 Prologue
 Topic wise breakup CDS Maths Papers
 Gather the weapons
 Warm up the brain
 [Block#1]: Basics + Algebra
 Number System
 Surds, Indices, Powers, Exponents
 Linear Equations
 Quadratic equations
 Appendix Download link: Topic wise Sorted NCERTs
Prologue
Studyplan for CDS GK paper already given click me. In this three part article series, we’ll how to prepare for the maths papers. This is different from CSAT and CAPF in following ways:
 No questions on reasoning.
 Plenty of questions Trigonometry, quadratic equations asked.
 They ask theory based geometry i.e. beyond the routine areavolumeperimeter type questions that you see in bank, LIC and state service exams.
 Even Statistics based theory questions are asked.
In recent years, SSC CGL has been moving towards Trigonometry, Geometry and Quadratic equations. CDS runs on parallel tract, but with higher difficulty level.
Topic wise breakup CDS Maths Papers
Duration: 2 hours; 100 MCQs; 100 Marks; NegativeMarking for wrong answers: yes.
Block  CDS Exam  2012(I)  2012(II)  2013(I)  2013(II) 
BASICS: need to be prepared for any aptitude exam.  BoDMAS/Simplification  2  1  1  0 
surds indices  2  3  2  5  
number system  12  11  7  11  
linear equation  3  3  3  2  
BANK: these topics are important for Bank, IBPS, LIC, PSU type exam.  % (profit loss, Interest rate)  5  7  2  2 
RatioProportion  1  1  1  0  
MixtureAlligiation  0  0  2  1  
statistics, Data Interpretation  6  7  7  5  
TimeSpeedDistanceWork  3  5  9  10  
SSCCDS block: more than 50% of the Questions come from this block.  quadratic equations  11  9  13  13 
Trigonometry  10  14  18  14  
Geometry  39  34  33  36  
Misc: asked in SSS/CDS/CAT. This should be prepared at last, once you’re done with priority topics viz. trig, QE and geometry.  functions, Coordinate Geometry  2  1  0  0 
logarithms  3  2  0  0  
Venn Diagrams  1  2  2  1  
total MCQs in CDS  100  100  100  100 
Let’s plot this data on a graph.
From the above graph you can see in last two papers 2013(I) and 2013(II) nearly 80% of the questions came from only five topics viz.
 Number System
 Quadratic Equations (And Polynomials)
 TimeSpeedDistanceWork
 Geometry
 Trigonometry
so the only question remains is: how to prepare? I’m dividing it into four blocks, as show in the following chart. Topics highlighted in red, are high priority.
in this article, we’ll see how to handle block#1.
 Now in the second article, we’ll see how to approach block#2: percentage, profitloss, simplecompound interest rate, timespeeddistancework and statisticsData interpretation related problems. click me
 in this third and last article, we’ll see block#3: how to approach geometry, trigonometry and remaining misc. Topics(block#4) .click me
But first….
Gather the weapons
ESSENTIAL 

OPTIONAL 

*Which book to use for CDS Maths?
NCERTs only clear the basics but for competitive exam level maths, you need a book on quantitative aptitude to learn and practice advanced concepts. In the market there are plenty of names. My recommendation is as usual Quantam CAT by Sarvesh Kumar Verma.Reasons:
 RS Aggarwal, M.Tyra, Guha etc. don’t cover geometry theory (cords, bisectors, orthocenter etc.); trigonometry, quadratic equations, logarithms, etc. in detail. While they help for bank, LIC level exams but hardly useful for CDS.
 Sarvesh Kumar’s geometry chapter is thorough, particularly the summary tables of triangles, quadrilaterals and circles. Those of you already know the basics of geometry, can directly use without having to go through NCERTs.
 For the given price range this book helps in all competitive exams: starting from SSC CGL, PSU, IBPS, UPSC to all the way upto CAT. Each chapter contains introductory exercises, level 1, level2 and final round exercises. For CDS do upto level 1. Thus saves your time and money in not having to buy new book for every exam.
Warm up the brain
In CDS, there is minimum physical requirements for height, chest, eyesight. Similarly to glide through Maths paper, you need to meet following requirements:
Minimum:
 Memorize the multiplication tables of 2 to 9; 12, 15, 16 and 25.
 Memorize squares upto 19 and cubes upto 9. (necessary for number system, HCFLCM and divisibility related MCQs )
Preferred:
 Memorize the multiplication tables of 2 to 9; 12 to 25; finally 29
 Memorize squares upto 29 and cubes upto 15.
 Memorize all prime numbers between 1 to 100
 Trachtenberg’s speed multiplication rules for 5, 9 and 11. (http://en.wikipedia.org/wiki/Trachtenberg_system)
 two digit long division click me
Note: An excel file containing multiplication tables and prime numbers in given the NCERT zip file itself.
[Block#1]: Basics + Algebra
Under this block: total four areas
topic  priority  avg.MCQs in each of the last four CDS exams 

