Practice Question Papers · with Answers

CBSE / NCERT Class 6 Maths Practice Question Papers

Download free CBSE / NCERT Class 6 Maths practice question papers with full answer keys. These are original Brain Grain model papers — built from our verified question bank to the real exam blueprint (sections, marks and solutions) — perfect for board revision and model tests.

Brain Grain · braingrain.in
Maths — Practice Paper · Set 1
Class: 6CBSE / NCERTMax Marks: 26
Name: ____________________Reg No: ____________
Part I — Multiple Choice Questions 2 × 1 = 2

Choose the correct answer. (Answer all questions.)

1.A square piece of paper is folded in half. The square is then cut into two rectangles along the fold. Regardless of the size of the square, one of the following statements is always true. Which statement is true here? a. The area of each rectangle is larger than the area of the square. b. The perimeter of the square is greater than the perimeters of both the rectangles added together. c. The perimeters of both the rectangles added together is always 1 1/2 times the perimeter of the square. d. The area of the square is always three times as large as the areas of both rectangles added together.a. The area of each rectangle is larger than the area of the square.b. The perimeter of the square is greater than the perimeters of both the rectangles added together.c. The perimeters of both the rectangles added together is always 1 1/2 times the perimeter of the square.d. The area of the square is always three times as large as the areas of both rectangles added together.[1]
2.Which of the following is not a name for this square? 1. PQSR 2. SPQR 3. RSPQ 4. QRSP1. PQSR2. SPQR3. RSPQ4. QRSP[1]
Part II — Short Answer Questions 12 × 2 = 24

Answer briefly. (Answer all questions.)

