# How to Solve Algebra Questions in CDS Exam

By Naveen Singh|Updated : January 17th, 2019

Algebra makes an important part of the CDS mathematics exam as 17-20 questions out of the 100 questions are asked from this topic. Here we will discuss some important tips and tricks along with all the important formulae of algebra that you will need in the CDS exam. This article will help you in understanding the approach to solve questions and also will be helpful in your revision of this topic before exam.

## Tips to solve Algebra Questions for CDS Exam

Following are the topics covered under algebra:

• Basic Operations, simple factors, Remainder Theorem.
• Theory of polynomials, Solutions of quadratic equations, relation between its roots and coefficients
• Simultaneous linear equations in two unknowns-analytical and graphical solutions. Simultaneous linear in equations in two variables and their solutions.
• Practical problems leading to two simultaneous linear equations or in equations in two Variables or quadratic equations in one variable & their solutions.
• Set language and set notation, rational expressions and conditional identities, Laws of indices.

### Important formulae and theorems of Algebra

1. a2 – b2 = (a – b)(a + b)
2. (a + b)2 = a2 + 2ab + b2
3. a2  +b2  = (a – b)2 + 2ab
4. (a – b)2  = a2  – 2ab + b2
5. (a + b + c)2  = a2  + b2  + c2 + 2ab + 2ac + 2bc
6. (a + b + c)3  =  a3  + b3 + c3 + 3(a + b)(b + c)(c + a)
7. a3 + b3 + c3 - 3abc = (a + b+ c) ( a2  + b2  + c2 - ab - ac - bc) = 12(a+b+c) [(a-b)2  + (b-c)2  + (c-a)2 ]
if (a+b+c) = 0, then a3 + b3 + c3 = 3abc
8. (a + b)3 = a3 + 3a2b + 3ab2 + b3 ;
or, (a + b)
= a3 + b3 + 3ab(a + b)
9. (a – b)3 = a3 – 3a2b + 3ab2 – b3
10.  a– b3 = (a – b)(a2 + ab + b2)
11. a3 + b3 = (a + b)(a2 - ab + b2)
12. x2+ x(a + b) + ab = (x + a) (x + b)
13. Rules of indices
• a-n = 1/an
• (am)(an) = am+n
• (ab)m = ambm
• (am)n = amn
• am/an = am-n
• a0 = 1
14. Remainder Theorem – Let f(x) be a polynomial of a degree greater than or equal to one and α be any real number, if f(x) is divided by (x-α) then the remainder is f(α).
15. Factor theorem – Let f(x) be a polynomial of degree greater than or equal to one and α be any real number such that f(α) = 0, then (x-α) is a factor of f(x).
16. Relation between roots and coefficients of a quadratic equation
17. A quadratic equation is of the form ax2+bx+c = 0, where a, b and c are real numbers and a≠0. Let α and β be the roots of the quadratic equation, then
Sum of roots i.e. (α+β) = -b/a, and
Product of roots i.e. αβ = c/a, and ### Tips and tricks for solving algebra problems

• A lot of questions in algebra can be solved by putting some values of variables in the question, and it can help you in solving the question in no time. But this method needs to be applied very carefully. Your first approach to solve the problem should always be through basic method especially when you are practising at home.
• Even if you solve a problem correctly by putting values in variables, you must be aware of the basic method to solve the question. So after solving questions in quizzes you must look for basic/alternative methods in the solutions provided.
• Variety of questions in algebra is more as compared to other topics in mathematics. In order to solve a question easily in exam you should be familiar with different types of questions that are asked in CDS exam. If you would have solved the similar questions before, it will be quite easy for you to attempt them in the exam. So we sincerely advise you to solve previous year question papers of at least 5 years before appearing in the exam.
• You must remember all the important formulae in algebra. There is just no way around it.

To give you guys some idea about the type of questions asked in the CDS exam, here are some questions asked in the previous exams of CDS.

1. If x = y1/a, y = z1/b, and z = x1/c where x≠1, y≠1, z≠1, then what is the value of abc?

1. -1
2. 1
3. 0
4. 3

Solution:

x = y1/a, y = z1/b, and z = x1/c 2. If the roots of the equation px2 + x + r = 0 are reciprocal to each other, then which one of the following is correct?

1. P = 2r
2. P = r
3. 2p = r
4. P = 4r

Solution:

Let the roots be x and 1/x.

Use the property of quadratic equations {x+y = -b/a , xy = c/a};
x*1/x = r/p
1 = r/p
r = p
Thus option (b) is correct.

3. What is the value of α (α≠0) for which x2 - 5x + α and x2 - 7x + 2α have a common factor?

1. 6
2. 4
3. 3
4. 2

Solution:

Let (x - a) be the factor of both quadratic equation.
i.e. x = a is the root of both equation. Then x = a will satisfy both the equation.
So, a2 - 5a + a = 0... (i) and
a2 - 7a + 2a = 0... (ii)
Using quadratic formula for both (i) and (ii), we get: Thus option (a) is the correct answer.

Lastly practice of previous year papers and solving mock test would benefit the candidate in scoring good marks in the exam.

Note: Students who are going to appear for the CDS-I 2019 exam are requested to fill out the form below:

All the best for your exams,
Team BYJU'S Exam Prep

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