Learning the important Class 10 Maths formulas can make Maths easier. Formulas help us solve questions quickly and correctly. However, it is also important to understand when and how to use each formula.
In this guide, we will look at some useful Class 10 Maths formulas with simple examples.
1. Real Numbers
The Euclid’s division formula is:
a = bq + r
Here, a is the dividend, b is the divisor, q is the quotient, and r is the remainder.
For example:
17 = 5 × 3 + 2
Therefore, the quotient is 3 and the remainder is 2.
2. Quadratic Equations
For a quadratic equation:
ax² + bx + c = 0
the quadratic formula is:
x = (-b ± √(b² – 4ac)) / 2a
This formula helps us find the roots of a quadratic equation.
3. Arithmetic Progression
The formula for the nth term is:
aₙ = a + (n – 1)d
The sum of the first n terms is:
Sₙ = n/2 [2a + (n – 1)d]
Here, a is the first term and d is the common difference.
4. Coordinate Geometry
The distance between two points is:
√[(x₂ – x₁)² + (y₂ – y₁)²]
The midpoint formula is:
((x₁ + x₂)/2, (y₁ + y₂)/2)
These formulas help us find the distance and middle point between two places on a graph.
5. Trigonometry
Some important trigonometric ratios are:
sin θ = Perpendicular / Hypotenuse
cos θ = Base / Hypotenuse
tan θ = Perpendicular / Base
One important identity is:
sin² θ + cos² θ = 1
6. Areas and Volumes
Area of a circle:
Area = πr²
Circumference of a circle:
Circumference = 2πr
Volume of a cylinder:
Volume = πr²h
Here, r is the radius and h is the height.
7. Statistics
The mean of observations can be found using:
Mean = Sum of observations / Number of observations
For grouped data, students may also use the appropriate mean formulas based on the given frequency table.
8. Probability
The basic probability formula is:
P(E) = Number of favourable outcomes / Total number of outcomes
For example, when a fair coin is tossed, the probability of getting heads is:
P(Heads) = 1/2
Quick Revision Tip
First, understand the formula. Next, write down what each letter means. Then, solve a simple example. Finally, practise different questions.
In short, Class 10 Maths formulas are useful for quick revision, but understanding the concept behind each formula is just as important. Regular practice will help you use these formulas with confidence in your exams.