3.Which of the following numbers are prime: 23, 51, 37, 26?[2]
4.Compare the following fractions and justify your answers: a. 8/3, 5/2 b. 4/9, 3/7 c. 7/10, 9/14 d. 12/5, 8/5 e. 9/4, 5/2[2]
5.Find the prime factorisations of the following numbers: 64, 104, 105, 243, 320, 141, 1728, 729, 1024, 1331, 1000.[2]
6.Try to subtract: – 3 – (+ 5). How many zero pairs will you have to put in? What is the result?[2]
7.What happens when you start to add up hexagonal numbers, i.e., take 1, 1 + 7, 1 + 7 + 19, 1 + 7 + 19 + 37, … ? Which sequence do you get? Can you explain it using a picture of a cube?[2]
8.Add the following fractions using Brahmagupta’s method: a. 2/7 + 5/7 + 6/7 b. 3/4 + 1/3 c. 2/3 + 5/6 d. 2/3 + 2/7 e. 3/4 + 1/3 + 1/5 f. 2/3 + 4/5 g. 4/5 + 2/3 h. 3/5 + 5/8 i. 9/2 + 5/4 j. 8/3 + 2/7 k. 3/4 + 1/3 + 1/5 l. 2/3 + 4/5 + 3/7 m. 9/2 + 5/4 + 7/6[2]
9.We are the group of 5-digit numbers between 35,000 and 75,000 such that all of our digits are odd. Who is the largest number in our group? Who is the smallest number in our group? Who among us is the closest to 50,000?[2]
10.Can you create a similar table for 1/4?[2]
11.Always, Sometimes, Never? Below are some statements. Think, explore and find out if each of the statement is 'Always true', 'Only sometimes true' or 'Never true'. Why do you think so? Write your reasoning; discuss this with the class. a. 5-digit number + 5-digit number gives a 5-digit number b. 4-digit number + 2-digit number gives a 4-digit number c. 4-digit number + 2-digit number gives a 6-digit number d. 5-digit number - 5-digit number gives a 5-digit number e. 5-digit number - 2-digit number gives a 3-digit number[2]
12.If the game is played for the numbers 1 to 90, find out: a. How many times would the children say ‘idli’ (including the times they say ‘idli-vada’)? b. How many times would the children say ‘vada’ (including the times they say ‘idli-vada’)? c. How many times would the children say ‘idli-vada’?[2]
13.Find the common factors of: a. 20 and 28 b. 35 and 50 c. 4, 8 and 12 d. 5, 15 and 25[2]
14.Draw two figures other than a circle and a square that have both reflection symmetry and rotational symmetry.[2]
🔑 Show Answer Key — Set 1
  1. 1. c.
  2. 2. PQSR.
  3. 3. $23$ and $37$ .
  4. 4. a. $\frac{8}{3}>\frac{5}{2}$ ; b. $\frac{4}{9}>\frac{3}{7}$ ; c. $\frac{7}{10}>\frac{9}{14}$ ; d. $\frac{12}{5}>\frac{8}{5}$ ; e. $\frac{9}{4}<\frac{5}{2}$ .
  5. 5. $64=2^6$ ; $104=2^3\times13$ ; $105=3\times5\times7$ ; $243=3^5$ ; $320=2^6\times5$ ; $141=3\times47$ ; $1728=2^6\times3^3$ ; $729=3^6$ ; $1024=2^{10}$ ; $1331=11^3$ ; $1000=2^3\times5^3$ .
  6. 6. Put in $5$ zero pairs; the result is $-8$ .
  7. 7. You get cube numbers: $1,8,27,64,\ldots$ .
  8. 8. a. $\frac{13}{7}$ ; b. $\frac{13}{12}$ ; c. $\frac{3}{2}$ ; d. $\frac{20}{21}$ ; e. $\frac{77}{60}$ ; f. $\frac{22}{15}$ ; g. $\frac{22}{15}$ ; h. $\frac{49}{40}$ ; i. $\frac{23}{4}$ ; j. $\frac{62}{21}$ ; k. $\frac{77}{60}$ ; l. $\frac{199}{105}$ ; m. $\frac{83}{12}$ .
  9. 9. If repetition of digits is allowed: largest is 73,999, smallest is 35,111 and closest to 50,000 is 51,111. If digits are not repeated: largest is 73,951, smallest is 35,179 and closest to 50,000 is 51,379.
  10. 10. $\frac{1}{4}$ is one quarter; $\frac{1}{4}+\frac{1}{4}$ is two quarters; $\frac{1}{4}+\frac{1}{4}+\frac{1}{4}$ is three quarters; $\frac{1}{4}+\frac{1}{4}+\frac{1}{4}+\frac{1}{4}$ is four quarters.
  11. 11. a. Only sometimes true. b. Only sometimes true. c. Never true. d. Only sometimes true. e. Never true.
  12. 12. a. $30$ times; b. $18$ times; c. $6$ times.
  13. 13. a. $1,2,4$ ; b. $1,5$ ; c. $1,2,4$ ; d. $1,5$ .
  14. 14. Examples: a regular hexagon and an equilateral triangle.
Brain Grain · braingrain.in
Maths — Practice Paper · Set 2
Class: 6CBSE / NCERTMax Marks: 26
Name: ____________________Reg No: ____________
Part I — Multiple Choice Questions 2 × 1 = 2

Choose the correct answer. (Answer all questions.)

1.A square piece of paper is folded in half. The square is then cut into two rectangles along the fold. Regardless of the size of the square, one of the following statements is always true. Which statement is true here? a. The area of each rectangle is larger than the area of the square. b. The perimeter of the square is greater than the perimeters of both the rectangles added together. c. The perimeters of both the rectangles added together is always 1 1/2 times the perimeter of the square. d. The area of the square is always three times as large as the areas of both rectangles added together.a. The area of each rectangle is larger than the area of the square.b. The perimeter of the square is greater than the perimeters of both the rectangles added together.c. The perimeters of both the rectangles added together is always 1 1/2 times the perimeter of the square.d. The area of the square is always three times as large as the areas of both rectangles added together.[1]
2.Which of the following is not a name for this square? 1. PQSR 2. SPQR 3. RSPQ 4. QRSP1. PQSR2. SPQR3. RSPQ4. QRSP[1]
Part II — Short Answer Questions 12 × 2 = 24

Answer briefly. (Answer all questions.)

