RRB NTPC (Non-Technical Popular Categories) 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 (Non-Technical Popular Categories), not a summary of it.

1. 1

   Number System and Arithmetic Foundations

   5 topics

   • Types and Properties of Numbers
     • Natural, whole, integer, rational and irrational numbers
     • Even, odd, prime and composite numbers
     • Face value and place value
   • Divisibility, HCF and LCM
     • Divisibility rules for 2 to 11
     • HCF and LCM by factorisation and division
     • Relation between HCF, LCM and product of numbers
     • HCF and LCM of fractions and decimals
   • Fractions, Decimals and Surds
     • Conversion between fractions and decimals
     • Recurring decimals
     • Simplification of surds and indices
   • BODMAS and Simplification
     • Order of operations
     • Vinculum and bracket simplification
     • Approximation techniques
   • Square Roots, Cube Roots and Powers
2. 2

   Ratio, Proportion and Commercial Arithmetic

   6 topics

   • Ratio and Proportion
     • Compound and continued proportion
     • Componendo and dividendo
     • Partnership and division of amounts
   • Percentage
     • Percentage increase and decrease
     • Successive percentage change
     • Application in population and depreciation
   • Profit, Loss and Discount
     • Cost price, selling price and marked price
     • Successive discounts
     • Dishonest dealer and false weights
   • Simple and Compound Interest
     • SI formula and applications
     • CI compounded annually, half-yearly and quarterly
     • Difference between SI and CI
   • Average
     • Average of numbers and series
     • Weighted average
     • Average speed problems
   • Mixture and Alligation
3. 3

   Time, Speed, Work and Distance

   4 topics

   • Time and Work
     • Work efficiency and man-days
     • Pipes and cisterns
     • Wages distribution
   • Time, Speed and Distance
     • Conversion of units
     • Relative speed
     • Average and variable speed
   • Trains, Boats and Streams
     • Trains crossing poles, platforms and trains
     • Upstream and downstream speed
   • Problems on Ages
4. 4

   Algebra and Elementary Statistics

   4 topics

   • Basic Algebraic Identities and Expressions
   • Linear and Quadratic Equations
     • Solving linear equations in one and two variables
     • Roots of quadratic equations
   • Elementary Statistics
     • Mean, median and mode
     • Frequency distribution
     • Range and basic measures of dispersion
   • Data Interpretation
     • Tables and bar graphs
     • Pie charts and line graphs
5. 5

   Geometry and Mensuration

   4 topics

   • Lines, Angles and Triangles
   • Mensuration of 2D Figures
     • Area and perimeter of squares, rectangles and triangles
     • Circle, sector and ring
   • Mensuration of 3D Solids
     • Cube, cuboid and cylinder
     • Cone, sphere and hemisphere
   • Basic Trigonometry and Heights and Distances

Mathematics (Quantitative Aptitude) flashcards for RRB NTPC (Non-Technical Popular Categories)

18 of 55 cards from the Mathematics (Quantitative Aptitude) deck — real questions with worked answers.

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

   A rational number can be expressed as p/q (q not equal to 0) where p and q are integers; its decimal form terminates or repeats. An irrational number cannot be written as p/q and its decimal is non-terminating and non-repeating (e.g. root 2, pi).

2. Classify numbers into prime, composite, and the special case of 1.

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

3. How many prime numbers are there below 50, and what are they?

   There are 15 primes below 50: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47.

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

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

5. State the divisibility rules for 4 and 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.

6. What is the key relationship between HCF and LCM of two numbers?

   HCF x LCM = product of the two numbers. So for numbers a and b: HCF(a,b) x LCM(a,b) = a x b.

7. 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.

8. What is a surd, and how do you rationalise the denominator of 1/(a + root b)?

   A surd is an irrational root that cannot be simplified to a rational number (e.g. root 2). To rationalise 1/(a + root b), multiply numerator and denominator by the conjugate (a - root b), giving (a - root b)/(a^2 - b).

9. What is the BODMAS order of operations?

   Brackets, Orders (powers/roots), Division, Multiplication, Addition, Subtraction. Division and Multiplication are done left to right, then Addition and Subtraction left to right.

10. State the laws of exponents for multiplication, division, and power of a power.

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

11. How do you simplify root a x root b and the square root of a fraction?

    root a x root b = root(ab). The square root of (a/b) = root a / root b. Also root(a^2 b) = a root b.

12. What is the cube root relationship: if a number ends in certain digits, what is the unit digit of its cube root?

    Cubes preserve unit-digit mapping: cube ending in 1->1, 8->2, 7->3, 4->4, 5->5, 6->6, 3->7, 2->8, 9->9, 0->0. Useful for finding cube roots of perfect cubes quickly.

13. If a:b = 2:3 and b:c = 4:5, what is a:b:c?

    Make b common: a:b = 8:12 and b:c = 12:15, so a:b:c = 8:12:15.

14. What is the difference between direct and inverse proportion?

    In direct proportion, as one quantity increases the other increases (x/y = constant). In inverse proportion, as one increases the other decreases (xy = constant).

15. How do you find the fourth proportional to three numbers a, b, c?

    If a:b = c:x, then the fourth proportional x = (b x c)/a.

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

    To convert to percentage, multiply by 100 (e.g. 0.25 = 25 percent, 1/4 = 25 percent). To convert a percentage to a fraction, divide by 100 (e.g. 40 percent = 40/100 = 2/5).

17. If a value increases by x percent and then decreases by x percent, what is the net effect?

    There is a net decrease of (x^2/100) percent. For example, +10 percent then -10 percent gives a net 1 percent decrease.

18. What is the formula for percentage increase and percentage decrease?

    Percentage increase = (Increase / Original) x 100. Percentage decrease = (Decrease / Original) x 100.

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