Everyone starts the QA (Quantitative Aptitude) then they try to start a CAT mock. Then they see an algebra question and then your brain just stops. You know the equation, but the change in it throws you off. Two minutes pass and you are still rewriting the same line as the clock keeps moving.
If this feels like you, then pause for a second. It usually means the test style is new, not that you are bad at maths. In school you practice algebra in one way. In CAT, the questions are set up differently. This Algebra for CAT 2026 helps you focus on the parts that matter, shows what exam questions look like, and teaches you how to stay calm while solving.
The test date is Sunday, November 29, 2026. You have around eight weeks. That is enough time to turn algebra into something you can score on, but only if you plan and study with care.
Why Algebra for CAT 2026 Can Affect Your Quant Score
Start with a simple check of the exam pattern. CAT 2026 has 68 questions in three sections. Each section gets 40 minutes. In Quantitative Aptitude, there are 22 questions. Some are MCQs, and some are TITA, where you type the answer. Negative marking is only for MCQs. So your Quant score depends a lot on which questions you pick and how fast you solve them within the time.
Now, where does algebra sit in all this? Most breakdowns place it at about 5 to 8 questions out of the 22. The number varies because different sources group topics in different ways. Some count logs, progressions, and functions as algebra. Others place them under other labels. Still, arithmetic and algebra together make up close to 60% of the section.
Recent papers give a clear picture.
- In 2023, algebra made up around 7 to 8 questions in each slot.
- In 2024, Slot 1 had close to seven algebra questions. Slot 2 had nearly five. Most of them were about quadratics, and also about inequalities shown through graphs and functions.
- In 2025, algebra and geometry were marked as the harder, more time heavy areas.
So yes, algebra shows up a lot and it can be tough. That is not all bad. A lot of students leave these questions. If you solve three or four correctly, your percentile can jump ahead of the average group.
CAT 2026: Algebra topics to focus on
You should not treat every chapter the same way. For the CAT algebra section, the key areas are linear and quadratic equations, functions, logarithms, inequalities, sequences and series, plus maxima and minima.
Below is a simple order of what to prioritize first.
Tier 1. Don’t miss these.
- Quadratic equations. Focus on the sum and product of roots, the discriminant, common roots, and symmetric forms. In most sets, one or two questions in each slot go straight to quadratics.
- Inequalities and modulus. Use the wavy curve idea, then handle modulus in cases. Be clear about the parts of the graph you need. This area repeats often, and small sign mistakes cost easy marks.
- Functions. Work on functional equations, composition, domain and range, and counting style functions.
Tier 2. Worth the time.
- Logarithms. Check the base and the domain first. It matters more than mugging up rules.
- Progressions. AP and GP basics should be quick and solid. That usually earns easy marks.
- Linear equations and integer solutions.
- Maxima and minima. AM-GM is a key tool here.
- Surds, indices, and polynomials. In one 2025 slot, there were single questions from surds, indices, logarithms, and functions.
If you are also gearing up for IPMAT or CUET, you can breathe a bit. Those tests still rest on the same core topics, like quadratics, logs, and inequalities, so your prep helps in both places.
CAT 2026 Algebra: Key Questions (Solutions Included)
Theory helps, but you need practice. These algebra questions for CAT come from the last two CAT papers. I have changed the wording only. The actual math stays the same. Try each one for three full minutes. Then check the solution.
Question 1: A simple link between roots (CAT 2024, Slot 2)
For the equation 3x² + λx − 1 = 0, let the roots be α and β. You are told that
1/α² + 1/β² = 15.
Now find (α³ + β³)².
Solution
First, use basic root facts.
α + β = −λ/3
αβ = −1/3
Now handle the given condition.
1/α² + 1/β² = (α² + β²) / (αβ)²
Next, rewrite α² + β² using (α + β)² − 2αβ.
So the expression becomes
(α + β)² − 2αβ, all divided by (αβ)²
After simplification, it turns into
9[(α + β)² − 2αβ] = λ² + 6
We are told this equals 15.
