6th Maths - Quarterly Exam 2024 - Original Question Paper | Thanjavur Dsitrict | English Medium

6th Std Maths Quarterly Exam 2024 - Solutions

QUARTERLY COMMON EXAMINATION – 2024 Subject: MATHS Std: 6 Time: 2.00 Hrs. Marks: 60

I Choose the correct answer. (10 X 1 = 10)

1. 1 billion is equal to

a) 100 crore    b) 100 million    c) 100 lakh    d) 10000 lakh

Answer: a) 100 crore

Explanation: 1 billion = 1,000,000,000. 1 crore = 1,00,00,000. Therefore, 1 billion = 100 x 1,00,00,000 = 100 crore.

2. The estimation to the nearest hundred of 76812 is

a) 77000    b) 76000    c) 76800    d) 76900

Answer: c) 76800

Explanation: To round to the nearest hundred, we look at the tens digit. In 76812, the tens digit is 1. Since 1 is less than 5, we keep the hundreds digit (8) as it is and change the tens and ones digits to zero. So, the estimated number is 76800.

3. Which of the following expressions is not zero?

a) 0 X 0    b) 0 + 0    c) 2 / 0    d) 0 / 2

Answer: c) 2 / 0

Explanation: Division by zero is undefined, not zero. 0 X 0 = 0, 0 + 0 = 0, and 0 / 2 = 0.

4. The number of days in 'w' weeks is

a) 30 + w    b) 30 w    c) 7 + w    d) 7 w

Answer: d) 7 w

Explanation: There are 7 days in one week. So, in 'w' weeks, the number of days is 7 multiplied by w, which is 7w.

5. The ratio of the number of sides of a triangle to the number of sides of a rectangle is

a) 4 : 3    b) 3 : 4    c) 3 : 5    d) 3 : 2

Answer: b) 3 : 4

Explanation: A triangle has 3 sides. A rectangle has 4 sides. The ratio is 3 to 4, written as 3:4.

6. An equivalent ratio of 4 : 7 is

a) 1 : 3    b) 8 : 15    c) 14 : 8    d) 12 : 21

Answer: d) 12 : 21

Explanation: To find an equivalent ratio, multiply both parts of the ratio by the same non-zero number. 4 x 3 = 12 and 7 x 3 = 21. So, 4:7 is equivalent to 12:21.

7. If a barbie doll costs Rs. 90, then the cost of 3 such dolls is Rs.

a) 260    b) 270    c) 30    d) 93

Answer: b) 270

Explanation: Cost of 1 doll = Rs. 90. Cost of 3 dolls = 3 x 90 = Rs. 270.

8. A line is denoted as

a) AB    b) → over AB    c) ↔ over AB    d) ‾ over AB

Answer: c) ↔ over AB   

Explanation: A line extends indefinitely in both directions, which is denoted by a double-headed arrow over the letters representing two points on the line.

9. The tally marks for the number 7 in standard form is

Answer: b) |||| ||

Explanation: Tally marks are grouped in fives. The number 7 is represented as a group of five (||||) and two additional marks (||).

10. The representation of "one picture to many objects" in a pictograph is called

a) Tally mark    b) Pictoword    c) scaling    d) frequency

Answer: c) scaling

Explanation: In a pictograph, scaling is the key used to define how many objects each picture represents (e.g., 1 car picture = 100 cars).

II Fill in the blanks. (5 X 1 = 5)

11. The largest 8 digit number is ____________.

Answer: 99,999,999

12. The algebraic statement of 'S divided by 5' is ____________.

Answer: S / 5

13. Ratio of 75 paise to Rs. 2 = ____________.

Answer: 3 : 8

Explanation: Convert Rs. 2 to paise: Rs. 2 = 200 paise. The ratio is 75 : 200. Dividing both by their greatest common divisor (25), we get 3 : 8.

14. A line through two end points 'A' and 'B' is denoted by ____________.

Answer:

15. The tally marks for number 8 in standard form is ____________.

Answer:

III True (or) False. (5 X 1 = 5)

16. Successor of a one digit number is always a one digit number.

Answer: False

Explanation: The successor of 9 (a one-digit number) is 10 (a two-digit number).

17. Both addition and multiplication are associative for whole numbers.

Answer: True

Explanation: The associative property (a + b) + c = a + (b + c) and (a × b) × c = a × (b × c) holds for whole numbers.

18. The product of 'q' and 20 is '20q'.

Answer: True

19. The ratio of 130cm to 1m is 13 : 10.

Answer: True

Explanation: 1m = 100cm. The ratio is 130cm : 100cm. Dividing by 10, we get 13 : 10.

20. 20° and 70° are complementary.

Answer: True

Explanation: Complementary angles are two angles that add up to 90°. 20° + 70° = 90°.

IV Answer any 10 of the following. (10 X 2 = 20)

21. How many thousands are there in 1 lakh?

1 lakh = 1,00,000

1 thousand = 1,000

Number of thousands in 1 lakh = 1,00,000 / 1,000 = 100.

There are 100 thousands in 1 lakh.

22. Use the properties of whole numbers and simplify: 50 X 102.

Using the distributive property of multiplication over addition:

50 x 102 = 50 x (100 + 2)

= (50 x 100) + (50 x 2)

= 5000 + 100

= 5100

Answer: 5100

23. Arivazhagan is 30 years younger to his father. Write Arivazhagan's age in terms of his father's age.

Let the father's age be 'f' years.

Since Arivazhagan is 30 years younger, his age is the father's age minus 30.

Arivazhagan's age = f - 30

24. Find the simplified form of the following ratio 15 : 20.

To simplify the ratio 15 : 20, we find the greatest common divisor (GCD) of 15 and 20, which is 5.

Divide both parts of the ratio by 5:

15 ÷ 5 = 3

20 ÷ 5 = 4

The simplified form is 3 : 4.

25. Which of the two ratios is larger? 4 : 5 or 8 : 15.

To compare the ratios, we can convert them to fractions: 4/5 and 8/15.

Find a common denominator, which is 15.

