CDS (Combined Defence Services) Exam Elementary Mathematics (IMA, INA and AFA only) Syllabus

Elementary Mathematics (IMA, INA and AFA only) syllabus — full chapter and topic list

Expand any chapter to see its topics and sub-topics. This is the whole examinable outline for Elementary Mathematics (IMA, INA and AFA only) in CDS (Combined Defence Services) Exam, not a summary of it.

1. 1

   Arithmetic

   6 topics

   • Number System
     • Natural, integer, rational and real numbers
     • Tests of divisibility, HCF and LCM
     • Decimal fractions and operations
   • Square Roots and Cube Roots
     • Finding square and cube roots
   • Ratio, Proportion and Variation
     • Direct and inverse proportion
     • Partnership and mixtures
   • Percentage and Commercial Mathematics
     • Profit, loss and discount
     • Simple and compound interest
   • Time, Work, Speed and Distance
     • Time and work problems
     • Trains, boats and streams
   • Unitary Method and Averages
     • Average of numbers and ages
2. 2

   Algebra

   6 topics

   • Basic Operations and Identities
     • Polynomials and algebraic identities
     • Remainder and factor theorem
   • HCF and LCM of Polynomials
     • Factorization methods
   • Linear Equations
     • Equations in one and two variables
     • Simultaneous equations and applications
   • Quadratic Equations
     • Roots and nature of roots
     • Relation between roots and coefficients
   • Linear Inequations and Sets
     • Solving inequations in two variables
     • Set theory, Venn diagrams and laws
   • Laws of Indices and Logarithms
     • Exponent rules
     • Logarithm laws and applications
3. 3

   Trigonometry

   3 topics

   • Trigonometric Ratios
     • Ratios of standard angles
     • Complementary angles
   • Trigonometric Identities
     • Fundamental identities and simplification
   • Heights and Distances
     • Angles of elevation and depression
4. 4

   Geometry

   5 topics

   • Lines and Angles
     • Parallel lines and transversals
   • Triangles
     • Congruence and similarity
     • Properties and centres of a triangle
   • Quadrilaterals and Polygons
     • Properties of parallelograms
     • Interior and exterior angles
   • Circles
     • Chords, tangents and angle properties
   • Loci
     • Basic loci constructions
5. 5

   Mensuration

   3 topics

   • Areas of Plane Figures
     • Triangles, quadrilaterals and circles
   • Surface Area and Volume of Solids
     • Cube, cuboid and cylinder
     • Cone, sphere and hemisphere
   • Perimeter and Circumference
     • Composite figures
6. 6

   Statistics

   3 topics

   • Data Collection and Representation
     • Frequency distribution tables
     • Bar charts, histograms and pie charts
   • Measures of Central Tendency
     • Mean, median and mode
   • Graphical Interpretation
     • Reading and analyzing graphs

Elementary Mathematics (IMA, INA and AFA only) flashcards for CDS (Combined Defence Services) Exam

25 of 50 cards from the Elementary Mathematics (IMA, INA and AFA only) deck — real questions with worked answers.

1. What is the divisibility rule for 11?

   A number is divisible by 11 if the difference between the sum of digits in odd positions and the sum of digits in even positions is 0 or a multiple of 11.

2. How are HCF and LCM of two numbers related to the numbers themselves?

   Product of two numbers = HCF x LCM. So a x b = HCF(a,b) x LCM(a,b).

3. State the test for divisibility by 8.

   A number is divisible by 8 if the number formed by its last three digits is divisible by 8.

4. How do you find the unit digit of a large power, e.g. units digit of 7^n?

   Use the cyclicity of the unit digit. For 7 the cycle is 7, 9, 3, 1 (length 4). Take the exponent mod 4 to pick the position in the cycle.

5. What is the simplest method to find the square root of a perfect square by prime factorisation?

   Express the number as a product of prime factors, pair the identical primes, and take one factor from each pair; the product of these is the square root.

6. What is the cube root of a number found by prime factorisation?

   Factor the number into primes, group identical primes in triplets, and take one factor from each triplet; their product is the cube root.

7. If a : b = 2 : 3 and b : c = 4 : 5, what is a : b : c?

   Make b common: a:b = 8:12, b:c = 12:15, so a:b:c = 8:12:15.

8. State the rule of direct and inverse variation.

   Direct variation: y = kx (y increases as x increases). Inverse variation: y = k/x (y decreases as x increases). k is a constant.

9. What is the mean proportional between two numbers a and b?

   The mean proportional is the square root of their product, i.e. sqrt(a x b).

10. What is the formula for simple interest?

    SI = (P x R x T)/100, where P = principal, R = rate per annum, T = time in years.

11. What is the compound interest formula for amount compounded annually?

    A = P(1 + R/100)^T, and CI = A - P.

12. How do you convert a fraction to a percentage and vice versa?

    Fraction to percent: multiply by 100. Percent to fraction: divide by 100 (and simplify).

13. What is the formula relating cost price, selling price and profit percentage?

    Profit% = ((SP - CP)/CP) x 100. Loss% = ((CP - SP)/CP) x 100.

14. If an article is sold at SP with profit P%, how do you find CP?

    CP = SP x 100/(100 + P). For loss L%, CP = SP x 100/(100 - L).

15. State the basic formula linking speed, distance and time.

    Speed = Distance / Time; Distance = Speed x Time; Time = Distance / Speed.

16. How do you convert km/h to m/s?

    Multiply by 5/18. To convert m/s to km/h, multiply by 18/5.

17. What is relative speed for two objects moving in the same and opposite directions?

    Opposite directions: add the speeds. Same direction: subtract the speeds.

18. In a work problem, if A does a job in n days, what fraction does A do in one day?

    A's one-day work = 1/n of the job.

19. If A can do work in x days and B in y days, how long together?

    Together they take xy/(x + y) days, since combined one-day work = 1/x + 1/y.

20. What is the unitary method?

    A method to find the value of many units by first finding the value of one unit, then multiplying by the required number of units.

21. What is the formula for the average (arithmetic mean) of n quantities?

    Average = (sum of all quantities) / (number of quantities).

22. State the algebraic identity for (a + b)^2 and (a - b)^2.

    (a + b)^2 = a^2 + 2ab + b^2; (a - b)^2 = a^2 - 2ab + b^2.

23. What is the identity for a^2 - b^2?

    a^2 - b^2 = (a + b)(a - b).

24. State the identity for (a + b)^3 and a^3 + b^3.

    (a + b)^3 = a^3 + b^3 + 3ab(a + b); a^3 + b^3 = (a + b)(a^2 - ab + b^2).

25. What is the identity for a^3 + b^3 + c^3 - 3abc?

    a^3 + b^3 + c^3 - 3abc = (a + b + c)(a^2 + b^2 + c^2 - ab - bc - ca).

See more Elementary Mathematics (IMA, INA and AFA only) flashcards →

Planning Elementary Mathematics (IMA, INA and AFA only) for CDS (Combined Defence Services) Exam

Elementary Mathematics (IMA, INA and AFA only) (CDS (Combined Defence Services) Exam) FAQ