Preparing for the Class 6 Maths Half Yearly Examination becomes easier with regular practice and proper revision. This Class 6 Maths Model Test Paper is designed to help students assess their understanding of important concepts covered in the half-yearly syllabus.
The sample paper covers key chapters including Patterns in Mathematics, Lines and Angles, Number Play, Data Handling and Presentation, and Prime Time. It includes a variety of questions to strengthen mathematical concepts, improve problem-solving skills, and build confidence for the examination.
Students can use this Class 6 Mathematics Sample Paper as a practice test to revise important topics, identify areas that need improvement, and become familiar with the type of questions they may encounter in their Half Yearly Exam.
Chapters Covered:
- Patterns in Mathematics
- Lines and Angles
- Number Play
- Data Handling and Presentation
- Prime Time
Try to solve the paper independently within the given time and check your answers afterward. Regular practice with model papers can help students improve accuracy, speed, conceptual understanding, and exam readiness.
SECTION A: MULTIPLE CHOICE QUESTIONS (10 × 1 = 10 Marks)
1. What is the 6th triangular number in the sequence 1, 3, 6, 10, 15, …?
(a) 20 (b) 21 (c) 28 (d) 36
2. An angle whose measure is greater than 180° and less than 360° is called:
(a) An obtuse angle (b) A straight angle
(c) A reflex angle (d) An acute angle
3. At 4 o’clock, the angle formed between the hour hand and the minute hand of a clock is:
(a) 90° (b) 120° (c) 150° (d) 60°
4. The remainder of Question 4 is cut off in the supplied screenshot; its complete wording cannot be recovered accurately.
5. The remainder of Question 5 is cut off in the supplied screenshot; its complete wording cannot be recovered accurately.
6. In a pictograph, if 1 symbol (■) = 5 students, how many symbols are required to represent 35 students?
(a) 5 (b) 6 (c) 7 (d) 8
7. The only even prime number is:
(a) 0 (b) 1 (c) 2 (d) 4
8. Which of the following pairs of numbers are co-prime?
(a) 15 and 39 (b) 18 and 35
(c) 30 and 415 (d) 81 and 18
9. A number is divisible by 8 if:
(a) Its last digit is 8
(b) The sum of its digits is divisible by 8
(c) The number formed by its last two digits is divisible by 8
(d) The number formed by its last three digits is divisible by 8
10. What sequence do you get when you add consecutive pairs of triangular numbers (1 + 3, 3 + 6, 6 + 10, 10 + 15, …)?
SECTION B: VERY SHORT ANSWER QUESTIONS (6 × 2 = 12 Marks)
11. Without adding term-by-term, compute the sum of the first 12 odd counting numbers:
1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 + 23.
Explain the mathematical pattern/rule used.
12. In the given figure, line BR is a straight line. If ∠TER = 80° and ∠SER = 90°:
(a) Find the measure of ∠BET.
(b) Find the measure of ∠SET.
13. I am a 5-digit palindrome number: I am an odd number; my tens (t) digit is double my units (u) digit; my hundreds (h) digit is double my tens (t) digit; my thousands digit is 1 more than my hundreds digit; my ten-thousands digit is the same as my thousands digit. Find the number and write it in words.
14. Check whether 8536 is divisible by 4 and whether 14560 is divisible by 8. Show the divisibility rule/working.
15. Find all common factors of 20 and 28.
16. State whether each statement is Always True, Sometimes True, or Never True. The individual statements are cut off in the supplied screenshot.
SECTION C: SHORT ANSWER QUESTIONS (6 × 3 = 18 Marks)
17. Patterns in Geometry:
(a) Count the number of line segments in complete graphs K₂, K₃, K₄, K₅.
(b) Which special number sequence does this form?
(c) How many lines will the complete graph K₇ contain?
18. Angle Bisectors & Types:
(a) If a straight angle of 180° is bisected, what is the measure and name of each resulting angle?
