Test: Patterns in Mathematics - 2 - Class 6 MCQ

A square number is a number that can be expressed as the square of an integer (e.g., 1² = 1, 2² = 4, 3² = 9, etc.).

Among the options:

• 20 is not a square number.
• 24 is not a square number.
• 25 is a square number because 5² = 25.
• 30 is not a square number.

So, the correct answer is C: 25.

The numbers 3, 6, 9, 12 are increasing by 3 each time.

• 3 + 3 = 6
• 6 + 3 = 9
• 9 + 3 = 12

This shows that the numbers are multiples of 3.

So, the correct answer is C: Multiple of 3.

The triangular numbers are formed by arranging dots in an equilateral triangle. The sequence of triangular numbers is:

1st triangular number: 1 dot
2nd triangular number: 1 + 2 = 3 dots
3rd triangular number: 1 + 2 + 3 = 6 dots
4th triangular number: 1 + 2 + 3 + 4 = 10 dots

So, the third triangular number has 6 dots.

The correct answer is B: 6.

The first three odd numbers are:

1, 3, and 5.

To find their sum:

1 + 3 + 5 = 9

So, the correct answer is C: 9.

A three-dimensional object has depth in addition to length and width. Among the options:

• A square is a 2D shape, having only length and width.
• A triangle is also a 2D shape, having length and width.
• A circle is a 2D shape, having only radius and no depth.
• A cube is a 3D shape, having length, width, and depth.

So, the correct answer is D: Cube.

The sequence of numbers representing the number of sides in regular polygons starts with a triangle (3 sides), followed by a square (4 sides), pentagon (5 sides), hexagon (6 sides), and so on.

So, the correct sequence is C: 3, 4, 5, 6..., which represents the number of sides in regular polygons.

The sequence related to triangular numbers is formed by the sum of consecutive integers:

• 1st triangular number: 1
• 2nd triangular number: 1 + 2 = 3
• 3rd triangular number: 1 + 2 + 3 = 6
• 4th triangular number: 1 + 2 + 3 + 4 = 10
• 5th triangular number: 1 + 2 + 3 + 4 + 5 = 15

Thus, the sequence 1, 3, 6, 10, 15... is related to triangular numbers.

The correct answer is A: 1, 3, 6, 10, 15....

A number that is both a square number and a triangular number is a special number that can be expressed as both the square of an integer and the sum of consecutive natural numbers (triangular number).

Let's check the options:

• 16 is a square number (4² = 16), and it's also a triangular number because 1 + 2 + 3 + 4 = 10 (not 16).
• 25 is a square number (5² = 25), but it's not a triangular number.
• 36 is a square number (6² = 36), and it is also a triangular number (1 + 2 + 3 + 4 + 5 + 6 = 21, but still not the correct triangular number for 36).
• 49 is a square number (7² = 49) but not a triangular number.

Hence, 36 is both a square and a triangular number.

The correct answer is C: 36.

Regular polygons and number sequences both follow specific patterns. Regular polygons have a consistent number of sides and angles, while number sequences follow particular rules, such as adding or multiplying by the same value to form the next number. Both concepts are predictable and structured, which is why they can be described by patterns.