Important Theorems & Formulas Every Class 10 Student Must Remember
Success in Class 10 Board Exams depends a lot on your understanding of concepts and quick recall of important theorems and formulas. Mathematics, especially, becomes easier if you have all the key results at your fingertips. In this article, we have compiled a complete list of important theorems and formulas for Class 10 students, as per the CBSE syllabus, to help you prepare effectively.
📘 Important Theorems for Class 10
Pythagoras Theorem
(Hypotenuse)2 = (Base)2 + (Perpendicular)2
👉 Very important for coordinate geometry, trigonometry, and applications.
Theorem on Similar Triangles
If a line is drawn parallel to one side of a triangle, it divides the other two sides in the same ratio.
👉 Used in proving similarity of triangles.
Basic Proportionality Theorem (Thales Theorem)
If a line is drawn parallel to one side of a triangle, it divides the other two sides proportionally.
Tangents to a Circle Theorems
- The tangent at any point of a circle is perpendicular to the radius at the point of contact.
- The lengths of tangents drawn from an external point to a circle are equal.
📘 Important Formulas for Class 10
Algebra Formulas
- (a+b)2 = a2 + 2ab + b2
- (a-b)2 = a2 - 2ab + b2
- (a+b)(a-b) = a2 - b2
Mensuration (Surface Area & Volume)
- Surface area of sphere = 4πr2
- Volume of sphere = (4/3)πr3
- Surface area of cone = πr(l + r)
- Volume of cone = (1/3)πr2h
- Volume of cylinder = πr2h
Geometry
- Area of triangle (Heron’s Formula): √[s(s-a)(s-b)(s-c)], where s = (a+b+c)/2
Coordinate Geometry
- Distance formula: √[(x2-x1)2 + (y2-y1)2]
- Mid-point formula: ((x1+x2)/2, (y1+y2)/2)
Trigonometry
- sin2θ + cos2θ = 1
- 1 + tan2θ = sec2θ
- 1 + cot2θ = csc2θ
- Values of trigonometric ratios at 0°, 30°, 45°, 60°, 90° must be memorised
Arithmetic Progression (AP)
- nth term: an = a + (n-1)d
- Sum of n terms: Sn = n/2 [2a + (n-1)d]
Probability
- Probability = Favourable Outcomes / Total Outcomes
📝 Quick Tips to Remember These Formulas
- Maintain a separate formula notebook and revise it daily.
- Solve NCERT Examples & Exercises regularly.
- Use flashcards for trigonometric values and algebraic identities.
- Practice previous year question papers for better recall in exams.
📌 Final Words
Remember, formulas and theorems are the backbone of Class 10 Mathematics. Once you have them at your fingertips, solving problems becomes much easier. Keep practicing regularly, revise daily, and you’ll surely score well in your exams.