high  10 

medium*  3 

medium*  3 

high  11 
*although barely 3 MCQs are asked, still you need good grip over them, because indirectly these concepts are essential for solving other MCQs in compound interest rate, profit loss, quadratic eq. etc.
Number System
In CDS paper, a good number of questions directly come from theory/definitions. Hence NCERTs important. Example:
Q. The set of integers is closed with respect to which one of the following?
 Addition only
 Multiplication only
 Both A and B
 Division
You’ll find the answer in Class 7 NCERT. I’ve arranged the NCERT maths chapters from class7 to 10 (+a few from 11) topic wise according to their utility in the aptitude exams. Zip file is at bottom. Even in worst case scenario, at least go through the Summary at the end of each chapter. And don’t just ‘read’ the NCERT solve all the sums given in it, including the illustrations and examples.
Secondly, I’m providing reference tables about the NCERT chapters for each topic. Abbreviations:
 “7_1 integers”= class 7 maths textbook, chapter 1
 DQ=direct questions asked in CDS from the theory/definition/examples given in this chapter. Hence even if you “know” the topic, DO go through those chapters.
 IAK=”I already know”. Meaning you can ignore this chapter, if you’re basics are already good. (i.e. you’ve already cleared written stage of bank, SSC or LIC.)
 ICD=”I can’t do”. Meaning you the theory/ concept is just not going inside your head. versus barely 12 MCQs are asked from that particular in CDS exam. Then you take ‘risk’ to ignore/skip. As such I don’t recommend you skip anything but at the same time, there is no point in being stuck at just one topic when exam is just ~eight weeks away from now. (9 Feb.2014)
 “Bold”: topics highlighted in bold are MUST DO, Most important because MCQs routinely appearing from there.
Here starts the first table.
7_1 Integers  number line and properties of integers (associative, distributive etc)  DQ 
7_2 Fractions and Decimals  proper and improper fractions, comparing fractions  IAK 
7_9 Rational Numbers  comparing rational numbers  IAK 
8_1 Rational number  table 1.2 (properties of rational numbers) very important for MCQs.  DQ 
8_16 Playing with Numbers  Reversing digits.  DQ 
Divisibility rules for 2,3,5,9  IAK  
9_1 Number systems  recurring decimals  DQIAK 
real numbers geometry connection  DQ  
10_1 Real Numbers  Euclid’s division algorithm  ICD* 
Irrational numbers, prime numbers  DQ 
*Euclid’s division algorithm helps finding HCFLCM of big numbers quickly but if it’s not going in your head (=”I can’t do”), then you can just use desimethod to find HCFLCM (i.e. via factorization).
After this is done,
 http://mrunal.org/2013/03/aptitudelcmhcfgcdbasicconceptcalculationapplicationsexplained.html
 http://mrunal.org/2013/01/aptituderemainderonenumberandtwodivisorsnumbertheory.html
Lastly Sarvesh Kumar’s chapter on fundamentals. focus especially on the following topics
 Divisibility rules with special focus on (7,11,13,17,19,23) Because for prime number related MCQs you’ll need it. then solve all the MCQs in his first introductory exercise
 properties of squares
 table of prime numbers from 1100
 How to test whether a number is prime or not? what is coprime, what is composite number?
 rules of simplification or calculation (BODMAS)
 Remainders
 HCF with remainders
 LCM with remainders
 HCM and LCM of fractions and decimals
 square roots and cube roots of fractions
 recurring decimals
 conjugate surds and the sums related to them
 concept of unit digit (e.g. what is the unit digit of 2^{35})
You may ignore following topics from his chapter on fundamentals
 Concept of remainder in huge numbers (e.g find remainder when 5^{123} divided by 7)
 imaginary numbers, complex numbers (i=root minus1)
 m^{th }root of unity
 digital number systems (converting decimal into binary etc)
 coding decoding
now let’s check the…
Demo MCQs from previous CDS exams
NUMBERS CLASSIFICATION  PRIME NUMBER 


DIVISIBILITY RELATED  REMAINDER THEOREM RELATED 


LAST DIGIT  RECURRING DECIMALS 

(Note in following number, assume underline is “bar” above the number.)

HCFLCM variety of questions
GENERIC  REAL LIFE SITUATIONS 


FRACTIONS AND DECIMALS  POLYNOMIALS** 


**for this type of MCQs, first go through quadratic equations related block.
Surds, Indices, Powers, Exponents
7_13 Exponents and Powers  comparing numbers with powers, how evenodd powers change the sign of negative numbers, expressing large numbers in std.form  IAK 
8_06 Squares and Square Roots  finding square root through repeated subtraction, square roots of decimals, estimating square root  DQ 
8_07 Cube and Cube Roots  finding cube roots  ICD 
8_12 Powers  laws of exponents, expressing numbers in standard form.  DQ 
Demo MCQs from previous CDS exams
comparing quantities  solving unknown powers 
Which is the smallest number of the following?
Which of the following is largest?


