Class 10 Mathematics
Last Minute Formula Book – All Chapters
1. Real Numbers
• Euclid’s Division Lemma: a = bq + r, 0 ≤ r < b
• HCF × LCM = Product of two numbers
• Fundamental Theorem of Arithmetic: Unique prime factorization
2. Polynomials
• Number of zeroes = Number of x-axis intersections
• For quadratic ax² + bx + c: Sum of roots = -b/a
• Product of roots = c/a
3. Pair of Linear Equations
• Unique solution if a1/a2 ≠ b1/b2
• Infinite solutions if a1/a2 = b1/b2 = c1/c2
• No solution if a1/a2 = b1/b2 ≠ c1/c2
4. Quadratic Equations
• Quadratic Formula: x = (-b ± √(b² - 4ac)) / 2a
• Discriminant D = b² - 4ac
• If D > 0 → Real & distinct roots
• If D = 0 → Equal roots
• If D < 0 → No real roots
5. Arithmetic Progressions (AP)
• nth term: an = a + (n-1)d
• Sum of first n terms: Sn = n/2 [2a + (n-1)d]
• Sn = n/2 (a + l)
Last Minute Formula Book – All Chapters
1. Real Numbers
• Euclid’s Division Lemma: a = bq + r, 0 ≤ r < b
• HCF × LCM = Product of two numbers
• Fundamental Theorem of Arithmetic: Unique prime factorization
2. Polynomials
• Number of zeroes = Number of x-axis intersections
• For quadratic ax² + bx + c: Sum of roots = -b/a
• Product of roots = c/a
3. Pair of Linear Equations
• Unique solution if a1/a2 ≠ b1/b2
• Infinite solutions if a1/a2 = b1/b2 = c1/c2
• No solution if a1/a2 = b1/b2 ≠ c1/c2
4. Quadratic Equations
• Quadratic Formula: x = (-b ± √(b² - 4ac)) / 2a
• Discriminant D = b² - 4ac
• If D > 0 → Real & distinct roots
• If D = 0 → Equal roots
• If D < 0 → No real roots
5. Arithmetic Progressions (AP)
• nth term: an = a + (n-1)d
• Sum of first n terms: Sn = n/2 [2a + (n-1)d]
• Sn = n/2 (a + l)
