March 3, 2022
The Central Board of Secondary Education had developed a new elective course for the class 12 Commerce stream i.e. Applied Maths. Algebra is considered one of the main topics of applied maths in class 12.
In the CBSE Class 12 Board Exam, Algebra covers 10 marks out of 80 marks. This post takes you through detailed information about CBSE Class 12 Applied Maths Algebra.
As per the CBSE Class 12 Applied Maths Syllabus the main topics that you will be studying in Algebra are:
Read About CBSE Class 12 Applied Maths Probability
Read About CBSE Class 12 Applied Maths Basic Financial with Mathematics
You will be studying various topics in the Applied maths Algebra section that are Matrices, Determinants, Cramer’s rule and its application, and Simple applications of matrices and determinants including Leontief input-output model for two variables.
Knowing the syllabus will help you know important Applied Maths Algebra CBSE class 12 topics and focus more on those topics to score good marks in the exam. The table below shows the CBSE class 12 Applied Maths Algebra syllabus 2021:
Topics | Explanation of Topics |
Matrices | Concept of matrices, Notation, order, equality, types of matrices, zero and identity matrix, transpose of a matrix, symmetric and skew-symmetric matrices. Operation on matrices: Addition and multiplication and multiplication with a scalar. Simple properties of addition, multiplication, and scalar multiplication. Non-commutativity of multiplication of matrices and existence of non-zero matrices whose product is the zero matrices (restricted to square matrices of order 2). Concept of elementary row and column operations. Invertible matrices and proof of the uniqueness of inverse, if it exists; (Here all matrices will have real entries). |
Determinants | Concept of Determinant, Determinant of a square matrix (up to 3 × 3 matrices), properties of determinants, minors, cofactors, and applications of determinants in finding the area of a triangle Adjoint and inverse of a square matrix Consistency, inconsistency, and number of solutions of a system of linear equations by examples, solving system of linear equations in two or three variables (having a unique solution) using an inverse of a matrix |
Cramer’s rule and its Application | Concept of Cramer’s rule and its Application, Derivation of application. |
Simple applications of matrices and determinants including Leontiff input-output model for two variables | Concept of Simple applications of matrices and determinants including Leontiff input-output model for two variables. |
Read about: CBSE Class 12 Linear programming
To help you better understand the type of questions asked from the algebra topic, we have provided few sample questions here.
Question 1: Under what conditions on the real numbers a, b, c, d, e, f do the simultaneous equations ax + by = e and cx + dy = f have (a) a unique solution, (b) no solution, (c) infinitely many solutions in x and y. Select values of a, b, c, d, e, f for each of these cases, and sketch on separate axes the lines ax+by = e and cx+dy = f.
Question 2: For what values of a do the simultaneous equations x + 2y + a2z = 0, x + ay + z = 0, x + ay + a2z = 0 have a solution other than x = y = z = 0. For each such a find the general solution of the above equations.
Question 3: Do 2 × 2 matrices exist satisfying the following properties? Either find such matrices or show that no such exist.
Question 4: (a) Find the remainder when n2 + 4 is divided by 7 for 0 ≤ n < 7. Deduce that n2 + 4 is not divisible by 7, for every positive integer n. [Hint: write n = 7k + r where 0 ≤ r < 7.] (b) Now k is an integer such that n3 + k is not divisible by 4 for all integers n. What are the possible values of k?
Read About CBSE Class 12 Applied Maths Inferential Statistics
Frequently Asked Questions
What is the weightage of Algebra section in Applied maths subject of class 12?
The Algebra section holds a weightage of 13 marks in Applied Maths subject of class 12.
What are the topics which will be taught in Applied Maths Algebra section class 12?
The topics which will be taught in Applied maths Algebra section class 12 are: -
What are the best reference books for the CBSE class 12 Applied Maths Subject?
The best reference books are: -
Which Mathematics is tougher, the pure one or the Applied one?
Both the mathematics subjects are tougher in their own way. The science stream students study pure mathematics, it is tough and beneficial for them, and the Commerce and Arts stream students generally now opt Applied mathematics subject because it is beneficial for their future career options also. So , both are tough in their own respect fields.