4/5 = (4 x 3) / (5 x 3) = 12/15

Now compare 12/15 and 8/15. Since 12 > 8, 12/15 is larger.

Therefore, the ratio 4 : 5 is larger.

26. Fill in the box: 3 : 5 :: [ ] : 20.

Let the missing number be x. The proportion is 3/5 = x/20.

To get from 5 to 20, we multiply by 4.

So, we multiply the numerator by 4 as well: x = 3 x 4 = 12.

The missing number is 12.

27. Find the complementary angle of a) 30° b) 26°

Complementary angles add up to 90°.

a) Complement of 30° = 90° - 30° = 60°

b) Complement of 26° = 90° - 26° = 64°

28. Draw any 3 lines to have a point of concurrency.

To draw three concurrent lines:

1. Draw a single point on the paper and label it 'O'.
2. Draw a straight line that passes through point O.
3. Draw a second straight line that also passes through point O.
4. Draw a third straight line that also passes through point O.

All three lines intersect at the same single point P, which is the point of concurrency.

29. How many triangles are there in the given figure.

The figure shows a large triangle with its interior divided by connecting the midpoints of its sides. This creates 4 smaller triangles inside and 1 large outer triangle.

1. The top small triangle.
2. The bottom-left small triangle.
3. The bottom-right small triangle.
4. The central inverted small triangle.
5. The large outer triangle itself.

Total number of triangles = 5.

30. Define: "Ray".

Ray: A ray is a part of a line that has one fixed starting point (called an endpoint) and extends infinitely in one direction.

31. Name the following angles as shown in the figure. i) ∠1 = ? ii) ∠2 = ?

Based on the typical labeling in the figure provided:

i) ∠1 = ∠DBC (or ∠CBD)

ii) ∠2 = ∠EBD (or ∠DBE)

V Answer any 5 of the following. (5 X 3 = 15)

32. Arrange the following numbers in the descending order : 128435, 10835, 21354, 6348, 25840.

Descending order means arranging numbers from the largest to the smallest.

1. 128435 (the only 6-digit number)
2. 25840 (largest of the 5-digit numbers)
3. 21354
4. 10835
5. 6348 (the only 4-digit number)

The descending order is: 128435, 25840, 21354, 10835, 6348.

33. The number of people who visited the public library for the past 5 months were 1000, 2000, 2450, 3060 and 3200 respectively. How many people visited the library in the last 5 months.

To find the total number of visitors, we add the numbers for each month:

Total visitors = 1000 + 2000 + 2450 + 3060 + 3200

1000 + 2000 = 3000

3000 + 2450 = 5450

5450 + 3060 = 8510

8510 + 3200 = 11710

A total of 11,710 people visited the library in the last 5 months.

34. What is the value of 'S' if '2S - 6' gives 30?

We are given the equation: 2S - 6 = 30

Step 1: Add 6 to both sides of the equation.

2S - 6 + 6 = 30 + 6

2S = 36

Step 2: Divide both sides by 2.

S = 36 / 2

S = 18

The value of S is 18.

35. The cost of parking a bicycle is Rs. 5 and the cost of parking a scooter is Rs. 15. Find the simplest ratio of the parking cost of the a bicycle to that of a scooter.

Cost of parking a bicycle = Rs. 5

Cost of parking a scooter = Rs. 15

The ratio of the cost of parking a bicycle to a scooter is 5 : 15.

To simplify, divide both numbers by their greatest common divisor, which is 5.

5 ÷ 5 = 1

15 ÷ 5 = 3

The simplest ratio is 1 : 3.

36. A line segment 63cm long is to be divided into two parts in the ratio 3 : 4. Find the length of each part.

Total length = 63 cm

Ratio = 3 : 4

Sum of the ratio parts = 3 + 4 = 7

This means the line segment is divided into 7 equal parts.

Length of one part = 63 cm / 7 = 9 cm

Length of the first part (3 parts) = 3 x 9 cm = 27 cm

Length of the second part (4 parts) = 4 x 9 cm = 36 cm

The lengths of the two parts are 27 cm and 36 cm.

37. Draw a pictograph for the given data.

Month	June	July	August	September
Number of Computers sold	300	450	600	550

Pictograph: Computers Sold Last 4 Months

Scale: Each 💻 symbol represents 100 computers.

Month	Number of Computers (Pictorial)
June	💻 💻 💻
July	💻 💻 💻 💻 (and a half symbol)
August	💻 💻 💻 💻 💻 💻
September	💻 💻 💻 💻 💻 (and a half symbol)

VI Answer any one of the following. (1 X 5 = 5)

38. Construct a line segment using ruler and compass AB = 7.5cm. (OR)

Steps for Construction:

1. Draw a line and mark a point 'A' on it.
2. Place the metal tip of the compass on the '0' mark of the ruler.
3. Extend the pencil tip of the compass to the 7.5 cm mark on the ruler.
4. Without changing the compass width, place the metal tip on point 'A'.
5. Draw a small arc on the line to cut it at a point. Mark this point as 'B'.
6. The line segment AB is the required segment of length 7.5 cm.

39. Draw the following angle using the protractor ∠NAS = 90°.

Steps for Construction:

1. Draw a ray AS. This will form one side of the angle.
2. Place the center of the protractor on the vertex 'A'.
3. Align the base line of the protractor with the ray AS.
4. Look for the 90° mark on the protractor scale and make a small dot. Label this point 'N'.
5. Remove the protractor.
6. Draw a ray from the vertex 'A' through the point 'N'.
7. The resulting angle, ∠NAS, is the required 90° angle.

6th Std Maths Quarterly Exam Question Paper 2024 with Solutions | Krishnagiri District | English Medium

6th Std Maths Quarterly Exam 2024 - Solutions

QUARTERLY COMMON EXAMINATION – 2024 Subject: MATHS Std: 6 Time: 2.00 Hrs. Marks: 60

I Choose the correct answer. (10 X 1 = 10)

1. 1 billion is equal to

a) 100 crore    b) 100 million    c) 100 lakh    d) 10000 lakh

Answer: a) 100 crore

Explanation: 1 billion = 1,000,000,000. 1 crore = 1,00,00,000. Therefore, 1 billion = 100 x 1,00,00,000 = 100 crore.

