CBSE Class 6 Mathematics Chapter 10 The Other Side of Zero Worksheet with Answers

This printable worksheet is designed for CBSE Class 6 students studying Chapter 10 – The Other Side of Zero – from the NCERT Mathematics textbook. The worksheet comprises six distinct sections with varying difficulty levels, from basic multiple-choice questions to higher-order thinking problems and a case-study-based question. The difficulty level is MODERATE, suitable for students who have completed the chapter once and want to consolidate their understanding. The suggested time to complete this worksheet is 60 minutes under exam conditions, though students may take longer during initial practice. Parents and teachers should encourage students to attempt all sections in sequence without looking at the answer key first. Each question has been carefully crafted to align with the 2025 CBSE examination pattern and NCERT terminology. The answer key provided at the end includes brief explanations to help students learn from their mistakes and understand the reasoning behind each correct answer. Students should keep a notebook handy to show all working, especially for arithmetic questions involving addition and subtraction of integers.

Before you begin the worksheet, here is a quick recap of the essential concepts from Chapter 10. Integers are an extension of the whole numbers and include negative numbers as well. The complete set of integers is {..., −3, −2, −1, 0, 1, 2, 3,...}. Zero is the dividing point: numbers greater than zero are positive integers, and numbers less than zero are negative integers. On the number line, positive integers appear to the right of zero and negative integers to the left. The farther right a number is, the greater its value. This is why −1 is greater than −10, even though 10 is greater than 1 in the world of natural numbers. Every integer has an opposite: the opposite of +7 is −7, and the opposite of −4 is +4. Integers have numerous real-life applications. Temperatures can drop below zero degrees Celsius (negative temperatures), sea levels are measured as heights above sea level (positive) or depths below sea level (negative), and financial transactions include profits (positive) and losses (negative). Addition and subtraction of integers follow consistent rules that students must practice to internalize. For instance, subtracting a negative integer is equivalent to adding its positive counterpart: 5 − (−3) = 5 + 3 = 8.

This section contains six multiple-choice questions designed to test your foundational understanding of integers, number line representation, and basic properties. Each question has four options, and only one is correct. Read each question carefully, especially those involving negative numbers, as the signs can be tricky. Remember that the value of an integer is determined by its position on the number line, not by the size of the numeral alone. For example, −100 is less than −1 because it lies farther to the left on the number line. When comparing integers, always visualize or sketch a quick number line if needed. MCQs often test conceptual clarity rather than computational ability, so focus on understanding the 'why' behind each answer. These questions cover introduction to integers, properties of zero, comparison of integers, and identification of integers in real-life situations. Attempt all six questions and mark your answers clearly. Each correct answer earns you 1 mark, and there is no negative marking. Take approximately 8-10 minutes for this section, ensuring you do not spend too much time on any single question.

This section comprises six fill-in-the-blank statements that require you to recall key terminology, definitions, and properties of integers from Chapter 10. Each blank corresponds to a single word, number, or short phrase directly related to NCERT Class 6 Mathematics content. Unlike MCQs, you must produce the answer from memory rather than recognize it among options. Pay close attention to the context of each sentence. For example, if a sentence discusses the number line, think about the direction of increase (left to right) and the properties of negative and positive integers. Blanks may ask for specific integers, definitions such as 'integers', 'opposite', or 'zero', or properties like 'neither positive nor negative'. Spelling and exact terminology matter, so ensure your answers match the language used in your NCERT textbook. These questions test both conceptual understanding and precise recall. Allocate around 6-8 minutes for this section. Write your answers neatly on the worksheet or in your notebook, maintaining the question numbers for easy cross-referencing with the answer key later. This section carries a total of 6 marks.

Section C presents six statements about integers, number lines, and operations. Your task is to determine whether each statement is True or False. This format tests your ability to evaluate the correctness of mathematical assertions, a skill essential for logical reasoning and critical thinking. Some statements may appear obviously true or false, while others are designed to be subtle and require careful thought. For instance, a statement like 'Zero is a positive integer' is false because zero is neither positive nor negative, as clearly stated in the NCERT textbook. When you encounter a statement involving comparisons (such as '−8 is greater than −3'), visualize the number line: −3 is to the right of −8, so −3 is greater, making the statement false. Do not rush through this section; even a single word like 'always', 'never', 'all', or 'some' can change the truth value of a statement. Write 'True' or 'False' next to each statement number. Each correct answer earns 1 mark, for a total of 6 marks in this section. Budget approximately 6-8 minutes. If a statement seems ambiguous, consider the definitions and properties covered in Chapter 10 of your NCERT Class 6 Mathematics textbook.

This section contains five short-answer questions, each carrying 3 marks. These questions require you to write brief explanations, perform simple calculations, or illustrate concepts using examples or diagrams. Unlike objective-type questions, short-answer questions demand that you demonstrate your understanding through written responses. A complete answer typically includes a clear statement, the necessary working or reasoning, and a final answer. For example, if asked to arrange a set of integers in ascending order, you should write the integers in the correct sequence and may also draw a number line to support your answer. Marks are often awarded in steps: one mark for the correct method or reasoning, one mark for accurate computation, and one mark for the final answer. Therefore, even if your final answer is incorrect due to a calculation error, you can still earn partial credit by showing proper working. Each question should take 3-4 minutes to complete. Use your notebook or the worksheet margins for rough work, and write your final answers neatly. This section tests your ability to apply concepts of integers to solve problems involving comparison, ordering, real-life contexts, and simple arithmetic operations. Total marks for Section D: 15.

Section E comprises three long-answer or higher-order thinking skills (HOTS) questions, each worth 4 marks. These questions are designed to challenge your deeper understanding and ability to apply concepts of integers to complex or unfamiliar situations. HOTS questions may involve multi-step problem solving, analysis of real-life scenarios, or explanation of why certain mathematical statements are true or false. For example, you might be asked to solve a word problem involving temperature changes over several hours, requiring you to perform multiple additions and subtractions with negative integers. Or you might need to explain the concept of opposite integers using examples from daily life. Each question should be answered in a structured manner: begin by identifying what is given and what is required, then show all steps of your working clearly, and conclude with a well-stated final answer. Marks are distributed across understanding the problem (1 mark), correct method and reasoning (2 marks), and accurate final answer (1 mark). Allocate 12-15 minutes for this section, spending about 4-5 minutes per question. These questions assess your analytical thinking, problem-solving skills, and ability to communicate mathematical ideas clearly. Total marks for Section E: 12.

The case study question presents a real-world scenario involving integers, followed by a set of sub-questions that you must answer based on the information provided. This format, increasingly common in CBSE examinations, tests your ability to extract relevant data, interpret it mathematically, and apply your knowledge of Chapter 10 concepts. A typical case study in this chapter might describe a city's temperature fluctuations over a week, bank account transactions showing deposits and withdrawals, or elevation data for different geographical locations relative to sea level. You will be given a short paragraph (4-6 sentences) setting up the context, followed by 3-4 sub-questions worth 1-2 marks each, totaling 5 marks. Read the case study passage carefully, underlining or highlighting key numerical information and relationships. Then attempt each sub-question in order, referring back to the passage as needed. Show all calculations clearly. This section assesses your comprehension skills alongside your mathematical ability, making it a holistic test of learning. Allocate about 8-10 minutes for the case study. Even if you find one sub-question difficult, attempt the others, as they are often independent of one another.

The answer key below provides correct answers for all sections of the worksheet, along with brief explanations to help you understand the reasoning. After completing the worksheet on your own, use this key to check your answers and identify areas that need more practice. For objective questions (MCQs, fill-ups, true/false), the answers are straightforward. For subjective questions (short answer, long answer, case study), compare your method and working with the model solutions provided. If your approach differs but is mathematically sound, you may still award yourself full or partial credit. Pay special attention to questions you answered incorrectly: revisit the relevant section in your NCERT Class 6 Mathematics textbook, review your class notes, or seek help from a teacher or tutor. Consistent practice using worksheets like this one builds confidence and ensures you are well-prepared for term exams. If you need personalized support, platforms like CBSETUTOR.ai offer 24×7 AI-powered tutoring where you can upload photos of tricky questions and receive step-by-step solutions – all for a flat fee of ₹999 per month across all subjects and classes 6-12, with a 3-day free trial to get started. Regular revision and self-assessment using such worksheets are key strategies for mastering integers and scoring well in CBSE examinations.