3.Now join A to other grid points in the figure by a straight line to get a right angle. What are all the different ways of doing it?[2]
4.Write three pairs of prime numbers less than 20 whose sum is a multiple of 5.[2]
5.What could be so special about these grids? Is the magic in the numbers or the way they are arranged or both? Can you make more such grids?[2]
6.The following pictograph shows the number of books borrowed by students, in a week, from the library of Middle School, Ginnori: a. On which day were the minimum number of books borrowed? b. What was the total number of books borrowed during the week? c. On which day were the maximum number of books borrowed? What may be the possible reason?[2]
7.Suppose you start with ₹0 in your bank account, and then you have debits of ₹1, 2, 4, 8, 16, 32, 64, and 128, and then a single credit of ₹256. What is your bank account balance now?[2]
8.Draw the letter 'Y' such that the three angles formed are 150°, 60° and 150°.[2]
9.Complete the additions using tokens. a. (+ 6) + (+ 4) b. (– 3) + (– 2) c. (+ 5) + (– 7) d. (– 2) + (+ 6)[2]
10.Look at the list of primes till 100. What is the smallest difference between two successive primes? What is the largest difference?[2]
11.2024 is a leap year (as February has 29 days). Leap years occur in the years that are multiples of 4, except for those years that are evenly divisible by 100 but not 400. a. From the year you were born till now, which years were leap years? b. From the year 2024 till 2099, how many leap years are there?[2]
12.Estimate the number of holidays you get in a year including weekends, festivals and vacation. Then, try to get an exact number and see how close your estimate is.[2]
13.How does the farthest distance between X and Y compare with the length of AC? BD?[2]
14.Can you explain each of Brahmagupta’s rules in terms of Bela’s Building of Fun, or in terms of a number line?[2]
🔑 Show Answer Key — Set 2
  1. 1. c.
  2. 2. PQSR.
  3. 3. Join $A$ to any grid point lying on a line through $A$ that is perpendicular to line $AB$ .
  4. 4. Examples: $(2,3)$ , $(3,7)$ , and $(2,13)$ .
  5. 5. The special feature is in both the numbers and their arrangement.
  6. 6. a. Thursday; b. $24$ books; c. Saturday.
  7. 7. $Rs\ 1$ .
  8. 8. Draw a Y with the upper two arms separated by $60^\circ$ , and each upper arm making $150^\circ$ with the lower stem on the outside.
  9. 9. a. $+10$ ; b. $-5$ ; c. $-2$ ; d. $+4$ .
  10. 10. Smallest difference: $1$ ; largest difference: $8$ .
  11. 11. a. The answer depends on the student's birth year. b. $19$ leap years.
  12. 12. A sample estimate is about 120 holidays in a year.
  13. 13. The farthest distance between $X$ and $Y$ is equal to $AC$ or $BD$ .
  14. 14. Yes. Each rule describes movement on the number line or in the lift.
Brain Grain · braingrain.in
Maths — Practice Paper · Set 3
Class: 6CBSE / NCERTMax Marks: 26
Name: ____________________Reg No: ____________
Part I — Multiple Choice Questions 2 × 1 = 2

Choose the correct answer. (Answer all questions.)

1.A square piece of paper is folded in half. The square is then cut into two rectangles along the fold. Regardless of the size of the square, one of the following statements is always true. Which statement is true here? a. The area of each rectangle is larger than the area of the square. b. The perimeter of the square is greater than the perimeters of both the rectangles added together. c. The perimeters of both the rectangles added together is always 1 1/2 times the perimeter of the square. d. The area of the square is always three times as large as the areas of both rectangles added together.a. The area of each rectangle is larger than the area of the square.b. The perimeter of the square is greater than the perimeters of both the rectangles added together.c. The perimeters of both the rectangles added together is always 1 1/2 times the perimeter of the square.d. The area of the square is always three times as large as the areas of both rectangles added together.[1]
2.Which of the following is not a name for this square? 1. PQSR 2. SPQR 3. RSPQ 4. QRSP1. PQSR2. SPQR3. RSPQ4. QRSP[1]
Part II — Short Answer Questions 12 × 2 = 24

Answer briefly. (Answer all questions.)

