Linear and Quadratic Equations for CAT 2025 QA Preparation

You need to have a thorough knowledge of Linear and Quadratic equations if you are going to score marks in the Quantitative Aptitude section of the CAT 2025 exam. They are easy algebra concepts, but they greatly influence how quickly you will be able to answer difficult questions. In the previous CAT exams, the candidates typically got around 1 to 2 questions from these subjects, and these are primarily scoring subjects if you practice them regularly. Because QA has too much weightage and is also time-bound, accuracy in such equation-type questions in such core subjects could improve your overall percentile. Compared to lengthy arithmetic or geometry problems, these questions based on equations are time-saving, which actually works in your favour during the exam.

Also Read: Topics You Should Not Skip in CAT Quant 2025

What are Linear and Quadratic Equations?

As you start learning algebra, two of the most important topics you will come across are Linear and Quadratic equations in the CAT QA section. These concepts serve as lead-ins to more complex math and have numerous practical applications, ranging from business profit to forecasting outcomes.

Linear Equations

• A linear equation is an algebraic expression in which the variable contains the highest power of 1. It takes the form ax + b = c, where
  • a, b, and c are constants, and x represents the variable.
  • Its graph, if plotted, always yields a straight line as output.
  • Equation value refers to the position at which the line touches the x-axis.
• For two variables, i.e., in cases such as in equations, a1x + b1y = c1 and a2x + b2y = c2.
  • In this instance, there will be a single common solution.
  • If lines are parallel, there is no solution.
  • If they overlap entirely, there are an infinite number of solutions.

Quadratic Equations

A quadratic equation takes the form ax² + bx + c = 0, in which a ≠ 0. The highest exponent of x in this one happens to be 2, and this produces, on the graph, a U-shaped curve known as a parabola. That kind of solution depends on the discriminant value D = b2 − 4ac:

• If D>0, two distinct real roots exist.
• If D=0, one real root (repeated) exists.
• If D<0, the roots are imaginary.

Key Concepts and Formulas for Linear and Quadratic Equations for CAT

Refer to the table given below to learn and get familiar with the key concepts and formulas related to Linear and Quadratic Equations for the CAT 2025 QA section:

Preparation Tips to Solve Linear and Quadratic Equations in CAT QA

If you are preparing for the CAT QA section, understanding Linear and Quadratic Equations can significantly help you achieve a high score. These topics frequently appear in questions and also serve as the basis for more advanced problems in Algebra and Arithmetic. Recently, about 12 to 15% of QA questions in CAT exams related to Algebra have been directly on these topics, so it is essential to practise them.

Importance of Linear and Quadratic Equation Topics

• Linear and Quadratic equations topics keep appearing in CAT and other MBA entrance exams like XAT and SNAP in their straightforward forms or in the form of camouflaged word problems.
• Having a good grasp of them enhances your speed while performing tougher topics like inequalities, functions, or logarithms.

How to Prepare

• Reinforce foundations: Be comfortable with simultaneous equations, factorising, using the quadratic formula, and examining the nature of roots using the help of the discriminant.
• Practice mixed questions: Work on modulus equations, absolute value equations, and word problems that involve constructing equations from everyday life.
• Quick tips:
  • Use factorising if possible.
  • Use the quadratic formula if the roots are not factorable.
  • Split terms carefully for rational roots.
  • Split modulus questions into tractable cases.

Practical Tips

• Begin with linear equations to get a feel and idea, and then shift to quadratic equation topics and questions.
• Practice substituting options while solving MCQs under time limits. This is a good practice in the CAT's time-strapped scenario.
• Regular CAT mock tests and sectional tests should be attempted. It can be ensured that you eliminate careless mistakes and achieve accuracy at the right time by solving 20 to 25 algebra questions per week.

By focusing on key strategies, you can ace Linear and Quadratic equations in the CAT 2025 Quant section. Begin with easy and medium questions, taking care to maintain precision and pace. Apply shortcuts like substitution and option elimination to quickly solve questions. Practice frequent question types like word problems, ratios, and time-work. Avoid calculation mistakes and practice answers to gain confidence and overall CAT Quant scores. With 22 questions in 40 minutes, time management is very important; calm down and leave difficult questions for later to reach the highest marks.

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