Kendriya Vidyalaya Sangathan
Periodic Test 1 (PT-1) — 2026–27
Class: VII
Subject: Mathematics (Ganita Prakash)
Time Allowed: 90 Minutes
Maximum Marks: 40
Marks Blueprint & Chapter Breakdown
| Section | Question Type | No. of Questions | Marks per Question | Total Marks |
| Section A | Multiple Choice Questions (MCQs) | 5 | 1 | 5 |
| Section B | Very Short Answer (VSA) | 4 | 2 | 8 |
| Section C | Short Answer (SA) | 4 | 3 | 12 |
| Section D | Long Answer (LA) | 3 | 5 | 15 |
| Total | 16 | 40 Marks |
Chapter 1: Large Numbers Around Us ~ 13 Marks
Chapter 2: Arithmetic Expressions ~ 13 Marks
Chapter 3: A Peek Beyond the Point ~ 14 Marks
SECTION A: Multiple Choice Questions (1 Mark Each)
Q1. What is 1 crore written in numbers as per the Indian System of Numeration? (Chapter 1)
(a) $10,000$
(b) $1,00,000$
(c) $10,00,000$
(d) $1,00,00,000$
Q2. Which of the following equals the fraction $\dfrac{7}{10}$ in decimal form? (Chapter 3)
(a) $7.0$
(b) $0.7$
(c) $0.07$
(d) $70.0$
Q3. According to the order of operations (BODMAS), which operation should be performed first in the expression $15 - (4 + 2) \times 2$? (Chapter 2)
(a) Subtraction
(b) Addition inside brackets
(c) Multiplication
(d) Subtraction from 15
Q4. How many one-tenths make 1 whole unit? (Chapter 3)
(a) 1
(b) 10
(c) 100
(d) $0.1$
Q5. Estimation of $4,892 + 3,105$ rounded off to the nearest thousand is: (Chapter 1)
(a) $7,000$
(b) $8,000$
(c) $8,500$
(d) $9,000$
SECTION B: Very Short Answer Questions (2 Marks Each)
Q6. Insert commas according to the Indian System of Numeration and write the number name for:
(Chapter 1)
Q7. Simplify the expression step-by-step: (Chapter 2)
Q8. Convert the mixed fraction $4 \dfrac{3}{10}$ into a decimal and write its expansion in terms of units and one-tenths. (Chapter 3)
Q9. State whether the following statement is True or False, and give a reason:
"Changing the order of numbers in subtraction does not change the result." (Chapter 2)
SECTION C: Short Answer Questions (3 Marks Each)
Q10. The population of three towns in a district are $2,45,600$, $1,89,750$, and $3,12,400$.
(a) Find the total population of the district.
(b) How much greater is the population of the largest town compared to the smallest town? (Chapter 1)
Q11. Solve the following arithmetic expressions: (Chapter 2)
(a) $18 + 6 \div 3 - 2 \times 4$
(b) $5 \times (12 - 4) \div 2$
Q12. Arrange the following numbers in increasing (ascending) order: (Chapter 3)
Q13. A piece of cloth measures $12 \dfrac{4}{10}\text{ meters}$. A tailor cuts away $6 \dfrac{7}{10}\text{ meters}$ from it. Calculate the length of the remaining cloth piece. (Chapter 3)
SECTION D: Long Answer / Case-Based Questions (5 Marks Each)
Q14. (Case Study - Large Numbers in Daily Life) (Chapter 1)
A state library has $1,25,000$ books in total. Out of these, $45,230$ are in English, $38,900$ are in Hindi, and the rest are regional language books.
(a) Find the number of regional language books in the library. (2 Marks)
(b) Express the total number of books ($1,25,000$) in expanded form. (1.5 Marks)
(c) Round off the total number of English books ($45,230$) to the nearest hundred. (1.5 Marks)
Q15. (Order of Operations) (Chapter 2)
(a) Simplify completely:
(3 Marks)
(b) Frame a mathematical expression using brackets for the given phrase, and then solve it:
"Subtract 4 from 10, then multiply the result by 6." (2 Marks)
Q16. (Measurement & Decimal Application) (Chapter 3)
Sonu is measuring different stationery items using a ruler divided into tenths:
Pencil length = $3 \text{ units and } 4 \text{ one-tenths}$
Eraser length = $1 \text{ unit and } 8 \text{ one-tenths}$
Sharpener length = $2 \text{ units and } 5 \text{ one-tenths}$
(a) Write the length of each item as a fractional expression (e.g., $3 \dfrac{4}{10}$) and convert each to decimal form. (3 Marks)
(b) Find the total combined length of the pencil and the sharpener. (2 Marks)
SECTION A: MCQs (1 Mark Each)
Q1. Answer: (d) $1,00,00,000$
Solution: 1 crore is represented as 1 followed by 7 zeros in the Indian system ($1,00,00,000$).
Q2. Answer: (b) $0.7$
Solution: $\dfrac{7}{10}$ means 7 divided by 10, which places the decimal point one digit to the left of 7, giving $0.7$.
