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RRB JE Mathematics Syllabus
The Mathematics syllabus for RRB JE in full: 5 chapters and 19 topics, every one listed below, plus 55 Mathematics flashcards with answers.
Mathematics syllabus: all 5 chapters
Expand any chapter to see its topics and sub-topics.
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Algebra
4 topics- Simplification
- Polynomials
- Quadratic Equations
- Linear Equations
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Arithmetic
5 topics- Percentage
- Ratio and Proportion
- Average
- Time and Work
- Time, Speed and Distance
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Geometry
4 topics- Triangles
- Circles
- Quadrilaterals
- Coordinate Geometry
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Trigonometry
3 topics- Trigonometric Ratios
- Height and Distance
- Trigonometric Identities
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Statistics
3 topics- Mean, Median, Mode
- Probability
- Standard Deviation
RRB JE Mathematics flashcards — 55 questions with answers
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).
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.
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).
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.
State the Remainder Theorem.
If a polynomial p(x) is divided by (x − a), the remainder equals p(a).
State the Factor Theorem.
(x − a) is a factor of polynomial p(x) if and only if p(a) = 0.
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.
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).
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).
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).
For ax² + bx + c = 0, what are the sum and product of the roots?
Sum of roots = −b/a; Product of roots = c/a.
How do you form a quadratic equation when the sum (S) and product (P) of its roots are known?
x² − Sx + P = 0.
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).
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.
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).
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).
If a value increases from A to B, how is the percentage increase calculated?
Percentage increase = [(B − A)/A] × 100.
If a number is increased by x% and then decreased by x%, what is the net percentage change?
A net decrease of (x²/100)%.
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).
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.
Show the other 35 Mathematics flashcards
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.
How do you divide a quantity Q in the ratio a:b?
First part = Q × a/(a+b); Second part = Q × b/(a+b).
What is the formula for the average (arithmetic mean) of n numbers?
Average = (Sum of all observations) / (Number of observations).
What is the average of the first n natural numbers?
Average = (n + 1)/2.
If two groups have averages A₁ (n₁ items) and A₂ (n₂ items), what is the combined average?
Combined average = (n₁A₁ + n₂A₂)/(n₁ + n₂).
If A can do a work in x days and B in y days, how long do they take working together?
Together they take xy/(x + y) days (their combined one-day work is 1/x + 1/y).
In time and work, what is the relationship between efficiency and time taken?
Efficiency is inversely proportional to time: if A is twice as efficient as B, A takes half the time B takes. Ratio of work done in equal time = ratio of efficiencies.
State the basic relationship between speed, distance and time.
Speed = Distance / Time; therefore Distance = Speed × Time and Time = Distance / Speed.
How do you convert a speed from km/h to m/s and vice versa?
km/h to m/s: multiply by 5/18. m/s to km/h: multiply by 18/5.
What is the relative speed of two objects moving in the same direction and in opposite directions?
Same direction: relative speed = difference of speeds (s₁ − s₂). Opposite directions: relative speed = sum of speeds (s₁ + s₂).
What is the average speed for a journey covering equal distances at speeds u and v?
Average speed = 2uv/(u + v) (the harmonic mean of the two speeds).
State the Pythagoras theorem for a right-angled triangle.
In a right-angled triangle, the square of the hypotenuse equals the sum of the squares of the other two sides: c² = a² + b².
State the angle sum property of a triangle and the exterior angle property.
The three interior angles of a triangle sum to 180°. An exterior angle equals the sum of the two opposite (remote) interior angles.
Give the formulas for the area of a triangle by base-height and by Heron's formula.
Area = ½ × base × height. Heron's formula: Area = √[s(s−a)(s−b)(s−c)], where s = (a+b+c)/2.
What does it mean for two triangles to be similar, and what is the ratio of their areas?
Two triangles are similar if their corresponding angles are equal and corresponding sides are proportional. The ratio of their areas equals the square of the ratio of corresponding sides.
State the standard congruence criteria for triangles.
SSS, SAS, ASA, AAS, and RHS (right angle–hypotenuse–side, for right triangles).
