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

The Mathematics (CBT Stage 1 & Stage 2 Part A) syllabus for RRB ALP (Assistant Loco Pilot) in full: 5 chapters, 20 topics and 41 sub-topics, every one listed below, plus 50 Mathematics (CBT Stage 1 & Stage 2 Part A) flashcards with answers.

5Chapters
20Topics
41Sub-topics
50Flashcards

Mathematics (CBT Stage 1 & Stage 2 Part A) syllabus: all 5 chapters

Expand any chapter to see its topics and sub-topics.

  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. 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. 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. 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. 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

RRB ALP (Assistant Loco Pilot) Mathematics (CBT Stage 1 & Stage 2 Part A) flashcards — 50 questions with 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).

Show the other 30 Mathematics (CBT Stage 1 & Stage 2 Part A) flashcards

  1. 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).

  2. How do you calculate Profit percentage?

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

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

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

  4. 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.

  5. What is the formula for Simple Interest (SI)?

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

  6. What is the formula for Amount under Compound Interest, compounded annually?

    A = P(1 + R/100)^T; Compound Interest = A - P.

  7. For the same principal, rate and 2 years, how much more is CI than SI?

    The difference for 2 years = P(R/100)^2, i.e. interest on the first year's interest.

  8. What is the formula for the average (arithmetic mean) of n quantities?

    Average = (Sum of all quantities) / (Number of quantities).

  9. What is the average of the first n natural numbers?

    Average = (n + 1) / 2.

  10. How does the average change if every number in a set is increased by 5?

    The average also increases by 5.

  11. State the basic relationship between speed, distance and time.

    Speed = Distance / Time; Distance = Speed x Time; Time = Distance / Speed.

  12. How do you convert a speed from km/h to m/s?

    Multiply by 5/18. (And multiply by 18/5 to convert m/s to km/h.)

  13. How long does a train of length L metres take to cross a stationary pole at speed v m/s?

    Time = L / v, because the train only needs to cover its own length.

  14. How do you find the relative speed of two objects moving in opposite directions?

    Add their speeds (speed1 + speed2). For the same direction, subtract them.

  15. If A can do a work in 10 days and B in 15 days, what is their combined one-day work?

    1/10 + 1/15 = 3/30 + 2/30 = 5/30 = 1/6, so together they finish in 6 days.

  16. In time and work, what does the unitary method assume about a person's daily output?

    If a person completes a job in n days, their one-day work is 1/n of the total work (rate is constant).

  17. A pipe fills a tank in 6 hours and an outlet empties it in 8 hours. What is the net fill rate per hour?

    1/6 - 1/8 = 4/24 - 3/24 = 1/24, so the tank fills in 24 hours when both are open.

  18. In pipes and cisterns, how is an emptying (outlet) pipe represented in the rate equation?

    As a negative rate, because it removes water; its work is subtracted from the filling pipes' work.

  19. What are the algebraic identities for (a+b)^2 and (a-b)^2?

    (a+b)^2 = a^2 + 2ab + b^2; (a-b)^2 = a^2 - 2ab + b^2.

  20. State the identity for a^2 - b^2.

    a^2 - b^2 = (a + b)(a - b).

  21. What is the quadratic formula for solving ax^2 + bx + c = 0?

    x = [-b +/- sqrt(b^2 - 4ac)] / (2a).

  22. What are the formulas for area and perimeter of a rectangle?

    Area = length x breadth; Perimeter = 2(length + breadth).

  23. What are the formulas for area and circumference of a circle?

    Area = pi x r^2; Circumference = 2 x pi x r, where r is the radius.

  24. What is the formula for the area of a triangle given base and height?

    Area = (1/2) x base x height.

  25. What are the formulas for the volume and total surface area of a cube of side a?

    Volume = a^3; Total Surface Area = 6a^2.

  26. What is the formula for the volume of a cylinder?

    Volume = pi x r^2 x h, where r is the base radius and h is the height.

  27. What is the sum of the interior angles of a triangle, and of a quadrilateral?

    Triangle = 180 degrees; Quadrilateral = 360 degrees.

  28. State the Pythagoras theorem.

    In a right-angled triangle, the square of the hypotenuse equals the sum of the squares of the other two sides: c^2 = a^2 + b^2.

  29. Define sin, cos and tan of an angle in a right-angled triangle.

    sin = Opposite/Hypotenuse; cos = Adjacent/Hypotenuse; tan = Opposite/Adjacent.

  30. How many times do the hands of a clock overlap in 12 hours, and how do you find the angle of a clock?

    The hands overlap 11 times in 12 hours. Angle between hands = |30H - 5.5M| degrees, where H = hour, M = minutes.

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

What is in the RRB ALP (Assistant Loco Pilot) Mathematics (CBT Stage 1 & Stage 2 Part A) syllabus?

RRB ALP (Assistant Loco Pilot) Mathematics (CBT Stage 1 & Stage 2 Part A) is split into 5 chapters: Number System & Arithmetic Operations, Commercial Arithmetic, Time-Based and Rate Problems, Algebra and Mensuration and Geometry, Trigonometry and Data Interpretation. Together they contain 20 topics and 41 sub-topics.

How many chapters are in RRB ALP (Assistant Loco Pilot) Mathematics (CBT Stage 1 & Stage 2 Part A)?

5 chapters, containing 20 topics and 41 sub-topics. The largest chapter is Commercial Arithmetic, with 5 topics.

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

Yes — a 50-card Mathematics (CBT Stage 1 & Stage 2 Part A) deck, printed in full in the flashcards section of this page and available in the Examius app with spaced repetition. The free plan covers one exam of your choice, including its flashcards; Examius Pro, a one-time purchase, unlocks every other exam and deck.