Important Questions: CBSE Class 6 Mathematics Chapter 10 The Other Side of Zero
Chapter 10 The Other Side of Zero introduces integers—positive and negative whole numbers—and zero itself. This chapter forms the foundation for algebraic thinking in higher classes. CBSE exam papers typically allocate 4-6 marks to this chapter through a mix of 1-mark MCQs, 2-3 mark application problems, and occasionally a 5-mark case study. Below you will find 18 carefully curated questions mirroring actual CBSE patterns, complete with model answers to help you score full marks.
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Key takeaways
- ✓Chapter 10 typically carries 4-6 marks in CBSE Class 6 term exams, with questions on integer operations and number line representation.
- ✓Understanding negative numbers through real-life contexts like temperature below zero, debt, and depths below sea level is essential.
- ✓Sign errors during addition and subtraction of integers are the most common mistakes; always determine the operation and resultant sign carefully.
- ✓Number line questions test both plotting integers and understanding direction (left for negatives, right for positives).
- ✓Case-based questions often combine temperature changes, banking transactions, or elevation scenarios requiring multi-step integer operations.
- ✓Comparing integers: among negatives, the number with larger absolute value is actually smaller (e.g., -15 < -8).
- ✓Practice at least 15 varied questions to cover all question types: MCQ, VSA, short answer, long answer, and application-based problems.
Chapter Overview and Marks Weightage in CBSE Exam
The Other Side of Zero extends the number system beyond counting numbers into the realm of integers, both positive and negative. CBSE Class 6 Mathematics papers usually dedicate 4-6 marks to this chapter, distributed across objective (MCQ or fill-in-the-blank), very short answer (VSA), and short-answer questions. Occasionally, a case-based or application question worth 4-5 marks appears in term exams or sample papers. The chapter covers five core topics: introduction to integers, representation on the number line, comparing integers, addition and subtraction of integers, and real-life contexts such as temperature (degrees above and below zero), banking (credit and debit), and geography (depth below sea level and height above). Mastery of integer operations and number line plotting is critical because these concepts recur in Class 7 rational numbers and Class 8 linear equations.
- Typical weightage: 4-6 marks per term exam
- Question types: 1-2 MCQs, 1-2 VSAs, one 3-mark short answer, and sometimes one 4-5 mark case study
- Core skills tested: plotting on number line, ordering integers, adding/subtracting with correct signs, applying integers to real scenarios
- Difficulty level: Moderate; errors usually stem from sign confusion rather than concept gaps
1-Mark Questions (MCQ and Very Short Answer)
One-mark questions test quick recall and basic comprehension. Expect 2-3 such questions in your term exam. MCQs often ask you to identify the correct integer representation, compare two integers, or solve a simple addition/subtraction. Fill-in-the-blank or one-step numerical problems also appear. Practice these to build speed and accuracy, because every mark counts. Below are six representative 1-mark questions with model answers that mirror CBSE patterns. Pay attention to sign notation and number line direction, as these are frequent traps in objective questions. Even a small slip can cost you the entire mark, so double-check your work before moving to the next question during the actual exam.
2-Mark Questions (Short Answer Type)
Two-mark questions require a short working or explanation, typically one or two steps. They test whether you can apply integer rules correctly and show reasoning. Common formats include comparing a set of integers, performing addition or subtraction with explanation, or drawing a simple number line. CBSE marking schemes award 1 mark for method and 1 mark for the correct final answer, so always write your steps clearly. Below are four high-quality 2-mark questions with model answers. Practice writing concise yet complete solutions—avoid lengthy explanations but do not skip intermediate steps, especially sign changes and directional moves on the number line.
3-Mark Questions (Application and Reasoning)
Three-mark questions demand multi-step reasoning or application to a real-life scenario. You might compare multiple integers, solve a word problem involving temperature or banking, or explain a concept with a number line diagram. CBSE allocates 1 mark for correct method, 1 mark for intermediate working, and 1 mark for the final answer with proper units or statement. These questions assess conceptual clarity and the ability to translate words into integer operations. Below are four carefully designed 3-mark questions with full model answers. Write each step on a separate line during the exam; examiners award partial marks even if the final answer is wrong, provided your approach is sound.
5-Mark Questions and Case-Based Problems
Five-mark questions or case studies test comprehensive understanding and multi-step problem-solving. They integrate multiple sub-concepts—comparison, operations, and real-world application—in a single scenario. CBSE introduced case-based questions from 2021 onwards; expect a short paragraph describing a situation (e.g., mountaineering expedition with altitude changes, weekly temperature log, or a shopkeeper's profit-loss ledger) followed by 3-4 sub-questions totalling 4-5 marks. Award distribution is typically 1 mark per correct sub-answer plus 1 mark for correct interpretation. Below are two full case-based examples with model solutions. Read the case carefully, underline key numerical data, and tackle sub-questions one at a time. Show all working to earn partial credit even if you miss one sub-part.
