Mathematics is a crucial subject for students in Class 10 as it lays the foundation for higher studies and competitive exams. Remembering all the formulas can be challenging, but having them in one place can make problem-solving easier. At Alva’s Pre-University College, we believe in simplifying learning, and here’s a comprehensive list of important Class 10 Maths formulas categorized by topics.
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1. Algebra Formulas
Quadratic Equations:
The standard form of a quadratic equation: ax² + bx + c = 0
Quadratic formula: x = (-b ± ) / 2a
Sum of roots: α + β = -b/a
Product of roots: αβ = c/a
Arithmetic Progression (AP):
nth term of an AP: aₙ = a + (n-1)d
Sum of n terms: Sₙ = (n/2) × (2a + (n-1)d)
Polynomials:
Sum of zeros: -b/a
Product of zeros: c/a
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2. Trigonometry Formulas
Basic Identities:
sin²θ + cos²θ = 1
1 + tan²θ = sec²θ
1 + cot²θ = cosec²θ
Trigonometric Ratios:
sinθ = Opposite / Hypotenuse
cosθ = Adjacent / Hypotenuse
tanθ = Opposite / Adjacent
cotθ = 1/tanθ
secθ = 1/cosθ
cosecθ = 1/sinθ
Values of Standard Angles:
Angle 0° 30° 45° 60° 90°
Sinθ 0 1/2 1/√2 √3/2 1
Cosθ 1 √3/2 1/√2 ½ 0
Tanθ 0 1/√3 1 √3 Undefined
Cotθ Undefined √3 1 1/√3 0
Secθ 1 2/√3 √2 2 Undefined
Cosecθ Undefined 2 √2 2/√3 1
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3. Coordinate Geometry Formulas
Distance Formula:
d = √((x〖2-x1〗_ )^2+(y2-y1)^2 )
Midpoint Formula:
M = (x1+x2/2,y1+y2/2)
Section Formula:
P = (m1x2+m2x1/(m1+m2),m1y2+m2y1/(m1+m2))
Area of a Triangle:
A = 1/2|x1(y2-y3)+x2(y3-y1)+x3(y1-y2)|
Where (x1,y1)(x2,y2) and (x3,y3) are the coordinates of the triangle’s vertices.
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4. Geometry and Mensuration Formulas
Circle:
Circumference: C = 2πr
Area: A = πr²
Surface Areas and Volumes:
Cube: Volume = a³, Surface area = 6a²
Cuboid: Volume = l × b × h, Surface area = 2(lb + bh + hl)
Sphere: Volume = (4/3)πr³, Surface area = 4πr²
Cylinder: Volume = πr²h, Surface area = 2πr(h + r)
Cone: Volume = (1/3)πr²h, Curved surface area = πrl
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5. Probability and Statistics Formulas
Probability:
Probability of an event occurring: P(E)=Number of favourable outcomes/Total number of outcomes
Mean, Median, and Mode:
Mean: Σx/n
Median: The middle value in an ordered dataset: Median=L+(n/2-CF/f)*h
Mode: The most frequently occurring value in a dataset: Mode=L+(f1-f0/2f1-f0-f2)*h
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Conclusion
Mastering these formulas will help you score well in your Class 10 Maths Exams and strengthen your conceptual understanding. At Alva’s Pre-University College, we provide in-depth coaching, practice sessions, and expert guidance to ensure our students excel in Mathematics and other subjects.
All the Best for your Examination!
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