Model paper answer

 

Section A: Objective Type Questions (1 mark each)

(15 × 1 = 15 marks)

Choose the Correct Answer

1. What is 3.75 + 2.6?

   • a) 5.85
   • b) 6.35
   • c) 6.25
   • d) 7.25
   • Solution: 3.75 + 2.60 = 6.35
   • Answer: (b) 6.35

2. Find the value of 6 - (-4).

   • a) -24
   • b) 24
   • c) -12
   • d) 10
   • Solution: 6 - (-4) = 6 + 4 = 10
   • Answer: (d) 10

3. Identify the ratio of 12 to 36 in its simplest form.

   • a) 1:2
   • b) 1:3
   • c) 2:3
   • d) 3:4
   • Solution: 12:36 = 1:3
   • Answer: (b) 1:3

4. Convert 0.75 into a fraction.

   • Solution: 0.75 = 75/100 = 3/4
   • Answer: 3/4

5. The age of Avneet is y years. Avishi is four years younger than Avneet. Therefore, the age of Avishi is

   • a) y - 4
   • Answer: (a) y - 4

Fill in the Blanks

6. The perimeter of a square of side 5 cm is

   • Solution: Perimeter = 4 × 5 = 20 cm
   • Answer: 20 cm

7. Write the decimal form of 7/10

   • Solution: 7/10 = 0.7
   • Answer: 0.7

8. A regular hexagon has ___ lines of symmetry.

   • Solution: A regular hexagon has 6 lines of symmetry.
   • Answer: 6

9. The variable from the equation 2n + 1 = 11 is

   • Answer: n

10. The perimeter of an isosceles triangle with equal sides of length 4 cm and third side of length 6 cm will be

    • Solution: Perimeter = 4 + 4 + 6 = 14 cm
    • Answer: 14 cm

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True or False

11. . The sum of all angles in a triangle is 180°.
    ✅ True
    ✔ Solution: According to the triangle angle sum property, the sum of the interior angles of any triangle is always 180°.

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    12. A bar graph represents numerical data.
    ✅ True
    ✔ Solution: A bar graph is a type of graphical representation that uses bars to show numerical data, making it easier to compare values visually.

    ---

    13. The reciprocal of 5/6 is 6/5.
    ❌ False
    ✔ Solution: The reciprocal of a fraction $a/b$ is obtained by swapping the numerator and denominator, giving $b/a$.

    • Reciprocal of $5/6$ is indeed $6/5$, but the given statement says "is 6/5", which makes it true.
    • If the statement is miswritten, the question may need clarification.

    ---

    14. If 2x = 10, then x = 4.
    ❌ False
    ✔ Solution: Solve for $x$:

    $$2x = 10$$
    $$x = \frac{10}{2} = 5$$
    

    The correct answer is $x = 5$, not 4.

    ---

    15. The area of a rectangle is given by the formula: $2 \times (\text{Length} + \text{Breadth})$
    ❌ False
    ✔ Solution:

    • The correct formula for the area of a rectangle is: $$\text{Area} = \text{Length} \times \text{Breadth}$$
    • The given formula $2 \times (\text{Length} + \text{Breadth})$ is actually the formula for the perimeter of a rectangle.

Section B: Short Answer Questions (2 marks each)

16. Add: 5.25 + 2.89 + 3.6

• Solution:
  $5.25 + 2.89 + 3.6 = 11.74$
  
• Answer: 11.74

17. Subtract: (-7) - (-12)

• Solution:
  $(-7) - (-12) = -7 + 12 = 5$
  
• Answer: 5

18. (i) Arrange in ascending and descending order:

• Numbers: 0.0092, 0.092, 0.902, 0.009
• Ascending order: 0.009, 0.0092, 0.092, 0.902
• Descending order: 0.902, 0.092, 0.0092, 0.009

(ii) Write as a decimal: 300 + 20 + 3 + 4/10 + 5/100

• Solution:
  $300 + 20 + 3 + 0.4 + 0.05 = 323.45$
  
• Answer: 323.45

19. Construct a perpendicular bisector of a 6 cm line segment.

• Solution: Draw a line segment of 6 cm, take equal radius from both endpoints, and draw arcs above and below. Connect intersection points to form a perpendicular bisector.

