CLASS X MATHEMATICS
Complete Quick Revision Formula Sheet (Full Syllabus)
1. Real Numbers
• Fundamental Theorem of Arithmetic: Every composite number can be expressed as a product
of primes uniquely.
• HCF and LCM Relation: For any two positive integers a and b:
HCF(a, b) × LCM(a, b) = a × b
2. Polynomials
• General Form: P(x) = ax2 + bx + c
• Sum of Zeroes (α + β): -b / a
• Product of Zeroes (αβ): c / a
• Forming Quadratic Polynomial: x2 - (Sum of Zeroes)x + (Product of Zeroes)
3. Pair of Linear Equations in Two Variables
• Standard Pair: a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0
• Unique Solution (Intersecting Lines): a1/a2 ≠ b1/b2
• Infinite Solutions (Coincident Lines): a1/a2 = b1/b2 = c1/c2
• No Solution (Parallel Lines): a1/a2 = b1/b2 ≠ c1/c2
4. Quadratic Equations
• Standard Form: ax2 + bx + c = 0 (where a ≠ 0)
• Discriminant (D): D = b2 - 4ac
• Nature of Roots:
• If D > 0: Two distinct real roots.
• If D = 0: Two equal real roots.
• If D < 0: No real roots.
• Quadratic Formula: x = (-b ± √D) / 2a
5. Arithmetic Progressions (AP)
• General AP Form: a, a+d, a+2d, a+3d, ...
• n-th Term (an): an = a + (n - 1)d
Complete Quick Revision Formula Sheet (Full Syllabus)
1. Real Numbers
• Fundamental Theorem of Arithmetic: Every composite number can be expressed as a product
of primes uniquely.
• HCF and LCM Relation: For any two positive integers a and b:
HCF(a, b) × LCM(a, b) = a × b
2. Polynomials
• General Form: P(x) = ax2 + bx + c
• Sum of Zeroes (α + β): -b / a
• Product of Zeroes (αβ): c / a
• Forming Quadratic Polynomial: x2 - (Sum of Zeroes)x + (Product of Zeroes)
3. Pair of Linear Equations in Two Variables
• Standard Pair: a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0
• Unique Solution (Intersecting Lines): a1/a2 ≠ b1/b2
• Infinite Solutions (Coincident Lines): a1/a2 = b1/b2 = c1/c2
• No Solution (Parallel Lines): a1/a2 = b1/b2 ≠ c1/c2
4. Quadratic Equations
• Standard Form: ax2 + bx + c = 0 (where a ≠ 0)
• Discriminant (D): D = b2 - 4ac
• Nature of Roots:
• If D > 0: Two distinct real roots.
• If D = 0: Two equal real roots.
• If D < 0: No real roots.
• Quadratic Formula: x = (-b ± √D) / 2a
5. Arithmetic Progressions (AP)
• General AP Form: a, a+d, a+2d, a+3d, ...
• n-th Term (an): an = a + (n - 1)d
