Indian Army GD / Technical Recruitment Mathematics Syllabus

Mathematics syllabus — full chapter and topic list

Expand any chapter to see its topics and sub-topics. This is the whole examinable outline for Mathematics in Indian Army GD / Technical Recruitment, not a summary of it.

1. 1

   Arithmetic

   5 topics

   • Number System and Simplification
     • Types of Numbers and Operations
     • HCF and LCM
     • BODMAS and Simplification
   • Fractions, Decimals and Square Roots
     • Fractions and Decimals
     • Square Roots and Cube Roots
   • Percentage, Profit and Loss
     • Percentage Calculations
     • Profit, Loss and Discount
   • Ratio, Proportion and Average
     • Ratio and Proportion
     • Averages
   • Interest and Time-based Problems
     • Simple and Compound Interest
     • Time and Work
     • Time, Speed and Distance
2. 2

   Algebra

   3 topics

   • Basic Algebraic Operations
     • Algebraic Identities
     • Polynomials and Factorisation
   • Linear and Quadratic Equations
     • Linear Equations in One and Two Variables
     • Quadratic Equations
   • HCF, LCM of Polynomials
     • HCF and LCM of Algebraic Expressions
3. 3

   Geometry

   3 topics

   • Lines, Angles and Triangles
     • Lines and Angles
     • Triangles and Congruence
   • Circles and Polygons
     • Properties of Circles
     • Quadrilaterals and Polygons
   • Constructions and Theorems
     • Geometric Constructions
     • Pythagoras and Other Theorems
4. 4

   Mensuration

   3 topics

   • Area and Perimeter (2D)
     • Triangle, Rectangle and Square
     • Circle and Parallelogram
   • Surface Area and Volume (3D)
     • Cube, Cuboid and Cylinder
     • Cone, Sphere and Hemisphere
   • Combined Solids and Applications
     • Frustum and Combined Solid Figures
     • Real-life Mensuration Problems
5. 5

   Trigonometry and Statistics

   3 topics

   • Trigonometric Ratios and Identities
     • Trigonometric Ratios
     • Trigonometric Identities
   • Heights and Distances
     • Angles of Elevation and Depression
   • Data Handling and Statistics
     • Mean, Median and Mode
     • Bar Graphs, Pie Charts and Tables
     • Probability Basics

Mathematics flashcards for Indian Army GD / Technical Recruitment

21 of 58 cards from the Mathematics deck — real questions with worked answers.

1. In the number system, how are natural numbers, whole numbers, and integers distinguished?

   Natural numbers are counting numbers (1, 2, 3, ...); whole numbers add 0 (0, 1, 2, ...); integers add negatives (..., -2, -1, 0, 1, 2, ...).

2. What is the difference between rational and irrational numbers?

   A rational number can be written as p/q (q not 0) and has a terminating or repeating decimal; an irrational number cannot be written as p/q and has a non-terminating, non-repeating decimal (e.g. sqrt2, pi).

3. What is the BODMAS/BODMAS order used for simplification?

   Brackets, Of (or Orders/powers), Division, Multiplication, Addition, Subtraction - the sequence in which operations must be performed.

4. State the divisibility rule for 3 and for 9.

   A number is divisible by 3 if the sum of its digits is divisible by 3, and divisible by 9 if the digit sum is divisible by 9.

5. State the divisibility rule for 11.

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

6. What is the sum of the first n natural numbers?

   The sum is n(n+1)/2.

7. How do you convert a fraction to a percentage and a decimal?

   To a percentage, multiply the fraction by 100; to a decimal, divide the numerator by the denominator. For example 3/4 = 75% = 0.75.

8. How do you find the square root of a number by the long division (digit-pairing) method?

   Pair digits from the decimal point outward, find the largest divisor whose square fits the first pair, bring down pairs, and at each step double the quotient as the new divisor's leading part until you reach the desired accuracy.

9. What are the first ten perfect squares (1 to 10)?

   1, 4, 9, 16, 25, 36, 49, 64, 81, 100.

10. What is the rule for adding fractions with different denominators?

    Find the LCM of the denominators, convert each fraction to that common denominator, then add the numerators and keep the common denominator.

11. What is the formula relating percentage to the actual value?

    Percentage value = (rate/100) x base; conversely, rate = (part/whole) x 100.

12. How do you calculate profit percent and loss percent?

    Profit% = (Profit/Cost Price) x 100 and Loss% = (Loss/Cost Price) x 100, both taken on the cost price.

13. How do you find Selling Price from Cost Price and profit/loss percent?

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

14. What is the formula for discount and marked price relationship?

    Discount = Marked Price - Selling Price, and Discount% = (Discount/Marked Price) x 100.

15. If an article is sold at the same percentage gain and loss on two items at the same price, what is the net result?

    There is always a net loss, equal to (common%)^2/100 percent of the total.

16. What is a ratio and how is it different from a proportion?

    A ratio compares two quantities (a:b); a proportion states that two ratios are equal (a:b = c:d), where a and d are extremes and b and c are means.

17. State the property of means and extremes in a proportion.

    In a:b = c:d, the product of the extremes equals the product of the means, so a x d = b x c.

18. How do you find the average of a set of numbers?

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

19. What is the average of the first n consecutive natural numbers?

    The average is (n+1)/2.

20. If two quantities are in ratio a:b and their sum is S, how do you find each part?

    First part = S x a/(a+b) and second part = S x b/(a+b).

21. What is the simple interest formula?

    Simple Interest = (P x R x T)/100, where P is principal, R is annual rate percent, and T is time in years.

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