What algebraic identities are required for the CAT exam?

For the CAT exam, you should be familiar with the following algebraic identities: *Basic Identities:* 1. a^2 - b^2 = (a + b)(a - b) 2. a^2 + b^2 = (a + ib)(a - ib) (i = imaginary unit) 3. a^3 + b^3 = (a + b)(a^2 - ab + b^2) 4. a^3 - b^3 = (a - b)(a^2 + ab + b^2) 5. (a + b)^2 = a^2 + 2ab + b^2 6. (a - b)^2 = a^2 - 2ab + b^2 *Quadratic Equations:* 1. ax^2 + bx + c = 0 (sum and product of roots) 2. Quadratic formula: x = (-b ± √(b^2 - 4ac)) / 2a *Polynomial Equations:* 1. Remainder theorem 2. Factor theorem *Inequalities:* 1. Linear inequalities (e.g., 2x + 3 > 5) 2. Quadratic inequalities (e.g., x^2 + 2x - 3 > 0) *Functions:* 1. Domain and range 2. Even and odd functions 3. Composite functions 4. Inverse functions *Other Important Concepts:* 1. Linear equations in two variables 2. Systems of linear equations 3. Matrix algebra (basic operations) 4. Determinants (2x2 and 3x3) *CAT-Specific Topics:* 1. Functions (odd, even, composite) 2. Graphs (basic understanding) 3. Inequalities (linear, quadratic) 4. Quadratic equations (roots, sum, product) 5. Algebraic manipulations (simplifying expressions) *Recommended Study Materials:* 1. "Quantitative Aptitude" by RS Agarwal 2. "Algebra" by SK Goyal 3. CAT official study materials 4. Online resources (e.g., Khan Academy, Magoosh) *Tips:* 1. Practice solving problems regularly. 2. Focus on understanding concepts rather than just memorizing formulas. 3. Use online resources for additional practice. Would you like information on: 1. CAT exam syllabus and pattern? 2. Study materials and resources? 3. Time management techniques? 4. Mock test strategies? 5. CAT exam results and selection process? read less