RRB JE Mathematics Syllabus

Mathematics syllabus — full chapter and topic list

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

1. 1

   Algebra

   4 topics

   • Simplification
   • Polynomials
   • Quadratic Equations
   • Linear Equations
2. 2

   Arithmetic

   5 topics

   • Percentage
   • Ratio and Proportion
   • Average
   • Time and Work
   • Time, Speed and Distance
3. 3

   Geometry

   4 topics

   • Triangles
   • Circles
   • Quadrilaterals
   • Coordinate Geometry
4. 4

   Trigonometry

   3 topics

   • Trigonometric Ratios
   • Height and Distance
   • Trigonometric Identities
5. 5

   Statistics

   3 topics

   • Mean, Median, Mode
   • Probability
   • Standard Deviation

Mathematics flashcards for RRB JE

21 of 55 cards from the Mathematics deck — real questions with worked answers.

1. In simplification, what does the BODMAS rule stand for and in what order are operations performed?

   Brackets, Orders (powers/roots), Division, Multiplication, Addition, Subtraction — performed in that order (with division/multiplication left to right, then addition/subtraction left to right).

2. What is the value of a^0 for any non-zero a, and what is a^(-n)?

   a^0 = 1; a^(-n) = 1/a^n.

3. State the laws of indices for a^m × a^n and (a^m)^n.

   a^m × a^n = a^(m+n); (a^m)^n = a^(mn). Also a^m ÷ a^n = a^(m−n).

4. What is a polynomial, and what is meant by its degree?

   A polynomial is an expression of the form a_n x^n + ... + a_1 x + a_0 with non-negative integer powers of the variable. Its degree is the highest power of the variable with a non-zero coefficient.

5. State the Remainder Theorem.

   If a polynomial p(x) is divided by (x − a), the remainder equals p(a).

6. State the Factor Theorem.

   (x − a) is a factor of polynomial p(x) if and only if p(a) = 0.

7. Expand (a + b)^2, (a − b)^2, and (a + b)(a − b).

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

8. Give the identities for a^3 + b^3 and a^3 − b^3.

   a^3 + b^3 = (a+b)(a^2 − ab + b^2); a^3 − b^3 = (a−b)(a^2 + ab + b^2).

9. What is the standard form of a quadratic equation and the quadratic formula for its roots?

   Standard form: ax^2 + bx + c = 0 (a ≠ 0). Roots: x = [−b ± √(b² − 4ac)] / (2a).

10. What is the discriminant of a quadratic, and how does its value determine the nature of the roots?

    Discriminant D = b² − 4ac. If D > 0: two distinct real roots; D = 0: two equal real roots; D < 0: no real roots (complex conjugate roots).

11. For ax² + bx + c = 0, what are the sum and product of the roots?

    Sum of roots = −b/a; Product of roots = c/a.

12. How do you form a quadratic equation when the sum (S) and product (P) of its roots are known?

    x² − Sx + P = 0.

13. What is the condition for a pair of linear equations a₁x + b₁y = c₁ and a₂x + b₂y = c₂ to have a unique solution?

    A unique solution exists when a₁/a₂ ≠ b₁/b₂ (the lines intersect at one point).

14. What are the conditions for a pair of linear equations to have no solution and infinitely many solutions?

    No solution (parallel lines): a₁/a₂ = b₁/b₂ ≠ c₁/c₂. Infinitely many (coincident lines): a₁/a₂ = b₁/b₂ = c₁/c₂.

15. Name three algebraic methods for solving a pair of linear equations in two variables.

    Substitution method, elimination method, and cross-multiplication method (graphical method is the non-algebraic option).

16. How do you convert a fraction to a percentage and a percentage to a fraction?

    Fraction to percent: multiply by 100 (e.g., 1/4 = 25%). Percent to fraction: divide by 100 (e.g., 25% = 25/100 = 1/4).

17. If a value increases from A to B, how is the percentage increase calculated?

    Percentage increase = [(B − A)/A] × 100.

18. If a number is increased by x% and then decreased by x%, what is the net percentage change?

    A net decrease of (x²/100)%.

19. What is a ratio, and what does proportion mean?

    A ratio a:b compares two quantities of the same kind by division. A proportion states that two ratios are equal, a:b = c:d (i.e., a/b = c/d).

20. In a proportion a:b = c:d, what is the rule of cross products (and what are the means and extremes)?

    ad = bc (product of extremes = product of means). Here a and d are the extremes; b and c are the means.

21. What is the mean proportional (geometric mean) between two numbers a and b?

    The mean proportional is √(ab); it is the value x such that a:x = x:b.

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