So λ² + 6 = 15
λ² = 9
λ = 3 or λ = −3
Case 1: λ = 3
Then α + β = −1
Also αβ = −1/3
Compute α³ + β³.
α³ + β³ = (α + β)³ − 3αβ(α + β)
= (−1)³ − 3(−1/3)(−1)
= −1 − 1
= −2
So (α³ + β³)² = (−2)² = 4.
Case 2: λ = −3
Then α + β = 1
The same step gives α³ + β³ = 2
So (α³ + β³)² is again 4.
Final answer: (α³ + β³)² = 4
Question 2: Three equations and one shared root (CAT 2024, Slot 1)
We have these quadratics:
x² + mx + 9 = 0
x² + nx + 17 = 0
x² + (m + n)x + 35 = 0
All three have the same negative root. We need 2m + 3n.Let the common root be r. Take the first two equations and add them:
(x² + mx + 9) + (x² + nx + 17) = 0
So we get:
2x² + (m + n)x + 26 = 0
Now plug in x = r:
2r² + (m + n)r + 26 = 0 ....(1)
Next, compare with the third equation. Subtract the third equation from what we get after using the first two.
That leaves:
r² − 9 = 0
So r = −3.
Now use r = −3 in the first quadratic:
r² + mr + 9 = 0
9 − 3m + 9 = 0
18 − 3m = 0
m = 6
Use r = −3 in the second quadratic:
r² + nr + 17 = 0
9 − 3n + 17 = 0
26 − 3n = 0
n = 26/3
Finally:
2m + 3n = 2(6) + 3(26/3) = 12 + 26
= 38
Takeaway: if two expressions share a root, write them as a matched pair, then combine or cancel before you start solving.
Question 3: CAT 2024, Slot 2
A hidden sum of squares
Given 4x^2 + 4y^2 − 4xy − 6y + 3 = 0, determine 4x + 5y.
Solution: Since there is one equation but two variables, a rewrite should help. Try grouping in a way that forms squares:
(2x − y)^2 + 3(y − 1)^2 = 0.
Each part is never below zero. If their sum is zero, each part must be zero.
So y − 1 = 0, which gives y = 1.
Also 2x − y = 0, so 2x = 1 and x = 1/2.
Answer: 7
Question 4: CAT 2024, Slot 2
The inequality trap
Find all x such that 1/(x + 5) ≤ 1/(2x − 3).
Solution: Do not rush to multiply across. The signs of x + 5 and 2x − 3 are not fixed. First bring both sides to one side:
(x − 8) / [(x + 5)(2x − 3)] ≤ 0.
Now look at key values where the expression can change sign: x = −5, x = 3/2, and x = 8.
Use those points to split the number line and pick where the fraction is at most zero.
At x = −5 and x = 3/2 the denominators blow up, so those x values are not allowed.
At x = 8 the numerator is zero, so x = 8 is allowed.
Answer: x < −5 or 3/2 < x ≤ 8
Question 5: Integer point count (CAT 2024, Slot 3)
How many different pairs of integers (x, y) make
|x + y| + |x − y| = 2 true?
Let A = |x + y| + |x − y|.
This quantity can be rewritten as 2 times the bigger of |x| and |y|.
So A = 2 · max(|x|, |y|).
Since A = 2, we get max(|x|, |y|) = 1.
That forces x and y to stay within −1, 0, 1, and at least one of them must be nonzero.
Now list the allowed pairs from the set (−1, 0, 1) × (−1, 0, 1).
There are 9 total pairs, but (0, 0) does not work.
So the count is 9 − 1 = 8.
Answer: 8
Question 6: Functional equation cleanup (CAT 2024, Slot 2)
A function f is defined on positive integers and obeys
f(xy) = f(x)f(y) + f(x) + f(y).
Also f(p) = 1 for every prime p.
Compute f(160000).
Start by changing variables.
Set g(n) = f(n) + 1.
