The combination of numbers, variables, constant, and mathematical operation is known as an expression in mathematics. For example, x3y+x2-x+y+1, x+y-3 and. They often called algebraic expressions, polynomials, multinomials, or sometimes equations.

These are some set of the equation which have common values of the variable, mainly in those equations in which we have more than one variable. For example, x+y=9 and 2x-y=15 form a system of equations in two variables.

Function 'f' from set A to Set B is a subset of the cartesian product of A and B. In mathematical notation, f:A→B⊂A×B. Function is a special type of Relation in which every element of A has unique image in set B. So 'r' is called image of 'a' under 'f' and 'a' is called pre image 'r' under 'f'. Collection of pre images is known as ‘domain’ of a function Collection of images is known as ‘range’ of a function

Collection of all numbers including natural number, 0, negative numbers, fractions, decimals, and irrational is known as real number. It is the greatest number system in this real world all types of number are included in there like whole numbers, integers, rational numbers.

When we have to compare two quantities, we use concept of inequalities in general and in mathematics we compare two algebraic expression or algebraic expression with constant using these (<, >, ≤and≥) signs

Mathematical expression of kind an where 'n' is called exponent and 'a' is called its base. And this represents that base 'a' will pe multiplied 'n' number of times. For example, 34=3×3×3×3

An algebraic expression is known as polynomials if the exponent of variables on each and every term are whole number.

For example, x2y+x-y+1 is a polynomial

But x+ 1x is not a polynomial.

Mathematical expression of kind a1n or na where '1n' or n.. is called radical and 'a' is called its radicand. And this represents that nth root of radicand is to be find. For example, 532=2

Expression in the form of fxgx in which both numerator and denominator are polynomials and gx≠0. For example, x2+3x+4x2+1 where x2+1 is not equal to zero for any real value of x.

Mathematically, sequence is f:N→A (a function f from natural number to a set A). In other words, sequence is a pattern between elements of a set in ordered way. For example, 1, 3, 32, 33………

Any function in the form of fx=ax2+bx+c, where a should not be equal to zero is known as quadratic function. It has its degree as 2, which means highest power of a term in that expression should be 2.

**Q1. Solve the following system of equation
2x+y=4,
3x+2y=7**

3x+2y=7………(2)

In order to solve this, we have make coefficient of one variable equal

2x+y=4………×2

3x+2y=7………×1

So, we have 4x+2y=8………(3)

3x+2y=7………(4)

Now to eliminate y we have to subtract the (3) and (4)

We get, x=1

Back substitute it in (1) we get

2(1)+y=4

y=4-2

y=2

**Q2. Find the zeros of the polynomial fx=x****^****2-5x-6**

**Sol. ** We have to factorise to find the zeros of the

f(x)=x**^**2-6x+x-6

f(x)=x(x-6)+1(x-6)

f(x)=(x-6)(x+1)

Now, f(x)=0

(x-6)(x+1)=0

Product of two factor will be zero if either of them is zero

x-6=0 or x+1=0

x-6 or x=-1

**Q3. Solve the inequality x-43 + x+54 >1**

**Sol.** (x-4)/3 + (x+5)/4 >1

(4x-16+3x+15)/12 >1

(7x-1)/12 >1

7x-1>12

7x>13

x> 137

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Algebra 1 is the second math course in high school, and it helps students learn real numbers and their operations in the very beginning. Typically, Algebra 1 is taught in high school in grade 9. However, depending on your school, you might learn algebra one concepts even in grade 7 and 8.

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The second Math course in high school is called Algebra 1. It is taught in 9th grade and focuses on solving equations and inequalities. It covers the following topics:

- Linear Equations
- Word problems
- Inequalities
- Sequences
- Functions
- Quadratic equations

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Algebra 1 is introduced in grade 9, and provides basic tools to the students to begin solving equations and inequalities. You will cover the following topics in this course:

- Functions and Relations
- Polynomials
- Radical expressions
- Linear Equations
- Quadratic Equations

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