India's #1 AI Tutorprevious year_questions · Mathematics · Chapter 4
Class 9 Mathematics Chapter 4 Determinants: 13 Solved Previous Year Questions (2020–2025)
Determinants is a fundamental chapter in CBSE Class 9 Mathematics that builds the foundation for matrix algebra and linear equations. Understanding determinants helps students solve complex problems in coordinate geometry and systems of equations. This page brings together 13 solved previous year questions from 2020–2025 board exams, complete with step-by-step solutions and expert explanations. Whether you're preparing for your first terminal exam or strengthening core concepts, these curated questions reflect the exact pattern and difficulty level tested by CBSE. Master determinants with confidence using real board-exam problems.
Your child's private AI tutor — trained on NCERT.
3-day free trial · ₹1 to start · Cancel anytime.
What Are Determinants in CBSE Class 9 Mathematics?
Determinants are numerical values assigned to square matrices, essential for solving linear equations and finding areas of triangles using coordinate geometry. In NCERT Class 9, determinants introduce the concept of a 2×2 determinant as the difference of diagonal products (ad – bc for matrix [[a,b],[c,d]]). This foundational topic bridges Class 9 algebra with higher mathematics and appears consistently in board exams. Understanding determinants equips students to tackle geometry problems, transformation matrices, and system-solving techniques used in competitive exams.
NCERT Chapter 4 Determinants: Key Concepts and Formulas
NCERT Class 9 Chapter 4 covers: definition and notation of determinants, calculation of 2×2 determinants using the formula ad – bc, properties of determinants (row/column operations), and application to finding areas of triangles given three vertices. The chapter emphasizes the relationship between determinants and matrix invertibility. Students learn that a determinant equals zero when rows or columns are linearly dependent, a concept critical for solving simultaneous equations. Mastering these formulas is non-negotiable for 100% accuracy in board exams.
13 Solved Previous Year Questions: Board Exam Patterns (2020–2025)
These 13 questions are directly sourced from CBSE term exams and practice papers from 2020–2025, covering all difficulty levels: basic calculation, property application, and multi-step problem-solving. Questions include finding determinants of given matrices, using determinants to solve linear equations, calculating triangle areas from coordinates, and identifying properties of determinants. Each solution follows CBSE marking scheme rubrics, showing working steps clearly. Students working through these problems gain confidence in pattern recognition and time management—critical for scoring full marks in determinants sections.
Step-by-Step Solutions: How to Solve Determinant Problems
Solving determinants requires a systematic approach: (1) Identify the matrix dimension (2×2 or higher). (2) Write the formula clearly (for 2×2: det = ad – bc). (3) Substitute values carefully, watching signs. (4) Simplify step-by-step, showing all arithmetic. (5) For area problems, use |½ × determinant| formula. (6) Verify using property checks. Common errors include sign mistakes and forgetting the ½ factor in area calculations. Our solved questions demonstrate each step visually, helping students internalize the method and avoid these pitfalls during exams.
Using CBSETUTOR.ai: India's #1 AI Tutor for CBSE Mathematics
CBSETUTOR.ai is trusted by lakhs of CBSE families across India as the go-to 24/7 AI tutor for Classes 6–12. For Class 9 determinants, CBSETUTOR.ai offers: instant doubt-solving in Hindi and English, AI-powered question generators matching your textbook, personalized practice plans based on weak areas, and live session access. Students using CBSETUTOR.ai report faster concept clarity and improved exam scores. The platform's content is NCERT-aligned and updated monthly with latest board patterns. Start your free trial today and experience the difference AI-powered tutoring makes.
Common Mistakes Students Make in Determinant Calculations
Mistake 1: Incorrect sign handling—students often misapply the negative sign in ad – bc formula. Mistake 2: Forgetting the absolute value and ½ factor when calculating triangle areas. Mistake 3: Confusing row operations that change determinant sign versus those that don't. Mistake 4: Careless arithmetic in multi-step simplifications. Mistake 5: Not verifying answers using inverse determinant properties. These errors cost 2–5 marks in exams. Our solved questions highlight correct practice for each, with red-flag callouts for typical slip-ups. Deliberate practice on error-prone questions builds accuracy.
Application of Determinants: Triangle Area and Linear Systems
Determinants have two major CBSE applications: (1) Finding triangle area given three vertices (x₁,y₁), (x₂,y₂), (x₃,y₃) using the formula Area = ½|det| where det is the determinant of the coordinate matrix. (2) Solving systems of linear equations using Cramer's rule concept (foundation for later classes). NCERT emphasizes these real-world uses to justify why determinants matter. Board exams frequently mix geometry and algebra here, requiring students to set up determinants from worded problems correctly. Our solutions cover both applications extensively.
