6^{3} \times 0, 4^{7}$

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