2. The estimation to the nearest hundred of 76812 is

a) 77000    b) 76000    c) 76800    d) 76900

Answer: c) 76800

Explanation: To round to the nearest hundred, we look at the tens digit. In 76812, the tens digit is 1. Since 1 is less than 5, we keep the hundreds digit (8) as it is and change the tens and ones digits to zero. So, the estimated number is 76800.

3. Which of the following expressions is not zero?

a) 0 X 0    b) 0 + 0    c) 2 / 0    d) 0 / 2

Answer: c) 2 / 0

Explanation: Division by zero is undefined, not zero. 0 X 0 = 0, 0 + 0 = 0, and 0 / 2 = 0.

4. The number of days in 'w' weeks is

a) 30 + w    b) 30 w    c) 7 + w    d) 7 w

Answer: d) 7 w

Explanation: There are 7 days in one week. So, in 'w' weeks, the number of days is 7 multiplied by w, which is 7w.

5. The ratio of the number of sides of a triangle to the number of sides of a rectangle is

a) 4 : 3    b) 3 : 4    c) 3 : 5    d) 3 : 2

Answer: b) 3 : 4

Explanation: A triangle has 3 sides. A rectangle has 4 sides. The ratio is 3 to 4, written as 3:4.

6. An equivalent ratio of 4 : 7 is

a) 1 : 3    b) 8 : 15    c) 14 : 8    d) 12 : 21

Answer: d) 12 : 21

Explanation: To find an equivalent ratio, multiply both parts of the ratio by the same non-zero number. 4 x 3 = 12 and 7 x 3 = 21. So, 4:7 is equivalent to 12:21.

7. If a barbie doll costs Rs. 90, then the cost of 3 such dolls is Rs.

a) 260    b) 270    c) 30    d) 93

Answer: b) 270

Explanation: Cost of 1 doll = Rs. 90. Cost of 3 dolls = 3 x 90 = Rs. 270.

8. A line is denoted as

a) AB    b) → over AB    c) ↔ over AB    d) ‾ over AB

Answer: c) ↔ over AB   

Explanation: A line extends indefinitely in both directions, which is denoted by a double-headed arrow over the letters representing two points on the line.

9. The tally marks for the number 7 in standard form is

Answer: b) |||| ||

Explanation: Tally marks are grouped in fives. The number 7 is represented as a group of five (||||) and two additional marks (||).

10. The representation of "one picture to many objects" in a pictograph is called

a) Tally mark    b) Pictoword    c) scaling    d) frequency

Answer: c) scaling

Explanation: In a pictograph, scaling is the key used to define how many objects each picture represents (e.g., 1 car picture = 100 cars).

II Fill in the blanks. (5 X 1 = 5)

11. The largest 8 digit number is ____________.

Answer: 99,999,999

12. The algebraic statement of 'S divided by 5' is ____________.

Answer: S / 5

13. Ratio of 75 paise to Rs. 2 = ____________.

Answer: 3 : 8

Explanation: Convert Rs. 2 to paise: Rs. 2 = 200 paise. The ratio is 75 : 200. Dividing both by their greatest common divisor (25), we get 3 : 8.

14. A line through two end points 'A' and 'B' is denoted by ____________.

Answer:

15. The tally marks for number 8 in standard form is ____________.

Answer:

III True (or) False. (5 X 1 = 5)

16. Successor of a one digit number is always a one digit number.

Answer: False

Explanation: The successor of 9 (a one-digit number) is 10 (a two-digit number).

17. Both addition and multiplication are associative for whole numbers.

Answer: True

Explanation: The associative property (a + b) + c = a + (b + c) and (a × b) × c = a × (b × c) holds for whole numbers.

18. The product of 'q' and 20 is '20q'.

Answer: True

19. The ratio of 130cm to 1m is 13 : 10.

Answer: True

Explanation: 1m = 100cm. The ratio is 130cm : 100cm. Dividing by 10, we get 13 : 10.

20. 20° and 70° are complementary.

Answer: True

Explanation: Complementary angles are two angles that add up to 90°. 20° + 70° = 90°.

IV Answer any 10 of the following. (10 X 2 = 20)

21. How many thousands are there in 1 lakh?

1 lakh = 1,00,000

1 thousand = 1,000

Number of thousands in 1 lakh = 1,00,000 / 1,000 = 100.

There are 100 thousands in 1 lakh.

22. Use the properties of whole numbers and simplify: 50 X 102.

Using the distributive property of multiplication over addition:

50 x 102 = 50 x (100 + 2)

= (50 x 100) + (50 x 2)

= 5000 + 100

= 5100

Answer: 5100

23. Arivazhagan is 30 years younger to his father. Write Arivazhagan's age in terms of his father's age.

Let the father's age be 'f' years.

Since Arivazhagan is 30 years younger, his age is the father's age minus 30.

Arivazhagan's age = f - 30

24. Find the simplified form of the following ratio 15 : 20.

To simplify the ratio 15 : 20, we find the greatest common divisor (GCD) of 15 and 20, which is 5.

Divide both parts of the ratio by 5:

15 ÷ 5 = 3

20 ÷ 5 = 4

The simplified form is 3 : 4.

25. Which of the two ratios is larger? 4 : 5 or 8 : 15.

To compare the ratios, we can convert them to fractions: 4/5 and 8/15.

Find a common denominator, which is 15.

4/5 = (4 x 3) / (5 x 3) = 12/15

Now compare 12/15 and 8/15. Since 12 > 8, 12/15 is larger.

Therefore, the ratio 4 : 5 is larger.

26. Fill in the box: 3 : 5 :: [ ] : 20.

Let the missing number be x. The proportion is 3/5 = x/20.

To get from 5 to 20, we multiply by 4.

So, we multiply the numerator by 4 as well: x = 3 x 4 = 12.