How CBSE Frames Questions from This Chapter
CBSE question setters follow predictable patterns when designing integer questions. Objective questions (MCQ, true/false, fill-in-the-blank) test definitions and basic properties: recognising opposites, identifying the smallest or largest integer in a list, or choosing the correct operation. Short-answer questions (2-3 marks) typically embed integers in practical contexts—temperature changes, altitude (above or below sea level), profit and loss (credit and debit), or movement on a number line. Long-answer and case-based questions integrate multiple operations: you might need to compare, add, subtract, and interpret results in one go. Watch for keywords: 'below' or 'loss' or 'owe' signal negative integers; 'above' or 'gain' or 'rise' signal positive. CBSE also loves number line diagrams: you may be asked to plot integers, show an operation visually, or read positions from a given line. Familiarise yourself with the exact NCERT terminology—'opposite of an integer', 'absolute value' (though not named explicitly in Class 6, the concept appears), and 'ascending/descending order'—because examiners lift phrasing directly from the textbook.
- Objective questions: definitions, opposites, ordering, simple one-step operations
- 2-3 mark questions: real-world scenarios (temperature, banking, depth), number line plotting
- 4-5 mark case studies: multi-step problems with sub-questions on comparison, operations, interpretation
- Diagrams: number line sketches worth 1-2 marks; label clearly and use uniform scale
- Language cues: 'below', 'loss', 'descent', 'owe' → negative; 'above', 'gain', 'rise', 'credit' → positive
Common Mistakes Students Make and How to Avoid Them
Sign errors top the list of mistakes in integer questions. Students often write -3 + 5 = -8 by adding absolute values without considering different signs. Remember: different signs mean subtract and take the sign of the number with larger absolute value. Another frequent error is ordering negatives incorrectly; many assume -20 > -5 because 20 > 5, forgetting that among negatives, larger absolute value means smaller integer. On the number line, mixing up left and right is common—always recall that right is positive, left is negative. In word problems, students miss keywords: 'debt of ₹100' must be written as -100, not +100. Also, when temperature drops, you subtract; when it rises, you add—sounds obvious, yet under exam pressure, mistakes happen. Finally, in case-based questions, students skip intermediate steps to save time and lose method marks. Even if your final answer is wrong, showing -20 + 8 = -12 earns you partial credit. Write every step, double-check signs, and verify your answer by plotting on a rough number line if time permits. These small habits can boost your score by 3-4 marks per paper.
- Sign confusion: different signs → subtract absolute values, same signs → add and keep the sign
- Ordering negatives: -25 < -10 because -25 is farther left on the number line
- Number line direction: left = negative, right = positive; plot carefully with uniform spacing
- Keyword misreading: 'below', 'owe', 'loss', 'descent' → use negative integers
- Skipping steps: always write intermediate working to earn method marks even if final answer is incorrect
- Calculation errors: double-check subtraction; |-3 - 5| ≠ -3 + 5; it equals -8, not +2
Practice Strategy and Exam Preparation Tips
Start by reading NCERT Class 6 Mathematics Chapter 10 thoroughly and solving every in-text example and exercise question. NCERT questions form the backbone of CBSE papers; many exam questions are direct adaptations. Next, practice the 18 questions in this bank under timed conditions—allocate about 1 minute per mark, so a 5-mark question should take roughly 5 minutes. After solving, compare your answers with the model solutions provided here. If you made a mistake, write the correct solution again on a fresh sheet; this repetition reinforces the correct method. Create a personal error log: note down every mistake (sign error, ordering error, number line plotting error) and review it the night before the exam. Use the number line liberally during practice; visualising integer positions reduces abstract confusion. For case-based questions, underline all numerical data in the paragraph before attempting sub-questions. Finally, take at least two full-length sample papers or previous years' question papers that include Chapter 10. This builds exam temperament and reveals any lingering weak spots. If you need step-by-step photo-upload solving and doubt clearing at any hour, CBSETUTOR.ai offers a 24×7 AI tutor for Classes 6-12 at a flat ₹999/month for all subjects. Start with a 3-day free trial to experience instant solutions and personalised practice sets tailored to your learning pace.
