The CAT 2023 will be conducted in three sessions and is a mandatory requirement for admission to various management programs offered by IIMs.
The CAT 2023 syllabus includes questions in three key areas: Quantitative Aptitude (QA), Verbal Ability and Reading Comprehension (VARC), and Data Interpretation and Logical Reasoning (DILR).
In this article, we will discuss how to prepare for the Algebra section of Quantitative Aptitude (QA). The Algebra section includes topics like linear and quadratic equations, inequalities, functions, graphs, and progressions.
Understand the Basics: Start by building a strong foundation in algebra. Understand concepts like linear and quadratic equations, inequalities, functions, graphs, and progressions. Ensure you know the fundamentals well.
Learn Key Formulas: Memorize essential algebraic formulas and identities. This will help you solve problems more efficiently during the exam.
Here are five key algebraic formulas that are useful for the CAT exam’s Algebra section:
- Quadratic Equation Formula:
- The solutions for a quadratic equation, ax² + bx + c = 0, are given by the quadratic formula:
- x = (-b ± √(b² – 4ac)) / (2a)
- Arithmetic Progression (AP) Formula:
- The nth term of an arithmetic progression with the first term ‘a’ and common difference ‘d’ is given by:
- An = a + (n – 1)d
- Geometric Progression (GP) Formula:
- The nth term of a geometric progression with first term ‘a’ and common ratio ‘r’ is given by:
- An = a * r^(n – 1)
- Quadratic Equation Discriminant:
- The discriminant, D, of a quadratic equation ax² + bx + c = 0 determines the nature of its solutions:
- D = b² – 4ac
- If D > 0, the equation has two distinct real solutions.
- If D = 0, the equation has one real solution (a repeated root).
- If D
- Inequalities Formula:
- For solving linear inequalities, you can use rules like:
- If a > b, then a + c > b + c (Adding the same value to both sides of an inequality).
- If a > b and c > 0, then ac > bc (Multiplying both sides of an inequality by a positive value).
These formulas are essential for solving various types of algebraic problems in the CAT exam’s Quantitative Aptitude section. Understanding and applying these formulas will help you approach algebra questions more effectively.
ALSO READ: CAT 2023 — 10 Tips to Prepare for Logical Reasoning Questions
Practice Regularly: Practice is the key to success. Solve a variety of algebra problems from different sources, including CAT preparation books, online resources, and previous year’s question papers.
Time Management: While practising, focus on improving your speed and accuracy. Time management is crucial in the CAT exam, so practice solving problems within time constraints.
Use Study Materials: Utilize CAT preparation books and study materials specifically designed for the exam. These resources often contain a wide range of algebra problems.
Online Mock Tests: Take online mock tests and CAT sample papers. These simulate the real exam environment and help you gauge your performance.
Analyze Your Mistakes: After solving problems, review your mistakes and understand the concepts you struggled with. Focus on improving in those areas.
Seek Help: If you find certain algebraic concepts challenging, don’t hesitate to seek help from mentors, teachers, or online tutorials. It’s essential to clarify your doubts.
Create a Study Schedule: Develop a study plan that allocates sufficient time for each topic, including algebra. Consistency is key.
Focus on Weaknesses: Identify your weaknesses within the algebra section and dedicate more time to improving in those areas.
Practice Mental Calculation: Develop your mental calculation skills to perform quick calculations during the exam. This will save time.
Stay Relaxed: Maintain a positive mindset and stay relaxed during the exam. Stress can affect your performance.
Simultaneous Equations: Practice solving systems of linear equations and simultaneous equations. These often appear in CAT questions.
Inequalities and Progressions: Understand the properties and rules of inequalities and arithmetic and geometric progressions. These are frequently tested in the CAT exam.
Graphs and Functions: Be familiar with various types of functions and their graphs. Practice interpreting and manipulating them.
Previous Year’s Papers: Solve previous year’s CAT question papers to get a sense of the types of algebra questions that have been asked in the past.
Take Breaks: While studying, remember to take short breaks to refresh your mind. Overexertion can lead to burnout.
Stay Updated: Stay updated with the latest CAT exam pattern and changes in the syllabus. The official CAT website is a valuable resource for this information.
Here are some examples to solve
Question: Solve the equation 2x^2 + 5x – 3 = 0.
Question: Find the roots and intercepts of the equation y = 3x^2 – 4x + 2.
Question: Sketch the graph of the equation y = x^2 – 2x – 3.
Question: Factor the expression 2x^2 + 7x – 15.
Question: A car travels at a constant speed of 50 mph for 2 hours. How far does it travel?
Question: Two workers can complete a job in 3 hours working together. If one worker can complete the job in 6 hours, how long can the other worker complete the job on their own?
Question: A company sells widgets for $20 each. The company’s variable cost per widget is $10. What is the company’s breakeven point?
Question: A mixture of water and alcohol has a volume of 10 litres. The mixture is 40% alcohol. How much alcohol must be added to the mixture to make the alcohol concentration 50%?
Question: A company wants to minimize the cost of producing a box with a volume of 100 cubic inches. The cost of the material for the box is $0.10 per square inch. What are the dimensions of the box that will minimize the cost?
These are just a few examples, and many other types of questions could be asked. The best way to prepare for the CAT exam is to practice solving a variety of linear and quadratic equations.