The missing number is 12.

27. Find the complementary angle of a) 30° b) 26°

Complementary angles add up to 90°.

a) Complement of 30° = 90° - 30° = 60°

b) Complement of 26° = 90° - 26° = 64°

28. Draw any 3 lines to have a point of concurrency.

To draw three concurrent lines:

1. Draw a single point on the paper and label it 'O'.
2. Draw a straight line that passes through point O.
3. Draw a second straight line that also passes through point O.
4. Draw a third straight line that also passes through point O.

All three lines intersect at the same single point P, which is the point of concurrency.

29. How many triangles are there in the given figure.

The figure shows a large triangle with its interior divided by connecting the midpoints of its sides. This creates 4 smaller triangles inside and 1 large outer triangle.

1. The top small triangle.
2. The bottom-left small triangle.
3. The bottom-right small triangle.
4. The central inverted small triangle.
5. The large outer triangle itself.

Total number of triangles = 5.

30. Define: "Ray".

Ray: A ray is a part of a line that has one fixed starting point (called an endpoint) and extends infinitely in one direction.

31. Name the following angles as shown in the figure. i) ∠1 = ? ii) ∠2 = ?

Based on the typical labeling in the figure provided:

i) ∠1 = ∠DBC (or ∠CBD)

ii) ∠2 = ∠EBD (or ∠DBE)

V Answer any 5 of the following. (5 X 3 = 15)

32. Arrange the following numbers in the descending order : 128435, 10835, 21354, 6348, 25840.

Descending order means arranging numbers from the largest to the smallest.

1. 128435 (the only 6-digit number)
2. 25840 (largest of the 5-digit numbers)
3. 21354
4. 10835
5. 6348 (the only 4-digit number)

The descending order is: 128435, 25840, 21354, 10835, 6348.

33. The number of people who visited the public library for the past 5 months were 1000, 2000, 2450, 3060 and 3200 respectively. How many people visited the library in the last 5 months.

To find the total number of visitors, we add the numbers for each month:

Total visitors = 1000 + 2000 + 2450 + 3060 + 3200

1000 + 2000 = 3000

3000 + 2450 = 5450

5450 + 3060 = 8510

8510 + 3200 = 11710

A total of 11,710 people visited the library in the last 5 months.

34. What is the value of 'S' if '2S - 6' gives 30?

We are given the equation: 2S - 6 = 30

Step 1: Add 6 to both sides of the equation.

2S - 6 + 6 = 30 + 6

2S = 36

Step 2: Divide both sides by 2.

S = 36 / 2

S = 18

The value of S is 18.

35. The cost of parking a bicycle is Rs. 5 and the cost of parking a scooter is Rs. 15. Find the simplest ratio of the parking cost of the a bicycle to that of a scooter.

Cost of parking a bicycle = Rs. 5

Cost of parking a scooter = Rs. 15

The ratio of the cost of parking a bicycle to a scooter is 5 : 15.

To simplify, divide both numbers by their greatest common divisor, which is 5.

5 ÷ 5 = 1

15 ÷ 5 = 3

The simplest ratio is 1 : 3.

36. A line segment 63cm long is to be divided into two parts in the ratio 3 : 4. Find the length of each part.

Total length = 63 cm

Ratio = 3 : 4

Sum of the ratio parts = 3 + 4 = 7

This means the line segment is divided into 7 equal parts.

Length of one part = 63 cm / 7 = 9 cm

Length of the first part (3 parts) = 3 x 9 cm = 27 cm

Length of the second part (4 parts) = 4 x 9 cm = 36 cm

The lengths of the two parts are 27 cm and 36 cm.

37. Draw a pictograph for the given data.

Month	June	July	August	September
Number of Computers sold	300	450	600	550

Pictograph: Computers Sold Last 4 Months

Scale: Each 💻 symbol represents 100 computers.

Month	Number of Computers (Pictorial)
June	💻 💻 💻
July	💻 💻 💻 💻 (and a half symbol)
August	💻 💻 💻 💻 💻 💻
September	💻 💻 💻 💻 💻 (and a half symbol)

VI Answer any one of the following. (1 X 5 = 5)

38. Construct a line segment using ruler and compass AB = 7.5cm. (OR)

Steps for Construction:

1. Draw a line and mark a point 'A' on it.
2. Place the metal tip of the compass on the '0' mark of the ruler.
3. Extend the pencil tip of the compass to the 7.5 cm mark on the ruler.
4. Without changing the compass width, place the metal tip on point 'A'.
5. Draw a small arc on the line to cut it at a point. Mark this point as 'B'.
6. The line segment AB is the required segment of length 7.5 cm.

39. Draw the following angle using the protractor ∠NAS = 90°.

Steps for Construction:

1. Draw a ray AS. This will form one side of the angle.
2. Place the center of the protractor on the vertex 'A'.
3. Align the base line of the protractor with the ray AS.
4. Look for the 90° mark on the protractor scale and make a small dot. Label this point 'N'.
5. Remove the protractor.
6. Draw a ray from the vertex 'A' through the point 'N'.
7. The resulting angle, ∠NAS, is the required 90° angle.

6th Standard Maths First Term Chengalpattu District Summative Exam Question Paper 2024 with Answer Key | English Medium

6th Maths - Term 1 Exam 2024 - Original Question Paper & Answer Key

FIRST TERM SUMMATIVE EXAMINATION - 2024

Standard: VI | Subject: MATHEMATICS

Time: 2.00 hrs | Marks: 60

Part I - Objective Type Questions (Page 1)

I. Choose the Correct answer (5x1=5)

1. The successor of 10 million is

• a) 100001
• b) 10000001
• c) 9999999
• d) 100001

Answer: b) 10000001

2. The number of days in 'W' weeks is

• a) 30+W
• b) 30W
• c) 7+W
• d) 7W

Answer: d) 7W

3. The ratio of the number of sides of a triangle to the number of sides of a rectangle is

• a) 4:3
• b) 3:4
• c) 3:5
• d) 3:2

Answer: b) 3:4

4. A line is denoted as

Answer: c) AB (with arrows on both ends)

