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Question (11)

QN0030868

A point R is equidistant from the endpoints of a line segment ST. Which construction helps locate the line on which R must lie?

(A) Angle bisector of ∠SRT
(B) Perpendicular bisector of ST
(C) Parallel line to ST
(D) Median of triangle SRT

Correct Answer: B

Explanation:

Every point equidistant from the endpoints of a line segment lies on its perpendicular bisector.

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Question (12)

QN0030869

A student bisects a 120° angle and then copies one of the resulting angles. The copied angle measures

(A) 30°
(B) 45°
(C) 60°
(D) 120°

Correct Answer: C

Explanation:

120° ÷ 2 = 60°. Copying preserves the angle measure.

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Question (13)

QN0030870

Which of the following constructions is based on the property of congruent triangles?

(A) Constructing the angle bisector
(B) Measuring an angle with a protractor
(C) Drawing a freehand sketch
(D) Drawing a bar graph

Correct Answer: A

Explanation:

Angle bisection is justified using congruent triangles.

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Question (14)

QN0030871

A rectangular board has 72 unit squares. What is the least number of 2 × 1 tiles needed to cover it completely?

(A) 24
(B) 30
(C) 36
(D) 72

Correct Answer: C

Explanation:

Each tile covers 2 unit squares, so 72 ÷ 2 = 36.

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Question (15)

QN0030872

A floor has dimensions 12 × 15 unit squares. If 2 × 1 tiles are used, how many tiles are required?

(A) 75
(B) 90
(C) 120
(D) 180

Correct Answer: B

Explanation:

Total unit squares = 12 × 15 = 180. Required tiles = 180 ÷ 2 = 90.

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Question (16)

QN0030873

Which statement about tiling is correct?

(A) Every tiling uses only one kind of shape.
(B) A tiling may use more than one shape without gaps or overlaps.
(C) Only regular polygons can be used for tiling.
(D) Tiling is possible only with squares.

Correct Answer: B

Explanation:

A plane can be tiled using one or more shapes, including non-regular polygons.

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Question (17)

QN0030874

Which natural structure is an example of hexagonal tiling?

(A) Spider web
(B) Bee hive
(C) Tree trunk
(D) Lotus leaf

Correct Answer: B

Explanation:

Honeycombs are made of hexagonal cells that tile the surface efficiently.

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Question (18)

QN0030875

A student constructs a perpendicular to a given line at a point on it. Which earlier construction is directly modified to obtain this construction?

(A) Construction of a regular hexagon
(B) Construction of a perpendicular bisector
(C) Construction of a circle
(D) Construction of a rectangle

Correct Answer: B

Explanation:

The construction of a perpendicular at a point on a line is a modification of the perpendicular bisector construction.

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Question (19)

QN0030876

A square floor of side 14 unit squares is to be tiled using 2 × 1 tiles. How many tiles are needed?

(A) 49
(B) 98
(C) 196
(D) 28

Correct Answer: B

Explanation:

Total unit squares = 14 × 14 = 196. Tiles required = 196 ÷ 2 = 98.

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Question (20)

QN0030877

Which statement best explains why mathematicians continue to study tilings?

(A) There is only one possible tiling for every shape.
(B) New tiling patterns and mathematical discoveries are still being made.
(C) Tiling is useful only in school geometry.
(D) All possible tilings have already been discovered.

Correct Answer: B

Explanation:

Tiling remains an active area of mathematical research, with new patterns continuing to be discovered.

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Question (11)

A point R is equidistant from the endpoints of a line segment ST. Which construction helps locate the line on which R must lie?

Explanation:

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Question (12)

A student bisects a 120° angle and then copies one of the resulting angles. The copied angle measures

Explanation:

Link:

Question (13)

Which of the following constructions is based on the property of congruent triangles?

Explanation:

Link:

Question (14)

A rectangular board has 72 unit squares. What is the least number of 2 × 1 tiles needed to cover it completely?

Explanation:

Link:

Question (15)

A floor has dimensions 12 × 15 unit squares. If 2 × 1 tiles are used, how many tiles are required?

Explanation:

Link:

Question (16)

Which statement about tiling is correct?

Explanation:

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Question (17)

Which natural structure is an example of hexagonal tiling?

Explanation:

Link:

Question (18)

A student constructs a perpendicular to a given line at a point on it. Which earlier construction is directly modified to obtain this construction?

Explanation:

Link:

Question (19)

A square floor of side 14 unit squares is to be tiled using 2 × 1 tiles. How many tiles are needed?

Explanation:

Link:

Question (20)

Which statement best explains why mathematicians continue to study tilings?

Explanation:

Link:

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