RRB Group D maths formula sheet

In the last two weeks, you should not be learning new maths. You should be making sure that every rule you already know comes to mind in two seconds. That is what this sheet is for.

Read it once before every mock test. After the mock, mark the lines behind each wrong answer. Those marked lines are your revision list for the next day. The topic guides linked below explain each rule properly; this page only reminds you of them.

Numbers

• 1 is neither prime nor composite. 2 is the only even prime.
• Divisible by 3 or 9: the digit sum is divisible by 3 or 9. By 4: the last two digits form a multiple of 4. By 8: the last three digits. By 11: the difference between the sums of alternate digits is 0 or a multiple of 11.
• Unit-digit cycles: 2 → 2, 4, 8, 6; 3 → 3, 9, 7, 1; 7 → 7, 9, 3, 1; 8 → 8, 4, 2, 6. Digits 0, 1, 5 and 6 never change. Divide the power by 4 and use the remainder (remainder 0 means the 4th digit in the cycle).
• If N = aᵖ × bʳ (a and b prime), the number of factors of N is (p + 1)(r + 1).
• For two numbers: HCF × LCM = product of the numbers.
• BODMAS: brackets, then "of", then division and multiplication (left to right), then addition and subtraction.

Squares, cubes and fractions to know by heart

• Squares from 1 to 30 and cubes from 1 to 15. See squares and square roots.
• Fraction–percentage pairs:

Percentage and ratio

• Change % = change ÷ original × 100.
• Successive changes of a% and b%: a + b + ab/100 (use a minus sign for a fall).
• If a price rises by r%, consumption must fall by r ÷ (100 + r) × 100% to keep spending the same.
• Share a total in a : b as a/(a + b) and b/(a + b) of the total.
• Mean proportional of a and b = √(ab).

Averages

• Total = average × number.
• Replacement: new person = old person + (number × change in average).
• Combined average = (n₁a₁ + n₂a₂) ÷ (n₁ + n₂). Never average two averages directly.

Profit, loss and discount

• Profit % and loss % are on the cost price. Discount % is on the marked price.
• SP = CP × (100 + profit%) ÷ 100. SP = MP × (100 − discount%) ÷ 100.
• Two discounts of a% and b% equal one discount of a + b − ab/100.

Interest

• SI = P × R × T ÷ 100. Under simple interest, a sum doubles when R × T = 100.
• CI amount = P(1 + R/100)ᵀ, where T is the number of years.
• CI − SI for 2 years = P(R/100)².

Time, work and pipes

• Take total work = LCM of the days. Add the daily work of people working together.
• Workers × days is constant for the same job (more workers, fewer days).
• A filling pipe adds and a leak or emptying pipe subtracts.

Speed and trains

• km/h × 5/18 = m/s. m/s × 18/5 = km/h.
• Average speed for a round trip at a and b: 2ab ÷ (a + b).
• A train crossing a pole or a person covers its own length. Crossing a platform or bridge: train + platform.
• Opposite directions: add the speeds. Same direction: subtract them.

Algebra

• (a + b)² = a² + 2ab + b²; (a − b)² = a² − 2ab + b²; a² − b² = (a + b)(a − b).
• x² + 1/x² = (x + 1/x)² − 2.

Geometry and mensuration

• Triangle angles: 180°. Polygon interior sum: (n − 2) × 180°. Exterior angles: 360°.
• Triplets: 3, 4, 5 · 5, 12, 13 · 8, 15, 17 · 7, 24, 25.
• Circle: area πr², circumference 2πr.
• Cylinder: volume πr²h, curved surface 2πrh. Cone: volume ⅓πr²h, curved surface πrl. Sphere: volume (4/3)πr³, surface 4πr².

Trigonometry and statistics

• sin 30° = 1/2, sin 45° = 1/√2, sin 60° = √3/2; the cos values are the same list reversed.
• tan 30° = 1/√3, tan 45° = 1, tan 60° = √3.
• sin²θ + cos²θ = 1; sec²θ − tan²θ = 1; cosec²θ − cot²θ = 1.
• Median: sort first. Mode: most frequent value. Range: largest − smallest.

The sheet in action

Example 1: A price rises by 10% and then by 20%. What is the total rise?

• 10 + 20 + (10 × 20)/100 = 32%.

Example 2: Find the difference between CI and SI on ₹10,000 at 10% a year for 2 years.

• P(R/100)² = 10,000 × (1/10)² = ₹100.

Example 3: A train 150 m long runs at 54 km/h. How long does it take to pass a pole?

• 54 × 5/18 = 15 m/s. Time = 150 ÷ 15 = 10 seconds.

Example 4: How many factors does 72 have?

• 72 = 2³ × 3². Factors = (3 + 1)(2 + 1) = 12.

Quick self-test

1. Find 15% of 240.
2. Find the simple interest on ₹5,000 at 8% a year for 3 years.
3. Convert 72 km/h to m/s.
4. One person can finish a job in 12 days and another in 18 days. How long will they take together?
5. Find each interior angle of a regular octagon.
6. Find the volume of a cylinder of radius 7 cm and height 10 cm.
7. Find the unit digit of 7²³.
8. A person drives to a town at 40 km/h and returns by the same road at 60 km/h. Find the average speed for the whole journey.

Answers:

1. 36. 10% is 24 and 5% is 12.
2. ₹1,200. 5,000 × 8 × 3 ÷ 100.
3. 20 m/s. 72 × 5/18.
4. 7.2 days. Total work 36 units; they do 3 + 2 = 5 units a day; 36 ÷ 5.
5. 135°. Each exterior angle is 360 ÷ 8 = 45°, and 180 − 45 = 135.
6. 1,540 cm³. 22/7 × 7 × 7 × 10.
7. 3. 23 ÷ 4 leaves remainder 3, and the 3rd digit in the cycle 7, 9, 3, 1 is 3.
8. 48 km/h. 2 × 40 × 60 ÷ (40 + 60) = 4,800 ÷ 100. Not 50.

Two-week revision plan

Alongside the plan, take a full mock every two or three days. Our guide to mock tests explains how to review them.

What to do next

• Read this sheet before every mock for the next two weeks.
• After each mock, tick the formula behind every maths mistake and reread those lines the next morning.
• Redo the self-test on day 7 and day 14. Aim for all eight right in under eight minutes.
• If a whole section feels shaky, go back to its guide, starting with the maths plan.