How To Prepare Maths For Cds

Are you planning to appear for the UPSC CDS exam this year? The UPSC conducts the Combined Defence Services (CDS) test twice a year. The Combined Defence Services written exam consists of three papers: Mathematics (optional for OTA), English, and General Knowledge.

The CDS I 2023 test was held on April 16, 2023, and according to the UPSC official calendar, the CDS II 2023 exam will be held on September 3, 2023. To excel in this exam, you need to develop a competitive edge by scoring well in the math section. It is because math is the only section where candidates stand a chance of losing maximum marks owing to their inaccuracy and inefficiency. This space will cover in detail how to prepare Maths for the UPSC CDS Examination. The Combined Defence Services Exam 2023 preparation suggestions mentioned here would be useful for all applicants preparing to take the next CDS test. You may also read CDS Eligibility 2022

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Maths is probably the highest-scoring section for candidates who are not that comfortable with English. Besides a good score in maths provides certainty in the examination as the answers can hardly vary as per the official answer key. You can very easily score 65+ marks out of the total 100 marks in the mathematics section by following the below-mentioned key points:

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1. Strategic approach: To be able to score marks in the math section, you need to make sure that you attempt questions with accuracy. The number of attempts should be balanced as the negative marking does exist in the CDS exam. Each question carries one mark.

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The key point to ace this section is to maintain a balance of accuracy and efficiency.

2. Set realistic goals: Have a look at the math syllabus and then divide your preparation time into different topics. Allot more time for difficult topics like trigonometry and mensuration. Set weekly goals so that you can track your progress on different topics and also identify the topics you are weak in. Try to give some extra time to strengthen your weaker topics by solving more and more questions related to that topic.

While studying, make notes of important formulas so that you can revise them from time to time. This will help you to learn those formulas by heart.

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3. Follow the right study material: Some of the books you can go for to prepare the CDS syllabus include:

NCERT
Arihant Pathfinder
Mathematics for CDS by RS Aggarwal
Quantum CAT by Sarvesh Verma,
Quantitative Aptitude for examinations paperback by RS Aggarwal, etc.

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4. Topic-wise weightage: Analyze the previous year's question papers to determine the pattern of the exam. Focus more on topics accordingly. For instance, you get very easy questions based on chapters related to statistics like bar charts, pie charts, measuring central tendency frequency polygons, etc.

Given below is some analysis drawn from the previous year's question papers. You can schedule your study plan according to it but remember, it can change. So, make sure you cover the entire syllabus.

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Most Difficult Questions

The level of questions you get on concepts like surface area and volume of rectangles, parallelograms, cuboids, etc. will be slightly difficult. To prepare for these concepts you need to learn the formulas by heart and also work on your calculation speed. Try solving more and more questions based on these concepts as this will help you to memorize the formulas quite well.

HIGH WEIGHTAGE TOPICS:

Questions on Geometry and trigonometry-related concepts such as properties of angles, congruency of triangles, medians, tangents, etc. are most commonly asked. Hence, these topics carry very high weight in CDS exams. Try to develop full command of chapters like line & angles, triangles, circles, trigonometry, and applications of trigonometry by thoroughly understanding the concepts involved.

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BASIC Topics:

Topics like number systems, time and work, percentages, averages, HCF, LCM, and quadratic equations are very easy to understand and consume less time. Therefore, if you are not that good in math then you can start your preparation with such topics. It will help to develop conceptual clarity along with boosting your confidence.

5. Revise: Until and unless you revise you won’t be able to memorize things. This can cause problems for you in the final exam. All the formulas and concepts should be at your fingertips only then will you be able to complete your exam correctly and on time.

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UPSC NDA Maths Syllabus

Topic	NDA Syllabus
ALGEBRA	Concept of set, operations on sets, Venn diagrams. De Morgan laws, Cartesian product, relation, equivalence relation. Representation of real numbers on a line. Complex numbers—basic properties, modulus, argument, cube roots of unity. Binary system of numbers. Conversion of a number in a decimal system to a binary system and vice-versa. Arithmetic, Geometric, and Harmonic progressions. Quadratic equations with real coefficients. Solution of linear inequations of two variables by graphs. Permutation and Combination. Binomial theorem and its applications. Logarithms and their applications.
MATRICES AND DETERMINANTS	Types of matrices, operations on matrices. Determinant of a matrix, basic properties of determinants. Adjoint and inverse of a square matrix, Applications-Solution of a system of linear equations in two or three unknowns by Cramer’s rule and by Matrix Method.
TRIGONOMETRY	Angles and their measures in degrees and radians. Trigonometrical ratios. Trigonometric identities Sum and difference formulae. Multiple and Sub-multiple angles. Inverse trigonometric functions. Applications and distance, properties of triangles.
ANALYTICAL GEOMETRY OF TWO AND THREE DIMENSIONS	Rectangular Cartesian Coordinate system. Distance formula. Equation of a line in various forms. The angle between two lines. Distance of a point from a line. Equation of a circle in standard and general form. Standard forms of parabola, ellipse, and hyperbola. Eccentricity and axis of a conic. Point in a three-dimensional space, the distance between two points. Direction Cosines and direction ratios. Equation two points. Direction Cosines and direction ratios. Equation of a plane and a line in various forms. Angle between two lines and angle between two planes. Equation of a sphere
DIFFERENTIAL CALCULUS	Concept of a real-valued function–domain, range, and graph of a function. Composite functions, one-to-one, onto, and inverse functions. The notion of limit, Standard limits—examples. Continuity of functions—examples, algebraic operations on continuous functions. Derivative of function at a point, geometrical and physical interpretation of a derivative—applications. Derivatives of sum, product, and quotient of functions, derivative of a function concerning another function, derivative of a composite function. Second-order derivatives. Increasing and decreasing functions. Application of derivatives in problems of maxima and minima.
INTEGRAL CALCULUS AND DIFFERENTIAL EQUATIONS	Integration as inverse of differentiation, integration by substitution and by parts, standard integrals involving algebraic expressions, trigonometric, exponential and, hyperbolic functions. Evaluation of definite integrals—determination of areas of plane regions bounded by curves—applications. Definition of order and degree of a differential equation, formation of a differential equation by examples. General and particular solutions of differential equations, solutions of the first order, and first-degree differential equations of various types—examples. Application in problems of growth and decay.
VECTOR ALGEBRA	Vectors in two and three dimensions, magnitude, and direction of a vector. Unit and null vectors, the addition of vectors, scalar multiplication of a vector, scalar product, or dot product of two vectors. Vector product or cross product of two vectors. Applications—work done by a force and moment of a force and in geometrical problems.
STATISTICS AND PROBABILITY	Statistics : Classification of data, Frequency distribution, cumulative frequency distribution—examples. Graphical representation—Histogram, Pie Chart, frequency polygon— examples. Measures of Central tendency—Mean, median, and mode. Variance and standard deviation—determination and comparison. Correlation and regression. Probability : Random experiment, outcomes, and associated sample space, events, mutually exclusive and exhaustive events, impossible and certain events. Union and Intersection of events. Complementary, elementary, and composite events. Definition of probability—classical and statistical—examples. Elementary theorems on probability—simple problems. Conditional probability, Bayes’ theorem—simple problems. Random variable as function on a sample space. Binomial distribution, examples of random experiments giving rise to Binomial distribution.

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