Algebra, the pure branch of mathematics and many students are algebra phobic, they like other branch of mathematics but algebra is something like horror movies for them. Many students only fear from algebra and many of them fears even by the name of mathematics. Kids you should not fear from such an interesting subject, math is such an easy subject that if you start learning its concepts then automatically you start inducing in this subject. Algebra is the very first topic or we can say subject that is taught to students from the very first class of their school. Algebra is one of the most important branches of mathematics that deals with the numbers, constants, variables, operators and their relation. The main definition of algebra moves around these few things only but it has wide applications. Algebra moves around these few things still it is so wide that it has various sub branches. Mainly Algebra is divided in few branches that are algebra 1, algebra 2, algebra 3 and college algebra.
Algebra 1 (get more detail here) is the basic of algebra and it contains several topics. Topics involved in algebra 1 are linear equations, Simultaneous equations, Quadratic equation, binomial theorem and functions. Linear equations are something that students learn throughout their studies. Before we move to linear equations, let’s understand what are equations? Equations are those mathematical statements that are connected through an equal to symbol. This equal symbol plays a major rule in the equations or we can say it is the only thing that defines an equation. Linear equations are generally defined as those equations which show result as a straight line. They are generally given in the form of
x = my + c, you can also play number sets algebra 1 worksheets.
In this equation m is defined as the slope of the line and c is the y intercept. Linear equations can have many numbers of variables but, the variable must be of single power i.e the exponent of the variable must be only one. If the degree of variable is more than one then it is not linear equation. Linear equations can’t have x2, y2, x3, z6 and many other variables like this. With this the variables should also not be in the form like xy, yz, xyz, abcd, etc. Let’s have an example of linear equation to understand the concept of the equation and specially linear equations properly with this students can see how should they solve an linear equations problem.
Question: 2x + 7 = 3,
Solution: This is a linear equation having one variable. Solving the linear equation of one variable is very simple and you can easily solve this type of equations by taking the values one side and variable one side.
After this let's move to the linear equation of two variables, by linear equation of two variables we mean that equations having two unknowns whose value we have to determine the value of two unknowns. To the linear equations of two variables generally we use graph method. The graph of the linear equation must result a straight line if not then the equation is not linear. Every solution of the linear equation gives result as a point on the graph of the linear equation. Linear equation of two variables are like x + y =0, 2x + y =9, etc.
Now, move to the linear equations in the form of word problems. As you move to higher classes you will find several word problems and to solve such problems you first have to convert them in equation form. Let’s see an example of this: The sum of 2 times a number and 12 is 24. Find the number.
Solution: let’s assume the unknown as ‘x’. On doing two times of this we get,
2x and above problem says that the 2x+ 12 = 24,
2x = 24 - 12,
2x = 12,
x = 12/2,
x = 6.
Now, move to the other topic of algebra 1 i.e Simultaneous equations. These equations are a set of different equations with two or more variables. In Simultaneous equations we have multiple numbers of variables. Sometimes Simultaneous equations are also known as system of equations. There are several methods used to solve these types of equations out of which substitution and elimination method are most often used. The general form of Simultaneous equation is given as:
px +qy = r,
sx +ty = u.
All the equations that comes under simultaneous equation fall under this form only. To understand how to implement elimination method while solving the equations take an example and implement the method on that.
Let's take an example of two variables and two equations:
4x + 6y = 10,
4x + 20 = 4y,
To solve this system of equation we will use the elimination method it is the easiest method used to solve the Simultaneous equations.
In both the equations x is having the same value i.e. 4 so we can subtract equation one from two on doing this we get,
4x + 6y = 10,
4x – 4y = -20,
Subtract equation 1- equation 2,
4x + 6y = 10,
-(4x – 4y = -20),
10y = 30,
y = 30/10,
y = 3
In this way we eliminate the variable x and get the value of variable y. Now, put the value y in any of the above equation and with this we can easily calculate the value of x.
So first put the value of y in equation one on doing this we get,
4x + 6(3) = 10,
4x + 18 = 10,
4x = 10- 18,
4x = -8,
x = -8/4,
x = -2.
Thus x =-2 and y =3.
In this we way can use elimination method to solve the problems of the system of equations.
Quadratic equation is the other important topic that is covered under algebra 1. Quadratic equations are in the form of ax2 + by + c =0.
In the above equation a, b and c are the constant terms and x and y are the two variables. In this equation the value of ‘a’ can’t be equal to zero. It should always be greater than zero.
