Every Class 10 Maths exam has certain formulas that appear again and again. If you know these 10 formulas by heart — with understanding — you can solve most questions in your exam without getting stuck.
1. Quadratic Formula
For any quadratic equation ax² + bx + c = 0, the roots are:
x = (-b ± √(b² - 4ac)) / 2a
The value b² - 4ac is called the Discriminant (D).
If D > 0 → two distinct real roots
If D = 0 → two equal roots
If D < 0 → no real roots
Tip: Always calculate D first before finding the roots.
2. Distance Formula
Distance between two points (x₁, y₁) and (x₂, y₂):
d = √[(x₂ - x₁)² + (y₂ - y₁)²]
Use this whenever the question asks for the length between two coordinates on a graph.
3. Section Formula
Point dividing line segment joining (x₁, y₁) and (x₂, y₂) in ratio m:n is:
P = [(mx₂ + nx₁)/(m+n), (my₂ + ny₁)/(m+n)]
For midpoint, m = n = 1, so: P = [(x₁+x₂)/2, (y₁+y₂)/2]
4. Area of Triangle (Coordinate Geometry)
Area = ½ |x₁(y₂ - y₃) + x₂(y₃ - y₁) + x₃(y₁ - y₂)|
If area = 0, the three points are collinear.
5. Trigonometric Identities
These three must be memorised perfectly:
sin²θ + cos²θ = 1
1 + tan²θ = sec²θ
1 + cot²θ = cosec²θ
Tip: Learn the first one and derive the other two by dividing by cos²θ and sin²θ.
6. Pythagoras Theorem
In a right-angled triangle:
Hypotenuse² = Base² + Perpendicular²
c² = a² + b²
Used in trigonometry, coordinate geometry and mensuration problems.
7. Surface Area and Volume Formulas
Cylinder:
Curved Surface Area = 2πrh
Total Surface Area = 2πr(r + h)
Volume = πr²h
Cone:
Curved Surface Area = πrl (where l = slant height = √(r² + h²))
Total Surface Area = πr(r + l)
Volume = ⅓πr²h
Sphere:
Surface Area = 4πr²
Volume = 4/3 πr³
Tip: The volume of cone is exactly ⅓ of cylinder with same r and h.
8. Arithmetic Progression (AP) Formulas
nth term: aₙ = a + (n-1)d
Sum of n terms: Sₙ = n/2 [2a + (n-1)d]
Or: Sₙ = n/2 [first term + last term]
Where a = first term, d = common difference
9. Probability Formula
P(Event) = Number of favourable outcomes / Total number of outcomes
Always remember:
0 ≤ P(E) ≤ 1
P(E) + P(not E) = 1
10. Similar Triangles — Basic Proportionality Theorem
If a line is drawn parallel to one side of a triangle, it divides the other two sides proportionally.
AB/AD = AC/AE
Also: Ratio of areas of similar triangles = Square of ratio of their corresponding sides
Area(△ABC) / Area(△DEF) = (AB/DE)²
How to Use This List
Print this page and stick it near your study table. Read through all 10 formulas every morning for 2 weeks before your exam. Do not just memorise — understand each formula and solve at least 5 questions based on each one.
With these 10 formulas firmly in your memory, you are already 70% prepared for your Class 10 Maths exam. All the best from Shweta ma'am!