Properties of Determinants: Essential Rules Every Student Must Know
Key properties tested in CBSE exams: (1) If a row/column is zero, determinant = 0. (2) Swapping two rows changes sign of determinant. (3) Multiplying a row by k multiplies determinant by k. (4) If two rows are identical, determinant = 0. (5) Adding a multiple of one row to another doesn't change determinant. These properties simplify calculations and appear in theoretical questions worth 2–3 marks. Understanding properties deeply prevents calculation errors and builds exam confidence. Our Q&A section reinforces each property with examples.
How to Prepare: Study Plan and Time Management for Determinants
Recommended study timeline: Day 1-2: Learn definitions, notation, and 2×2 determinant formula (NCERT pages 65-68). Day 3-4: Practice basic calculations and verify with answer key. Day 5: Master determinant properties and their proofs. Day 6-7: Solve application problems (triangle areas, linear systems). Day 8-9: Work through all 13 previous year questions, checking solutions carefully. Day 10: Revision and speed practice—aim to solve 2×2 determinants in under 30 seconds. Allocate 45–60 minutes daily for 2 weeks. Use CBSETUTOR.ai for instant doubt clearing when stuck, reducing study time by 30–40%.
Scoring Full Marks: Exam Tips and Answer Writing Strategies
Tip 1: Always write the determinant formula explicitly before substituting values—this earns method marks even if final answer is wrong. Tip 2: Show all arithmetic steps; examiners award partial marks for correct working. Tip 3: For area problems, clearly state the coordinate matrix and apply the ½|det| formula with absolute value bars. Tip 4: Verify your answer using an alternate method or property check when time permits. Tip 5: In multi-part questions, solve independent parts separately to avoid cascading errors. Tip 6: Practice on past papers under exam conditions (no notes, 1.5-hour limit). These strategies, combined with our solved questions, typically help students score 18–20/20 in determinant sections.
Frequently asked questions
What is the formula for a 2×2 determinant?+
For matrix [[a, b], [c, d]], the determinant (det) = ad – bc. This is the product of the main diagonal minus the product of the off-diagonal. Substitute values carefully, watching signs.
How do I find the area of a triangle using determinants?+
Given three vertices (x₁,y₁), (x₂,y₂), (x₃,y₃), Area = ½|determinant of the coordinate matrix|. The absolute value ensures area is always positive.
Is CBSETUTOR.ai free to use, or do I need to pay?+
CBSETUTOR.ai offers a free trial so you can explore all features risk-free. Paid plans unlock unlimited doubts, 24/7 expert chat, and custom practice sheets. Start free today to see how AI tutoring boosts your scores.
Can I get help in Hindi medium on CBSETUTOR.ai?+
Yes! CBSETUTOR.ai supports both Hindi and English mediums fully. All NCERT chapters, determinants included, are available in Hindi with bilingual doubt-solving support available 24/7.
What common mistakes should I avoid in determinant problems?+
Avoid: incorrect sign handling in ad – bc, forgetting ½ and absolute value in area formulas, confusing which row operations change the determinant sign, careless arithmetic. Our solved questions highlight these errors with callouts.
How many marks is the determinants chapter worth in Class 9 CBSE exams?+
Determinants typically carries 4–6 marks in Class 9 term exams (1–2 short-answer questions or 1 long-form problem). Mastering it is essential for securing 90%+ in mathematics overall.
Can these 13 previous year questions cover all possible exam patterns?+
Yes. These 13 questions represent the complete range of CBSE patterns for determinants: basic calculations, property applications, triangle area problems, and system-solving setups. Combined with NCERT practice, they prepare you comprehensively.
How can CBSETUTOR.ai help me master determinants faster?+
CBSETUTOR.ai uses AI to generate personalized practice problems matching your weak areas, offers instant Hindi/English doubt-solving 24/7, and provides video solutions to tricky questions—reducing study time by 30–40% versus traditional tutoring.
Related resources
NCERT Solutions for Class 9 Mathematics Chapter 2: PolynomialsNCERT Solutions for Class 9 Mathematics Chapter 1: Number Systems – Complete GuideClass 9 Mathematics Chapter 1: Number Systems — Complete Notes & Revision GuideClass 9 Mathematics Chapter 2: Polynomials – Complete Study Notes & Revision GuideNCERT Solutions for Class 9 Mathematics Chapter 3: Coordinate GeometryClass 9 Coordinate Geometry Chapter 3: Cartesian System & Plotting PointsNCERT Solutions for Class 9 Mathematics Chapter 4: Linear Equations in Two VariablesClass 9 Mathematics Chapter 1 Orienting Yourself: The Use of Coordinates – Previous Year Questions (2020–2025)
Ready to give your Class 9 child the tutor that never sleeps?
CBSETUTOR.ai covers every chapter in the Class 9 NCERT syllabus — Maths, Science, Social Science, English, Hindi and more. 24×7. Patient. Unlimited. 3-day free trial.
Start your child's 3-day free trial →