(b) If each resulting angle from part (a) is bisected again, what is the measure of each smaller angle formed?
(c) Classify an angle measuring 135°.
19. Supercell Puzzle:
A cell in a grid is called a supercell if the number in it is strictly greater than all of its adjacent/neighbouring cells.
(a) Can a cell with the smallest number in a table ever be a supercell? Why or why not?
(b) Arrange the digits 1, 2, 3, 4, 5, 6, 7, 8, 9 in a row of 9 cells such that you get the maximum possible number of supercells. How many supercells did you obtain?
20. Find the prime factorisation of 1728 using the factor tree or repeated division method. Express it in product form.
21. The Ashoka Chakra:
The Ashoka Chakra on the Indian national flag has 24 equally spaced spokes.
(a) What is the angle between two consecutive spokes?
(b) What is the largest acute angle that can be formed between any two spokes?
22. A survey of 120 school students asked about their preferred leisure activity. The table gives:
- Playing – 45
- Reading story books – 30
- Watching TV – 20
- Painting – 15
- Listening to music – 10
Answer the questions based on this data.
SECTION D: LONG ANSWER QUESTIONS (3 × 4 = 12 Marks)
23. Collatz Conjecture & Powers of 2:
(a) Explain the two rules of the Collatz sequence for even and odd numbers.
(b) Write down the complete Collatz sequence starting from the number 13 until it reaches 1.
(c) Why does any starting number that is a power of 2 (e.g., 16, 32, 64) always reach 1 directly without increasing?
24. Number Properties & Prime Tests:
(a) Write down all the prime numbers between 90 and 100.
(b) Find seven consecutive composite numbers between 1 and 100.
(c) Write two numbers whose product is 10000 such that neither of the two numbers has 0 as its units digit.
25. Constructing & Interpreting Data:
The table below shows the number of saplings planted by a school club during a week of “Van Mahotsav”:
- Monday – 50
- Tuesday – 40
- Wednesday – 30
- Thursday – 40
- Friday – 50
- Saturday – 60
- Sunday – 40
(a) What was the total number of saplings planted during the entire week?
(b) On which day was the maximum number of saplings planted, and on which day was the minimum planted?
(c) If you represent this data on a vertical bar graph with a scale of 1 unit length = 10 saplings, find the height (in units) of the bars for Tuesday and Saturday.
SECTION E: CASE-BASED / SOURCE-BASED INTEGRATED QUESTIONS (2 × 4 = 8 Marks)
26. Case Study 1: The Idli-Vada Game & LCM
A mathematics teacher conducts the “Idli-Vada” circle game in class. Students count in order: 1, 2, 3, …; multiples of 4 say “idli”; multiples of 6 say “vada”; common multiples of both 4 and 6 must say “idli-vada”.
Based on this context, answer:
(i) What is the very first number at which a student calls out “idli-vada”? (1 mark)
(ii) If the game is played up to 60, how many times in total will “idli-vada” be called out? (1 mark)
(iii) Are the numbers 4 and 6 co-prime? Justify your answer using prime factorisation. (2 marks)
27. Case Study 2: Height of Global Peaks (Infographics)
A geography and mathematics interdisciplinary project recorded the highest peaks across continents:
- Asia (Everest) – 8848 m
- South America (Aconcagua) – 6962 m
- North America (Denali) – 6194 m
- Africa (Kilimanjaro) – 5895 m
- Europe (Elbrus) – 5642 m
- Australia (Kosciuszko) – 2228 m
Based on this data, answer:
(i) How much taller is Mount Everest than Mount Kosciuszko? (1 mark)
(ii) If an infographic represents mountain heights using triangular shapes where taller peaks are also drawn wider at the base, why might this be mathematically misleading? (1 mark)
(iii) The supplied screenshot cuts off the remainder of this sub-question after “If an artist chooses a scale of 1 unit = 1000 m for a column…”. The exact remaining wording is not visible, so it has not been invented.
