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.

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    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.

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    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.

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    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