3.Can you help Rihan and Sheetal find their answers?[2]
4.Suppose the number of children is kept the same, but the number of units that are being shared is increased? What can you say about each child’s share now? Why? Discuss how your reasoning explains 1/5 < 2/5, 3/7 < 4/7 and 1/2 < 5/8.[2]
5.Construct a rectangle in which one of the diagonals divides the opposite angles into 45° and 45°. What do you observe about the sides?[2]
6.Compare the following numbers using the Building of Fun and fill in the boxes with < or >. a. – 2 __ +5 b. – 5 __ + 4 c. – 5 __ – 3 d. + 6 __ – 6 e. 0 __ – 4 f. 0 __ + 4[2]
7.Draw a picture and write an addition statement as above to show: a. 5 times 1/4 of a roti b. 9 times 1/4 of a roti[2]
8.Can you think of other examples where mathematics helps us in our everyday lives?[2]
9.Find any three numbers that are multiples of 25 but not multiples of 50.[2]
10.Draw a rectangle of size 12 units × 8 units. Draw another rectangle inside it, without touching the outer rectangle that occupies exactly half the area.[2]
11.Fill a table such that the cell having the second largest number is not a supercell but the second smallest number is a supercell. Is it possible?[2]
12.The number of tigers in India went down drastically between 1900 and 1970. Project Tiger was launched in 1973 to track and protect the tigers in India. Starting in 2006, the exact number of tigers in India was tracked. Shagufta and Divya looked up information about the number of tigers in India between 2006 and 2022 in four-year intervals. They prepared a frequency table for this data and a bar graph to present this data, but there are a few mistakes in the graph. Can you find those mistakes and fix them?[2]
13.Are the following pairs of numbers co-prime? Guess first and then use prime factorisation to verify your answer. a. 30 and 45 b. 57 and 85 c. 121 and 1331 d. 343 and 216[2]
14.Make some more Collatz sequences like those above, starting with your favourite whole numbers. Do you always reach 1? Do you believe the conjecture of Collatz that all such sequences will eventually reach 1? Why or why not?[2]
🔑 Show Answer Key — Set 3
  1. 1. c.
  2. 2. PQSR.
  3. 3. Rihan can draw infinitely many lines through one point. Sheetal can draw exactly one line through two given distinct points.
  4. 4. Each child's share becomes larger when more units are shared among the same number of children.
  5. 5. The rectangle becomes a square; adjacent sides are equal.
  6. 6. a. $<$ ; b. $<$ ; c. $<$ ; d. $>$ ; e. $>$ ; f. $<$ .
  7. 7. a. $\frac{1}{4}+\frac{1}{4}+\frac{1}{4}+\frac{1}{4}+\frac{1}{4}=\frac{5}{4}$ ; b. nine quarters $=\frac{9}{4}=2\frac{1}{4}$ .
  8. 8. Yes. Mathematics helps in shopping, cooking, reading time, measuring distance, counting money, planning travel, sharing food equally, measuring cloth, designing buildings and comparing scores in games.
  9. 9. $25,75,$ and $125$ .
  10. 10. The inner rectangle should have area $48$ square units.
  11. 11. Yes. One valid row is $2,1,3,4,5,6,7,9,8$ .
  12. 12. The bars for 2006, 2010, 2014, and 2018 are incorrect and should be corrected to match the table.
  13. 13. a. No; b. Yes; c. No; d. Yes.
  14. 14. Example sequences: starting at 28 gives 28, 14, 7, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1. Starting at 19 gives 19, 58, 29, 88, 44, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1.

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Class 6 does not have a public board examination, so there are no official board question papers for this class. The papers above are Brain Grain practice papers built to the standard exam pattern — ideal for unit tests, monthly tests and revision.

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