1. Prologue
2. [Block#3] Geometry + Trig.
   1. [Geo] AVP/Mensuration
   2. [Geo] theory / non-AVP
      1. [Geo_theory1]Lines and Angles
      2. [Geo_theory2] Triangles
      3. [Geo_theory3]Quadrilaterals
      4. [Geo_theory4]Circles
   3. Trigonometry
      1. [Trig] Height and Distance (HnD)
      2. [Trig] non-height distance
3. [Block#4] Misc.Topix
   1. #1: Set Theory / Venn Diagrams
   2. #2: Logarithms
   3. #3: AP-GP Progression
   4. Topics to ignore
4. Epilogue
   1. Rule#1: Must finish entire block in one go
   2. Rule#2: Winners don’t make excuses
   3. Rules#3: Must get hands dirty, must maintain a diary of mistakes
5. Appendix Download link: Topic wise Sorted NCERTs

Prologue

1. In the first article, we saw how to prepare number system, surds-indices, linear and quadratic equations for CDS maths paper. click me
2. Now in the second article, we’ll see how to approach percentage, profit-loss, simple-compound interest rate, time-speed-distance-work and statistics-Data interpretation related problems. click me
3. in this third and last article, we’ll see how to approach geometry, trigonometry and remaining misc. Topics.

[Block#3] Geometry + Trig.

topics in this block	avg. MCQs in each of the last four CDS exams.	priority
Geometry	36	highest of all topics
Trigonometry	14	2nd highest of all topics

You should prepare this block only after finishing earlier block because

1. Some of the geometry MCQ require understanding of percentages, ratios and linear equations.
2. Some of the trigonometry MCQ require understanding of quadratic equations and geometry.

[Geo] AVP/Mensuration

Officially called “Mensuration”, this involves

1. Area and perimeter (A+P) of 2D figures: triangles, squares, rectangles, parallelogram, hexagons
2. Surface area, volume and perimeter (A+V+P) of 3D figures: spheres, cones, cylinders. Occasionally prism (tents), frustums (buckets) and pyramids.

Approach

1. From all the following NCERT chapters, memorize all the formulas given in the end summary of every chapter. Better write them down in your diary of mistakes.
2. for class 9 and class 10 NCERT chapters given below, you must solve all the examples and exercises given in them
3. Avoid silly mistakes e.g.
   • putting value of diameter instead of radius in the formula
   • not converting everything in same unit (cm/m/km)

7_11_Perimeter and Area	Basics about area-perimeters of parallelograms and circles.	IAK
8_11_Mensuration Modified	Area of Trapezium, polygon. General formula for quadrilaterals via diagonals.	DQ
8_11_Mensuration Modified	Cube, Cuboid and Cylinder- their area Volume and Capacity.	DQ | IAK
9_12_Herons formula	for finding area using ‘semi-perimeter’ concept for triangles and Quadrilaterals.	DQ | IAK
9_13_Surface areas and volumes	of cuboid, cylinder, cone, sphere. Solve all the examples and exercises from this chapter.	DQ | IAK
10_12 Areas Related to Circles	Solve all the problem figures given in this chapter.	DQ
10_13_Surface Areas and Volumes	More complex sums involving combination of solids e.g. two half spheres and a cylinder in between etc. Solve all the examples and exercises given in this chapter	DQ*

After this goto Sarvesh Kumar’s chapter on Mensuration and  Solve all the examples, introductory exercises and level 1 exercises. Note: he has given a big table at the beginning of this chapter, dealing with area, perimeter – Memorize it entirely.

*abbreviations used in above table

• “7_11 Perimeter and Area”= class 7 maths textbook, chapter 11
• 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.)
•  “Bold”: topics highlighted in bold are MUST DO, Most important because MCQs routinely appearing from there.

