MATH 2 PAPER OF LAST YEAR (2025) SOLVED

Based on the provided examination paper for Class 6 Mathematics from National Public School, HSR, Bengaluru, here are the questions and their respective solutions in Q&A format.

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Part I: 1 Mark Questions

Q1. Each angle in a rectangle is an/a: (A) acute angle (B) right angle (C) obtuse angle (D) straight angle Answer: (B) right angle. Every interior angle of a rectangle measures 90°.

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Q2. A tetrahedron is a pyramid whose base is a: (A) triangle (B) rectangle (C) square (D) quadrilateral Answer: (A) triangle. A tetrahedron is also known as a triangular pyramid.

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Q3. Which three-dimensional shape does this net create?

(Note: Referring to the image of a circle attached to a sector of a larger circle) (A) triangular Pyramid (B) cylinder (C) cone (D) none of them Answer: (C) cone. The sector forms the curved surface, and the circle forms the base.

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Q4. I am a quadrilateral with only one pair of parallel sides. Who am I? Answer: A Trapezium.

Q5. Which 3D shape looks like a can of soup? Answer: A Cylinder.

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Part II: 2 Mark Questions

Q6. Give one difference and one common property between a square and a rectangle. Answer:

• Common Property: Both shapes have four interior angles that are all right angles (90°).

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• Difference: In a square, all four sides are equal in length, whereas in a rectangle, only the opposite sides are equal.

Q7. Draw a cone and label its key components (base, height, curved surface). Answer:

• Base: The circular bottom of the cone.
• Height: The vertical distance from the center of the base to the apex.
• Curved Surface: The side area that wraps around the cone.

Q8. Construct a line perpendicular to a given line XY from a point 'P' on the line using a compass and ruler. (Steps not required) Answer:

1. Place the compass pointer on point P and draw arcs on both sides of P on line XY to mark points A and B.
2. Using a radius greater than AP, draw arcs from points A and B above the line so they intersect at point Q.
3. Join P and Q. Line PQ is perpendicular to line XY at point P.

Q9. Write two key properties of the diagonals of a rhombus. Answer:

1. The diagonals of a rhombus bisect each other at right angles (90°).
2. The diagonals bisect the vertex angles of the rhombus.

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Part III: 3 Mark Questions

Q10. Write any two 3D shapes depicted in the famous Indian monument Taj Mahal. Write the number of faces, edges, and vertices of each shape. Answer:

1. Cylinder (The Minarets):
• Faces: 3 (2 flat circular faces, 1 curved face)
• Edges: 2 (circular)
• Vertices: 0
2. Hemisphere (The Domes):
• Faces: 2 (1 flat circular face, 1 curved face)
• Edges: 1 (circular)
• Vertices: 0

Q11. Construct a 75∘ angle and bisect it. What is the measure of each of the angles formed? (Steps not required) Answer:

• A 75∘ angle is constructed by bisecting the region between 60∘ and 90∘.
• When a 75∘ angle is bisected, each resulting angle measures 37.5∘.

Q12. The angles of a quadrilateral are in the ratio 2:3:4:6. Find the measure of each of the angles. Answer: The sum of angles in a quadrilateral is 360∘. Let the angles be 2x,3x,4x, and 6x.

2x+3x+4x+6x=360

15x=360⟹x=24

• Angle 1: 2×24=48∘
• Angle 2: 3×24=72∘
• Angle 3: 4×24=96∘
• Angle 4: 6×24=144∘

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Part IV: 4 Mark Questions

Q13. (a) Identify the 3D shapes in the figure below. (b) Write any two differences between them. (Note: Figure A is a Square Pyramid; Figure B is a Triangular Prism) Answer:

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• (a) Identification: Figure (A) is a Square Pyramid. Figure (B) is a Triangular Prism.
• (b) Differences:
1. The Square Pyramid (A) has one base and triangular faces that meet at a single vertex (apex). The Triangular Prism (B) has two congruent triangular bases and rectangular side faces.
2. The Square Pyramid has 5 faces, 8 edges, and 5 vertices. The Triangular Prism has 5 faces, 9 edges, and 6 vertices.

Q14. Construct an angle of 135∘ using a compass and ruler. (Steps not required) Answer:

1. Draw a straight line and mark a point O.
2. Construct a 90∘ angle and a 180∘ (straight) angle.
3. Bisect the angle between 90∘ and 180∘.
4. 90∘+45∘=135∘.

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Would you like me to explain the step-by-step construction for the 135∘ angle?