Maths Formulas For Class 10 PDF Free Download

Maths Formulas For Class 10 PDF Download Info

CBSE Class 10th Mathematics 2023 : Chapter-Wise Important Formulas & Questions Download PDF Free Download.

Maths Formulas For Class 10 PDF Free Download

1. Algebra Formulas

a. Quadratic Formula:

• The quadratic formula is used to find the solutions (roots) of a quadratic equation in the form ax² + bx + c = 0.
• For a quadratic equation ax² + bx + c = 0, the solutions are given by:
• x = (-b ± √(b² – 4ac)) / 2a.

b. Arithmetic Progression (AP) Formulas:

• In an arithmetic progression, where a is the first term, d is the common difference, and nth term is an:
• nth term (an) = a + (n – 1)d.
• Sum of the first n terms (Sn) = (n/2)[2a + (n – 1)d].

c. Geometric Progression (GP) Formulas:

• In a geometric progression, where a is the first term, r is the common ratio, and nth term is an:
• nth term (an) = a * r^(n-1).
• Sum of the first n terms (Sn) = a * (1 – r^n) / (1 – r).

2. Geometry Formulas

a. Area of Common Shapes:

• Area of a rectangle = length × width.
• Area of a square = side × side.
• Area of a triangle = (1/2) × base × height.
• Area of a parallelogram = base × height.
• Area of a trapezoid = (1/2) × (sum of parallel sides) × height.

b. Perimeter of Common Shapes:

• Perimeter of a rectangle = 2 × (length + width).
• Perimeter of a square = 4 × side.
• Perimeter of a triangle = sum of the lengths of its three sides.
• Perimeter of a parallelogram = 2 × (sum of adjacent sides).
• Perimeter of a trapezoid = sum of all four sides.

c. Circle Formulas:

• Circumference of a circle = 2πr (r is the radius).
• Area of a circle = πr².

d. Volume and Surface Area:

• Volume of a cuboid = length × width × height.
• Surface area of a cuboid = 2lw + 2wh + 2lh.
• Volume of a cylinder = πr²h (r is the radius, h is the height).
• Surface area of a cylinder = 2πr² + 2πrh.

e. Pythagoras’ Theorem:

• In a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
• a² + b² = c², where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.

f. Similar Triangles:

• Two triangles are similar if their corresponding angles are equal and their corresponding sides are proportional.

3. Trigonometry Formulas

a. Sine, Cosine, and Tangent:

• In a right triangle, for an angle θ, where opposite side is ‘o,’ adjacent side is ‘a,’ and hypotenuse is ‘h’:
• Sine (sin θ) = o / h.
• Cosine (cos θ) = a / h.
• Tangent (tan θ) = o / a.

b. Pythagorean Trigonometric Identities:

• Sin² θ + cos² θ = 1.
• 1 + tan² θ = sec² θ.
• 1 + cot² θ = csc² θ.

c. Angle Sum and Difference Identities:

• sin(A + B) = sin A cos B + cos A sin B.
• cos(A + B) = cos A cos B – sin A sin B.
• tan(A + B) = (tan A + tan B) / (1 – tan A tan B).

d. Double Angle Formulas:

• sin(2θ) = 2sinθ cosθ.
• cos(2θ) = cos²θ – sin²θ.
• tan(2θ) = 2tanθ / (1 – tan²θ).

4. Statistics and Probability Formulas

a. Mean (Average):

• Mean (μ) = (Sum of all data values) / (Number of data values).

b. Median:

• Median is the middle value of a data set when it is arranged in ascending order.

c. Mode:

• Mode is the data value that occurs most frequently in a data set.

d. Probability:

• Probability of an event A is denoted as P(A) and is calculated as the ratio of favorable outcomes to total possible outcomes.

e. Probability of Independent Events:

• P(A and B) = P(A) × P(B), where A and B are independent events.