finding roots**  

for these type of MCQs, first go through quadratic equation block.
Linear Equations
@Those from Science/engineering background: directly goto Sarvesh Kumar=>chapter on “Elements of Algebra” =>Linear Equation. Mugup the theory bullets, do all the examples, introductory exercises and level1.
@Those from nonscience stream and/or very weak in Maths:
Linear equation means unknown variable (x or y) doesn’t have anything above their ‘head’. e.g.
x^{2}+2x+1  This is not linear equation because x has “2” above its head. 
2x+1  This is linear equation because x doesn’t have anything above its head. (Actually its x^{1 }but for our understanding purpose, take it as just “x”) 
Linear equations are very important for aptitude exams. Both as ‘direct MCQs’ (for age, salary, spending related problems) as well as indirect applications in Geometry; timespeeddistancework; profitlossSICI problems etc. first go through following NCERT chapters:
7_4 Simple Equations  how to convert statements into simple equation.  IAK 
7_12 Algebraic Expressions  MONOMIALS, BINOMIALS, TRINOMIALS AND POLYNOMIALS  DQ 
7_12 Algebraic Expressions  addingsubtracting simple equations  IAK 
8_2 Linear Equation  Age based questions  DQIAK 
8_2 Linear Equation  Notes and coins denominations  DQIAK 
10_3 Pair of Linear Equations in Two Variables 

DQ 

DQ  

ICD 
Then goto Sarvesh Kumar=>chapter on “Elements of Algebra” =>Linear Equation. Mugup the theory bullets, do all the examples, introductory exercises and level1
Two things to be kept in mind, while solving questions on linear equation:
#1: keep minimum variables
Suppose the question runs like this “The sum of present ages of father and son is 56, and 5 years ago Son’s age was……….blah blah blah….find the present age of Father. ”
avoid this  do this 




#2: Cannot be determined
Suppose you end up with two equations like this:
 x+y=5
 y+z=6
Here you’ve two equations but three variables (x, y and z). You can never find out the unique value of x, y, z in such situation. Hence answer = “Cannot be determined”.
But sometimes, even two variabletwo equation set can be impossible to solve. For example
No solution  infinite solution 

2x+ 3y=94x+ 6y=18 
To learn more about ^this, refer to NCERT Maths Class 10, Chapter3, table given on the page #9. CDS directly asks MCQs from this.
Linear equations: Variety of MCQs
From previous CDS exam
Age  digit reversal / unknown numbers 


Nature of solutions  nature of solutions 
The system of equations x+2y=3 and 3x+6y=9 has?

Under what condition do the equation kxy=2 and 6x2y=3 have a unique solution?

Quadratic equations
High priority topic, ~11 MCQs each year in last four exams.
8_9 Algebraic Expressions  Polynomials: additions, subtraction, multiplication.  IAK 
8_14 Factorization  making Factors of the form (x + a) (x+ b); division of polynomials  IAK 
9_2_Polynomials 

DQ 
10_2 Polynomials  sum of roots, product of zeros (given on pg.30)  DQ 
10_4 Quadratic Equations 

DQ 
Then Sarvesh Kumar’s chapter on
 Elements of algebra. And memorize all the formulas given in this chapter e.g. a^{3}+b^{3}=(a+b)(a^{2}+b^{2}ab)
 Theory of equations. (You may ignore the graphs, maximum minimum values.). Sometimes CDS even asks Quadratic inequalities it is explained in this chapter, but if that theory is not going in your head then ignore because at most only one MCQ comes that too not on regular basis.
For additional practice on polynomials and quadratic equations, you can solve the last three years’ SSCCGL papers (tier 1 Maths section and Tier II maths paper).
Demo MCQs from previous CDS exams
FACTORS  REMAINDERS 


ROOTS  HCF, LCM 


This concludes the block#1. In the next article, we’ll see how to approach block#2 (%, profit loss, SICI, timespeedwork).
Appendix Download link: Topic wise Sorted NCERTs
You’ve two choices
Choice #1: good internet connection: And you want to download entire zip file at once (size 35MB) then use following link: https://files.secureserver.net/0sYHJ029rgUbrg
Choice #2: not so good internet connection: and / or You want to download small zip files or selective topics only, then goto following link (e.g. geometry zip file separately, trigonometry zip file separately and so on) then use following link: https://files.secureserver.net/0fmaNqqBDslHlc
Hello Sir,
Please give the analysis of UPSC 2013 mains paper questionwise.i.e, From which book did the questions appeared and how to cover the syllabus?
I am thinking to start my preparations after your analysis.
Thank you.
eagerly waiting 4 ur phd on GS papers
Sir, I have only one month for study. can you tell me some important topics of maths & G.K regarding CDS 1 2014.
dear sir, I want best book for level upcoming cds 2 2014 mathematics preparation. thank you
Sir , i want study plan of UPSC pre exam both papers. please give me a right direction.
i am using fast track objective mathematics by rajesh verma For CDS is it okie ?