12th Maths Formulas List PDF

12th Maths Formulas List PDF Download

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PDF Name	12th Maths Formulas List
No. of Pages	39
PDF Size	1.22 MB
PDF Category	Education & Jobs
Last Updated	July 4, 2020July 4, 2020
Source / Credits	vthometutor.com
Comments ✎	0
Uploaded By	Pradeep

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12th Maths Formulas List

12th Maths Formulas List PDF read online or download for free from the vthometutor.com link given at the bottom of this article.

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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