RRB Group D Mathematics (Arithmetic) Syllabus

Mathematics (Arithmetic) syllabus — full chapter and topic list

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

1. 1

   Number System and Basic Arithmetic

   5 topics

   • Number Systems
     • Natural, whole, integer, rational and irrational numbers
     • Place value and face value
     • Comparison and ordering of numbers
   • BODMAS and Simplification
     • Order of operations (BODMAS rule)
     • Simplification of bracketed expressions
     • Surds and indices basics
   • Divisibility and Factors
     • Divisibility rules for 2, 3, 4, 5, 6, 8, 9, 11
     • Prime and composite numbers
     • Unit digit and remainder problems
   • LCM and HCF
     • Prime factorization and division methods
     • LCM and HCF of fractions
     • Word problems on bells, races and pipes alignment
   • Fractions and Decimals
     • Conversion between fractions and decimals
     • Operations on fractions and decimals
     • Recurring decimals
2. 2

   Ratio, Proportion and Percentage

   4 topics

   • Ratio and Proportion
     • Simplest form and equivalent ratios
     • Direct, inverse and compound proportion
     • Dividing a quantity in a given ratio
   • Percentage
     • Conversion between percentage, fraction and ratio
     • Percentage increase and decrease
     • Successive percentage change
   • Average
     • Average of numbers and observations
     • Weighted average
     • Change in average on addition or removal of items
   • Mixture and Alligation
     • Rule of alligation
     • Mixing of two or more ingredients
     • Replacement of part of a mixture
3. 3

   Commercial Mathematics

   3 topics

   • Profit and Loss
     • Cost price, selling price, marked price
     • Profit and loss percentage
     • Discount and successive discount
     • Dishonest dealer and false weights
   • Simple Interest
     • Principal, rate, time and amount
     • Finding any unknown quantity
   • Compound Interest
     • Annual, half-yearly and quarterly compounding
     • Difference between SI and CI
     • Growth and depreciation
4. 4

   Time, Work, Speed and Distance

   4 topics

   • Time and Work
     • Individual and combined work rates
     • Work and wages distribution
     • Efficiency-based problems
   • Pipes and Cisterns
     • Filling and emptying pipes
     • Leak problems
   • Time, Speed and Distance
     • Conversion of units (km/h to m/s)
     • Average speed and relative speed
   • Trains, Boats and Streams
     • Train crossing pole, platform and another train
     • Upstream and downstream speed
5. 5

   Algebra, Geometry and Mensuration

   4 topics

   • Elementary Algebra
     • Algebraic identities and factorization
     • Linear equations in one and two variables
   • Geometry Basics
     • Lines, angles and triangles
     • Circles and quadrilaterals
     • Similarity and congruence
   • Mensuration
     • Area and perimeter of 2D figures
     • Volume and surface area of cube, cuboid, cylinder, cone and sphere
   • Trigonometry Basics
     • Trigonometric ratios and standard angles
     • Heights and distances
6. 6

   Statistics, Calendar and Clock

   4 topics

   • Elementary Statistics
     • Mean, median and mode
     • Data interpretation from tables and graphs
   • Calendar
     • Odd days and leap year concept
     • Finding day of the week
   • Clock
     • Angle between hour and minute hands
     • Coincidence and opposite positions of hands
   • Age Problems
     • Present, past and future age relations
     • Ratio-based age problems

Mathematics (Arithmetic) flashcards for RRB Group D

22 of 50 cards from the Mathematics (Arithmetic) deck — real questions with worked answers.

1. What are natural numbers?

   The counting numbers starting from 1: 1, 2, 3, 4, ... (positive integers, excluding 0).

2. What are whole numbers?

   All natural numbers together with 0: 0, 1, 2, 3, 4, ...

3. What is the difference between a prime number and a composite number?

   A prime number has exactly two factors (1 and itself), e.g. 2, 3, 5, 7. A composite number has more than two factors, e.g. 4, 6, 8, 9. (1 is neither prime nor composite.)

4. What is the only even prime number?

   2 is the only even prime number; all other even numbers are divisible by 2 and hence composite.

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

   A rational number can be expressed as p/q where q ≠ 0 (e.g. 1/2, 0.75). An irrational number cannot be written as a fraction; its decimal is non-terminating and non-repeating (e.g. √2, π).

6. What is the place value vs. face value of a digit?

   Face value is the digit itself, regardless of position. Place value is the digit multiplied by its positional value. In 352, the digit 5 has face value 5 and place value 50.

7. What does BODMAS stand for and what order does it impose?

   Brackets, Orders (powers/roots), Division, Multiplication, Addition, Subtraction — the order of operations to simplify expressions. Division and Multiplication rank equally (left to right), as do Addition and Subtraction.

8. In BODMAS, which is solved first in brackets: which order of brackets?

   Innermost first: ( ) round brackets, then { } curly brackets, then [ ] square brackets (vinculum/bar even before round brackets).

9. Using BODMAS, simplify 2 + 3 × 4.

   14. Multiplication first: 3 × 4 = 12, then 2 + 12 = 14 (not 20).

10. What is the divisibility rule for 3?

    A number is divisible by 3 if the sum of its digits is divisible by 3. E.g. 372 → 3+7+2 = 12, divisible by 3.

11. What is the divisibility rule for 4?

    A number is divisible by 4 if the number formed by its last two digits is divisible by 4. E.g. 1316 → 16 is divisible by 4.

12. What is the divisibility rule for 8?

    A number is divisible by 8 if the number formed by its last three digits is divisible by 8. E.g. 7128 → 128 ÷ 8 = 16.

13. What is the divisibility rule for 9?

    A number is divisible by 9 if the sum of its digits is divisible by 9. E.g. 729 → 7+2+9 = 18, divisible by 9.

14. What is 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. E.g. 4829 → (9+8) − (2+4) = 11.

15. What is the divisibility rule for 6?

    A number is divisible by 6 if it is divisible by both 2 and 3 (i.e. it is even and its digit sum is divisible by 3).

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

    If N = a^p × b^q × c^r, the number of factors = (p+1)(q+1)(r+1). E.g. 72 = 2³×3² → (3+1)(2+1) = 12 factors.

17. What is the HCF (GCD) of two numbers?

    The Highest Common Factor is the largest number that divides both numbers exactly (the greatest common divisor).

18. What is the LCM of two numbers?

    The Least Common Multiple is the smallest number that is exactly divisible by both numbers.

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

    For two numbers a and b: LCM × HCF = a × b. So one can be found if the other three are known.

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

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

21. What is a proper fraction vs. an improper fraction?

    A proper fraction has numerator less than denominator (e.g. 3/5). An improper fraction has numerator greater than or equal to the denominator (e.g. 7/4).

22. How do you convert a fraction to a decimal and vice versa?

    Fraction to decimal: divide numerator by denominator. Decimal to fraction: write the decimal over the appropriate power of 10 and simplify, e.g. 0.25 = 25/100 = 1/4.

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