Whenever any problem related to quadratic equation occurs, we use two methods to solve such problems one is known as factoring method and other is known as quadratic formula. In the essential phase of quadratic equations we learn the factoring method and later on we learn its formula. The quadratic equation formula is given as:
Whenever we solve quadratic equation we get two roots or two answers having the same value but different signs i.e. one positive and one negative like, (-2 + 2).
Algebra 1 also contains binomial theorem, but before we move to theorem first study what Is binomial expression. Any algebraic expression containing two terms is defined as binomial expression. The general form of Binomial expression is defined as (x + y) or (x +y)n and it is called as binomial theorem. Binomial theorem is given as:
Let’s take an example and see how to solve binomial problems.
Question: ( 2x+ 1)5
Solution: Using the Binomial theorem,
( 2x+ 1)5 = 5C0(2x)5 10 + 5C1(2x)5-1 11 + 5C2(2x)5-2 12 + 5C3(2x)5-3 13 + 5C4(2x)5-4 14 + 5C5(2x)5-5 15
= 5C0(2x)5 + 5C1(2x)4 + 5C2(2x)3 + 5C3(2x)2 + 5C4(2x)1 + 5C5(2x)0
= 5C032x5 + 5C116x4 + 5C28x3 + 5C34x2 + 5C4 2x1 + 5C5
= 32x5 + (5) 16x4+ (10)8x3 + (10) 4x2 + (5) 2x + 1
= 32x5 + 80x4+ 80x3 + 40x2 + 10x + 1
In this way we get the solution of binomial problems.
Apart from all the above described topics, algebra 1 has many other topics such as exponents, radicals, one variables, ratios and percentage, common error and extra challenging problems, graphing of equation, complex numbers, special factorization, and many other topics. You can learn algebra 1 topics easily with little efforts. As you all know mathematics is that subject that needs lots of deviation towards the subject with regular practice. If you solve daily sheets then no one can stop you to become master of the subject. Algebra 1 is the base of algebra as it is the very first branch of algebra. When you move to higher classes you will go through Algebra 2, algebra 3 and college algebra. And college algebra is generally the last course of algebra that most of the students study.
In present time when whole world is running on internet, many websites are developed to help students so that they can easily learn mathematics. You can take online help to solve several math problems and even in online help you will find various resources using which you can easily learn different math topics. Take online help and solve all queries related to this subject and get out of the math problems and start scoring good grades.
In upcoming posts we will discuss about How to Graph Equations and Special names for sides and angles. Visit our website for information on school of secondary education Andhra Pradesh
Algebra 1 (get more detail here) is the basic of algebra and it contains several topics. Topics involved in algebra 1 are linear equations, Simultaneous equations, Quadratic equation, binomial theorem and functions. Linear equations are something that students learn throughout their studies. Before we move to linear equations, let’s understand what are equations? Equations are those mathematical statements that are connected through an equal to symbol. This equal symbol plays a major rule in the equations or we can say it is the only thing that defines an equation. Linear equations are generally defined as those equations which show result as a straight line. They are generally given in the form of
x = my + c, you can also play number sets algebra 1 worksheets.
In this equation m is defined as the slope of the line and c is the y intercept. Linear equations can have many numbers of variables but, the variable must be of single power i.e the exponent of the variable must be only one. If the degree of variable is more than one then it is not linear equation. Linear equations can’t have x2, y2, x3, z6 and many other variables like this. With this the variables should also not be in the form like xy, yz, xyz, abcd, etc. Let’s have an example of linear equation to understand the concept of the equation and specially linear equations properly with this students can see how should they solve an linear equations problem.
Question: 2x + 7 = 3,
Solution: This is a linear equation having one variable. Solving the linear equation of one variable is very simple and you can easily solve this type of equations by taking the values one side and variable one side.
- 2x = 3 -7,
- 2x = - 4,
- x = - 4/2,
- x =-2.
After this let's move to the linear equation of two variables, by linear equation of two variables we mean that equations having two unknowns whose value we have to determine the value of two unknowns. To the linear equations of two variables generally we use graph method. The graph of the linear equation must result a straight line if not then the equation is not linear. Every solution of the linear equation gives result as a point on the graph of the linear equation. Linear equation of two variables are like x + y =0, 2x + y =9, etc.
Now, move to the linear equations in the form of word problems. As you move to higher classes you will find several word problems and to solve such problems you first have to convert them in equation form. Let’s see an example of this: The sum of 2 times a number and 12 is 24. Find the number.