5. Algebraic Identities

a. (a + b)² = a² + 2ab + b²

b. (a – b)² = a² – 2ab + b²

c. (a + b)(a – b) = a² – b²

d. (a + b)³ = a³ + 3a²b + 3ab² + b³

e. (a – b)³ = a³ – 3a²b + 3ab² – b³

6. Coordinate Geometry Formulas

a. Distance Formula:

• The distance (d) between two points with coordinates (x₁, y₁) and (x₂, y₂) is given by:
• d = √((x₂ – x₁)² + (y₂ – y₁)²).

b. Midpoint Formula:

• The midpoint between two points with coordinates (x₁, y₁) and (x₂, y₂) is:
• Midpoint = ((x₁ + x₂) / 2, (y₁ + y₂) / 2).

7. Number Systems

a. Real Numbers:

• Real numbers include all rational and irrational numbers.

b. Rational Numbers:

• Rational numbers can be expressed as the ratio of two integers, where the denominator is not zero.

c. Irrational Numbers:

• Irrational numbers cannot be expressed as a simple fraction and have non-terminating, non-repeating decimal expansions.

d. Complex Numbers:

• Complex numbers are written in the form a + bi, where ‘a’ and ‘b’ are real numbers, and ‘i’ is the imaginary unit (i² = -1).

8. Practical Geometry Formulas

a. Construction of Tangents to a Circle:

• To draw a tangent from a point outside the circle, the length of the tangent (T) is given by:
• T = √(OP² – r²), where ‘OP’ is the distance from the point to the center of the circle and ‘r’ is the radius.

9. Mensuration Formulas

a. Surface Area of 3D Shapes:

• Surface area of a cube = 6s² (s is the side length).
• Surface area of a sphere = 4πr² (r is the radius).
• Surface area of a cylinder = 2πrh + 2πr² (h is the height, r is the radius).
• Surface area of a cone = πrl + πr² (l is the slant height, r is the radius).

b. Volume of 3D Shapes:

• Volume of a cube = s³ (s is the side length).
• Volume of a sphere = (4/3)πr³ (r is the radius).
• Volume of a cylinder = πr²h (h is the height, r is the radius).
• Volume of a cone = (1/3)πr²h (h is the height, r is the radius).

10. Probability Formulas

a. Probability of an Event:

• Probability (P) = (Number of favorable outcomes) / (Total number of possible outcomes).

b. Probability of Complementary Events:

• Probability of event A (P(A)) + Probability of event not A (P(not A)) = 1.

c. Probability of Independent Events:

• Probability of events A and B both occurring = P(A) × P(B).

d. Probability of Mutually Exclusive Events:

• Probability of either event A or event B occurring = P(A) + P(B).

11. Coordinate Geometry Formulas

a. Slope of a Line:

• The slope (m) of a line passing through two points (x₁, y₁) and (x₂, y₂) is given by:
• m = (y₂ – y₁) / (x₂ – x₁).

b. Equation of a Line:

• The equation of a line with slope ‘m’ and passing through point (x₁, y₁) is given by:
• y – y₁ = m(x – x₁).

12. Probability Formulas

a. Probability of an Event:

• Probability (P) = (Number of favorable outcomes) / (Total number of possible outcomes).

b. Probability of Complementary Events:

• Probability of event A (P(A)) + Probability of event not A (P(not A)) = 1.

c. Probability of Independent Events:

• Probability of events A and B both occurring = P(A) × P(B).

d. Probability of Mutually Exclusive Events:

• Probability of either event A or event B occurring = P(A) + P(B).

These Are A Few Of The Most Important Mathematical Formulae That Are Taught In Class 10 Math. It Is Essential To Comprehend And Use These Formulae In Order To Solve Problems And Do Well On Math Tests. These Formulae Are Employed In Many Real-world Applications, Ranging From Geometry And Algebra To Statistics And Probability, And They Serve As The Basis For More Complex Mathematical Concepts.