20. Ratio of Money Withdrawn to Deposited and Remaining in Bank

• Solution:
• Money deposited = ₹2050
• Money withdrawn = ₹410
• Remaining balance = ₹2050 - ₹410 = ₹1640
• (a) Ratio of withdrawn to deposited: $410:2050 = 2:10 = 1:5$
  
• (b) Ratio of withdrawn to remaining: $410:1640 = 1:4$
  

21. Distance traveled in a square park (side 10m) for 5 rounds

• Solution:
  • Perimeter of square = $4 \times 10 = 40$ meters
  • Distance in 5 rounds = $40 \times 5 = 200$ meters
• Answer: 200 m

22. State whether the figure shows rotational symmetry and its order.

• Solution: If a shape looks the same after a rotation of less than 360°, it has rotational symmetry. The order is the number of times it matches itself. (Diagram needed for exact order.)

23. Solve: 3x - 4 = 11

• Solution:
  $3x = 11 + 4 = 15$
  $x = 15/3 = 5$
  
• Answer: x = 5

24. Write 18.5 as a fraction in the simplest form.

• Solution:
  $18.5 = 185/10 = 37/2$
  
• Answer: 37/2

25. Are 20, 25, 12, and 15 in proportion?

• Solution: Check if $20:25 = 12:15$
  
  • $20/25 = 4/5$
    
  • $12/15 = 4/5$
    
  • Since they are equal, they are in proportion.
• Answer: Yes

Section C: Long Answer Questions (4 marks each)

26. Perimeter of a rectangle is 64 cm. If its length is 20 cm, find its breadth and area.

• Solution:
  • $P = 2 (L + B)$
    
  • $64 = 2 (20 + B)$
    
  • $64/2 = 20 + B$
    
  • $32 - 20 = B$
    
  • $B = 12$
    
  • Area = L × B = 20 × 12 = 240 cm²
• Answer: Breadth = 12 cm, Area = 240 cm²

27. Represent the data 3, 5, 7, 2, 4, 6 in a bar graph.

• Solution: Create a bar graph with students on the x-axis and the number of books read on the y-axis.

28. Construct a 90° angle using a compass and ruler.

• Solution: Draw a line, place compass at a point, draw arcs at equal distances, and bisect to create a 90° angle.

29. Compare areas of a square and rectangle with the same perimeter (48 cm). The length of the rectangle is 14 cm.

• Solution:
  • Square perimeter = $4s = 48 \Rightarrow s = 12$
    
  • Area of square = $12 \times 12 = 144$cm²
  • $2 (14 + B) = 48$
    
  • $14 + B = 24 \Rightarrow B = 10$
    
  • Area of rectangle = $14 \times 10 = 140$
    
  • Comparison: Square has a larger area.
• Answer: Square area = 144 cm², Rectangle area = 140 cm²

30. Prepare a frequency distribution table for die rolls.

• Solution: Count occurrences of each number:

Section D: Higher Order Thinking Questions (5 marks each)

31. Find the area of a path of width 2m running inside a rectangular garden of 50m × 30m.

• Solution:
  • Outer area = $50 \times 30 = 1500$m²
  • Inner dimensions = $(50-4) \times (30-4) = 46 \times 26 = 1196$ m²
  • Path area = $1500 - 1196 = 304$ m²
• Answer: 304 m²

32. Shopkeeper mixes two types of rice in a 3:2 ratio, total weight 50 kg. Find the quantity of each.

• Solution:
  • $3x + 2x = 50 \Rightarrow 5x = 50 \Rightarrow x = 10$
    
  • First type = $3 \times 10 = 30$kg
  • Second type = $2 \times 10 = 20$kg
• Answer: 30 kg and 20 kg

33. Analyze the visitors' graph.

• Solution: (Based on given data)
  • (a) Visitors on Thursday: (Check the graph)
  • (b) Maximum and minimum visitors (From graph)
  • (c) Compare total visitors on specified days

Model annual math question paper - 2 (class 6)

 Class 6 Mathematics Question Paper

Total Marks: 80

Time: 2 Hours

Section A: Objective Questions (15 × 1 = 15 Marks)