Observe the MCQs from past CDS exams

TRIANGLES	QUADRILATERAL
The area of a triangle ABC is equal to area of square of side length 6cm.What is the length of the altitude to AB where AB=9 cm? If the area of a circle, inscribed in an equilateral triangle is 4pi cm2, then what is the area of the triangle?	A man walking at the rate 3km/h crosses a square field diagonally in 1 min. What is the area of the field? A circle is inscribed in an equilateral triangle of side “A”. What is the area of any square inscribed in this circle?
Circle	Sphere
Three congruent circles each of radius 4 cm touch one another. What is the area (in cm2) of the portion included between them? A circle circumscribes a rectangle with sides of 16cm x 12 cm. find area of the circle region outside this rectangle. the areas of two circles are in the ratio of 1:2m if the two circles are bent in the form of squares, what is the ratio of their areas?	What is the number of wax balls, each of radius 1 cm that can be molded out of a sphere of radius 8 cm? The surface area of a sphere is 616 sq cm. If its radius is changed so that the area gets reduced by 75%, then find radius? A hemispherical bowl of internal radius 20 cm contains sauce. The sauce is to be filled in a conical shaped bottles of radius 5 cm and height 8 cm. What is the number of bottles required?
CYLINDER	CONE / FRUSTUM
A roller of diameter 70 cm and length 2m is rolling on the ground. What is the area covered by the roller in 50 revolutions? Form a wooden cylindrical block, whose diameter is equal to its height, a sphere of maximum possible volume is carved out. What is the ratio of the volume of the utilized wood to that of the wasted wood?	a right circular cone is cut by a plane parallel to its base in such a way that slant highest of the original and smaller cone thus obtained are in the ratio of 2:1. If V1 and V1 are the respective volumes of the original cone and the new cone, then what is the ratio of V1: V2? let C be a right circular cone with two ends of a frustum C are of radii 3cm and +6 cm. And the height of frustum C is 9cm. Find the slant height of frustum and total surface area of this frustum.

+ Variety of diagram/figure based questions. But for the lack of time, I’m not inserting their scanned photos here in the article.

[Geo] theory / non-AVP

• Questions involving sides, angles, midpoints, bisectors, centroid etc. topics related to 2D figures (lines, triangles, quadrilaterals and circles.)
• In CDS, usually they give a problem figure that has one or more combination of triangle + parallelogram + circle. So, first you need master the individual figures (triangles, parallelogram and circle) before you attempt the MCQs involving their combination.

[Geo_theory1]Lines and Angles

Superficially this might look like a ‘chillar’ topic but good number of MCQs come every year from here.

7_5 Lines and Angles	types of angles, pair of angles	IAK
9_6_Lines and angle	Intersecting lines and the angels made by them. corresponding, interior etc.	IAK
9_5_Introduction to Euclid’s geometry	basics of axioms and theorem	IAK

Then move to Sarevsh Kumar=>Geometry=> starting part of the chapter and the big table of lines-angle and first introductory exercise.

Observe the MCQs from past CDS exams

1. Three lines intersect each other in pairs. What is the number of angles so formed? (3/6/9/12)
2. Assertion (A) two distinct lines cannot have more than one point in common. Reasoning (R) any number of lines can be drawn through one point.
3. What is the least number of straight lines for a bounded plane figure?(1/2/3/4)
4. What is the angle which equals one –fifth of its supplement (15/30/36/75)
5. If two parallel lines are intersected by a transversal, then
   1. Each pair of corresponding angles are equal.
   2. each pair of alternate are unequal.
   3. both A and B correct
   4. None
6. + Variety of diagram/figure based questions. But for the lack of time, I’m not inserting them here in the article.

[Geo_theory2] Triangles

Similarity and congruence are most important because in variety of MCQ figures involving – you’ll have to apply these concepts to get the value of any side/angle/area. Master them from NCERTs.

7_6 The Triangle and its Properties	altitude, angle sum property, sums of sides and inequalities related to it, Pythagoras	IAK
7_7 Congruence of Triangles	SSS, SAS, ASA congruence	IAK
9_7_Triangles	advanced concepts related to Congruence, sides-altitude and base	DQ
9_12_Herons formula	for finding area using ‘semi-perimeter’ concept for triangles and Quadrilaterals. Mugup the Summary	DQ | IAK
10_6 Triangles	Similarity of triangles/	DQ

Then, Sarevsh Kumar=>Geometry=>Triangle related table and introductory exercises.

1. Mugup the table related to altitude, median, angle bisector, circumcenter / orthocenter/ incenter/ centroid of a triangle.
2. He has also given a separate table important theorems on triangles. Within that important are:
   1. BPT, midpoint, Apollonius, interior exterior bisector.
   2. You can ignore 45-45-90 and 30-60-90 theorem because I’ve already covered its applications in trigonometry – in separate articles and videos.

Triangles: Demo MCQs from previous exam

1. The point of concurrence of the altitudes of a triangle is called? (circumcenter / orthocenter/ incenter/ centroid)
2. find correct statement
   1. Congruent triangles are similar.
   2. If the hypotenuse and a side of one right triangle are equal to the hypotenuse and a side of another right triangle respectively, then the two right triangles are congruent.
   3. both A and B
   4. neither A nor B
3. What is the number of points in the plane of a triangle ABC are at equal distance from the vertices of the triangle?
4. Assertion (A) If two triangles are congruent, then their corresponding angles are equal. Reason (R) Two congruent triangles have same area.
5. A triangle DEF is formed by joining the midpoints of the sides of triangle ABC. Similarly a triangle PQR is formed by joining the mid-points of the sides of the triangle DEF. If the sides of the triangle PQR are of lengths 1, 2 and 3 units, what is the perimeter of the triangle ABC?
   1. 18 units
   2. 24 units
   3. 48 units
   4. Cannot be determined due to insufficient data
6. The centroid of a triangle ABC is 8cm from the vertex A. What is the length of the median of the triangle through A?
7. A piece of wire 78 cm long is bent in the form of an isosceles triangle. If the ratio of one of the equal sides to the base is 5:3, then what is the length of the base?
8. + Variety of diagram/figure based questions. But for the lack of time, I’m not inserting their scanned photos here in the article.

[Geo_theory3]Quadrilaterals

Quadrilateral means four sided 2D figure: square, rectangle, kite, trapezium, rhombus etc.

8_3 Understanding Quadrilaterals	Angle-sum property, exterior angles, Parallelogram: diagonals, sides, angles, rhombus. properties of quadrilaterals (given at bottom of chapter)	DQ
9_8_Quadrilaterals	Theorems related to quadrilaterals, diagonals, midpoints, bisectors	DQ
9_9_Areas of parallelograms and triangles	this is not related to ‘formulas’ but theory about triangles-parallelograms on same base, one figure inside another etc. must be thoroughly prepared	DQ
8_10 Visualizing Shapes_euler’s formula	only one topic: Euler’s formula for polyhedron (F+V-E=2), given under topic Number 10.4	DQ

Then Sarevsh Kumar=>Geometry=>Quadrilaterals related table and introductory exercises.

He has summarized the bullets related to quadrilateral properties. Religiously memorize them for the theory/definition based MCQs. also do the ‘polygon’ related section – particularly the table about sum of all angles, no. of diagonals for triangle, quadri., pentagon, hexagon etc.

Triangles: Demo MCQs from previous CDS exams

1.Find correct statement If the diagonals of a parallelogram ABCD are perpendicular, then ABCD may be a rhombus. If the diagonals of a quadrilateral ABCD are equal and perpendicular, then ABCD is a square. both A and B Neither A nor B	2.Correct statement about quadrilateral In a the line segments joining the mid-points of two pairs of opposite sides bisect each other at the point of intersection area of quadrilateral formed by joining the mid-points of the four adjacent sides is half the total area of the quadrilateral both A and B neither A nor B.
3.ABCD is a quadrilateral such that BC = BA and CD > AD. Which one of the following is correct? ZBAD = LBCD ZBAD < LBCD ZBAD > ZBCD 2ZBAD = ZBCD	4.Assertion (A) if the sides of a rhombus is 10 cm. its diagonals should have values of 16cm and 12 cm. Reason(R) The diagonals of a rhombus cut at right angles.5. + Variety of diagram/figure based questions. But for the lack of time, I’m not inserting their scanned photos here in the article.

