Maths Formulas for Class 10 Math: Essеntial Formulas, Chaptеr by Chaptеr

Maths formulas for  Class 10 is dividеd into various chaptеrs, еach focusing on diffеrеnt concеpts and skills. Hеrе’s a comprеhеnsivе guidе to thе kеy math formulas for еach chaptеr, еnsuring you havе a handy rеfеrеncе for your studiеs.

Chapter 1: Real Numbers

1. Euclid’s Division Lemma: For any two positive integers aaa and bbb, there exist unique integers qqq and rrr such that a=bq+ra = bq + ra=bq+r where 0≤r<b0 \le r < b0≤r<b.
2. Fundamental Theorem of Arithmetic: Every composite number can be expressed (factorized) as a product of primes, and this factorization is unique, apart from the order of the factors.

Chapter 2: Polynomials

1. Polynomial: An expression of the form anxn+an−1xn−1+…+a1x+a0a_n x^n + a_{n-1} x^{n-1} + \ldots + a_1 x + a_0an​xn+an−1​xn−1+…+a1​x+a0​.
2. Zeroes of a Polynomial: If kkk is a zero of the polynomial p(x)p(x)p(x), then p(k)=0p(k) = 0p(k)=0.
3. Relationship between Zeroes and Coefficients:
   • For a quadratic polynomial ax2+bx+cax^2 + bx + cax2+bx+c:
     • Sum of zeroes = −ba-\frac{b}{a}−ab​
     • Product of zeroes = ca\frac{c}{a}ac​

Chapter 3: Pair of Linear Equations in Two Variables

1. Standard Form: a1x+b1y=c1a_1x + b_1y = c_1a1​x+b1​y=c1​ and a2x+b2y=c2a_2x + b_2y = c_2a2​x+b2​y=c2​.
2. Solutions:
   • Substitution Method
   • Elimination Method
   • Cross Multiplication Method: xb1c2−b2c1=yc1a2−c2a1=1a1b2−a2b1\frac{x}{b_1c_2 – b_2c_1} = \frac{y}{c_1a_2 – c_2a_1} = \frac{1}{a_1b_2 – a_2b_1}b1​c2​−b2​c1​x​=c1​a2​−c2​a1​y​=a1​b2​−a2​b1​1​

Chapter 4: Quadratic Equations

1. Standard Form: ax2+bx+c=0ax^2 + bx + c = 0ax2+bx+c=0.
2. Quadratic Formula:
   x=−b±b2−4ac2ax = \frac{-b \pm \sqrt{b^2 – 4ac}}{2a}x=2a−b±b2−4ac​​
3. Nature of Roots:
   • If b2−4ac>0b^2 – 4ac > 0b2−4ac>0, the roots are real and distinct.
   • If b2−4ac=0b^2 – 4ac = 0b2−4ac=0, the roots are real and equal.
   • If b2−4ac<0b^2 – 4ac < 0b2−4ac<0, the roots are complex.

Chapter 5: Arithmetic Progressions

1. nth Term of an AP:
   an=a+(n−1)da_n = a + (n-1)dan​=a+(n−1)d
2. Sum of First n Terms:
   Sn=n2[2a+(n−1)d]S_n = \frac{n}{2} [2a + (n-1)d]Sn​=2n​[2a+(n−1)d]

Chapter 6: Triangles

1. Similar Triangles: Two triangles are similar if their corresponding angles are equal and corresponding sides are in the same ratio.
2. Pythagorean Theorem:
   a2+b2=c2a^2 + b^2 = c^2a2+b2=c2
3. Area of a Triangle:
   Area=12×base×height\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}Area=21​×base×height

Chapter 7: Coordinate Geometry

1. Distance Formula:
   Distance=(x2−x1)2+(y2−y1)2\text{Distance} = \sqrt{(x_2 – x_1)^2 + (y_2 – y_1)^2}Distance=(x2​−x1​)2+(y2​−y1​)2​
2. Section Formula:
   (mx2+nx1m+n,my2+ny1m+n)\left( \frac{mx_2 + nx_1}{m+n}, \frac{my_2 + ny_1}{m+n} \right)(m+nmx2​+nx1​​,m+nmy2​+ny1​​)
3. Area of a Triangle:
   Area=12∣x1(y2−y3)+x2(y3−y1)+x3(y1−y2)∣\text{Area} = \frac{1}{2} \left| x_1(y_2 – y_3) + x_2(y_3 – y_1) + x_3(y_1 – y_2) \right|Area=21​∣x1​(y2​−y3​)+x2​(y3​−y1​)+x3​(y1​−y2​)∣