5. The representation of 'one picture to many objects' in a pictograph is called ______

• a) Tally mark
• b) Pictoword
• c) Scaling
• d) Frequency

Answer: c) Scaling

II. Fill in the blanks (5x1=5)

6. 48792 ___ 48972 [> or < or =]

Answer: <

7. 17 x ___ = 34 x 17

Answer: 34

8. If 'P-5' gives 12 then 'P' is ___

Answer: 17

9. Ratio of Rs.3 to Rs.5 = ___

Answer: 3:5

10. The collected information is called ___

Answer: Data

III. Say True or False (5x1=5)

11. 3 + 9 x 8 = 96

Answer: False (Correct: 3 + 72 = 75)

12. The product of 'q' and 20 is '20q'.

Answer: True

13. The ratio of 130c.m to 1m is 13:10.

Answer: True (1m = 100cm, so 130:100 = 13:10)

14. 5:7 is equivalent to 21:15.

Answer: False (21:15 simplifies to 7:5)

15. 88° and 12° are complementary.

Answer: False (Complementary angles sum to 90°. 88° + 12° = 100°)

IV. Match the following (5x1=5)

1. 10000 - 1   -   9999
2. 59/1   -   59
3. 4:5 = __ : 10   -   8
4. 90°   -   Right angle
5. ||||| ||||   -   9

Part V & VI - Short & Long Answers (Page 2)

V. Answer any six questions from the following (6x2=12)

21. How many ten thousands are there in the smallest 6 digit number?

Answer: The smallest 6-digit number is 100,000. To find the number of ten thousands, we divide: 100,000 / 10,000 = 10. There are 10 ten thousands.

22. Round off 4,065 to hundred place.

Answer: The digit in the tens place is 6, which is 5 or greater. So, we round up the hundreds digit. The rounded number is 4,100.

23. If 'u' is an even number, how would you represent (i) the next even number? (ii) The previous even number?

Answer:
(i) The next even number is u + 2.
(ii) The previous even number is u - 2.

24. The cost of parking a bicycle is Rs.5 and the cost of parking scooter is Rs.15. Find the simplest ratio of the parking cost of a bicycle to that of a scooter.

Answer: The ratio is 5:15. Dividing both by 5 gives the simplest ratio: 1:3.

25. Give two equivalent ratios for 3:2.

Answer: Two equivalent ratios are 6:4 (multiplied by 2) and 9:6 (multiplied by 3).

26. Find the complementary angle of 85°.

Answer: Complementary angle = 90° - 85° = 5°.

27. Give an example for Primary Data and Secondary data.

Answer:
Primary Data: Collecting the heights of students in your class yourself.
Secondary Data: Using weather information from a newspaper.

28. How many triangles are there in the given figures?

Answer: There are 5 triangles in the figure (3 small corner triangles, 1 large outer triangle, 1 inverted middle triangle).

29. In the following magic triangle, arrange the numbers from 1 to 6, so that you get the same sum on all its sides.

Answer: Place 4, 5, 6 at the corners. Place 3 between 4 and 5. Place 1 between 5 and 6. Place 2 between 6 and 4. The sum on each side is 12.

VI. Answer any four questions from the following (4x5=20)

30. Rajan writes a 3-digit number, using the digits 4, 7 and 9. What are the possible numbers he can write?

Answer: The possible 3-digit numbers are 479, 497, 749, 794, 947, 974.

31. Use the properties of whole numbers and simplify 50 x 102.

Answer: Using the distributive property:
50 x 102 = 50 x (100 + 2)
= (50 x 100) + (50 x 2)
= 5000 + 100
= 5100

32. Complete the table and find the value of 'K' for which 'K'/3 gives 5.

Answer: From the table pattern, when K/3 = 5, the value of K is 15.

Part VI Continued (Page 3)

33. Kumaran has Rs.600 and wants to divide it between Vimala and Yazhini in the ratio 2:3. Who will get more and how much?

Answer:
Total ratio parts = 2 + 3 = 5.
Value of 1 part = 600 / 5 = Rs. 120.
Vimala's share (2 parts) = 2 x 120 = Rs. 240.
Yazhini's share (3 parts) = 3 x 120 = Rs. 360.
Yazhini will get more. Vimala gets Rs. 240 and Yazhini gets Rs. 360.

34. From the given figure, name the (i) intersecting lines (ii) Points of intersection

Answer:
(i) Intersecting lines: (L1, L2), (L1, L3), (L1, L5), (L1, L4), (L4, L5),etc.
(ii) Points of intersection: P, Q, R.

35. Thamarai is fond of reading books. The number of pages read by her on each day during the last 40 days are given below. Make a Tally Marks table.

Answer:

Pages Read	Tally Marks	Frequency
1	||||| ||	7
2	||||| |	6
3	|||||	5
4	|||	3
5	||||| ||||| ||	12
6	||||| ||	7

36. Put the numbers 1, 2, 3, 4, 5, 6 & 7 in the circles so that each straight line of three numbers add up to the same total.

Answer: Place 4 in the center circle. Place the pairs (1,7), (2,6), and (3,5) on the ends of the three lines. Each line will add up to a total of 12.

Part VII - Construction (Page 4)

VII. Answer any one of the following (1x8=8)

37. With the help of a ruler and compass draw a line segment PQ=5.5cm.

Steps for construction:

1. Draw a line 'l' on the paper.
2. Mark a point 'P' on the line 'l'.
3. Place the pointer of the compass at the '0' mark of the ruler.
4. Open the compass to a width of 5.5 cm.
5. Place the compass pointer at point 'P' and draw an arc that cuts the line 'l'.
6. Mark the point where the arc intersects the line as 'Q'.
7. The line segment PQ is the required segment of length 5.5 cm.

38. Draw and label the angle ∠NAS=90°.

Steps for construction (using a protractor):

1. Draw a ray AS. This will be one arm of the angle.
2. Place the center of the protractor on the vertex A.
3. Align the baseline of the protractor with the ray AS.
4. Find the 90° mark on the protractor's scale and mark a point, N.
5. Remove the protractor and draw a ray from vertex A through point N.
6. The resulting angle, ∠NAS, is the required 90° angle (a right angle).

