Grade 6 : Mathematics (Ganita Prakash) - Patterns in Mathematics (Set 7) | Concept of Maths

Question 1

A space station constructs a solar array using hexagonal modules. To form a chain of $n$ hexagons where adjacent hexagons share exactly one side, how many total structural beams (sides) are required?

Accepted Answer

C) $5n + 1$

Answer

A) $6n$

Answer

B) $6n - (n - 1)$

Answer

D) $4n + 2$

Question 2

An astronomer observes a pattern of stars forming "Triangular Clusters". The first cluster has 1 star, the second has 3, the third has 6, and the fourth has 10. How many stars will be in the $15^{ ext{th}}$ cluster?

Accepted Answer

B) 120

Answer

A) 105

Answer

C) 135

Answer

D) 150

Question 3

In a mathematical pattern, a "Magic Square" of size $L$ has a perimeter of $4L$. If we place $n$ such squares side-by-side in a single row such that they touch but do not overlap, which expression represents the total perimeter of the resulting shape?

Accepted Answer

D) $L(2n + 2)$

Answer

A) $4nL$

Answer

B) $4L + (n-1)L$

Answer

C) $2nL + 2L$

Question 4

A sequence of numbers is defined by the rule: "Multiply the position number $n$ by itself, then subtract the previous position number $(n-1)$". What is the $10^{ ext{th}}$ term of this sequence?

Accepted Answer

A) 91

Answer

B) 81

Answer

C) 100

Answer

D) 89

Question 5

If $x$ represents an odd natural number, which of the following expressions will ALWAYS represent the next consecutive odd number?

Accepted Answer

B) $x + 2$

Answer

A) $x + 1$

Answer

C) $2x + 1$

Answer

D) $x^2$

Question 6

Consider the pattern: $1+3=4, 1+3+5=9, 1+3+5+7=16$. Based on this pattern, what is the sum of the first $k$ odd numbers?

Accepted Answer

C) $k^2$

Answer

A) $2k - 1$

Answer

B) $k(k+1)$

Answer

D) $k^2 + 1$

Question 7

A pattern of tiles is laid such that the $n^{ ext{th}}$ row has $2n^2 - 1$ tiles. How many more tiles are in the $5^{ ext{th}}$ row than in the $3^{ ext{rd}}$ row?

Accepted Answer

A) 32

Answer

B) 34

Answer

C) 49

Answer

D) 17

Question 8

Which property of operations is represented by the pattern: $a imes (b - c) = a imes b - a imes c$?

Accepted Answer

D) Distributive Property

Answer

A) Commutative Property

Answer

B) Associative Property

Answer

C) Closure Property

Question 9

If the $n^{ ext{th}}$ term of a sequence is given by $5n - 3$, which term of the sequence is equal to 497?

Accepted Answer

B) $100^{	ext{th}}$

Answer

A) $99^{	ext{th}}$

Answer

C) $101^{	ext{st}}$

Answer

D) $102^{	ext{nd}}$

Question 10

Look at the number pattern: $2, 6, 12, 20, 30, \dots$ What is the general rule for the $n^{ ext{th}}$ term?

Accepted Answer

C) $n(n + 1)$

Answer

A) $4n - 2$

Answer

B) $2n^2$

Answer

D) $n^2 + n + 1$