Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies.

Complete the table given below, based on the pattern of dots and line segments. Also generalise and find the expression for the number of dots and segments used in case of $n$ squares.

Mohit was observing a number pattern and noted the values.

What is $y$, when $x=n$?

Considering the sequence $6, 11, 16, 21, 26, ...$, its $n \mathrm{th}$ term is

Represent the following pattern as an algebraic expression.

Write the algebraic expression for the $\mathrm{nth}$ term of the number pattern $2, 5, 10, 17, 26... ?$

Write the algebraic expression for the $\mathrm{nth}$ term of the number pattern $0, 3, 8, 15, 24, ...$

Find the number of diagonals drawn from vertex A in figure $4$.

Given diagram shows a matchstick pattern of rhombus. Find the general rule that gives the number of matchsticks required for $8^{th}$ pattern.

The given diagram shows a matchstick pattern of the pentagon. Find the general rule that gives the number of matchsticks required for the $4^{th}$ pattern.

Observe the pattern of sides of a square. Find out the number of sides of a square of ${10}^{th}$ pattern.

Given diagram shows a matchstick pattern of triangles. Find the general rule that gives the number of matchsticks required for $3^{rd}$ pattern.

Sum of interior angles of a pentagon is _____   (in degree)

State True or False
Number of diagonals in a triangle is $0$

Number of distinct diagonals of a hexagon is _____

Complete the statement
Number of diagonals can drawn from one vertex of a hexagon is _____

State True or False
Number of diagonals can drawn from one vertex of  $n$ sided polygon is $\left(n-3\right)$.

Consider the following pyramid :

If we start with $2, 3, 4$, then find the final number.

Write the rule for the pattern shown below. How many matchsticks will be there in the ${10}^{\mathrm{th}}$ figure? 

 The expression for the number of diagonals that we can make from one vertex of a $n$ sided polygon is:

Which one of the following mixtures will act as buffer?