Then plug into the given rule:
g(xy) = g(x)g(y).
So g is completely multiplicative.
For any prime p, f(p) = 1, so g(p) = 2.
Now factor 160000.
160000 = 160 · 100 = (2⁵)(5) · (2²)(5²) = 2⁷ · 5³.
That gives 7 + 3 = 10 prime factors when counting repeats.
Thus g(160000) = 2¹⁰ = 1024.
Since f(n) = g(n) − 1, we get f(160000) = 1024 − 1 = 1023.
Answer: 1023
Question 7: The logarithm domain trap (CAT 2025)
Find the sum of all real x that satisfy log base (x − 3) of (x² − 9) equals log base (x − 3) of (x + 1), plus 2.
Solution: First check the log rules. The base x − 3 must be greater than 0 and must not be 1. So x > 3, and x − 3 ≠ 1, which means x ≠ 4.
Now use the log equation. Rewrite it by combining the two logs. After simplification, you get (x² − 9)/(x + 1) = (x − 3)².
Since x > 3, x − 3 is not 0, so you can divide safely. This turns into (x + 3)/(x + 1) = x − 3.
Expand and collect terms: x² − 3x − 6 = 0.
So x = (3 ± √33)/2.
Check the domain. The value (3 − √33)/2 is about −1.37, so it does not meet x > 3.
The other value works. That is (3 + √33)/2, about 4.37.
Answer: (3 + √33)/2
Also, the two roots add up to 3. That total matches what appeared in the options. The problem rewarded students who tested the allowed domain.
Question 8: Read before you calculate (CAT 2025)
How many different integers n make log base 1/4 of (n² − 7n + 11) greater than 0?
Solution: The base is 1/4, so it lies between 0 and 1. For such bases, log is positive only if the input is strictly bigger than 0 but also strictly less than 1.
Now look at n² − 7n + 11. For every integer n, this expression is an integer. An integer cannot be strictly between 0 and 1.
So there are no integers n that meet the condition.
Answer: 0
You did not need hard algebra. You just had to figure out what the question was checking.
More Algebra Practice for CAT 2026
Try these five new ones. Check the answers at the end.
Terms x₁, x₂, …, x₁₀₀ form an AP. Given x₅ = −4 and 2x₆ + 2x₉ = x₁₁ + x₁₃, what is x₁₀₀?
A quadratic f(x) has f(x) ≥ 0 for every real x. Also f(2) = 0 and f(4) = 6. What is f(−2)?
Hint: look at a graph that just touches the axis instead of going through it.
Let u = (log₂x)² − 6 log₂x + 12. How many solutions does xᵘ = 256 have?
Hint: set t = log₂x.
For what values of A does x² − 4x − log₂A = 0 have real and separate roots?
The equation x² + bx + c = 0 has roots 4a and 3a. Find b² + c in terms of a.
Answers: (1) −194. (2) 24. (3) 1 solution, x = 4. (4) A > 1/16. (5) 61a².
CAT QA Algebra Under Pressure: What to Do
You need the syllabus. You also need a steady plan when time starts to cut in. Use these steps on any algebra question.
- First, figure out the goal. What is the question really checking? I once spent about ten seconds on a full solution after I got the main trick. That did not happen until I understood the target. In your first 15 seconds, focus on the idea. Do not waste time on long expansion.
- Second, confirm that the algebra is allowed. Square roots, logs, and any fraction terms can bring extra conditions. In one question, people who skipped these rules lost marks fast. So check validity early, then move on.
- Third, scan for a shortcut. Before you expand everything, try to spot structure. Hidden square forms, quick add and subtract moves, and direct substitution can cut the work. These save real time.
- Fourth, try quick values. For inequality types, test one number from each side of the boundary. For multiple choice equations, start with simple values like 0, 1, or -1. This often removes options in a minute.
- Fifth, set a hard time limit for yourself. You have 40 minutes for 22 questions. That is close to two minutes per question on average. Many test takers aim for about 13 to 15 correct answers with strong accuracy to reach a top tier score. You do not need to attempt all items. Pick the ones that you can solve well.
