Important formulas of 10th class mathematics
Unit#1, Unit#2, Unit#3, Unit#5, Unit#6, Unit#7, Unit#8, Unit#10, Unit#12, Unit#13,
This post covers all the important formulas of 10th class mathematics. You’ll find formulas of each unit, including quadratic equations, trigonometric identities, arithmetic sequences and much more. Use this guide to quickly review and strengthen your math skills for exams. To quickly access a specific chapter, simply click or tap the chapter name and you’ll be taken directly to formulas of that chapter. Click here to access the full solutions for each chapter of 10th class mathematics, including step-by-step explanations for all key topics. Do visit our Face Book Page for more educational and mathematics related content.
Unit # 1 Quadratic Equations
- \[(a + b)^2 = a^2 + b^2 + 2ab\]
- \[(a – b)^2 = a^2 + b^2 – 2ab\]
- \[x = \frac{-b \pm \sqrt{b^2 – 4ac}}{2a}\]
Unit # 2 Theory of Quadratic Equations
- \[\text{Discriminant} = b^2 – 4ac\]
- \[x = \frac{-b \pm \sqrt{b^2 – 4ac}}{2a}\]
- \[1 + \omega + \omega^2 = 0\]
- \[\omega^3 = 1\]
- \[\omega = \frac{1}{\omega^2} \text { or } \omega^2 = \frac{1}{\omega}\]
- \[(x + y + z)(x^2 + y^2 + z^2 – xy – yz – xz)\] \[= x^3 + y^3 + z^3 – 3xyz\]
- \[S = -\frac{b}{a} = – \frac{\text{Coefficient of }(x)}{\text{Coefficient of} (x^2}\]
- \[P = \frac{c}{a} = \frac{\text{Constant term}}{\text{Coefficient of }(x^2)}\]
- \[x^2 – Sx + P = 0 \text{ or }\] \[x^2 – (\text{Sum of roots}) x + \text{Product of roots} = 0\]
- \[\text{Function is Symmetric if } f(\alpha, \beta) = f(\beta, \alpha)\]
- \[\alpha^2 + \beta^2 = (\alpha + \beta)^2 – 2\alpha \beta\]
- \[\alpha^3 + \beta^3 = (\alpha + \beta)^3 – 3\alpha \beta (\alpha + \beta)\]
- \[\alpha – \beta = \sqrt{(\alpha + \beta)^2 – 4\alpha \beta}\]
Unit # 3 Variations
- \[\text{Forth proportional: } d = \frac{bc}{a}\]
- \[\text{Third proportional: } c = \frac{b^2}{a}\]
- \[\text{Mean proportional: }b^2 = ac\]
- \[\text{Continued proportional: }b^2 = ac\]
- \[\text{Invertendo Theorem: If } \frac{a}{b} = \frac{c}{d} \text{ then }\frac{b}{a} = \frac{d}{c}\]
- Alternendo Theorem
- \[\text{if }\frac{a}{b} = \frac{c}{d} then (a:c = b:d)\]
- Componendo Theorem
- \[\text{if }\frac{a}{b} = \frac{c}{d}\text{ then}\]
- \[\text{(i) } a + b : b = c + d : d\]
- \[\text{(ii) } a + a : b = c + c : d\]
- Dividendo Theorem
- \[\text{ If }\frac{a}{b} = \frac{c}{d} \text{ then }\]
- \[\text{(i) }a – b : b = c – d : d\]
- \[\text{(ii) }a – a : b = c – c : d\]
- Componendo-Dividendo Theorem
- \[\text{if }\frac{a}{b} = \frac{c}{d}\text{ then }\]
- \[\text{(i) }a + b : a – b = c + d : c – d\]
- \[\text{(ii) }a – b : a + b = c – d : c + d\]
- K Method
- \[\text{Let }\frac{a}{b} = \frac{c}{d} = k\]
- \[\text{Then }a = bk, c = dk\]
Unit # 5 Sets and Functions
- \[\text{Number of all possible subsets} =2^n\]
- \[\text{Number of all possible proper subsets} =2^n – 1\]
- \[\text{Number of improper subsets} = 1\]
- \[\text{Formula for number of elements in the power set} =2^n\]
- \[A – B = {x | x \in A \text{ and } x \notin B}\]
