IISER IAT Mathematics: Exactness and Domain Awareness
What is tested
IISER IAT Mathematics is a speed-and-rigour paper: functions and domains, calculus, coordinate geometry, vectors, probability, matrices, and trigonometry. Most stems are designed so that a clean structural observation beats lengthy algebra. Before calculating, classify the object: is it a domain question, a one-to-one/onto question, a limiting case, or a counting question?
Worked example
Solve log₂(x − 1) + log₂(x − 3) = 2. First impose the domain: x − 1 > 0 and x − 3 > 0, so x > 3. Combine logs: log₂[(x − 1)(x − 3)] = 2, so (x − 1)(x − 3) = 4. Expand: x² − 4x + 3 = 4, hence x² − 4x − 1 = 0. Roots are x = 2 ± √5. Only 2 + √5 ≈ 4.24 satisfies x > 3; 2 − √5 is negative. Thus there is exactly one real solution.
Traps that cost marks
- Squaring both sides and accepting extraneous roots; always test in the original equation.
- Forgetting domain restrictions on log, square root, and inverse trig.
- Mixing permutations and combinations when order is or is not relevant.
- Treating vectors as scalars; direction and components matter.
- Using a matrix inverse without checking the determinant is nonzero.
- Reporting a probability greater than 1 after adding non-mutually-exclusive events.