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

The Elementary Mathematics (IMA, INA and AFA only) syllabus for CDS (Combined Defence Services) Exam in full: 6 chapters, 26 topics and 41 sub-topics, every one listed below, plus 50 Elementary Mathematics (IMA, INA and AFA only) flashcards with answers.

6Chapters
26Topics
41Sub-topics
50Flashcards

Elementary Mathematics (IMA, INA and AFA only) syllabus: all 6 chapters

Expand any chapter to see its topics and sub-topics.

  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. 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. 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. 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. 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. 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

CDS (Combined Defence Services) Exam Elementary Mathematics (IMA, INA and AFA only) flashcards — 50 questions with 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.

Show the other 30 Elementary Mathematics (IMA, INA and AFA only) flashcards

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

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

  2. 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.

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

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

  4. 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).

  5. 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).

  6. How do you find the HCF of two polynomials?

    Factorise each polynomial completely; the HCF is the product of the common factors taken with the lowest powers.

  7. How do you find the LCM of two polynomials?

    Factorise each polynomial; the LCM is the product of all distinct factors taken with the highest powers.

  8. What is the condition for a pair of linear equations to have a unique solution?

    For a1x+b1y+c1=0 and a2x+b2y+c2=0, a unique solution exists when a1/a2 != b1/b2.

  9. When does a pair of linear equations have no solution or infinitely many solutions?

    No solution when a1/a2 = b1/b2 != c1/c2 (parallel lines). Infinitely many when a1/a2 = b1/b2 = c1/c2 (coincident lines).

  10. What is the quadratic formula for ax^2 + bx + c = 0?

    x = (-b +/- sqrt(b^2 - 4ac)) / (2a).

  11. What does the discriminant of a quadratic tell you?

    D = b^2 - 4ac. If D>0: two real distinct roots; D=0: two equal real roots; D<0: no real (complex) roots.

  12. What are the sum and product of roots of ax^2 + bx + c = 0?

    Sum of roots = -b/a; Product of roots = c/a.

  13. What happens to an inequality when both sides are multiplied or divided by a negative number?

    The inequality sign reverses (e.g. < becomes >).

  14. State the formula for the number of elements in the union of two sets.

    n(A union B) = n(A) + n(B) - n(A intersection B).

  15. State the three basic laws of indices.

    a^m x a^n = a^(m+n); a^m / a^n = a^(m-n); (a^m)^n = a^(mn). Also a^0 = 1 and a^(-n) = 1/a^n.

  16. State the key laws of logarithms.

    log(mn) = log m + log n; log(m/n) = log m - log n; log(m^n) = n log m; log_a a = 1; log_a 1 = 0.

  17. Define sine, cosine and tangent in a right triangle.

    sin = opposite/hypotenuse; cos = adjacent/hypotenuse; tan = opposite/adjacent.

  18. What are the values of sin, cos and tan at 0, 30, 45, 60 and 90 degrees?

    sin: 0, 1/2, 1/sqrt2, sqrt3/2, 1. cos: 1, sqrt3/2, 1/sqrt2, 1/2, 0. tan: 0, 1/sqrt3, 1, sqrt3, undefined.

  19. State the three fundamental trigonometric identities.

    sin^2 A + cos^2 A = 1; 1 + tan^2 A = sec^2 A; 1 + cot^2 A = cosec^2 A.

  20. What are the complementary angle relations in trigonometry?

    sin(90-A)=cos A; cos(90-A)=sin A; tan(90-A)=cot A; sec(90-A)=cosec A.

  21. In heights and distances, what are the angle of elevation and angle of depression?

    Angle of elevation is the angle above the horizontal to an object higher than the observer; angle of depression is the angle below the horizontal to an object lower than the observer.

  22. What is the angle sum of a triangle and the exterior angle theorem?

    Angles of a triangle sum to 180 degrees. An exterior angle equals the sum of the two opposite interior angles.

  23. State the Pythagoras theorem and its converse.

    In a right triangle, hypotenuse^2 = sum of squares of the other two sides. Converse: if a^2 + b^2 = c^2, the triangle is right-angled.

  24. What is the sum of interior angles of a polygon with n sides?

    Sum of interior angles = (n - 2) x 180 degrees. Sum of exterior angles is always 360 degrees.

  25. State the relationship between the angle subtended by an arc at the centre and at the circumference.

    The angle at the centre is twice the angle subtended by the same arc at any point on the remaining circumference.

  26. What is the angle in a semicircle?

    The angle in a semicircle is a right angle (90 degrees).

  27. What is the formula for the area of a triangle and a circle?

    Area of triangle = (1/2) x base x height. Area of circle = pi r^2.

  28. State the curved surface area and volume of a sphere and a cylinder.

    Sphere: surface area = 4 pi r^2, volume = (4/3) pi r^3. Cylinder: curved surface area = 2 pi r h, volume = pi r^2 h.

  29. What is the volume and total surface area of a cone?

    Volume = (1/3) pi r^2 h; curved surface area = pi r l; total surface area = pi r (l + r), where l is slant height = sqrt(r^2 + h^2).

  30. How are mean, median and mode related (empirical relationship)?

    Mode = 3 Median - 2 Mean. The median is the middle value; the mode is the most frequent value; the mean is the arithmetic average.

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

What is in the CDS (Combined Defence Services) Exam Elementary Mathematics (IMA, INA and AFA only) syllabus?

CDS (Combined Defence Services) Exam Elementary Mathematics (IMA, INA and AFA only) is split into 6 chapters: Arithmetic, Algebra, Trigonometry, Geometry, Mensuration and Statistics. Together they contain 26 topics and 41 sub-topics.

How many chapters are in CDS (Combined Defence Services) Exam Elementary Mathematics (IMA, INA and AFA only)?

6 chapters, containing 26 topics and 41 sub-topics. The largest chapter is Arithmetic, with 6 topics.

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

Yes — a 50-card Elementary Mathematics (IMA, INA and AFA only) deck, printed in full in the flashcards section of this page and available in the Examius app with spaced repetition. The free plan covers one exam of your choice, including its flashcards; Examius Pro, a one-time purchase, unlocks every other exam and deck.