IPMAT Algebra Preparation 2028 — Equations, Inequalities, Functions & Complete Strategy

Why Algebra is the Second Most Important IPMAT QA Topic

Algebra contributes 5 to 7 questions in IPMAT Indore and a similar proportion in IPMAT Rohtak. After Arithmetic, Algebra is the highest-scoring QA area. The good news: unlike Number System or Geometry, Algebra problems follow predictable patterns. Once you know the core question types, you can recognise them instantly in the exam and solve at speed.

Jayant Prajapat, who received 12 IIM calls in CAT 2025, built his QA foundation on strong Algebra during his IPMAT preparation. “Algebra is not about memorising formulas. It is about recognising which technique applies to which problem type. Once you train that recognition, Algebra becomes one of the fastest sections to clear in any exam.”

IPMAT Algebra — Topic Breakdown

Linear Equations — Foundation of Algebra

IPMAT linear equation questions typically involve 1 or 2 variables. For 2-variable systems, use substitution or elimination. The IPMAT twist: questions often present equations in disguised form (word problems). Train yourself to convert word problems to equations quickly.

Key shortcut: For two equations ax + by = c and dx + ey = f, use Cramer's rule for fast solution. If the system has no solution, the lines are parallel (a/d = b/e ≠ c/f). If infinite solutions, the equations are identical (a/d = b/e = c/f). These conditions appear as direct IPMAT questions.

Quadratic Equations

For quadratic ax² + bx + c = 0, the roots are α and β where: Sum of roots = −b/a. Product of roots = c/a. Discriminant D = b² − 4ac determines nature of roots: D > 0 means two distinct real roots; D = 0 means two equal real roots; D < 0 means no real roots.

Common IPMAT question types: Given sum and product of roots, form the quadratic equation. Find the range of k for which roots are real. Find the quadratic if one root is given and the equation has rational coefficients.

Inequalities

Inequality rules to memorise: Adding or subtracting the same value to both sides does not change the inequality. Multiplying or dividing by a positive number does not change the direction. Multiplying or dividing by a negative number reverses the inequality sign. Squaring both sides is only valid if both sides are positive.

Quadratic inequalities: For ax² + bx + c > 0, if a > 0 and roots are α and β (α < β), the solution is x < α or x > β. For ax² + bx + c < 0, the solution is α < x < β. Sketch the parabola to visualise if needed.

Functions & Graphs

IPMAT function questions test: domain and range, modulus function (|x| = x if x ≥ 0, = −x if x < 0), greatest integer function, and composite functions f(g(x)). The modulus function appears most frequently.

For composite functions: f(g(x)) means apply g first, then f. If f(x) = 2x + 1 and g(x) = x², then f(g(x)) = 2x² + 1. Always substitute g(x) into f(x), not the other way around.

Logarithms & Surds

Key log rules: log(ab) = log a + log b. log(a/b) = log a − log b. log(a^n) = n·log a. log base b of a = log a / log b (change of base). log base a of a = 1. log base a of 1 = 0. These 6 rules cover 95% of IPMAT log questions.

Arithmetic and Geometric Progressions

AP: nth term = a + (n−1)d. Sum of n terms = n/2 × (2a + (n−1)d) = n/2 × (first + last). GP: nth term = ar^(n−1). Sum of n terms = a(r^n − 1)/(r − 1) for r ≠ 1. Sum of infinite GP = a/(1−r) for |r| < 1. IPMAT frequently asks: find the term given conditions on sum and nth term simultaneously.

Algebra Preparation Strategy

Frequently Asked Questions — IPMAT Algebra

How many Algebra questions appear in IPMAT?

5 to 7 questions in IPMAT Indore's QA section. Algebra is the second largest QA topic after Arithmetic.

What is the most important Algebra topic for IPMAT?

Quadratic Equations and Inequalities appear most consistently. Functions and Logarithms are also high priority.

What is the sum and product of roots formula?

For ax² + bx + c = 0, sum of roots = −b/a and product of roots = c/a.

How do I solve quadratic inequalities?

Find the roots, then check the sign of the quadratic between and outside the roots. For a > 0, the quadratic is positive outside the roots and negative between them.

What log rules are most tested in IPMAT?

Product rule (log ab = log a + log b), power rule (log a^n = n log a), and change of base (logᵇ a = log a / log b) cover most IPMAT log questions.

Is Class 10 Algebra enough for IPMAT?

Class 10 covers linear and quadratic equations which is the core. Functions and logarithms are Class 11 topics that also appear in IPMAT and require additional preparation.

How long should I spend on Algebra preparation?

3 to 4 weeks after completing Arithmetic. Algebra preparation runs parallel with Number System preparation in Month 2 of most preparation plans.

What is the difference between AP and GP?

AP has a constant difference between consecutive terms. GP has a constant ratio. IPMAT questions often combine both in one problem.

Can arts students prepare Algebra for IPMAT?

Yes. IPMAT Algebra is Class 10 to 11 level. With NCERT as a base and 4 weeks of practice, any student regardless of stream can master the IPMAT Algebra topics.

What is the modulus function and why does it appear in IPMAT?

|x| = x when x ≥ 0 and |x| = −x when x < 0. IPMAT uses modulus equations and inequalities to test whether students can handle piecewise definitions. Practice at least 15 modulus problems.

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