6th Maths - Term 1 Exam 2024 - Original Question Paper with Solutions | Theni District

I. Choose the Correct answer (5 x 1 = 5)

1. \(\frac{59}{1}\) is

• a) 1
• b) 0
• c) \(\frac{1}{59}\)
• d) 59

Answer: d) 59

2. If y + 7 = 13, then the value of y is

• a) y = 5
• b) y = 6
• c) y = 7
• d) y = 8

Answer: b) y = 6 (Since 13 - 7 = 6)

3. An equivalent ratio of 4 : 7 is

• a) 1 : 3
• b) 8 : 15
• c) 14 : 8
• d) 12 : 21

Answer: d) 12 : 21 (Since 4 x 3 = 12 and 7 x 3 = 21)

4. Which of the following represents a line segment?

Answer: d) \(\overline{AB}\)

5. The tally marks represent the number count

Note: The image shows '||||' with a slash and '||||', representing 5 + 4.

• a) 5
• b) 8
• c) 9
• d) 10

Answer: c) 9

II. Fill in the blanks (5 x 1 = 5)

6. The place value of 5 in 7005380 is __________.

Answer: 5000 (Five thousand)

7. If 7 x 46 = 322 then 46 x 7 = __________.

Answer: 322

8. 3 : 5 = 9 : __________.

Answer: 15 (Since 3 x 3 = 9, we have 5 x 3 = 15)

9. A ray has __________ end points.

Answer: one

10. The collected information is called __________.

Answer: Data

III. Say True or False (5 x 1 = 5)

11. 3 + 9 x 8 = 96

Answer: False (By BODMAS, 9 x 8 = 72, then 3 + 72 = 75)

12. 0 is the identity for multiplication of whole numbers.

Answer: False (1 is the multiplicative identity. 0 is the additive identity.)

13. The product of q and 20 is 20q.

Answer: True

14. If 40 is divided in the ratio 3:2, then the larger part is 24.

Answer: True (Total parts = 5. One part = 40/5 = 8. Larger part = 3 x 8 = 24)

15. 90° is the right angle.

Answer: True

IV. Match the following (5 x 1 = 5)

Question	Answer
16. The successor of 4576	4577
17. (53+49) x 0	0
18. Twice P	2P
19. 4 weeks	28 days
20. Pictograph	pictogram

V. Answer any 10 questions (10 x 2 = 20)

21. Simplify: (10+17) ÷ 3

Solution: (10 + 17) ÷ 3 = 27 ÷ 3 = 9

22. How many thousands are there in 1 lakh?

Solution: 1 lakh = 1,00,000. 1,00,000 ÷ 1,000 = 100 thousands.

23. Write the number name of the numeral 345,678 in the Indian System.

Answer: Three lakh forty-five thousand six hundred seventy-eight.

24. Complete the following Pattern.
9 - 1 = 8
98 - 21 = 77
987 - 321 = 666
9876 - 4321 = ?
98765 - 54321 = ?

Solution:
9876 - 4321 = 5555
98765 - 54321 = 44444

25. What is the value of S, if 2S - 6 gives 30?

Solution: 2S - 6 = 30 => 2S = 36 => S = 18.

26. Find the simplified form of the ratio 20 : 5.

Solution: Dividing both by 5, we get 4 : 1.

27. By proportionality law, check whether 3 : 2 and 30 : 20 are in proportion.

Solution: Product of extremes = 3 x 20 = 60. Product of means = 2 x 30 = 60. Since both are equal, yes, they are in proportion.

28. Akilan walks 10 k.m in an hour while Selvi walks 6 k.m. in an hour. Find the simplest ratio of the distance covered by Akilan to that of Selvi.

Solution: The ratio is 10 : 6. Dividing by 2 gives the simplest ratio: 5 : 3.

29. Find the complementary angle of 85°.

Solution: 90° - 85° = 5°.

30. What is the tally marks for the number 8?

Answer: 廿 ||| (or HH III)

31. How many triangles are there in the figure?

Solution: There are 4 small inner triangles and 1 large outer triangle. Total = 5 triangles.

VI. Answer any 5 questions (5 x 3 = 15)

32. Fill up the circle with the numbers from 1 to 6 without repetition so that each side of the magic triangle adds sum of 12.

Solution:
The numbers at the vertices (corners) should be 4, 5, and 6.
The numbers at the middle of the sides should be 1, 2, and 3.
Side 1: 4 + 3 + 5 = 12
Side 2: 5 + 1 + 6 = 12
Side 3: 6 + 2 + 4 = 12

33. Find the value of x in the given figure.

Solution: The angles on a straight line sum to 180°.
$x° + 25° = 180°$
$x = 180 - 25$
$x = 155°$

34. Write the following numbers in the descending order: 128435, 10835, 21354, 6348, 25840

Answer: 128435, 25840, 21354, 10835, 6348

35. Simplify: 24 + 2 x 8 ÷ 2 - 1

Solution (using BODMAS):
= 24 + 2 x 4 - 1 (Division first)
= 24 + 8 - 1 (Multiplication next)
= 32 - 1 (Addition next)
= 31 (Subtraction last)

36. Athiyan and Mugilan are brothers. Athiyan is P years old and Mugilan is elder to Athiyan by 6 years. Write an algebraic statement for this and find the age of Mugilan if Athiyan is 20 years old.

Solution:
Algebraic Statement: Mugilan's age = P + 6
If Athiyan's age (P) = 20, then Mugilan's age = 20 + 6 = 26 years.

37. Kumaran has Rs. 600 and wants to divide it between Vimala and Yazhini in the ratio 2:3. Who will get more and how much?

Solution:
Total ratio parts = 2 + 3 = 5.
Value of 1 part = Rs. 600 / 5 = Rs. 120.
Vimala's share (2 parts) = 2 x 120 = Rs. 240.
Yazhini's share (3 parts) = 3 x 120 = Rs. 360.
Yazhini will get more, and she will get Rs. 360.

38. Two complementary angles are in ratio 7:2. Find the angles.

Solution:
Let the angles be 7x and 2x. Complementary angles sum to 90°.
7x + 2x = 90°
9x = 90°
x = 10°
The angles are: 7x = 7(10) = 70° and 2x = 2(10) = 20°.

39. The number of pages read by a girl on each day during the last 40 days are given below. Make a Tally Marks table.
1 3 5 6 6 3 5 4 1 6 2 5 3 4 1 6 6 5 5 1 1 2 3 2 5 2 4 1 6 2 5 5 6 5 5 3 5 2 5 1

Solution:

Number of Pages	Tally Marks	Frequency
1	廿 ||	7
2	廿 |	6
3	廿	5
4	|||	3
5	廿 廿 ||	12
6	廿 ||	7
Total		40

40. Put the numbers from 1 to 7 in the circles so that each straight line of three numbers add up to the same total.

Solution:
Place the number 1 in the center circle. Each line will sum to 10.
Arrange the other numbers in pairs at the ends of the lines: (2, 7), (3, 6), (4, 5).
Line 1: 2 + 1 + 7 = 10
Line 2: 3 + 1 + 6 = 10
Line 3: 4 + 1 + 5 = 10

OR YOU MAY TRY THIS ANSWER ALSO ...

Place the number 4 in the center circle. Each line will sum to 12.
Arrange the other numbers in pairs at the ends of the lines: (1, 7), (2, 6), (3, 5).
Line 1: 1 + 4 + 7 = 12
Line 2: 2 + 4 + 6 = 12
Line 3: 3 + 4 + 5 = 12

VII. Answer any one question (1 x 5 = 5)

41. a) Use a protractor to draw an angle 90°.

Steps for drawing a 90° angle:
1. Draw a straight line (ray) and label its starting point as A and another point on it as B. This forms the arm AB.
2. Place the center of the protractor on the vertex A, and align the baseline of the protractor with the arm AB.
3. Find the 90° mark on the protractor's scale and make a small dot. Label this point C.
4. Remove the protractor and use a ruler to draw a straight line from the vertex C to the point A.
5. The angle ∠CAB is the required 90° angle.

(OR)

b) With the help of a ruler and compass, draw a line segment PQ = 5.5cm.

Steps:

1. Draw a line 'l' and mark a point P on it.
2. Place the compass pointer on the 0 mark of the ruler.
3. Open the compass to a width of 5.5 cm.
4. Place the compass pointer on point P and draw an arc that cuts the line 'l'.
5. Mark the point where the arc intersects the line as Q.
6. The line segment PQ is the required segment of length 5.5 cm.

6th Standard Maths Virudhunagar District Summative Assessment Question Paper with Solutions - September 2024

6th Maths - Term 1 Exam 2024 - Original Question Paper with Solutions

Standard: 6 Subject: Maths Assessment: Summative Assessment - September 2024 Marks: 60 Time: 2.00 Hrs

I. Choose the best answer: 5 x 1 = 5

The value of 3+5-7×1 is ______.

• a) 5
• b) 7
• c) 8
• d) 1

Answer: d) 1
Explanation: Using BODMAS, multiplication first: 7×1 = 7. Then 3+5-7 = 8-7 = 1.

Variable means that it ______.

• a) can take only a few values
• b) has a fixed value
• c) can take different values
• d) can take only 8 values

Answer: c) can take different values

If 7:5 is in proportion to x:25, then 'x' is ______.

• a) 27
• b) 49
• c) 35
• d) 14

Answer: c) 35
Explanation: 7/5 = x/25. So, x = (7 × 25) / 5 = 7 × 5 = 35.

A line is denoted as ______.

• a) AB
• b) AB
• c) A↔B
• d) AB→

Answer: c) A↔B (A line extends infinitely in both directions)

A pictograph is also known as ______.

• a) Pictoword
• b) Pictogram
• c) Pictophrase
• d) Pictograft

Answer: b) Pictogram

II. Fill in the blanks: 5 x 1 = 5

Multiplication by ______ leaves a number unchanged.

Answer: 1

If 'P-5' gives 12 then 'P' is ______.

Answer: 17 (Since P = 12 + 5)

Ratio of 75 paise to ₹ 2 = ______.

Answer: 3:8 (75 paise : 200 paise)

A ray has ______ end points.

Answer: one

The collected information is called ______.

Answer: Data

III. Say True / False: 5 x 1 = 5

Successor of a one digit number is always a one digit number.

False (Successor of 9 is 10, which is a two-digit number).

If the cost of 10 rice bags is 't', then the cost of 1 rice bag is ^t⁄₁₀.

True

If the weight of 40 books is 8 kg, then the weight of 15 books is 3 kg.

True (Weight of 1 book = 8/40 = 0.2 kg. Weight of 15 books = 15 × 0.2 = 3 kg).

88° and 12° are complementary.

False (They sum to 100°. Complementary angles sum to 90°).

The spaces between any two bars in a bar graph are the same.

True

IV. Match it: 5 x 1 = 5

Question	Given Answer Options	Correct Match
16) The whole number that does not have a predecessor is	5:4	0
17) The value of 'y' in y+7 = 13 is	9	6
18) Simplify the ratio 25:20	60°	5:4
19) Find the complementary angle of 30° is	6	60°
20) The tally marks 卌 |||| represents the number count	0	9

V. Answer any SIX questions: 6 x 2 = 12

How many thousands are there in 1 million?

1 Million = 10,00,000
1 Thousand = 1,000
Number of thousands = 10,00,000 / 1,000 = 1000.
There are 1000 thousands in 1 million.

Cheran had a bank savings of ₹ 7,50,250. He withdrew ₹ 5,34,500 for educational purpose. Find the balance amount in his account.

Initial Savings = ₹ 7,50,250
Amount Withdrawn = ₹ 5,34,500
Balance Amount = 7,50,250 - 5,34,500 = ₹ 2,15,750.
The balance amount is ₹ 2,15,750.

Name the property being illustrated in each of the cases given below:
i) 75+34 = 34+75
ii) 50×1 = 50

i) Commutative property of addition.
ii) Multiplicative identity.

If 'u' is an even number, how would you represent (i) the next even number? (ii) the previous even number?

Given 'u' is an even number.
(i) The next even number is u + 2.
(ii) The previous even number is u - 2.

Converting Algebraic statements to verbal statements:
(i) x+6
(ii) 2p-5

(i) x+6: "6 added to x" or "The sum of x and 6".
(ii) 2p-5: "5 subtracted from twice p" or "5 less than 2 times p".

What is the ratio of 40 minutes to 1 hour?

1 hour = 60 minutes.
Ratio = 40 minutes : 60 minutes
Simplifying by dividing by 20: 2:3.

By proportionality law, check whether 3:2 and 30:20 are in proportion.

For a:b and c:d to be in proportion, the product of extremes (ad) must equal the product of means (bc).
Here, a=3, b=2, c=30, d=20.
Product of extremes = a × d = 3 × 20 = 60.
Product of means = b × c = 2 × 30 = 60.
Since 60 = 60, they are in proportion.

Find the supplementary angle of 35°.

Supplementary angles add up to 180°.
Supplementary angle of 35° = 180° - 35° = 145°.

VI. Answer any SIX questions: 6 x 3 = 18

How many Triangles are there in each of the following figures?

(i) The first figure (2x2 grid with diagonals) has 16 triangles.
(ii) The second figure (triangle with 3 levels) has 13 triangles.

If ₹ 10,00,000 was distributed in a Government scheme to 500 women in the self help groups, then find the amount given to each woman.

Total Amount = ₹ 10,00,000
Number of women = 500
Amount per woman = Total Amount / Number of women
= 10,00,000 / 500 = 10,000 / 5 = 2,000.
Each woman received ₹ 2,000.

Simplify: 100+8÷2+{(3×2)-6}÷2

Using BODMAS/BIDMAS rule:
1. Innermost Brackets: (3 × 2) = 6
2. Braces: {6 - 6} = 0
3. Division: 8 ÷ 2 = 4 and 0 ÷ 2 = 0
4. Addition: 100 + 4 + 0 = 104.

Athiyan and Mugilan are brothers. Athiyan is 'p' years old and Mugilan is elder to Athiyan by 6 years. Write an algebraic statement for this and find the age of Mugilan if Athiyan is 20 years old.

Athiyan's age = p
Mugilan is 6 years elder, so Mugilan's age = p + 6 (This is the algebraic statement).
If Athiyan's age p = 20, then Mugilan's age = 20 + 6 = 26 years old.

Complete the table and find the value of 'K' for which K/3 gives 5.

To find K when K/3 = 5, we calculate K = 3 × 5 = 15.
The completed table is:

K	3	6	9	12	15	18
K/3	1	2	3	4	5	6

Out of 50 students in a class, 30 are boys. Find the ratio of
i) number of boys to the number of girls.
ii) number of girls to the total number of students.
iii) number of boys to the total number of students.

Total students = 50
Number of boys = 30
Number of girls = 50 - 30 = 20
i) Ratio of boys to girls = 30 : 20 = 3 : 2
ii) Ratio of girls to total students = 20 : 50 = 2 : 5
iii) Ratio of boys to total students = 30 : 50 = 3 : 5

A heater uses 3 units of electricity in 40 minutes. How many units does it consume in 2 hours?

2 hours = 2 × 60 = 120 minutes.
In 40 minutes, it uses 3 units.
In 120 minutes, it uses (120 / 40) × 3 units = 3 × 3 = 9 units.

From the given figure, name the (i) parallel lines (ii) intersecting lines (iii) points of intersection

Based on the visual representation:
(i) Parallel lines: Lines CD, EF and IJ.
(ii) Intersecting lines: Line AB intersects lines CD, EF, GH, and IJ..
(iii) Points of intersection: P, Q, R

Viji threw a die 30 times and noted down the result each time as follows. Prepare a table on the numbers shown using Tally marks.
1 4 3 5 5 6 6 4 3 5 4 5 6 5 2 4 2 6 5 5 6 6 4 5 6 6 5 4 1 1

Number	Tally Marks	Frequency
1	|||	3
2	||	2
3	||	2
4	卌 |	6
5	卌 ||||	9
6	卌 |||	8

Arrange the odd numbers from 1 to 17 without repetition to get a sum of 30 on each side of the magic triangle.

This Solution to the Problem.

VII. Answer the following questions: 2 x 5 = 10

Construct a line segment using ruler and compass
AB = 7.5 cm (OR) QR = 10 cm

Steps to construct AB = 7.5 cm:
1. Draw a line and mark a point 'A' on it.
2. Place the metal tip of the compass on the '0' mark of the ruler.
3. Extend the pencil tip of the compass to the 7.5 cm mark.
4. Without changing the compass width, place the metal tip on 'A' and draw a small arc to cut the line.
5. Mark the point of intersection as 'B'.
6. AB is the required line segment of length 7.5 cm.
(The steps for QR = 10 cm are identical, just using points Q, R and length 10 cm).

Draw and label each of the angles.
∠NAS = 90° (OR) ∠BIG = 35°

Steps to draw ∠NAS = 90°:
1. Draw a ray AS.
2. Place the center of the protractor on the vertex A and the baseline along the ray AS.
3. Mark a point 'N' at the 90° mark on the protractor.
4. Remove the protractor and draw a ray AN from the vertex A passing through the point N.
5. ∠NAS is the required right angle of 90°.

Steps to draw ∠BIG = 35°:
1. Draw a ray IG.
2. Place the center of the protractor on the vertex I and the baseline along the ray IG.
3. Mark a point 'B' at the 35° mark on the protractor (using the inner scale).
4. Remove the protractor and draw a ray IB from the vertex I passing through the point B.
5. ∠BIG is the required acute angle of 35°.