- Solve all NCERT exercise questions first; CBSE papers mirror NCERT style and difficulty
- Time yourself: 1 minute per mark, so complete a 5-mark question in about 5 minutes
- Maintain an error log; review common mistakes (sign errors, ordering) before the exam
- Draw number lines even for practice; visualisation prevents abstract confusion
- Attempt 2-3 full sample papers to build speed and identify weak areas
- Use CBSETUTOR.ai for 24×7 doubt solving and personalised question banks; ₹999/month, 3-day free trial
Real-Life Contexts and Application Questions
CBSE emphasises real-world relevance, so Chapter 10 questions often feature temperature (meteorology), banking (credit and debit), geography (altitude and depth), and sports (golf scores below par). Understanding these contexts helps you set up the integer model correctly. For temperature, zero is the freezing point of water; temperatures below zero are negative. In banking, money you owe (loan, overdraft) is negative, money you have is positive. For altitude, sea level is zero; depths below sea level (submarine, mines) are negative, heights above (mountain peaks, aircraft) are positive. In sports like golf, par is zero; strokes below par are negative (better score), above par are positive. When you encounter a word problem, first identify the 'zero reference point', then assign positive or negative integers accordingly. Write a clear statement: 'Let sea level = 0 m; depth below = negative.' This one-line clarification can earn you a method mark and keeps your solution organised. Practice at least five application problems covering different contexts to build confidence in translation from words to integers.
- Temperature: 0°C is freezing; below zero → negative, above zero → positive
- Banking: credit/deposit → positive, debit/withdrawal/loan → negative
- Geography: sea level = 0; below sea level (depth) → negative, above (height) → positive
- Sports (golf): par = 0; below par → negative, above par → positive
- Always state your zero reference explicitly in the solution for clarity and method marks
Links to Higher Classes and Why This Chapter Matters
Integers are the gateway to algebra. In Class 7, you will extend integers to rational numbers (fractions and decimals, both positive and negative). Class 8 introduces linear equations in one variable, where you solve for unknowns that can be negative. Class 9 number systems and Class 10 polynomials both rely on fluent integer arithmetic. Even in practical life, you use integers every day: checking bank statements (credits and debits), reading weather forecasts (sub-zero temperatures), understanding elevation maps (below and above sea level), and interpreting sports scores. A solid grasp of integers now saves you from confusion later and builds the algebraic intuition needed for higher mathematics. Spend extra time on this chapter if you find negative numbers counterintuitive; the investment pays dividends across secondary school. Mastery here means you will breeze through rational number operations, directed numbers in physics, and coordinate geometry in Classes 9-10, where the Cartesian plane uses both positive and negative coordinates.
- Class 7: rational numbers (positive and negative fractions)
- Class 8: linear equations (solving for negative unknowns)
- Classes 9-10: number systems, polynomials, coordinate geometry (four quadrants with negatives)
- Real-life: banking, weather, altitude maps, sports scoring
- Strong integer foundation → easier algebra and smoother transition to higher maths
Frequently asked questions
How many marks does Chapter 10 The Other Side of Zero carry in the CBSE Class 6 exam?+
Typically 4-6 marks across term exams, distributed as 1-2 one-mark MCQs or fill-in-the-blanks, one or two 2-3 mark short-answer questions, and occasionally a 4-5 mark case-based or application problem.
What is the most common mistake students make with integer addition and subtraction?+
Sign errors are the biggest pitfall. Students add absolute values even when signs differ, forgetting that different signs mean subtract and take the sign of the number with the larger absolute value. For example, -8 + 5 should be -3, not -13.
How do I compare negative integers correctly?+
On the number line, the integer farther to the left is smaller. Among negatives, the one with the larger absolute value is actually smaller. For instance, -20 < -5 because -20 is farther left, even though 20 > 5 in magnitude.
Why does CBSE use real-life contexts like temperature and banking in integer questions?+
CBSE emphasises application and conceptual understanding. Real-world scenarios—temperature below zero, loan as debt, depth below sea level—make integers meaningful and test whether you can translate words into correct integer operations.
Should I draw a number line for every integer problem in the exam?+
Not mandatory for every problem, but highly recommended during practice and for questions that ask you to show operations visually. A quick sketch can prevent sign errors and earns you method marks even if the final answer is wrong.
How can I avoid losing marks in case-based questions on integers?+
Read the case paragraph carefully and underline all numerical data. Tackle each sub-question separately, write intermediate steps, and state your final answer with units. Even if one sub-part is incorrect, clear working earns partial credit.
Are there any shortcut tricks for adding and subtracting integers quickly?+
Remember: same signs → add absolute values and keep the sign; different signs → subtract absolute values and take the sign of the larger. Visualise movements on a number line: right for addition, left for subtraction. Practice builds speed naturally.
Where can I find more practice questions beyond NCERT for Chapter 10?+
Solve NCERT Exemplar problems, previous years' CBSE question papers, and sample papers from CBSE official website. For instant doubt-solving and personalised question banks, try CBSETUTOR.ai—₹999/month for all subjects, Classes 6-12, with a 3-day free trial.
What is the zero reference point in geography-based integer problems?+
Sea level is zero. Depths below sea level (submarine, valley floor) are negative; heights above sea level (mountain peak, aircraft altitude) are positive. Always state this reference in your solution for clarity.
How important is Chapter 10 for higher classes?+
Very important. Integers form the foundation for Class 7 rational numbers, Class 8 linear equations, and Classes 9-10 coordinate geometry and polynomials. Weak integer understanding creates gaps that widen in algebra and higher maths.
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