Q3. Answer: (b) Addition inside brackets
Solution: Per BODMAS, operation inside brackets $(4 + 2)$ must be evaluated first.
Q4. Answer: (b) 10
Solution: $10 \times \dfrac{1}{10} = 1$. Ten one-tenths equal 1 whole unit.
Q5. Answer: (b) $8,000$
Solution:
$4,892 \rightarrow 5,000$ (rounded to nearest thousand)
$3,105 \rightarrow 3,000$ (rounded to nearest thousand)
Estimated Sum $= 5,000 + 3,000 = 8,000$.
SECTION B: Very Short Answer (2 Marks Each)
Q6.
Commas: $8,54,32,109$ (1 Mark)
Number Name: Eight crore fifty-four lakh thirty-two thousand one hundred nine. (1 Mark)
Q7.
Step 1 (Innermost Bracket): $8 - 3 = 5 \implies 25 - [10 + 5]$ (1 Mark)
Step 2 (Square Bracket & Subtract): $25 - 15 = 10$ (1 Mark)
Q8.
Decimal conversion: $4 \dfrac{3}{10} = 4 + 0.3 = 4.3$ (1 Mark)
Expansion: $4 \text{ units} + 3 \text{ one-tenths} = 4 + \dfrac{3}{10}$ (1 Mark)
Q9.
Answer: False (1 Mark)
Reason: Subtraction is not commutative. For example, $8 - 3 = 5$, but $3 - 8 = -5$, which gives a different result. (1 Mark)
SECTION C: Short Answer (3 Marks Each)
Q10.
(a) Total Population:
$$2,45,600 + 1,89,750 + 3,12,400 = 7,47,750 \text{ inhabitants}$$(1.5 Marks)
(b) Difference:
$$\text{Largest } (3,12,400) - \text{Smallest } (1,89,750) = 1,22,650$$(1.5 Marks)
Q11.
(a) $18 + 6 \div 3 - 2 \times 4$
Division first: $18 + 2 - 2 \times 4$
Multiplication next: $18 + 2 - 8$
Addition & Subtraction: $20 - 8 = 12$ (1.5 Marks)
(b) $5 \times (12 - 4) \div 2$
Brackets first: $5 \times 8 \div 2$
Division next: $5 \times 4 = 20$ (1.5 Marks)
Q12.
Convert all mixed/improper fractions to decimal forms to compare easily:
$$\dfrac{4}{10} = 0.4, \quad 4 \dfrac{1}{10} = 4.1, \quad \dfrac{41}{10} = 4.1, \quad 41 \dfrac{1}{10} = 41.1$$Ascending Order:
$$\dfrac{4}{10} < 4 \dfrac{1}{10} = \dfrac{41}{10} < 41 \dfrac{1}{10}$$(or $0.4 < 4.1 \le 4.1 < 41.1$) (3 Marks)
Q13.
Total Cloth: $12 \dfrac{4}{10} = \dfrac{124}{10} \text{ m}$
Cut Cloth: $6 \dfrac{7}{10} = \dfrac{67}{10} \text{ m}$ (1 Mark)
Remaining Cloth:
$$\dfrac{124}{10} - \dfrac{67}{10} = \dfrac{124 - 67}{10} = \dfrac{57}{10} = 5 \dfrac{7}{10} \text{ meters (or } 5.7\text{ m)}$$(2 Marks)
SECTION D: Long Answer / Case-Based (5 Marks Each)
Q14.
(a) Regional books:
$$\text{English + Hindi} = 45,230 + 38,900 = 84,130$$$$\text{Regional Language Books} = 1,25,000 - 84,130 = 40,870$$(2 Marks)
(b) Expanded form of 1,25,000:
$$1,25,000 = (1 \times 1,00,000) + (2 \times 10,000) + (5 \times 1,000)$$(1.5 Marks)
(c) Round off 45,230 to nearest hundred:
Tens digit is $3 (< 5)$, so round down.
Result: $45,200$ (1.5 Marks)
Q15.
(a) Simplify: $100 - \{20 + 2 \times (15 - 5)\}$
Innermost bracket: $100 - \{20 + 2 \times 10\}$
Multiplication inside curly brace: $100 - \{20 + 20\}$
Resolve curly brace: $100 - 40 = 60$ (3 Marks)
(b) Expression:
$$\text{Phrase: } (10 - 4) \times 6$$(1 Mark)
$$\text{Solution: } 6 \times 6 = 36$$(1 Mark)
Q16.
(a) Fractional and Decimal conversion:
Pencil: $3 \dfrac{4}{10} = 3.4 \text{ units}$
Eraser: $1 \dfrac{8}{10} = 1.8 \text{ units}$
Sharpener: $2 \dfrac{5}{10} = 2.5 \text{ units}$ (3 Marks)
(b) Combined length (Pencil + Sharpener):
$$3.4 + 2.5 = 5.9 \text{ units } \left(\text{or } 5 \dfrac{9}{10} \text{ units}\right)$$(2 Marks)
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