- 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
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 area-volume-perimeter 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.
Duration: 2 hours; 100 MCQs; 100 Marks; Negative-Marking for wrong answers: yes.
|BASICS: need to be prepared for any aptitude exam.||BoDMAS/Simplification||2||1||1||0|
|BANK: these topics are important for Bank, IBPS, LIC, PSU type exam.||% (profit loss, Interest rate)||5||7||2||2|
|statistics, Data Interpretation||6||7||7||5|
|SSC|CDS block: more than 50% of the Questions come from this block.||quadratic equations||11||9||13||13|
|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|
|total MCQs in CDS||100||100||100||100|
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)
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, profit-loss, simple-compound interest rate, time-speed-distance-work and statistics-Data 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
*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.
In CDS, there is minimum physical requirements for height, chest, eyesight. Similarly to glide through Maths paper, you need to meet following requirements:
- 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, HCF-LCM and divisibility related MCQs )
- 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.
Under this block: total four areas
|topic||priority||avg.MCQs in each of the last four CDS exams|
*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.
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
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 1-2 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||DQ|IAK|
|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 HCF-LCM of big numbers quickly but if it’s not going in your head (=”I can’t do”), then you can just use desi-method to find HCF-LCM (i.e. via factorization).
After this is done,
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 1-100
- How to test whether a number is prime or not? what is co-prime, what is composite number?
- rules of simplification or calculation (BODMAS)
- 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 235)
You may ignore following topics from his chapter on fundamentals
- Concept of remainder in huge numbers (e.g find remainder when 5123 divided by 7)
- imaginary numbers, complex numbers (i=root minus1)
- mth 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.)
HCF-LCM variety of questions
|GENERIC||REAL LIFE SITUATIONS|
|FRACTIONS AND DECIMALS||POLYNOMIALS**|
**for this type of MCQs, first go through quadratic equations related block.
|7_13 Exponents and Powers||comparing numbers with powers, how even-odd 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?
for these type of MCQs, first go through quadratic equation block.
@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 non-science stream and/or very weak in Maths:
Linear equation means unknown variable (x or y) doesn’t have anything above their ‘head’. e.g.
|x2+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 x1 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; time-speed-distance-work; profit-loss-SI-CI 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||adding-subtracting simple equations||IAK|
|8_2 Linear Equation||Age based questions||DQ|IAK|
|8_2 Linear Equation||Notes and coins denominations||DQ|IAK|
|10_3 Pair of Linear Equations in Two Variables||
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:
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 variable-two 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 kx-y=2 and 6x-2y=3 have a unique solution?
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|
|10_2 Polynomials||sum of roots, product of zeros (given on pg.30)||DQ|
|10_4 Quadratic Equations||
Then Sarvesh Kumar’s chapter on
- Elements of algebra. And memorize all the formulas given in this chapter e.g. a3+b3=(a+b)(a2+b2-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’ SSC-CGL papers (tier 1 Maths section and Tier II maths paper).
Demo MCQs from previous CDS exams
This concludes the block#1. In the next article, we’ll see how to approach block#2 (%, profit loss, SI-CI, time-speed-work).
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