Give the formulas for the circumference and area of a circle of radius r.
Circumference = 2πr; Area = πr².
What is the formula for the length of an arc and the area of a sector subtending angle θ (in degrees) at the centre?
Arc length = (θ/360) × 2πr; Sector area = (θ/360) × πr².
State the relationship between the angle subtended by an arc at the centre and at any point on the remaining circle.
The angle subtended at the centre is twice the angle subtended at any point on the remaining part of the circle (same arc).
What is the angle in a semicircle, and what is the property of the tangent to a circle at the point of contact?
The angle in a semicircle is a right angle (90°). A tangent is perpendicular to the radius drawn to the point of contact.
Classify quadrilaterals: how do a parallelogram, rectangle, rhombus, and square differ?
Parallelogram: opposite sides parallel and equal. Rectangle: parallelogram with all angles 90°. Rhombus: parallelogram with all sides equal. Square: rectangle with all sides equal (all angles 90° and all sides equal).
Give the area formulas for a parallelogram, rhombus (diagonals d₁, d₂), and trapezium.
Parallelogram: base × height. Rhombus: ½ × d₁ × d₂. Trapezium: ½ × (sum of parallel sides) × height.
What is the sum of the interior angles of any quadrilateral?
360°.
State the distance formula between two points (x₁, y₁) and (x₂, y₂).
Distance = √[(x₂ − x₁)² + (y₂ − y₁)²].
State the midpoint formula and the section formula (internal division in ratio m:n).
Midpoint = ((x₁+x₂)/2, (y₁+y₂)/2). Section (ratio m:n) = ((mx₂ + nx₁)/(m+n), (my₂ + ny₁)/(m+n)).
What is the slope of a line through (x₁, y₁) and (x₂, y₂), and what is the slope-intercept form?
Slope m = (y₂ − y₁)/(x₂ − x₁). Slope-intercept form: y = mx + c, where c is the y-intercept.
Define the six trigonometric ratios for an angle in a right triangle.
sin = opposite/hypotenuse; cos = adjacent/hypotenuse; tan = opposite/adjacent; cosec = 1/sin; sec = 1/cos; cot = 1/tan.
Give the values of sin, cos, and tan for 0°, 30°, 45°, 60°, and 90°.
sin: 0, 1/2, 1/√2, √3/2, 1. cos: 1, √3/2, 1/√2, 1/2, 0. tan: 0, 1/√3, 1, √3, undefined.
In a height and distance problem, define the angle of elevation and the angle of depression.
Angle of elevation: angle above the horizontal when looking up at an object. Angle of depression: angle below the horizontal when looking down at an object. (They are equal for the same line of sight.)
State the three Pythagorean trigonometric identities.
sin²θ + cos²θ = 1; 1 + tan²θ = sec²θ; 1 + cot²θ = cosec²θ.
How are mean, median, and mode defined for a data set?
Mean = sum of values ÷ number of values. Median = middle value when data is arranged in order (average of two middle values if even count). Mode = the most frequently occurring value.
State the empirical relationship between mean, median, and mode.
Mode = 3 × Median − 2 × Mean.
What is the formula for the probability of an event, and what is the range of probability values?
P(event) = (number of favourable outcomes)/(total number of equally likely outcomes). Probability ranges from 0 (impossible) to 1 (certain).
What is the relationship between the probability of an event and its complement?
P(not E) = 1 − P(E); i.e., P(E) + P(not E) = 1.
What does standard deviation measure, and what is its formula for a population of n values with mean x̄?
Standard deviation measures the spread/dispersion of data about the mean. σ = √[ Σ(xᵢ − x̄)² / n ]; it is the square root of the variance.
RRB JE Mathematics FAQ
What is in the RRB JE Mathematics syllabus?
RRB JE Mathematics is split into 5 chapters: Algebra, Arithmetic, Geometry, Trigonometry and Statistics. Together they contain 19 topics.
How many chapters are in RRB JE Mathematics?
5 chapters, containing 19 topics. The largest chapter is Arithmetic, with 5 topics.
Are there flashcards for RRB JE Mathematics?
Yes — a 55-card Mathematics 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.