[Geo_theory4]Circles

Another prominent topic under geometry MCQs. Often the problem figure would involve a triangle / quadrilateral embedded inside the circle. Hence, circle topic should be prepared only after mastering triangles and quadrilaterals topics first.

9_10_Circles	circle related terms, all the theorems given in this chapter	DQ
	distance of chord from center intersecting circles,	DQ
	All the Problem figures involving circle + triangles/quadrilaterals and various sides/angles. cyclic quadrilateral	DQ
10_10 Circles	number of tangents from a circle	DQ

After this, Sarvesh Kumar=>Geometry=>Circles and the introductory exercises. And memorize the table on circle theorems. That’ll help you directly solve variety of MCQs problem figures of circles+ (triangle/quadrilateral) combinations without having to do any calculations.

Once you’re finished with circle’s introductory exercises. do the level 1 sums from Geometry chapter. (and if you’ve time and mood- even do level2 for additional grip.)

Circles: Demo MCQs from previous CDS exams

A regular hexagon is inscribed in a circle of radius 5 cm. If x is the area inside the circle but outside the regular hexagon, then which one of the following is correct? 13  < x < 15 15  < x < 17 17  < x < 19 (d)  19  < X < 21	The diameter of a circle with centre at C is 50 cm. CF is a radial segment of the circle. AB is a chord perpendicular to CP and passes through P. CP produced intersects the circle at D. If DP = 18 cm, then what is the length of AB? 24 cm 32 cm 40 cm (d)  48 cm
What is the number of circles passing through all the vertices of a given triangle? (1/2/3/infinite) What is the number of circles passing through a given pair of points? (1/2/more than two but finite/infinite) ABCD is concyclic quadrilateral. The tangents at A and C intersect each other at P. If angle ABC=100 degrees, then what is angle APC equal to?	The distance between the centres of two circles having radii 4.5 cm and 3.5 cm respectively is 10 cm.What is the length of the transverse common tangent of these circles? + Variety of diagram/figure based questions. But for the lack of time, I’m not inserting their scanned photos here in the article.

Trigonometry

Trigonometry is an important topic for both CDS as well as SSC-CGL. but there are few differences

1. CDS doesn’t ask question on minimum-maximum values. (Atleast I didn’t notice in last five years’ papers)
2. CDS asks less questions from height distance and more questions from trig+algebra combo question.
3. CDS asks quadrant –sign based question (usually ignored in SSC CGL)

Anyways, how to approach?

First finish geometry and quadratic topics. Because many of these trig.MCQs require understanding of previous two blocks.

[Trig] Height and Distance (HnD)

observe the sample questions from past CDS exams

A radio transmitter antenna of height 100m stands at the top of a tall building.At a point on the ground,the angle of elevation of bottom of the antenna is 45degrees and that of top of antenna is 60degrees.What is the height of the building?

The angle of elevation of the top of a tower from the bottom of a building is twice that from its top. What is the height of the building, if the height of the tower is 75m and the angle of elevation of the top of the tower from the bottom of the building is 60 degrees?

in every CDS exam, alteast one-two MCQs are from this “height-distance” subtopic of trigonometry, To solve them, go through following articles cum YouTube videos (and solve all the questions given at the bottom of each article)

1. [Trigonometry] Introduction, Types of Questions, Shortcut for memorizing 30,45,60 for SSC CGL CDS
2. [Trigonometry] HnD Type #1: One Building One Angle finding height, distance or hypotenuse
3. [Trigonometry] HnD Type #2: Broken Trees and Telegraph Poles: Finding original height
4. [Trigonometry] HnD Type #3: One Building Two Angles made easy for SSC
5. [Trigonometry] HnD Type #4: Two Buildings-Two Angles made easy for SSC
6. [Trigonometry] HnD Type #5: Finding speed, time or distance made easy for SSC

^in the mock questions given in articles, I’ve covered all the good questions from NCERT. Still if you want to go through NCERTs, they’re included in the zip file.

• 10_8 Introduction to Trigonometry
• 10_9 Some Applications of Trigonometry

for additional practice: Sarvesh Kumar, and/or old papers for CDS, SSC.

[Trig] non-height distance

First observe MCQs from past exams

TYPE#2: TABLE (VALUE) BASED	TYPE#3: COMPLIMENTARY ANGLES
what is the value of cos1 x cos2 x cos3 x….xcos90.	what is the value of cot15 x cot 20 x cot70 x cot 5 (options: -1/0/1/2) if sin3A=cos(A-2) where 3A and (A-2) are acute angles, then what is the value of “A”?(options: 22/23/24/25)
TYPE#4: COMBO OF TRIG+ ALGEBRA	Type#5: Degrees and radians
if sinA+cosA=1 then what is the value of sinAcosA? if cotA=(2xy)/(x2-y2) then what is the  value of cosA in terms of x and y? what is the value of (sin4x-cos4x+1)cosec2x? (options: 1/2/0/-1) if 2sec2A+secA-6=0, what is the value of cosecA?	A unit radian is approximately equal to how many degrees? if pie=22/7, what is the approx. value of 1 radian? How many degrees are there in an angle which equals two-third of its complement? (36/45/48/60)
TYPE#6: QUADRANTS
Q.for the first quadrant, which of the following correct? sin2x <1/2 and cos2x >1/2 sin2x >1/2 and cos2x <1/2 sin2x <1/2 and cos2x <1/2 atleast one of the sin2x or cos2x is less than 1	Q.if cosA is greater than or equal to 1/2 in first quadrant then which of the following correct? A is less than or equal to pie/3 A is greater than or equal to pie/3 A is less than or equal to pie/6 A is greater than or equal to pie/6

How to approach type 2 to 4

Go through these articles and solve all the questions given at bottom of each article

1. [Trigonometry] Type#2: Table based questions, memorization technique, approach explained for SSC CGL
2. [Trigonometry] Type#3: Complimentary Angles related Questions and approach for SSC CGL
3. [Trigonometry] Type#4: Questions based on Trig and Algebra combo

For additional practice: Sarvesh Kumar, and/or old papers for CDS, SSC.

HOW TO APPROACH TYPE 5 (Quadrants)?

• NCERT class 11 ch.3 Trigonometric Functions: page 50 to55 (included in the zip file) solve all the sums as well.
• and / or Savesh Kumar’s chapter on trigonometry

HOW TO APPROACH TYPE 6 (radians / degrees)?

• NCERT class 11 ch.3 Trigonometric Functions: page 55 to59 (include in the zip file).
• and / or Sarvesh Kumar chapter on trigonometry

[Block#4] Misc.Topix

Overall lowest priority because the following topics, barely 2-3 MCQs come. Although their cost:benefit is still good (compared to amount of pages you’ve to mupup to get one geography question right) so, When you’re finished with everything else and still have time and mood, do go through these topics.

#1: Set Theory / Venn Diagrams

Usually 2-3 MCQs per exam. Although NCERT class 10 chapter 15 does cover set-theory but to save time, just mugup the bullets given in Sarvesh Kumar’s chapter on Set Theory and solve the practice sums.

Observe the MCQs from previous exam:

set theory	Venn diagram
If A={1,2,3,4}, what is the number of subsets of A with at least three elements? set S={x belongs to natural numbers and x+3=3} is a null set infinite set singleton none of these.	In an examination,52% candidates failed in English and 42% failed in Mathematics. If 17% candidates failed in both English and Mathematics, what percentage of candidates passed in both the subjects? in a school, there are 30 teachers who teach maths or physics. of these 20 teach maths and 15 teach physics. 5 teach both maths and physics. How many teachers only teach maths? (options: 5/10/15/20)

#2: Logarithms

• Questions not seen in the recent years and at most one MCQ comes. Although if you’re left with free time, doesn’t take much effort to master.
• for this directly go through Logarithm chapter in Sarvesh Kumar’s book, ignore details related to graphs and characteristics of Mantissa. Solve upto introductory exercise only.