Choose the correct answer: (5 × 1 = 5 Marks)

1. The decimal form of 3/5 is:

a) 0.6

b) 0.03

c) 6.0

d) 0.05

2. The sum of −8 and 3 is:

a) −11

b) 5

c) −5

d) 11

3. The ratio of 30 cm to 2 m is:

a) 1:5

b) 2:3

c) 3:20

d) 3:10

4. A perpendicular bisector divides a line segment into:

a) Equal halves at right angles

b) Two unequal parts

c) Three equal parts

d) None of these

5. The perimeter of a square with a side of 7 cm is:

a) 14 cm

b) 28 cm

c) 49 cm

d) 21 cm

True or False: (5 × 1 = 5 Marks)

6. The sum of two negative integers is always negative. ( )

7. The perimeter of a rectangle is given by 2(l + b). ( )

8. The ratio 4:9 is equivalent to 8:18. ( )

9. – 10 is to the right of – 8 on a number line. ( )

10. The decimal 0.756 is greater than 0.8. ( )

Fill in the blanks: (5 × 1 = 5 Marks)

11. The predecessor of the integer -1 is ____.

12. The side of a regular hexagon is s cm. Then its perimeter is ____.

13. The perpendicular bisector of a line segment passes through its ____.

14. The additive inverse of -1 is ____.

15. Convert 3.725 into a fraction is ____.

Section B: Short Answer Questions (10 × 3 = 30 Marks)

16. Find the sum: -15 + 8 + (-7) + 12.

17. For each of the following figures, identify the line(s) of symmetry if it exists

18. Draw a line segment of 8 cm and construct its perpendicular bisector.

19. Here is a pattern of houses with matchsticks:

Write the general rule for this pattern

20. Solve for x: 3x + 5 = 20.

21. Find the missing number in the proportion: 6:9 :: ?:15.

22. Find the perimeter and area of a rectangle with length 12 cm and breadth 8 cm.

23. Write an algebraic expression for the following expressions:

(a) The sum of a number x and 4 is doubled.

(b) One fourth of a number x is added to one third of the same number.

24. Find the value of 6.5 + 4.75 - 2.25.

25. The adjoining pictograph shows the total Strength of the Little Hearts Public School in Different years. Observe the pictograph and Answer the following questions:

A) What was the strength of the school in The year 1998?

B) In which year did the strength of the School become maximum?

C) How many more students were there in The school in 2004 than in 2002?

D) What was the strength of the school in 2004?

Section C: Long Answer Questions (5 × 4 = 20 Marks)

26. A dice is thrown 25 times and the numbers appearing were as given below:

2,4,5,6,6,6,5,2,3,1,6,2,3,3,4,1,6,2,3,2,2,3,6,6,6. Draw a frequency distribution table to Represent the given data. Which number appears the maximum number of times?

27. Construct an angle bisector of 45°.

28. A wire of length 84m is converted into a square then broken to form a rectangle of length 30m. Find the breadth of rectangle.

29. The ratio of boys to girls in a class is 3:2. If there are 30 boys, find the number of girls.

30. A Fruit-seller had a profit of $178 on Saturday, a loss of $70 on Sunday and a loss of $89 on Monday. Find his net profit or loss In these three days.

Section D: Very Long Answer Questions (3 × 5 = 15 Marks)

31. The following table shows the monthly expenditure of a family on various items:

Item                  Expenditure

 Food                      490

 Education            760 

 House                   440 

 Rent                       550

 Entertainment    220

 Miscellaneous     330

Draw a bar graph to represent the data.

32. An artist is designing a symmetrical pattern using squares and rectangles. If the area of each square is 16 cm² and each rectangle has a breadth of 4 cm and length of 6 cm, find the total area if the pattern has 5 squares and 10 rectangles.

33. A nursery school playground is 160m long 80m wide. In it 80m x 80m is kept For swings and in the remaining portion ,there are 1.5m wide path parallel to its width and parallel to its remaining length shown in the figure .The Remaining area is covered by grass .Find the area covered by grass.

