Class 10 Mathematics Formula Sheet
1. REAL NUMBERS
Euclid's Division Lemma:
a = bq + r, where 0 <= r < b
For two positive integers:
HCF × LCM = Product of the two numbers
2. POLYNOMIALS
For quadratic polynomial ax² + bx + c:
Sum of zeroes = -b/a
Product of zeroes = c/a
3. PAIR OF LINEAR EQUATIONS
For equations:
a1x + b1y + c1 = 0
a2x + b2y + c2 = 0
Unique solution: a1/a2 ≠ b1/b2
No solution: a1/a2 = b1/b2 ≠ c1/c2
Infinite solutions: a1/a2 = b1/b2 = c1/c2
4. QUADRATIC EQUATIONS
Standard form:
ax² + bx + c = 0
Quadratic Formula:
x = (-b ± √(b² - 4ac)) / 2a
Discriminant:
D = b² - 4ac
5. ARITHMETIC PROGRESSIONS (AP)
nth term:
an = a + (n - 1)d
Sum of n terms:
Sn = n/2 [2a + (n - 1)d]
6. TRIANGLES
Pythagoras Theorem:
Hypotenuse² = Base² + Perpendicular²
Area of triangle:
1. REAL NUMBERS
Euclid's Division Lemma:
a = bq + r, where 0 <= r < b
For two positive integers:
HCF × LCM = Product of the two numbers
2. POLYNOMIALS
For quadratic polynomial ax² + bx + c:
Sum of zeroes = -b/a
Product of zeroes = c/a
3. PAIR OF LINEAR EQUATIONS
For equations:
a1x + b1y + c1 = 0
a2x + b2y + c2 = 0
Unique solution: a1/a2 ≠ b1/b2
No solution: a1/a2 = b1/b2 ≠ c1/c2
Infinite solutions: a1/a2 = b1/b2 = c1/c2
4. QUADRATIC EQUATIONS
Standard form:
ax² + bx + c = 0
Quadratic Formula:
x = (-b ± √(b² - 4ac)) / 2a
Discriminant:
D = b² - 4ac
5. ARITHMETIC PROGRESSIONS (AP)
nth term:
an = a + (n - 1)d
Sum of n terms:
Sn = n/2 [2a + (n - 1)d]
6. TRIANGLES
Pythagoras Theorem:
Hypotenuse² = Base² + Perpendicular²
Area of triangle:
