🧮 Mock Test : 1– Chapter 3: A Story of Numbers (NEP 2025 format)
Subject: Mathematics
Level: Class 8
Chapter: 3 – A Story of Numbers
Time: 60 minutes Marks: 40
Competency Focus:
- Understanding evolution and diversity of number systems
- Analyzing mathematical ideas (base, place value, representation)
- Applying arithmetic reasoning to ancient systems
- Connecting mathematics with human history and culture
Section A: Objective Type (1×10 = 10 marks)
Choose the most appropriate answer.
-
Which ancient civilization used a base-60 number system?
(A) Egyptian (B) Mesopotamian (C) Mayan (D) Chinese -
The Roman numeral system is NOT suitable for which of the following?
(A) Counting up to 20 (B) Writing years (C) Performing multiplication (D) Representing 10 -
The symbol 0 as both a placeholder and a number was first fully developed in:
(A) Greece (B) Arabia (C) India (D) Egypt -
The term place value means:
(A) The name given to a number
(B) The position of a digit determining its value
(C) Counting by 5s
(D) Writing numerals with landmarks -
The Egyptian number system was a __________ system.
(A) Base-5 (B) Base-10 (C) Base-12 (D) Base-60 -
Who popularised the Hindu numerals in Europe through his book Liber Abaci?
(A) Aryabhata (B) Brahmagupta (C) Fibonacci (D) Al-Khwārizmī -
The Gumulgal people counted mainly in groups of:
(A) Two (B) Five (C) Ten (D) Twenty -
What mathematical tool did the Romans use for computations?
(A) Rods (B) Abacus (C) Counting stones (D) Tally bones -
The Mayan civilisation developed their number system independently with a base close to:
(A) 10 (B) 20 (C) 60 (D) 100 -
The digit forms (0–9) that we use today originated:
(A) In India (B) In Arabia (C) In Persia (D) During the Renaissance
Section B: Very Short Answer (2×5 = 10 marks)
Answer briefly in one or two sentences.
- What are landmark numbers in a number system? Give one example from the Roman system.
- Name the two mathematicians through whose works the Indian numerals reached the Arab world.
- Why is 0 (zero) essential in a place value system?
- Mention one advantage of a base-n system over a tally or Roman system.
- What is a one-to-one mapping in counting?
Section C: Short Answer (3×5 = 15 marks)
Answer in 3–5 sentences. Use diagrams/examples where needed.
-
Describe how ancient people used tally marks or bones to represent numbers.
- Mention two archaeological examples.
-
Explain the concept of base with reference to Egyptian and base-5 systems.
- Include what “powers of a base” means.
-
Compare the Roman and Hindu number systems in terms of:
- (a) Symbols
- (b) Ease of arithmetic operations
- (c) Use of zero
-
The Mesopotamian system sometimes caused confusion.
- Explain why spacing or blank positions created ambiguity and how it was later resolved.
-
Describe how the Hindu number system influenced world mathematics.
- Include its journey from India to Europe.
Section D: Application & Higher-Order Thinking (5 marks)
Answer any one.
- Suppose there were no symbol for zero in today’s number system.
- What challenges would we face in writing or computing numbers?
- Give at least two examples demonstrating these challenges.
OR
- Imagine you are an ancient scholar creating your own system of writing numbers.
- Choose a base (for example, base 4 or base 8).
- Create symbols for 1–4 (or 1–8).
- Show how you would write the number 25 using your system.
(Bonus marks for clear visualisation and logic!)
Section E: Reflection & Integration (Optional Enrichment – not for marks)
Think, discuss, or write in your journal.
🪔 The chapter called India’s invention of zero one of humanity’s greatest intellectual achievements.
Do you agree? Why do you think this single symbol changed the world?
Give examples of where zero shapes your life today — in technology, finance, or science.
Marking Scheme Summary (for teachers or self-evaluation)
| Section | Type | Marks | Focus Skills |
|---|---|---|---|
| A | Objective | 10 | Recall & conceptual clarity |
| B | Very Short | 10 | Understanding & concise expression |
| C | Short | 15 | Reasoning & explanation |
| D | HOTS | 5 | Creativity & deeper conceptual reasoning |
This mock test is designed based on the content of Chapter 3, "A Story of Numbers," emphasizing conceptual understanding, historical evolution, and comparative analysis, as is often prioritized in modern pedagogical frameworks like the suggested NEP 2025 approach.
Mock Test-2 : Chapter 3 – A Story of Numbers
Maximum Marks: 30
Time Allotted: 60 Minutes
General Instructions:
- This test consists of three sections (A, B, and C).
- All questions are compulsory.
- Use of notes or external aids is strictly prohibited.
- Current date reference: November 07, 2025.
Section A: Multiple Choice Questions (1 Mark Each)
1. Reema's father mentioned that the civilization that first used the symbols shown in the chapter (like T, TT, TTT) flourished in:
a) The Indus Valley
b) Mesopotamia
c) The Mayan region
d) Ancient China
2. The method of associating each object being counted with a corresponding stick or pebble, ensuring no two objects map to the same mark, is known as:
a) Place value mapping
b) Base-10 representation
c) One-to-one mapping
d) Landmark grouping
3. What is the primary drawback of the Roman numeral system that hindered efficient arithmetic operations like multiplication and division?
a) It lacked symbols for zero.
b) It did not use landmark numbers.
c) The grouping/rearranging rule for obtaining the next value was not consistently based on a single size (base).
d) It was exclusively a base-5 system.
4. In a base- number system, the landmark numbers are defined as the powers of starting from:
a)
b) and
c)
d) and only
5. The Babylonian (Mesopotamian) number system is primarily identified by its base, which is:
a) Base-10
b) Base-20
c) Base-60 (Sexagesimal system)
d) Base-5
6. The concept that represents the highest point in the history of number system evolution, where the position of a symbol determines its landmark value, is called:
a) Positional Number System (Place Value System)
b) Tally Marking
c) Landmark Numeration
d) Grouping by Twos
Section B: Conceptual Understanding and Comparison (2 Marks Each)
7. Define the term 'numeral' as used in the context of written number systems. Give one example from the Hindu system and one from the Roman system.
8. Explain the difference between the counting methods used by the Gumulgal people (counting in 2s up to 6) and the system used by the Egyptian civilization in terms of their landmark number concepts.
9. In the context of the Egyptian number system, what is the significance of the symbol (representing 10) relative to the symbol | (representing 1)? How does this structure relate to the definition of a base-n system?
10. Why is the Hindu-Arabic numeral system considered highly efficient for performing arithmetic operations compared to the Roman system? Reference the property of the digit zero in your answer.
11. The Mesopotamian system utilized a placeholder symbol for 'zero'. Explain one ambiguity or defect that remained in their system despite having this placeholder.
Section C: Analytical and Higher Order Thinking (HOTs) Questions (4 Marks Each)
12. Analyze the transition from non-positional systems (like Roman or Egyptian grouping) to positional systems (like Mesopotamian or Hindu). What foundational mathematical idea made the Hindu system universally superior in eliminating ambiguity?
14. Consider the Mayan Number System (almost base-20). They used $1, 20, 360, 7200, \dots as landmark numbers. Why is this sequence (\1, 20, 20\times18, 20^2 \times 18, \dots$) considered not a true base-20 system, and how does this relate to the limitations observed in number systems based on grouping by a fixed size?
Answer Key (For Reference Only)
Section A: MCQs
- b) Mesopotamia
- c) One-to-one mapping
- c) The grouping/rearranging rule for obtaining the next value was not consistently based on a single size (base). (e.g., grouping by 1s, 5s, and 10s arbitrarily).
- c)
- c) Base-60 (Sexagesimal system)
- a) Positional Number System (Place Value System)
Section B: Conceptual Understanding and Comparison
7. Numeral Definition: Numerals are the symbols used to represent numbers in a written number system.
- Hindu Example: 5, 9, 0.
- Roman Example: V, X, I.
8. Comparison of Landmark Concepts:
- Gumulgal: Used counting by a fixed group size (2) repeatedly to form names, but this system was only explicit up to 6 (). It lacked a systematic way to represent powers beyond this structure.
- Egyptian: Used a system where each landmark number was 10 times the previous one (powers of 10: $1, 10, 100, \dots$). This is a base-10 structure, but it is not positional; one must write out every required symbol (e.g., 324 requires three 100s symbols).
9. Significance of and Base Relation:
- The symbol (10) is the next landmark number obtained by grouping 10 collections of the previous landmark number (| = 1).
- This exemplifies the concept of a base: the next landmark number is obtained by multiplying the current landmark number by a fixed factor ().
10. Efficiency of Hindu System: The Hindu system's efficiency comes from two aspects related to zero:
- Place Value: Zero acts as a required positional digit, allowing symbols (1-9) to represent powers of 10 without ambiguity (e.g., 307 vs 37).
- Arithmetic Properties: Zero is treated as a number itself, enabling the establishment of algebraic structures like the ring, which underpins modern arithmetic rules (like the distributive law shown in the text).
11. Mesopotamian Ambiguity: Even with a placeholder symbol, ambiguity existed because the placeholder was primarily used in the middle of numbers (to separate powers of 60) and not consistently at the end. Therefore, a numeral representing only a power of 60 (like $1 \times 3600$) might look identical to a numeral representing a smaller quantity if the final placeholder was omitted.
Section C: Analytical and HOTs Questions
12. Transition to Positional Systems:
- Transition: Non-positional systems (Roman, early Egyptian) required a new, distinct symbol for every new power/landmark number, leading to unwieldy representations for large numbers (e.g., for 1000, for 100, etc., or writing out $1000 \times$ symbol).
- Hindu Superiority (Eliminating Ambiguity): The Hindu system's key breakthrough was not just using place value (which Mesopotamians also did) but the explicit use of zero (0) as a digit that can occupy any position, ensuring unambiguous representation across all powers, including at the end of a number.
13. Laplace Quote Analysis (Numeral 375):
- a) Absolute Value (1 Mark): The absolute value of a digit is the inherent value it represents regardless of its position. In 375, the absolute value of the digit '7' is simply 7.
- b) Place Value (3 Marks): The place value is the absolute value multiplied by the landmark number corresponding to its position. In 375, the digit '7' is in the tens place. Its place value is .
14. Mayan System Analysis:
- Why not true base-20? A true base-20 system would have landmark numbers as successive powers of 20: , , , , etc.
- Mayan Sequence: The Mayan sequence is $1, 20, 360, 7200, \dots20^2$).
- Relation to Base Limitations: This deviation (using 360 instead of 400) shows that the Mayan system adopted a modified positional structure, likely influenced by astronomical/calendrical factors (360 days in a year approximation) rather than strictly adhering to the pure mathematical definition of a base-n system where the multiplier () is constant between all successive powers. This lack of strict mathematical consistency impacts its reliability for generalized computation compared to a pure base-10 system.
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