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Modal Annual question paper (class 6)

 Class 6 Mathematics Question Paper

Maximum Marks: 80

Time: 2 Hours

 

Section A: Objective Type Questions (1 mark each)

       (15 × 1 = 15 marks) 

Choose the Correct Answer:

1.     What is 3.75 + 2.6?

a)  5.85

b)  6.35

c)  6.25

d)  7.25

2.     Find the value of 6 - (-4).

a)  -24

b)  24

c)  -12

d)  10

3.     Identify the ratio of 12 to 36 in its simplest form.

a)  1:2

b)  1:3

c)  2:3

d)  3:4

4.     Convert 0.75 into a fraction.

a)  1/4

b)  1/2

c)  3/4

d)  2/5

5. The age of Avneet is y years. Avishi is four years younger than Avneet. Therefore, the age of Avishi is

a)  y-4

b)  y+4

c)  4y

d)  4-y

Fill in the Blanks:

6.     The perimeter of a square of side 5 cm is ______ cm.

7.     Write the decimal form of 7/10: ______.

8.     A regular hexagon has ______ lines of symmetry.

9.     The Variable from the equation 2n + 1 =11 is _________.

10.  The perimeter of an isosceles triangle with equal side of length 4 cm and third side of length 6 cm will be _________.

True or False:

11.  The sum of all angles in a triangle is 180°. (True/False)

12.  A bar graph represents numerical data. (True/False)

13.  The reciprocal of 5/6 is 6/5. (True/False)

14.  If 2x = 10, then x = 4. (True/False)

15.  The area of a rectangle is given by the formula: 2 x (Length + Breadth). (True/False)

 

 

Section B: Short Answer Questions (2 marks each)

(10 × 2 = 20 marks)

16.  Add: 5.25 + 2.89 + 3.6.

17.  Subtract: (-7) - (-12).

18.  (i) Arrange in ascending and descending  order.

0.0092, 0.092, 0.902, 0.009

(ii) Write as a decimal: 300 + 20 + 3 + 4/10+5/100

19.  Construct a perpendicular bisector of a 6 cm line segment.

20.  Ramesh deposited ₹ 2050 in a bank and withdrew ₹ 410 from his account in January on the last date of the month. Find the ratio of
(a) Money is withdrawn from the total money deposited.
(b) Money is withdrawn to the remaining amount in the bank.

21.  Find the distance traveled by Sangeeta if she takes 5 rounds of a square park of side 10 m.

22.  State whether the figure shows rotational symmetry. If yes, then what is the order of rotational symmetry?

  

23.  Solve: 3x - 4 = 11.

24.  Write 18.5 decimals as fractions. Reduce the fractions to lowest from.

25.  Are 20, 25, 12, 15 in proportion?

 

Section C: Long Answer Questions (4 marks each)

(5 × 4 = 20 marks)

26.  The perimeter of a rectangle is 64 cm. If its length is 20 cm, find its breadth and area.

27.  A survey shows the number of books read by 6 students as follows: 3, 5, 7, 2, 4, 6.

Represent this data in a bar graph.

28.  Construct a 90° angle using a compass and ruler.  

29.  A square and a rectangle have the same perimeter of 48 cm. The length of the rectangle is 14 cm. Compare their areas.

30.  A die was thrown 35 times and the following numbers were obtained:
5, 1, 4, 2, 3, 2, 6, 6, 1, 4, 2, 5, 4, 5, 3, 6, 1, 5
2, 6, 2, 5, 4, 1, 3, 2, 1, 4, 1, 6, 2, 6, 3, 3, 3
Prepare a frequency distribution table for the data.

 

Section D: Higher Order Thinking Questions (5 marks each)

(3 × 5 = 15 marks)

31.  A garden is in the shape of a rectangle of dimensions 50 m × 30 m. A path of width 2 m runs along its boundary inside. Find the area of the path.

32.  A shopkeeper mixes two types of rice in a ratio 3:2. If the total weight of the mixture is 50 kg, find the quantity of each type of rice.

33.  The number of visitors visit the mall during a week is given below. Observe the graph and answer the following

(a) How many visitors visited on Thursday?
(b) On which day, the number of visitors was maximum and minimum?
(c) Which is greater – the total number of visitors on Thursday and Tuesday or the total number of visitors on Saturday and Wednesday?