Chapter 8: Introduction to Trigonometry

1. Trigonometric Ratios:
   • sin⁡θ=OppositeHypotenuse\sin \theta = \frac{\text{Opposite}}{\text{Hypotenuse}}sinθ=HypotenuseOpposite​
   • cos⁡θ=AdjacentHypotenuse\cos \theta = \frac{\text{Adjacent}}{\text{Hypotenuse}}cosθ=HypotenuseAdjacent​
   • tan⁡θ=OppositeAdjacent\tan \theta = \frac{\text{Opposite}}{\text{Adjacent}}tanθ=AdjacentOpposite​

1. Trigonometric Identities:
   • sin⁡2θ+cos⁡2θ=1\sin^2 \theta + \cos^2 \theta = 1sin2θ+cos2θ=1
   • 1+tan⁡2θ=sec⁡2θ1 + \tan^2 \theta = \sec^2 \theta1+tan2θ=sec2θ
   • 1+cot⁡2θ=csc⁡2θ1 + \cot^2 \theta = \csc^2 \theta1+cot2θ=csc2θ

Chapter 9: Applications of Trigonometry

1. Height and Distance:
   • Use trigonometric ratios to calculate heights and distances in real-life problems.

Chapter 10: Circles

​Tangent to a Circle: A line that passes through the circle at a single point known as the point of contact. 

 Properties of Tangents: 

 At any given point tangent will be perpendicular to the radius at that given point of the circle. 

 The lengths of the tangents drawn from a point outside the circle to the circle are the same.

Chapter 11: Constructions

1. Division of a Line Segment:
   • To divide a line segment ABABAB in a given ratio m:nm:nm:n.
2. Construction of Tangents to a Circle:
   • From a point outside the circle.

Chapter 12: Areas Related to Circles

1. Area of a Circle:
   πr2\pi r^2πr2
2. Circumference of a Circle:
   2πr2 \pi r2πr
3. Area of a Sector:
   Area=θ360∘×πr2\text{Area} = \frac{\theta}{360^\circ} \times \pi r^2Area=360∘θ​×πr2

Chapter 13: Surface Areas and Volumes

1. Surface Area and Volume of Solids:
   • Cube:
     • Surface Area = 6a26a^26a2
     • Volume = a3a^3a3
   • Cuboid:
     • Surface Area = 2(lb+bh+hl)2(lb + bh + hl)2(lb+bh+hl)
     • Volume = lbhlbhlbh
   • Sphere:
     • Surface Area = 4πr24 \pi r^24πr2
     • Volume = 43πr3\frac{4}{3} \pi r^334​πr3
   • Cylinder:
     • Surface Area = 2πr(r+h)2\pi r (r + h)2πr(r+h)
     • Volume = πr2h\pi r^2 hπr2h
   • Cone:
     • Surface Area = πr(r+l)\pi r (r + l)πr(r+l)
     • Volume = 13πr2h\frac{1}{3} \pi r^2 h31​πr2h

Chapter 14: Statistics

1. Mean:
   Mean=∑xiN\text{Mean} = \frac{\sum x_i}{N}Mean=N∑xi​​
2. Median:
   • The middle value in a sorted data set.
3. Mode:
   • The value that appears most frequently in a data set.
4. Standard Deviation:
   σ=∑(xi−μ)2N\sigma = \sqrt{\frac{\sum (x_i – \mu)^2}{N}}σ=N∑(xi​−μ)2​​

Chapter 15: Probability

1. Basic Probability Formula: Probability(P)=Number of Favorable OutcomesTotal Number of Outcomes\text{Probability} (P) = \frac{\text{Number of Favorable Outcomes}}{\text{Total Number of Outcomes}}Probability(P)=Total Number of OutcomesNumber of Favorable Outcomes​

Conclusion

Maths formulas for class 10 is Undеrstanding and mеmorizing thеsе formulas is crucial for solving mathеmatical problеms еfficiеntly in Class 10. Rеgular practicе and application of thеsе formulas will not only hеlp in scoring good marks but also in dеvеloping a strong foundation for highеr studiеs. Happy studying! By this website learn Maths formulas for class 10 easily.