Algebra is an important part of the CAT Quantitative Aptitude section, which comprises 6–8 of these questions each year, accounting for about 30–36% of the QA section. These questions come from a variety of topics including linear and quadratic equations, inequalities, functions, sequences and series, logarithms, and progressions.
For aspirants targeting the 99th percentile in the Quants section, proficiency in Algebra is non-negotiable. By focusing preparation on the most recurrent Algebra question types, aspirants can maximize their accuracy and score in Quants. Check CAT Syllabus 2025
Weightage of Algebra in CAT Quant
Over the last five CAT administrations (2020–2024), the Quantitative Aptitude section has consistently asked between 6 and 8 questions from Algebra each year, contributing roughly 32% of the Quant section annually, out of a total of 22 QA questions:
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Top 10 Algebra Question Types in CAT
In the CAT exam, algebra problems recur in predictable formats. Familiarity with these ten categories and their sub-types allows aspirants to spot easy questions quickly and apply the right techniques. Each category below shows what to expect and how questions have appeared in recent CAT Question Papers.
1. Quadratic Equations and Their Roots
1.1 Standard Form and Factorization Questions often present ax2+bx+c=0. You’ll need to factorise or apply the quadratic formula.
1.2 Discriminant-Based Roots Tests on determining the nature of roots using D = b2 - 4ac: whether they are real, equal, or complex.
1.3 Sum and Product of Roots Applications Applications of the relationships: α+β=−b/a and αβ=c/a in word problems or finding unknown coefficients.
1.4 Past CAT Variants & Difficulty Recent CAT papers have combined root-sum questions with parameter-based conditions like "for what value of kk are the roots real?" — usually easy to moderate in difficulty.
2. Linear Equations and Inequalities
2.1 Single-Variable Linear Equations Straightforward forms like ax+b=c often feature quick solvable questions.
2.2 Systems of Two or Three Equations Two-variable systems test substitution/elimination, while three-variable sets sometimes apply determinant methods.
2.3 Linear Inequalities with Modulus Requires case-based solving, splitting into x+a≥0 and x+a<0.
2.4 Time-Tested Shortcuts Techniques like adding equations directly or spotting symmetry save time.
3. Logarithms and Exponents
3.1 Laws of Logarithms Master the product, quotient, and power rules like log(ab)=loga+logb.
3.2 Change of Base Formula Questions may require rewriting logba in terms of natural or base-10 logarithms.
3.3 Exponential Equations and Simplification Forms like af(x)=bg(x) often reduce to linear forms using logarithms.
3.4 Common Pitfalls in CAT Be careful of domain restrictions like a>0 and a≠1, and avoid sign errors.
4. Functions and Graphs
4.1 Domain, Range, and Composite Functions Identify where f(x) is defined and compute (f∘g)(x).
4.2 Inverse Functions and Functional Equations Solving for f−1(x) or equations like f(x)+f(1−x)=c.
4.3 Graphical Interpretation Sometimes, questions are based on interpreting maxima/minima or graph intersections.
4.4 TITA vs. MCQ Strategies In TITA (Type In The Answer) questions, clarity in algebraic form helps avoid errors.
5. Sequences and Series (AP, GP, HP)
5.1 Arithmetic Progression (AP) Using a+(n−1)d and n2[2a+(n−1)d] for terms and sums.
5.2 Geometric Progression (GP) Questions involving arn−1 and Sn=a(rn−1/r−1).
5.3 Harmonic Progression (HP) Typically rephrased through the reciprocals of an AP.
5.4 Tricks for Rapid Computation Pair terms or use known identities to save time.
6. Binomial Theorem and Permutations
6.1 Expansion of (a+b)n. Finding specific terms using (nk)an−kbk.
6.2 Middle Term(s) and Coefficient Properties Determining middle terms when nn is even or odd.
6.3 Connection with Permutations & Combinations Link between binomial coefficients and nPr or nCr.
6.4 High-Frequency Templates Simplify expansions via variable substitution or telescoping sums.
7. Polynomials and Remainder/Factor Theorems
7.1 Remainder Theorem Applications Evaluate f(a) quickly to find remainders when divided by x−a.
7.2 Factor Theorem & Factorization Identify roots to factorise cubic or quartic polynomials.
7.3 Relationship Between Roots and Coefficients Use Viète’s formulas for the sum and product of roots.
7.4 Common CAT Patterns Some questions require blending the remainder theorem with maximum/minimum value reasoning.
8. Maxima and Minima of Algebraic Expressions
8.1 AM–GM and Cauchy–Schwarz Inequalities Apply these directly to bound expressions or determine equality conditions.
8.2 Quadratic Form Minima/Maxima without Calculus Complete the square or recognize standard forms.
8.3 Parameter-Based Optimization E.g., "For which value of k, does ax2+bx+k attain its minimum at x=m?"
8.4 Practice Sets for Speed Quick drills in inequality optimizations sharpen accuracy.
9. Complex Numbers in Algebra
9.1 Arithmetic of a+bi and Polar Form Master addition, multiplication, and conversions to reiθ.
9.2 Roots of Unity and Geometric Interpretations Plotting roots on the complex plane or summing roots.
9.3 Equation-Based Complex Number Problems Equations like z+z=2az or ∣z∣=r.
9.4 Simplification Techniques Use conjugates to rationalize denominators and simplify modulus.
10. Mixed Question Sets (Multi-Concept Integration)
Candidates can check the mixed question sets in Algebra in the table below. Check the type and the description below.
