Get all important math formulas for Class 10 in one place. This chapter-wise SSC formula sheet covers real numbers, polynomials, quadratic equations, trigonometry, mensuration, probability, statistics, and more for easy exam revision.
Looking for all important math formulas for Class 10 in one place? This chapter-wise formula sheet covers the Telangana SSC Mathematics syllabus and helps students quickly revise key formulas before exams.
Real Numbers Formulas
Euclid’s Division Lemma
a = bq + r
Where:
- a = Dividend
- b = Divisor
- q = Quotient
- r = Remainder
- 0 ≤ r < b
Important Note
This chapter mainly focuses on concepts such as HCF and LCM. Students should understand the method rather than memorise many formulas.
Sets Formulas
Number of Elements in a Set
n(A ∪ B) = n(A) + n(B) − n(A ∩ B)
Complement of a Set
n(A’) = n(U) − n(A)
Where:
- U = Universal Set
- A’ = Complement of Set A
Polynomials Formulas
For a quadratic polynomial:
ax² + bx + c
Sum of Zeroes
α + β = −b/a
Product of Zeroes
αβ = c/a
Important Exam Point
Students are frequently asked to find the relationship between zeroes and coefficients.
Pair of Linear Equations in Two Variables
General Form:
a₁x + b₁y + c₁ = 0
a₂x + b₂y + c₂ = 0
Conditions for Solutions
Unique Solution
a₁/a₂ ≠ b₁/b₂
No Solution
a₁/a₂ = b₁/b₂ ≠ c₁/c₂
Infinite Solutions
a₁/a₂ = b₁/b₂ = c₁/c₂
Quadratic Equations
General Form:
ax² + bx + c = 0
Quadratic Formula
x = [−b ± √(b² − 4ac)] / 2a
Discriminant
D = b² − 4ac
Nature of Roots
- D > 0 → Two distinct real roots
- D = 0 → Equal roots
- D < 0 → No real roots
Important Exam Tip
This is one of the most important chapters in the SSC exam. Practice using the quadratic formula regularly.
Progressions (Arithmetic Progression)
nth Term
aₙ = a + (n − 1)d
Sum of n Terms
Sₙ = n/2 [2a + (n − 1)d]
Alternative Formula
Sₙ = n/2 (First Term + Last Term)
Where:
- a = First Term
- d = Common Difference
Coordinate Geometry
Distance Formula
d = √[(x₂ − x₁)² + (y₂ − y₁)²]
Midpoint Formula
[(x₁ + x₂)/2, (y₁ + y₂)/2]
Important Exam Point
Distance and midpoint problems appear regularly in board examinations.
Similar Triangles
Basic Proportionality Theorem
If a line is drawn parallel to one side of a triangle, it divides the other two sides in the same ratio.
Similar Triangle Condition
Corresponding angles are equal, and corresponding sides are proportional.
Students should focus more on applying theorems than on memorising formulas in this chapter.
Tangents and Secants to a Circle
Important Facts
- Tangent is perpendicular to the radius at the point of contact.
- Lengths of tangents drawn from an external point are equal.
If PA and PB are tangents:
PA = PB
These facts are frequently used in proof-based questions.
Mensuration Formulas
Circle
Area = πr²
Circumference = 2πr
Cylinder
Curved Surface Area = 2πrh
Total Surface Area = 2πr(r + h)
Volume = πr²h
Cone
Curved Surface Area = πrl
Total Surface Area = πr(l + r)
Volume = 1/3 πr²h
Sphere
Surface Area = 4πr²
Volume = 4/3 πr³
Hemisphere
Curved Surface Area = 2πr²
Total Surface Area = 3πr²
Volume = 2/3 πr³
Trigonometry Formulas
Trigonometric Ratios
sin θ = Perpendicular / Hypotenuse
cos θ = Base / Hypotenuse
tan θ = Perpendicular / Base
cosec θ = Hypotenuse / Perpendicular
sec θ = Hypotenuse / Base
cot θ = Base / Perpendicular
Important Identity
sin² θ + cos² θ = 1
Standard Values
| θ | 0° | 30° | 45° | 60° | 90° |
| sin θ | 0 | 1/2 | 1/√2 | √3/2 | 1 |
| cos θ | 1 | √3/2 | 1/√2 | 1/2 | 0 |
Applications of Trigonometry
Height and Distance Formula
tan θ = Height / Distance
This formula is commonly used in tower, tree, and building-based problems.
Probability
Probability Formula
P(E) = Number of Favourable Outcomes / Total Number of Outcomes
Important Rules
0 ≤ P(E) ≤ 1
P(E) + P(Not E) = 1
Statistics
Mean
Mean = Σx / n
Median
Median = Middle Value of Ordered Data
Mode
Mode = Value Occurring Most Frequently
Students should practice calculation-based problems from this chapter.
Most Important Formulas for SSC Exams
If you are revising one day before the exam, focus on:
- Quadratic Formula
- Distance Formula
- Midpoint Formula
- Trigonometric Ratios
- Trigonometric Identity
- Area and Volume Formulas
- Arithmetic Progression Formulas
- Probability Formula
- Mean Formula
These formulas are used repeatedly in board examinations.
Last-Minute Formula Revision Checklist
✅ Quadratic Formula revised
✅ Trigonometry table memorised
✅ Mensuration formulas revised
✅ Coordinate Geometry formulas revised
✅ Arithmetic Progression formulas revised
✅ Probability formula revised
✅ Statistics formulas revised
✅ Similar Triangles theorems revised
✅ Tangent properties revised
Frequently Asked Questions
Which chapter contains the most formulas?
Trigonometry and mensuration contain the most formulas.
Which formulas are most important for SSC exams?
Quadratic equations, trigonometry, mensuration, coordinate geometry, and probability formulas are commonly used in exams.
Should I memorise every formula?
No. Focus on understanding where and how each formula is used. This helps you remember them more easily during exams.
How should I revise formulas before the exam?
Create a one-page formula sheet and revise it daily during the final week before the examination.