Solution: let’s assume the unknown as ‘x’. On doing two times of this we get,
2x and above problem says that the 2x+ 12 = 24,
2x = 24 - 12,
2x = 12,
x = 12/2,
x = 6.
Now, move to the other topic of algebra 1 i.e Simultaneous equations. These equations are a set of different equations with two or more variables. In Simultaneous equations we have multiple numbers of variables. Sometimes Simultaneous equations are also known as system of equations. There are several methods used to solve these types of equations out of which substitution and elimination method are most often used. The general form of Simultaneous equation is given as:
px +qy = r,
sx +ty = u.
All the equations that comes under simultaneous equation fall under this form only. To understand how to implement elimination method while solving the equations take an example and implement the method on that.
Let's take an example of two variables and two equations:
4x + 6y = 10,
4x + 20 = 4y,
To solve this system of equation we will use the elimination method it is the easiest method used to solve the Simultaneous equations.
In both the equations x is having the same value i.e. 4 so we can subtract equation one from two on doing this we get,
4x + 6y = 10,
4x – 4y = -20,
Subtract equation 1- equation 2,
4x + 6y = 10,
-(4x – 4y = -20),
10y = 30,
y = 30/10,
y = 3
In this way we eliminate the variable x and get the value of variable y. Now, put the value y in any of the above equation and with this we can easily calculate the value of x.
So first put the value of y in equation one on doing this we get,
4x + 6(3) = 10,
4x + 18 = 10,
4x = 10- 18,
4x = -8,
x = -8/4,
x = -2.
Thus x =-2 and y =3.
In this we way can use elimination method to solve the problems of the system of equations.
Quadratic equation is the other important topic that is covered under algebra 1. Quadratic equations are in the form of ax2 + by + c =0.
In the above equation a, b and c are the constant terms and x and y are the two variables. In this equation the value of ‘a’ can’t be equal to zero. It should always be greater than zero.
Whenever any problem related to quadratic equation occurs, we use two methods to solve such problems one is known as factoring method and other is known as quadratic formula. In the essential phase of quadratic equations we learn the factoring method and later on we learn its formula. The quadratic equation formula is given as:
Whenever we solve quadratic equation we get two roots or two answers having the same value but different signs i.e. one positive and one negative like, (-2 + 2).
Algebra 1 also contains binomial theorem, but before we move to theorem first study what Is binomial expression. Any algebraic expression containing two terms is defined as binomial expression. The general form of Binomial expression is defined as (x + y) or (x +y)n and it is called as binomial theorem. Binomial theorem is given as:
Let’s take an example and see how to solve binomial problems.
Question: ( 2x+ 1)5
Solution: Using the Binomial theorem,
( 2x+ 1)5 = 5C0(2x)5 10 + 5C1(2x)5-1 11 + 5C2(2x)5-2 12 + 5C3(2x)5-3 13 + 5C4(2x)5-4 14 + 5C5(2x)5-5 15
= 5C0(2x)5 + 5C1(2x)4 + 5C2(2x)3 + 5C3(2x)2 + 5C4(2x)1 + 5C5(2x)0
= 5C032x5 + 5C116x4 + 5C28x3 + 5C34x2 + 5C4 2x1 + 5C5
= 32x5 + (5) 16x4+ (10)8x3 + (10) 4x2 + (5) 2x + 1
= 32x5 + 80x4+ 80x3 + 40x2 + 10x + 1
In this way we get the solution of binomial problems.
Apart from all the above described topics, algebra 1 has many other topics such as exponents, radicals, one variables, ratios and percentage, common error and extra challenging problems, graphing of equation, complex numbers, special factorization, and many other topics. You can learn algebra 1 topics easily with little efforts. As you all know mathematics is that subject that needs lots of deviation towards the subject with regular practice. If you solve daily sheets then no one can stop you to become master of the subject. Algebra 1 is the base of algebra as it is the very first branch of algebra. When you move to higher classes you will go through Algebra 2, algebra 3 and college algebra. And college algebra is generally the last course of algebra that most of the students study.
In present time when whole world is running on internet, many websites are developed to help students so that they can easily learn mathematics. You can take online help to solve several math problems and even in online help you will find various resources using which you can easily learn different math topics. Take online help and solve all queries related to this subject and get out of the math problems and start scoring good grades.
In upcoming posts we will discuss about How to Graph Equations and Special names for sides and angles. Visit our website for information on school of secondary education Andhra Pradesh
