Agniveer (Agnipath Scheme) Quantitative Aptitude and Mathematics Syllabus

Quantitative Aptitude and Mathematics syllabus — full chapter and topic list

Expand any chapter to see its topics and sub-topics. This is the whole examinable outline for Quantitative Aptitude and Mathematics in Agniveer (Agnipath Scheme), not a summary of it.

1. 1

   Number System and Arithmetic Operations

   3 topics

   • Number system
     • Natural, whole, integer and rational numbers
     • HCF and LCM
     • Divisibility rules and factors
   • Simplification
     • BODMAS and order of operations
     • Surds and indices
     • Square roots and cube roots
   • Fractions and decimals
2. 2

   Commercial Mathematics

   6 topics

   • Ratio and proportion
   • Percentage
   • Profit, loss and discount
   • Simple and compound interest
   • Average
   • Partnership and mixtures
3. 3

   Time, Speed and Work

   3 topics

   • Time and distance
     • Relative speed
     • Trains, boats and streams
   • Time and work
     • Work efficiency
     • Pipes and cisterns
   • Problems on ages
4. 4

   Algebra

   3 topics

   • Basic algebraic operations
     • Polynomials and factorisation
     • Algebraic identities
   • Linear equations in one and two variables
   • Quadratic equations
5. 5

   Geometry and Mensuration

   4 topics

   • Lines, angles and triangles
   • Circles and polygons
   • Area and perimeter of plane figures
   • Surface area and volume of solids
     • Cube, cuboid and cylinder
     • Cone, sphere and hemisphere
6. 6

   Trigonometry and Statistics

   4 topics

   • Trigonometric ratios and identities
   • Heights and distances
   • Data interpretation
     • Bar graphs and pie charts
     • Tables and line graphs
   • Mean, median and mode

Quantitative Aptitude and Mathematics flashcards for Agniveer (Agnipath Scheme)

22 of 63 cards from the Quantitative Aptitude and Mathematics deck — real questions with worked answers.

1. What are the classifications of real numbers (the four main subsets)?

   Natural numbers (1,2,3,...), Whole numbers (0,1,2,...), Integers (...,-2,-1,0,1,2,...), and Rational + Irrational numbers. Real numbers = Rational ∪ Irrational.

2. What is the difference between a rational and an irrational number?

   A rational number can be written as p/q (q≠0) with terminating or recurring decimals (e.g., 1/2, 0.333...). An irrational number cannot be written as a fraction and has non-terminating, non-repeating decimals (e.g., √2, π).

3. State the divisibility rules for 3, 9, and 11.

   Divisible by 3: sum of digits divisible by 3. Divisible by 9: sum of digits divisible by 9. Divisible by 11: difference between sum of digits in odd places and even places is 0 or a multiple of 11.

4. What is the relationship between LCM, HCF, and two numbers?

   Product of two numbers = LCM × HCF. So LCM × HCF = a × b.

5. What is the BODMAS/order of operations rule for simplification?

   Brackets, Orders (powers/roots), Division, Multiplication, Addition, Subtraction — evaluated left to right. (BODMAS = Brackets, Of, Division, Multiplication, Addition, Subtraction.)

6. How do you convert a recurring decimal like 0.4545... to a fraction?

   For a pure recurring decimal, place the repeating block over as many 9s as there are repeating digits: 0.4545... = 45/99 = 5/11.

7. How do you add two fractions with different denominators?

   Find the LCM of the denominators, convert each fraction to an equivalent fraction with that common denominator, then add the numerators. E.g., 1/3 + 1/4 = 4/12 + 3/12 = 7/12.

8. How do you compare two fractions to find which is larger?

   Cross-multiply: for a/b vs c/d, compare a×d with c×b. If a×d > c×b then a/b > c/d. Alternatively convert to a common denominator or to decimals.

9. What is the difference between ratio and proportion?

   A ratio compares two quantities (a:b). A proportion is a statement that two ratios are equal (a:b = c:d). In a proportion, product of means = product of extremes (b×c = a×d).

10. In the proportion a:b = c:d, what are the mean and extreme terms, and what is the key property?

    a and d are extremes; b and c are means. Property: product of extremes = product of means, i.e., a×d = b×c.

11. 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.

12. What is the formula to convert a fraction or decimal to a percentage and vice versa?

    Fraction/decimal to percent: multiply by 100. Percent to fraction/decimal: divide by 100. E.g., 0.25 = 25%, 40% = 0.4 = 2/5.

13. How do you calculate percentage increase and percentage decrease?

    % increase = (Increase / Original) × 100. % decrease = (Decrease / Original) × 100, where Increase/Decrease = |New − Original|.

14. If a value increases by x% and then decreases by x%, what is the net change?

    There is always a net decrease of (x²/100)%. E.g., +20% then −20% gives a net 4% decrease.

15. State the basic formulas for profit, loss, and their percentages.

    Profit = SP − CP; Loss = CP − SP. Profit% = (Profit/CP)×100; Loss% = (Loss/CP)×100. (SP = selling price, CP = cost price.)

16. What is the formula for Selling Price given Cost Price and profit/loss percent?

    SP = CP × (100 + Profit%)/100, or SP = CP × (100 − Loss%)/100.

17. What is discount and how is it calculated?

    Discount is a reduction on the Marked Price (MP). Discount = MP − SP. Discount% = (Discount/MP) × 100. So SP = MP × (100 − Discount%)/100.

18. What is the formula for Simple Interest?

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

19. What is the formula for Compound Interest (compounded annually)?

    Amount A = P(1 + R/100)^T; Compound Interest = A − P, where P = principal, R = rate per annum, T = time in years.

20. For 2 years, what is the difference between Compound Interest and Simple Interest on principal P at rate R%?

    Difference = P × (R/100)². This formula applies only for a 2-year period.

21. How do you adjust the compound interest formula when interest is compounded half-yearly?

    Use rate R/2 and time 2T: A = P(1 + R/200)^(2T). For quarterly: A = P(1 + R/400)^(4T).

22. What is the formula for the average (arithmetic mean) of n numbers?

    Average = (Sum of all observations) / (Number of observations). So Sum = Average × n.

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