Logarithms: Demo Q. from previous CDS exams:

1. What is the value of [5 log₁₀ 100]²?
2. If log_r6=m and log_r3=n, then what is log_r(r/2)equal to?
3. What is the value of [Log₁₃(10)]/[Log₁₆₉(10)]?
4. What is the value of Log₁₀₀0.1

#3: AP-GP Progression

Arithmetic progression (AP)	geometric progression (GP)
if the 14th term of an arithmetic series is 6 and 6th term is 14 then what is the 95th term?	a ball is dropped from the height of 64m above the ground, and every time it hits the ground, it raises to a height equal to half of the previous. What is the height attained after it hits the ground for 16th time?

AP-GP are not asked on regular basis but once in a while randomly appear.

I’ve included the respective NCERT chapters from class 10 and 11. but to save time you may just directly go to Sarvesh Kumar’s chapter on “Sequence, series and progressions” : memorize the formulas and solve introductory exercises only.

Topics to ignore

1. Permutation Combination Probability
2. Coordinate Geometry

Because from above topics, I didn’t see any MCQs in recent years’ CDS papers. (or may be I didn’t look carefully!)

Epilogue

Epilogue, concluding words, sacred rules, unwanted advice, whatever you want to call it….

Rule#1: Must finish entire block in one go

• Suppose today you finished ‘triangle’ topic under geometry. Then you take a ‘break’ and focus on polity for next 2-3 day, then some history, geography etc.  Later you resume back geometry, prepare quadrilaterals after a week.= This type of scattered preparation won’t help you get a steel grip over mathematics.
• You’ve to finish entire block in one go (e.g. picked up geometry then do triangles, quadrilaterals, circles, area-volume-perimeter… everything continuously.)

Rule#2: Winners don’t make excuses

EXCUSES	WHY #EPICFAIL?
Maths is not my cup of tea. so, I’ll pay extra attention to GS/GK and English to clear this exam.	Many senior players re-appear in CDS because they failed in earlier CDS@interview level. They work hard for all three papers (GK, Maths and English) so don’t live in a fantasy world that just because you’re avoiding maths means everyone else is also going to avoid maths. Donot underestimate competition. Agreed, a few of these MCQs look tough upfront but a sincere preparation- anyone-irrespective of graduation stream-can accurately solve majority of these question.  so, “I can’t do maths” =that is a lame excuse.
I’ve so many things to prepare in current affairs, I’m unable to take out time for maths!	In CDS GK paper, majority of the MCQs are from static/theory portion. It doesn’t require detailed reading of newspapers on daily basis. Just glance over- note down important Persons in news, opinion/GD based topics (like Homosexuality/#377) for interviews, and be done with it. You don’t have to spend entire day in current affairs. So don’t make an ‘excuse’ that I had to finish current affairs/newspaper hence I couldn’t pick up maths.
Hotaa hai, chaltaa hai, thik hai, dekhenge, abhi bahot der hai,there is still lot of time left.	No. Today is 14th Dec. CDS(I)2013 is on 9th February 2013= that’s ~55 days =~8 weeks. You cannot afford to continue preparation in a casual manner anymore. Must pump maximum hours per day in reading-revision-practice.

Rules#3: Must get hands dirty, must maintain a diary of mistakes

Why? Explained in following link https://mrunal.org/2012/03/strategy-art-of-preparing-for-aptitude.html

Rules#4: Must solve alteast 3 previous papers

Once you finish the maths syllabus. download and solve atleast three original UPSC CDS maths paper from their official site within three hours time limit for each. At home, you can take 5-10-15 minutes to solve one sum but in the exam hall you cannot waste time like that. Sometimes it is better to leave a question involving lengthy calculation (or leave it for the end part of the exam). sometimes, if your answer doesn’t match any of the a/b/c/d option in the exam, then it’s better to move to next question rather than trying to find out the mistake. You can understand these lessons only after burning your hands on original papers. so Do solve previous papers-within the given time limit.

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