- \[\text{if }A \cap B = \phi \text{ then A and B are disjoint sets.}\]
- \[A’ = A^c = U – A\]
- Commutative property of Union
- \[A \cup B = B \cup A\]
- Commutative property of intersection
- \[A \cap B = B \cap A\]
- Associative property of union
- \[A \cup (B \cup C) = (A \cup B) \cup C\]
- Associative property of intersection
- \[A \cap (B \cap C) = (A \cap B) \cap C\]
- Distributive property of union over intersection
- \[A \cup (B \cap C) = (A \cup B) \cap (A \cup C)\]
- Distributive property of intersection over union
- \[A \cap (B \cup C) = (A \cap B) \cup (A \cap C)\]
- De-Morgan’s laws
- \[(A∪B)′=A′∩B′\text{ and }(A∩B)′=A′∪B′\]
- \[A−B=A∩B′\]
- \[(A−B)′=A′∪B\]
- \[\text{Elements in Cartesian product } X×Y=m×n\]
- \[\text{Number of binary relations} = 2^{m \times n}\]
- \[\text{If }A⊆B\text{ then }A∪B=A\]
- \[\text{If } A⊆B\text { and } B⊆A\text{ then }A=B\]
- \[A∩A^c=ϕ\]
- \[A∪A^c=U\]
Unit # 6 Basic Statistics
Unit # 7 Introduction to Trigonometry
\(1^\circ = \frac{\pi}{180}\) radians
\(x^\circ = \frac{x\pi}{180}\) radians
1 radian = \(\frac{180^\circ}{\pi}\)
\(x\) radians = \(\frac{x(180^\circ)}{\pi}\)
\(l = r\theta\)
\(A = \frac{1}{2}r^2\theta\)
\(\theta \pm 360k = \theta\), \(k \in \mathbb{Z}\)
- \[\sin(-\theta) = -\sin(\theta)\]
- \[\cos(-\theta) = \cos(\theta)\]
- \[\tan(-\theta) = -\tan(\theta)\]
- \[\csc(-\theta) = -\csc(\theta)\]
- \[\sec(-\theta) = \sec(\theta)\]
- \[\cot(-\theta) = -\cot(\theta)\]
- \[\sin \theta = \frac{y}{r}\]
- \[\cos \theta = \frac{x}{r}\]
- \[\tan \theta = \frac{y}{x}\]
- \[\sin^2 \theta + \cos^2 \theta = 1\]
- \[1 + \tan^2 \theta = \sec^2 \theta\]
- \[1 + \cot^2 \theta = \csc^2 \theta\]
\begin{aligned}
\sin 0^\circ &= 0, & \sin 30^\circ &= \frac{1}{2}, & \sin 45^\circ &= \frac{1}{\sqrt{2}}, & \sin 60^\circ &= \frac{\sqrt{3}}{2}\end{aligned}
\begin{aligned}
\sin 90^\circ &= 1, & \sin 180^\circ &= 0, & \sin 270^\circ &= -1\end{aligned}
\begin{aligned}
\cos 0^\circ &= 1, & \cos 30^\circ &= \frac{\sqrt{3}}{2}, & \cos 45^\circ &= \frac{1}{\sqrt{2}}, & \cos 60^\circ &= \frac{1}{2}\end{aligned}
\begin{aligned}\cos 90^\circ &= 0, & \cos 180^\circ &= -1, & \cos 270^\circ &= 0\end{aligned}
\begin{aligned}\tan 0^\circ &= 0, & \tan 30^\circ &= \frac{1}{\sqrt{3}}, & \tan 45^\circ &= 1, & \tan 60^\circ &= \sqrt{3}\end{aligned}
\begin{aligned}\tan 90^\circ &= \text{Undefined}, & \tan 180^\circ &= 0, & \tan 270^\circ &= \text{Undefined}
\end{aligned}
Unit # 8: Projection of a Side of a Triangle
\[(BC)^2 = (AB)^2 + (AC)^2 – 2mAB \cdot mAC\]\[\text{when angle opposite to (BC) is acute.} \]
\[(BC)^2 = (AC)^2 + (AB)^2 + 2(mAB) \cdot (mAD)\]\[\text{when angle opposite to (BC) is obtuse.}\]
- \[\text{If } (a^2 + b^2 = c^2), (\Delta)\text{ is a right angled} (\Delta).\]
- \[\text{If } (a^2 + b^2 < c^2), (\Delta)\text{ is an obtuse angled }(\Delta).\]
- \[\text{If } (a^2 + b^2 > c^2), (\Delta)\text{ is an acute angled }(\Delta).\]
\[\text{Where, (c) is the longest side.}\]
Unit # 10: Tangent to a Circle
- If two circles touch each other externally, then the distance between their centers is equal to the sum of radii.