- Sixth, follow TITA. If the answer is wrong and no penalty applies, then a guess from real elimination is better than leaving it blank. If you already know the direction, even an educated choice costs you little.
- Seventh, keep a small error journal. After each wrong answer, note why it happened. Was it a concept gap, a calculation slip, or a reading mistake? Look back after about two weeks. You will see the same type of error repeating.
An 8 week algebra plan that feels doable
You have around eight weeks, so use a steady rhythm.
Week 1 and 2: Fix the basics again.
Focus on quadratics, straight line equations, identities, and sequences.
Do practice sets each day by topic.
Go back to the notes only when you hit a wall.
Week 3 and 4: Handle the harder parts.
Work on inequalities, modulus, functions, and logs.
Use older exam questions for each chapter.
This is also where the 2024 and 2025 papers tend to focus.
Week 5 and 6: Combine topics and build speed.
Practice integer type questions.
Also do maxima and minima.
Use AM to GM style questions too.
Start doing short tests with 22 questions in 40 minutes.
Week 7 and 8: Full mock exams and careful checking.
Do complete mocks.
After each one, review every question you did not get.
Keep a simple note of the mistakes you repeat.
In the last few days, do not chase new methods.
Just tighten the things you already know.
Final Thoughts
In algebra, patience matters more than quickness. At first, each problem can feel heavy. After a short while, the same work starts to look clear. That is the lesson you are training. Keep your mind steady. Find the main idea fast. Then move on if a question is not worth your time.
TCM Education knows this well. TCM, or The Chamber of Mathematics, began as a place to train students in math for MBA and CAT prep. So algebra has always been part of the plan, not a side topic. If you are preparing for CAT, IPMAT, CLAT, or CUET, mentor input on how you think can change your results. Answers alone are not enough.
Want support for your last eight weeks? Contact the TCM Education team. For now, return to Question 1 and work through the practice set. Your score will show it later.
FAQ: Algebra for CAT 2026
How many algebra questions are in the CAT QA section?
Most times, algebra gives around 5 to 8 questions out of 22. The count is not the same in every slot. It also changes based on how the paper labels topics like logs, progressions, and functions. Some versions treat them as algebra, while others move them to modern maths.
Which algebra chapters matter most for CAT 2026?
Focus first on quadratic equations, inequalities, modulus, and functions. These parts usually get the most weight. After that, study logarithms, linear equations with integer solutions, and maxima-minima. If you do these well, you will cover a large share of the algebra items listed for CAT 2026.
Is algebra hard for CAT?
It can feel hard. In CAT 2025 QA, algebra and geometry were often seen as the toughest and slowest topics by many test takers. The challenge usually comes from the angle of the question, not from using very advanced methods. You gain more by checking patterns and verifying the setup than by only memorising formulas.
What is a good target for QA questions to reach a top score?
Most analysts say about 13 to 15 strong questions, answered correctly, can put you near the 99 percentile. You do not have to attempt every algebra item. Choose questions where you can spot a way forward in just a few minutes.
Does CAT have negative marking for algebra questions?
Yes, but only for MCQs. For those, the scheme gives +3 for a correct answer and −1 for a wrong one. The same penalty does not apply to TITA algebra. If you pick TITA and get it wrong, there is no loss, so attempting a solid guess is usually a better move than staying blank.
Are past year questions enough for algebra practice?
They are a great place to begin. You can see how CAT changes familiar ideas into something that looks different. Still, do not stop there. Use timed section tests and full mocks too. This helps you learn how to choose questions when time is tight. Keep a short note of mistakes you make, and check it later so you do not repeat the same error.
Can I skip algebra and focus only on arithmetic?
That can backfire. Arithmetic plus algebra makes up close to 60% of the QA set. If you skip algebra, you reduce your share of the available questions. Even if algebra feels weak, you should still be able to do the simpler ones, like basic quadratics and number progressions.
