RRB NTPC Mathematics (Quantitative Aptitude) Syllabus

Mathematics (Quantitative Aptitude) syllabus — full chapter and topic list

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

1. 1

   Number System and Arithmetic Foundations

   5 topics

   • Classification of Numbers
     • Natural, whole, integers, rational and irrational numbers
     • Even, odd, prime and composite numbers
     • Place value and face value
   • Divisibility and Factors
     • Divisibility rules for 2 to 11
     • Factors, multiples and number of divisors
     • Unit digit and cyclicity of powers
   • LCM and HCF
     • HCF and LCM by prime factorisation and division
     • Relation: product of numbers = HCF x LCM
     • LCM and HCF of fractions and word problems
   • Fractions, Decimals and Surds
     • Conversion and comparison of fractions
     • Recurring and terminating decimals
     • Simplification of surds and indices
   • BODMAS and Simplification
     • Order of operations
     • Approximation techniques
2. 2

   Ratio, Proportion and Commercial Arithmetic

   6 topics

   • Ratio and Proportion
     • Compound, duplicate and inverse ratio
     • Dividing a quantity in a given ratio
     • Componendo and dividendo
   • Percentage
     • Percentage increase and decrease
     • Successive percentage change
     • Population, depreciation and election problems
   • Profit, Loss and Discount
     • Cost price, selling price and marked price
     • Successive discounts
     • Dishonest dealer and false weight
   • Simple and Compound Interest
     • Simple interest formula and instalments
     • Compound interest annually, half-yearly and quarterly
     • Difference between SI and CI
   • Average
     • Average of numbers and series
     • Weighted average and change in average
     • Average speed problems
   • Mixture and Alligation
     • Rule of alligation
     • Replacement of mixture
3. 3

   Time, Work, Speed and Distance

   5 topics

   • Time and Work
     • Individual and combined efficiency
     • Pipes and cisterns
     • Work and wages
   • Time, Speed and Distance
     • Conversion of units (km/h and m/s)
     • Average and relative speed
   • Problems on Trains
     • Train crossing pole, platform and another train
     • Trains in same and opposite directions
   • Boats and Streams
     • Upstream and downstream speed
     • Average speed in still water
   • Problems on Ages
     • Present, past and future age ratios
4. 4

   Algebra and Elementary Statistics

   5 topics

   • Algebraic Identities and Expressions
     • Standard identities and expansions
     • Factorisation
   • Linear and Quadratic Equations
     • Linear equations in one and two variables
     • Roots of quadratic equations
   • Elementary Statistics
     • Mean, median and mode
     • Range and frequency distribution
   • Data Interpretation
     • Tables and bar graphs
     • Pie charts and line graphs
   • Fundamentals of Trigonometry
     • Trigonometric ratios and standard angles
     • Heights and distances (basic)
5. 5

   Geometry, Mensuration and Probability

   5 topics

   • Lines, Angles and Triangles
     • Properties of angles and triangles
     • Congruence and similarity
   • Circles and Quadrilaterals
     • Tangents and chords
     • Properties of quadrilaterals
   • Mensuration of 2D Figures
     • Area and perimeter of triangle, rectangle and circle
   • Mensuration of 3D Solids
     • Volume and surface area of cube, cuboid and cylinder
     • Cone, sphere and hemisphere
   • Permutation, Combination and Probability
     • Basic counting principle
     • Simple probability with coins, dice and cards

Mathematics (Quantitative Aptitude) flashcards for RRB NTPC

18 of 50 cards from the Mathematics (Quantitative Aptitude) deck — real questions with worked answers.

1. What is a rational number?

   A number that can be expressed in the form p/q, where p and q are integers and q is not equal to 0 (e.g., 3/4, -5, 0.25).

2. What is an irrational number? Give two examples.

   A number that cannot be expressed as p/q with integers p and q; its decimal is non-terminating and non-repeating. Examples: square root of 2, and pi.

3. What is a prime number? Which is the only even prime number?

   A natural number greater than 1 having exactly two factors, 1 and itself. The only even prime number is 2.

4. What are co-prime (relatively prime) numbers?

   Two numbers whose HCF (greatest common factor) is 1, e.g., 8 and 15. They need not individually be prime.

5. Classify whole numbers, natural numbers, and integers.

   Natural numbers: 1, 2, 3, ... Whole numbers: 0, 1, 2, 3, ... (natural numbers plus 0). Integers: ..., -2, -1, 0, 1, 2, ... (positive, negative, and zero).

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

   Divisible by 3 if the sum of digits is divisible by 3. Divisible by 9 if the sum of digits is divisible by 9.

7. State the divisibility rule for 4 and for 8.

   Divisible by 4 if the number formed by the last two digits is divisible by 4. Divisible by 8 if the number formed by the last three digits is divisible by 8.

8. State 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.

9. How do you find the total number of factors of a number from its prime factorization?

   If N = a^p × b^q × c^r (prime factorization), the number of factors = (p+1)(q+1)(r+1).

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

    Product of two numbers = HCF × LCM. So HCF × LCM = first number × second number.

11. What is the HCF (Highest Common Factor) of two or more numbers?

    The largest number that divides each of the given numbers exactly (without remainder).

12. What is the LCM (Least Common Multiple) of two or more numbers?

    The smallest number that is exactly divisible by each of the given numbers.

13. How do you find the LCM and HCF of fractions?

    LCM of fractions = (LCM of numerators) / (HCF of denominators). HCF of fractions = (HCF of numerators) / (LCM of denominators).

14. What is the smallest number which when divided by a, b, c leaves the same remainder r in each case?

    It is (LCM of a, b, c) + r.

15. What is a surd? Give an example.

    An irrational root of a rational number that cannot be simplified to remove the root, e.g., square root of 2 or cube root of 5.

16. How do you rationalize the denominator of 1/(a + sqrt(b))?

    Multiply numerator and denominator by the conjugate (a - sqrt(b)), giving (a - sqrt(b)) / (a^2 - b).

17. What does BODMAS stand for?

    Brackets, Orders (powers/roots), Division, Multiplication, Addition, Subtraction — the order of operations in simplification.

18. In BODMAS, what is the order for solving brackets?

    Solve brackets in order: first ( ), then { }, then [ ] — innermost brackets are solved first.

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