- Two circles with centers \[(C_1) \text{ and }(C_2)\], radii of measure \[(r_1) \text{ and }(r_2)\] \[\text{ such that }(mC_1C_2 = r_1 + r_2).\]
- If two circles touch each other internally, then the distance between their centers is equal to the difference of radii.
- Two circles with centers \[(C_1)\text{ and }(C_2), \text{ radii }(r_1) \text{ and }(r_2)\]
\[\text{such that }(mC_1C_2 = |r_1 – r_2|).\] - \[\text{Area of Circle} = (\pi r^2).\]
- \[\text{Area of semi circle} = (\frac{1}{2} \pi r^2).\]
- \[\text{Perimeter or Circumference of Circle} = (2\pi r = \pi d).\]
- \[\text{Semi Perimeter or Half Circumference of Circle} = (\pi r).\]
Unit # 12: Chords and Arcs
- \[(m \angle AOC = 2m \angle ABC)\]
\[{ where,}(m \angle AOC)\text{ is central angle}\]
\[\text{ and }(m \angle ABC) \text{ is circum angle.}\] - The angle in a semi-circle is a right angle,
- In a segment greater than a semi-circle is less than a right angle,
- In a segment less than a semi-circle is greater than a right angle.
- \[(m \angle A + m \angle C = 180^\circ) ,and, (m \angle B + m \angle D = 180^\circ),\]
\[ \text{where }(ABCD)\text{ is a cyclic quadrilateral.}\] - \[(m \angle ACB = m \angle ADB), where, (m \angle ACB)\text{ and }(m \angle ADB)\] are angles of the same segment.
Unit # 13: Angle in a Segment of a Circle
- Perimeter of a regular polygon = \[(n \times l),\]where (n) is the number of sides and (l) is the length of a side.
- The measure of the external angle of a regular hexagon is \[(\frac{\pi}{3}).\]
- The measure of the external angle of a regular octagon is \[(\frac{\pi}{4}).\]
- Formula for finding the angle subtended by the side of an n-sided polygon at the center of the circle = \[(\frac{360^\circ}{n}).\]
We hope this collection of important formulas of 10th class mathematics has helped you in preparing for your exams. Learning these formulas well is important because they will help you solve math problems faster and more easily. Remember to keep practicing these formulas by using them in different types of questions to improve your understanding. If you ever need more help or want to practice with real exam questions, you can check out our 10th class math past papers for detailed guidance and additional practice. Keep practicing, and best of luck with your studies! With regular practice, you’ll get better and feel more confident in your math skills.
Maths formulas for class 10 why they are important
As you continue your studies, remember that mastering the important formulas of 10th class mathematics is crucial for achieving success in your exams. These formulas not only serve as the foundation for solving various mathematical problems but also enhance your ability to tackle complex questions with confidence. Be sure to revisit the important formulas of 10th class mathematics regularly and apply them in different scenarios to solidify your understanding. With dedication and consistent practice, you’ll find yourself excelling in math and ready to take on any challenge that comes your way.