1. Which of the following is an integer? (a) 1.5 (b) −3 (c) 2/3 (d) 0.75. Answer: (b) −3. Explanation: Integers are whole numbers and their negatives; decimals and fractions are not integers. 2. The integer 0 is: (a) Positive (b) Negative (c) Neither positive nor negative (d) Both positive and negative. Answer: (c) Neither positive nor negative. Zero is the dividing point between positive and negative integers. 3. Which is greater: −10 or −2? (a) −10 (b) −2 (c) Both are equal (d) Cannot be determined. Answer: (b) −2. On the number line, −2 is to the right of −10, so it is greater. 4. The opposite of +15 is: (a) −15 (b) 15 (c) 0 (d) 1/15. Answer: (a) −15. Opposite integers are equidistant from zero but on opposite sides. 5. How many integers lie between −3 and +3? (a) 5 (b) 6 (c) 7 (d) 4. Answer: (a) 5. The integers are −2, −1, 0, 1, 2 (excluding −3 and +3). 6. Sea level is represented by which integer? (a) +1 (b) −1 (c) 0 (d) +10. Answer: (c) 0. Sea level is the reference point, hence represented by zero.

Section B (Fill in the Blanks): 1. The set of integers includes positive numbers, negative numbers, and zero. 2. On the number line, integers increase as we move from left to right. 3. The opposite of −20 is +20 or 20. 4. Zero is neither positive nor negative. 5. An integer greater than −5 but less than −1 is −4, −3, or −2 (any one). 6. The temperature 3 degrees below zero is written as −3°C. Section C (True/False): 1. True – Every positive integer is greater than every negative integer. 2. False – Zero is not a negative integer; it is neutral. 3. True – The opposite of a negative integer is a positive integer. 4. False – −8 is less than −3, not greater. 5. True – Integers are used to represent temperatures above and below freezing. 6. True – The integer 0 is greater than all negative integers. Section D (Short Answer): 1. Arrange −9, 4, −1, 0, 7 in ascending order. Answer: −9, −1, 0, 4, 7. 2. Write the integer representing 500 m below sea level. Answer: −500. 3. What is the successor of −6 on the number line? Answer: −5. 4. Compare −15 and −20 using > or <. Answer: −15 > −20. 5. If temperature drops from 2°C to −3°C, by how many degrees did it fall? Answer: 2 − (−3) = 5 degrees. Section E (Long Answer/HOTS): 1. A lift starts at ground floor (0), goes up 5 floors (+5), then down 8 floors. Where is it now? Answer: 5 − 8 = −3, i.e., 3 floors below ground (basement level 3). 2. Explain with examples why −1 is greater than −100. Answer: On the number line, −1 is closer to zero and lies to the right of −100, hence greater. Example: −1°C is warmer than −100°C. 3. A shopkeeper had a profit of ₹200 on Monday, a loss of ₹150 on Tuesday, and a profit of ₹50 on Wednesday. What is the net result? Answer: 200 + (−150) + 50 = 100. Net profit of ₹100. Section F (Case Study): Case: The table shows temperatures in five cities: Delhi 5°C, Shimla −2°C, Leh −10°C, Mumbai 25°C, Srinagar −5°C. (i) Which city is coldest? Answer: Leh (−10°C). (ii) Which city is warmest? Answer: Mumbai (25°C). (iii) Arrange cities in ascending order of temperature. Answer: Leh, Srinagar, Shimla, Delhi, Mumbai. (iv) What is the difference between the highest and lowest temperatures? Answer: 25 − (−10) = 35°C.