The UPSC administers the CDS exam to select applicants for the Indian Military Academy, Indian Naval Academy, Officers Training Academy, and Indian Air Force Academy.

Knowing the syllabus and the most recent CDS exam pattern is essential for strategically planning your preparation for the Combined Defense Services exam.

Geometry problems are included in the quantitative component, sometimes known as the numerical ability section, of the CDS exam.

In this article, let’s understand how to prepare for the geometry sections of the CDS exam.

Maths Syllabus of CDS Exam

CDS Syllabus – Elementary Mathematics
Algebra	Basic Operations, Simple factors, Remainder Theorem, HCF/LCM, Theory of polynomials, Quadratic equations, Relation between its roots and coefficients (Only real roots to be considered), Simultaneous linear equations in two unknowns—analytical and graphical solutions, Simultaneous linear inequations in two variables and their solutions, Practical problems leading to two simultaneous linear equations or inequations in two variables or quadratic equations in one variable & their solutions, Set language and set notation, Rational expressions and conditional identities, Laws of indices
Arithmetic	Number System: Natural numbers, Integers, Rational and Real numbers. Fundamental operations: addition, substraction, multiplication, division, Square roots, Decimal fractions Unitary method, Time and Distance, Time and work, Percentages, Simple and compound interest, Profit and loss Ratio and proportion, Variation, Elementary Number Theory: Division algorithm, Prime and composite numbers, Tests of divisibility by 2, 3, 4, 5, 9 and 11, Multiples and factors. Factorisation Theorem H.C.F. and L.C.M., Euclidean algorithm, Logarithms to base 10, Laws of logarithms and use of logarithmic tables
Geometry	Lines and angles, Plane and plane figures, Theorems on Properties of angles at a point, Parallel lines, Sides and angles of a triangle, Congruence of triangles, Similar triangles, Concurrence of medians and altitudes, Properties of angles, Sides and diagonals of a Parallelogram, Rectangle and square, Circles and its properties including tangents and normals and Loci
Trigonometry	Sine ×, cosine ×, Tangent × when 0° < × < 90° Values of sin ×, cos × and tan ×, for ×= 0°, 30°, 45°, 60° and 90° Simple trigonometric identities Use of trigonometric tables Simple cases of heights and distances
Statistics	Collection and tabulation of statistical data, Graphical representation frequency polygons, Histograms, Bar charts, Pie charts, etc., Measures of central tendency
Mensuration	Areas of squares, Rectangles, Parallelograms, Triangle and Circle. Areas of figures which can be split up into these figures (Field Book), Surface area and volume of cuboids, Lateral surface and volume of right circular cones and cylinders, Surface area and volume of spheres

For detailed CDS syllabus, check the linked article.

How to prepare for the Geometry section of the CDS Exam?

Mathematics is a required topic in the NDA/ CDS tests for all aspirants.

Coordinate geometry is an essential component that has significant question markings in the CDS Exam.

Tips to solve geometry problems in CDS Exam

In coordinate geometry, Points forming triangles, Distance formulae, line equations, section formulas, and their areas are a few of the topics you should learn for any defence exam.
To improve in this section, you must first understand all of the fundamental forms and geometry formulae.
You should review the formulae for perimeter, area, surface area, and volume of all two-dimensional and three-dimensional figures.
Questions regarding parallel lines and transversals are regularly asked in the CDS exam. When two parallel lines cross, a transversal is a line segment that forms a few pairs of angles such as matching angles, alternate interior angles, and more. To find the missing angle or identify the problem, you must be familiar with all of the qualities and angles.
Triangles are closed figures with three or more straight lines. They are four-sided forms (quadrilaterals), which include squares, parallelograms, rectangles, and others. You should be aware not only of their qualities but also know how to apply them to questions.
Make a mark to check that the figure drawn/given corresponds to the facts in the question.
Examine the question. Determine what is being asked, then combine factual information with the solution and link it backwards.
Visualize the problem in mind. This is vital in geometry since it is necessary to imagine and construct the shape/figure contained in the query.
Simplify difficult situations wherever feasible and apply the Basic Proportionality Theorem.
Basic concepts are required to solve difficult problems. To answer questions correctly in a short amount of time, you must be well-versed in each topic’s laws, rules, theorems, and so on.
Make a daily practice regimen for each topic. Attempt a range of questions from various areas so that you can answer such questions in a short period of time in the test. Practising is also a vital technique for preparedness.
Make a schedule for completing the quant part in the allotted time of one hour. Then, only attempt quant sets inside the specified timescale. This will assist you in improving your quantitative skills.
While studying the fundamentals, take careful notes on each important point and create appropriate takeaways. These handout notes will assist you in revising the whole study material summary right prior to the test. Make a list of all the quick tricks as well.
Do not try the questions unless you have read them thoroughly.
In math, don’t make erroneous assumptions. Without a solution, it may wipe off your marks as a result of negative marking.
Don’t spend more time than is necessary. Other exam sections will suffer as a result.
Make a list of the subjects you want to cover during the day and check them off as you finish them so you can evaluate how well you are prepared for the CDS test.
Always keep in mind that as time is limited, hopefuls shouldn’t learn any new subjects or ideas. Only choose that subject if you are certain about it and want to have a basic comprehension of the topic.
Starting something new at the last minute would just compromise the newly started topic and might also cause confusion on topics that have already been planned.

Important Geometry Topics For Defence Exams

The most common and the most important topics of geometry and mensuration for the defence exams are as follows:

Concepts	Explanation
Basic Shapes	Different types of geometrical figures and shapes
Angles	Angles are formed when two straight lines meet at a point.
Parallel Lines & Transversals	Two lines are parallel if they are on the same plane and do not intersect on any side, whereas a transversal is a line segment that intersects two or more lines.
Polygons	A closed figure made up of three or more straight lines.
Triangles	A closed three-sided polygon whose three internal angles add up to 180 degrees in all cases.
Quadrilaterals	A figure that forms with four sides, such as squares, parallelograms, rectangles, and others.
Circles	A polygon with infinite sides in which every point is equally spaced from the focus.

UPSC Syllabus	UPSC CAPF Syllabus	UPSC NDA Syllabus
UPSC Books	UPSC 2023	NDA Exam