RRB ALP (Assistant Loco Pilot) Mathematics (CBT Stage 1 & Stage 2 Part A) Syllabus

Mathematics (CBT Stage 1 & Stage 2 Part A) syllabus — full chapter and topic list

Expand any chapter to see its topics and sub-topics. This is the whole examinable outline for Mathematics (CBT Stage 1 & Stage 2 Part A) in RRB ALP (Assistant Loco Pilot), not a summary of it.

1. 1

   Number System & Arithmetic Operations

   4 topics

   • Number Systems
     • Natural, whole, integers, rational and irrational numbers
     • Factors, multiples, HCF and LCM
     • Divisibility rules and remainder theorem
   • BODMAS and Simplification
     • Order of operations
     • Surds and indices
     • Approximation techniques
   • Fractions and Decimals
     • Conversion between fractions and decimals
     • Comparison and ordering
   • Squares, Cubes and Roots
     • Square roots and cube roots
     • Estimation of roots
2. 2

   Commercial Arithmetic

   5 topics

   • Ratio and Proportion
     • Direct and inverse proportion
     • Partnership problems
   • Percentage
     • Percentage increase and decrease
     • Successive percentage change
   • Profit, Loss and Discount
     • Cost price, selling price, marked price
     • Successive discounts
   • Simple and Compound Interest
     • SI formula and applications
     • CI compounded annually, half-yearly
     • Difference between SI and CI
   • Average
     • Average of numbers and quantities
     • Weighted average
3. 3

   Time-Based and Rate Problems

   3 topics

   • Time, Speed and Distance
     • Relative speed
     • Problems on trains
     • Boats and streams
   • Time and Work
     • Work efficiency and rates
     • Pipes and cisterns
   • Pipes and Cisterns
     • Inlet and outlet pipes
4. 4

   Algebra and Mensuration

   3 topics

   • Elementary Algebra
     • Algebraic identities and expressions
     • Linear equations in one and two variables
   • Mensuration of 2D Figures
     • Area and perimeter of triangle, rectangle, circle
     • Area of parallelogram and trapezium
   • Mensuration of 3D Solids
     • Volume and surface area of cube, cuboid, cylinder
     • Cone, sphere and hemisphere
5. 5

   Geometry, Trigonometry and Data Interpretation

   5 topics

   • Basic Geometry
     • Lines, angles and triangles
     • Properties of circles
   • Elementary Trigonometry
     • Trigonometric ratios and identities
     • Heights and distances
   • Pythagoras and Statistics
     • Mean, median, mode
   • Calendar and Clock
     • Odd days and day determination
     • Angle between clock hands
   • Data Interpretation
     • Tables, bar graphs and pie charts

Mathematics (CBT Stage 1 & Stage 2 Part A) flashcards for RRB ALP (Assistant Loco Pilot)

24 of 50 cards from the Mathematics (CBT Stage 1 & Stage 2 Part A) deck — real questions with worked answers.

1. How do you classify real numbers into rational and irrational?

   A rational number can be written as p/q where p, q are integers and q is not zero (e.g. 3/4, 0.25, 7); an irrational number cannot be expressed as p/q and has a non-terminating, non-repeating decimal (e.g. sqrt2, pi).

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

   Two numbers whose Highest Common Factor (HCF) is 1, e.g. 8 and 15. They share no common factor other than 1.

3. State the relationship between HCF and LCM of two numbers.

   Product of two numbers = HCF x LCM. So LCM = (a x b) / HCF.

4. What is the divisibility rule for 11?

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

5. What does the BODMAS rule stand for and what order does it dictate?

   Brackets, Of, Division, Multiplication, Addition, Subtraction. Operations are solved in that order; brackets first, then of/division/multiplication (left to right), then addition/subtraction (left to right).

6. In BODMAS, in what order should brackets be opened?

   Innermost first: () round brackets, then {} curly brackets, then [] square brackets.

7. How do you convert the recurring decimal 0.bar(3) into a fraction?

   A single repeating digit over 9: 0.333... = 3/9 = 1/3.

8. How do you add two fractions with different denominators, e.g. 1/4 + 1/6?

   Take the LCM of the denominators (12), convert: 3/12 + 2/12 = 5/12.

9. How do you divide one fraction by another, e.g. (2/3) / (4/5)?

   Multiply by the reciprocal of the divisor: (2/3) x (5/4) = 10/12 = 5/6.

10. What is the value of a square of a number ending in 5, e.g. 35^2?

    Take the tens digit n, compute n(n+1) and append 25. For 35: 3x4=12, so 35^2 = 1225.

11. What is the cube of 12 and how is it derived?

    12^3 = 12 x 12 x 12 = 1728.

12. What is the square root of 1764?

    42, because 42 x 42 = 1764.

13. List the perfect squares from 11^2 to 15^2.

    121, 144, 169, 196, 225.

14. How do you simplify the ratio 18:24 to its lowest terms?

    Divide both terms by their HCF (6): 18/6 : 24/6 = 3:4.

15. 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.

16. In a proportion a:b = c:d, what is the rule of cross multiplication?

    The product of extremes equals the product of means: a x d = b x c.

17. How do you divide a sum of Rs 600 in the ratio 2:3?

    Total parts = 5; one part = 600/5 = 120; shares are 2x120 = Rs 240 and 3x120 = Rs 360.

18. How do you convert a fraction like 3/8 into a percentage?

    Multiply by 100: (3/8) x 100 = 37.5%.

19. What is the formula to find percentage increase?

    Percentage increase = (Increase / Original value) x 100.

20. If a number is increased by 20% then decreased by 20%, what is the net change?

    A net decrease of 4% (because 1.2 x 0.8 = 0.96, i.e. 96% of original).

21. What are the formulas for Profit and Loss in terms of Cost Price (CP) and Selling Price (SP)?

    Profit = SP - CP (when SP > CP); Loss = CP - SP (when CP > SP).

22. How do you calculate Profit percentage?

    Profit% = (Profit / Cost Price) x 100. Profit and loss percentages are always calculated on the cost price.

23. What is the relationship between Marked Price (MP), Discount and Selling Price?

    Selling Price = Marked Price - Discount; Discount = Discount% of Marked Price.

24. A shopkeeper marks an item at Rs 500 and gives 10% discount. What is the selling price?

    Discount = 10% of 500 = Rs 50; SP = 500 - 50 = Rs 450.

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