Updated On : March 3, 2022
The Central Board of Secondary Education had developed a new elective course for the class 12 Commerce stream i.e. Applied Maths. Algebra is considered one of the main topics of applied maths in class 12.
In the CBSE Class 12 Board Exam, Algebra covers 10 marks out of 80 marks. This post takes you through detailed information about CBSE Class 12 Applied Maths Algebra.
As per the CBSE Class 12 Applied Maths Syllabus the main topics that you will be studying in Algebra are:
Read About CBSE Class 12 Applied Maths Probability
Read About CBSE Class 12 Applied Maths Basic Financial with Mathematics
You will be studying various topics in the Applied maths Algebra section that are Matrices, Determinants, Cramer’s rule and its application, and Simple applications of matrices and determinants including Leontief input-output model for two variables.
Knowing the syllabus will help you know important Applied Maths Algebra CBSE class 12 topics and focus more on those topics to score good marks in the exam. The table below shows the CBSE class 12 Applied Maths Algebra syllabus 2021:
Topics | Explanation of Topics |
Matrices | Concept of matrices, Notation, order, equality, types of matrices, zero and identity matrix, transpose of a matrix, symmetric and skew-symmetric matrices. Operation on matrices: Addition and multiplication and multiplication with a scalar. Simple properties of addition, multiplication, and scalar multiplication. Non-commutativity of multiplication of matrices and existence of non-zero matrices whose product is the zero matrices (restricted to square matrices of order 2). Concept of elementary row and column operations. Invertible matrices and proof of the uniqueness of inverse, if it exists; (Here all matrices will have real entries). |
Determinants | Concept of Determinant, Determinant of a square matrix (up to 3 × 3 matrices), properties of determinants, minors, cofactors, and applications of determinants in finding the area of a triangle Adjoint and inverse of a square matrix Consistency, inconsistency, and number of solutions of a system of linear equations by examples, solving system of linear equations in two or three variables (having a unique solution) using an inverse of a matrix |
Cramer’s rule and its Application | Concept of Cramer’s rule and its Application, Derivation of application. |
Simple applications of matrices and determinants including Leontiff input-output model for two variables | Concept of Simple applications of matrices and determinants including Leontiff input-output model for two variables. |
Read about: CBSE Class 12 Linear programming
To help you better understand the type of questions asked from the algebra topic, we have provided few sample questions here.
Question 1: Under what conditions on the real numbers a, b, c, d, e, f do the simultaneous equations ax + by = e and cx + dy = f have (a) a unique solution, (b) no solution, (c) infinitely many solutions in x and y. Select values of a, b, c, d, e, f for each of these cases, and sketch on separate axes the lines ax+by = e and cx+dy = f.
Question 2: For what values of a do the simultaneous equations x + 2y + a2z = 0, x + ay + z = 0, x + ay + a2z = 0 have a solution other than x = y = z = 0. For each such a find the general solution of the above equations.
Question 3: Do 2 × 2 matrices exist satisfying the following properties? Either find such matrices or show that no such exist.
Question 4: (a) Find the remainder when n2 + 4 is divided by 7 for 0 ≤ n < 7. Deduce that n2 + 4 is not divisible by 7, for every positive integer n. [Hint: write n = 7k + r where 0 ≤ r < 7.] (b) Now k is an integer such that n3 + k is not divisible by 4 for all integers n. What are the possible values of k?
Read About CBSE Class 12 Applied Maths Inferential Statistics
Frequently Asked Questions
What is the weightage of Algebra section in Applied maths subject of class 12?
The Algebra section holds a weightage of 13 marks in Applied Maths subject of class 12.
What are the topics which will be taught in Applied Maths Algebra section class 12?
The topics which will be taught in Applied maths Algebra section class 12 are: -
What are the best reference books for the CBSE class 12 Applied Maths Subject?
The best reference books are: -
Which Mathematics is tougher, the pure one or the Applied one?
Both the mathematics subjects are tougher in their own way. The science stream students study pure mathematics, it is tough and beneficial for them, and the Commerce and Arts stream students generally now opt Applied mathematics subject because it is beneficial for their future career options also. So , both are tough in their own respect fields.