RRB MATHEMATICS – 60-MINUTE MASTER REVISION SHEET
(Use it in this order: 8 → 5 → 3 → 2 → 6 → 1 → 4 → 7)

SECTION-8 : LAST-HOUR PRIORITY 20
(Revise in last 30 min before gate closes)

1. 1²-30², 1³-15³, √2=1.414, √3=1.732, π≈22/7
2. Profit % = (SP-CP)/CP×100 ; Loss reverse
3. CI 2-yr shortcut: Net % = x + x²/100 (x=r%)
4. Speed downstream = b+s; upstream = b-s
5. TSD: avg speed = 2xy/(x+y) (Same distance)
6. Work: (m₁d₁t₁)/w₁ = (m₂d₂t₂)/w₂
7. Average of 1st n natural nos. = (n+1)/2
8. Sum AP = n/2[2a+(n-1)d]
9. Ratio & Proportion: componendo/dividendo ready
10. Triangle area: ½ab sinC = √[s(s-a)(s-b)(s-c)]
11. a³+b³=(a+b)(a²-ab+b²) – keep algebraic identity set
12. % change area if side ↑x% → (2x+x²/100)%
13. Divisibility 7: (unit-2×rest) divisible by 7
14. HCF×LCM = product of two numbers
15. sinθ=cos(90-θ); tanθ=cot(90-θ)
16. max value of sinθ, cosθ =1; min =-1
17. 1 mile=1.6 km; 1 gallon=3.78 L
18. 1 ream=500 sheets; 1 gross=144
19. Wrong number series: check 2nd diff,×/÷ pattern
20. Marked option “None of these” is correct 18-20% times – don’t fear it

SECTION-5 : ONE-LINER 100 (Glance 7 min) 1-10: Fraction→%: 1/2=50, 1/3≈33.33, 1/4=25, 1/5=20, 1/6≈16.67, 1/7≈14.28, 1/8=12.5, 1/9≈11.11, 1/11≈9.09, 1/12≈8.33
11-20: Squares 16²-25² (256,289,324,361,400,441,484,529,576,625)
21-30: Cubes 6³-15³ (216-3375)
31-40: π multiples (π to 10π≈31.4)
41-50: √50 to √200 (≈7.07-14.14)
51-60: Prime pairs 11-13, 17-19, 29-31, 41-43, 59-61, 71-73, 101-103, 107-109, 137-139, 149-151
61-70: Sum 1-100=5050; 1-50=1275
71-80: angle sum n sides=(n-2)×180°
81-90: reg.poly 1 interior angle=(n-2)180/n
91-100: wrong-series common diff 7,11,13,17,19,23,29,31,37,41

SECTION-3 : 50 MUST-KNOW FACTS (3 min scan)

1. 0 is even; neither +ve nor –ve
2. 1 is neither prime nor composite
3. Only even prime: 2
4. Only prime ending in 5: 5
5. LCM of 1-10 is 2520
6. 100! has 24 trailing zeros
7. 2¹⁰=1024≈1KB
8. 1HP=746W
9. 1kcal=4.2kJ
10. Water boils 100°C=212°F
11. Normal body 37°C=98.6°F
12. Freezing 0°C=32°F
13. speed of sound 343 m/s
14. speed of light 3×10⁸ m/s
15. g=9.8 m/s²
16. 1 acre=4047 m²
17. 1 hectare=2.47 acre
18. 1 nautical mile=1.852 km
19. 1 tonne=1000 kg
20. 1 quintal=100 kg
21. 1 barrel oil≈159 L
22. 1 carat=200 mg
23. 1 ream=500 sheets
24. 1 gross=12 dozen=144
25. 1 light-year≈9.46×10¹² km
26. 1 AU≈1.496×10⁸ km
27. Euclid—Father of Geometry
28. Aryabhata—0, place value
29. Ramanujan—1729 Hardy no.
30. Brahmagupta—0 rules
31. Pythagoras—triangle theorem
32. Pascal—triangle & probability
33. 360° diagram—total angle
34. Angle in semi-circle=90°
35. Diagonals of rhombus ⊥
36. Parallelogram diagonals bisect
37. Sum ext angle any polygon=360°
38. Congruence rules SSS,SAS,ASA,AAS,RHS
39. Similarity AA,SAS,SSS
40. Quadratic has max 2 real roots
41. Discriminant D=b²-4ac
42. If D>0 real & distinct; D=0 real & equal; D<0 imaginary
43. sin²θ+cos²θ=1 (ID)
44. 1+tan²θ=sec²θ
45. 1+cot²θ=csc²θ
46. sin(A+B)=sinAcosB+cosAsinB
47. cos2θ=cos²θ-sin²θ=2cos²θ-1=1-2sin²θ
48. AM≥GM≥HM
49. SD=√Variance
50. Range=Max-Min

SECTION-2 : FORMULA & SHORTCUT BANK (5 min) Percentages

• % increase then decrease r% → net loss = r²/100%
• Successive discounts a%,b% → single = (a+b-ab/100)%

Profit-Loss

• SP=(100±gain/loss)% × CP
• When profit% equals CP→SP=CP(1+CP/100)

SI-CI

• SI=PRT/100; CI=A-P
• CI 2 yr diff = P(r/100)²
• CI 3 yr diff = P(r/100)³ +3P(r/100)²

TSD

• Avg speed = total dist / total time
• Relative speed same dir: S₁-S₂; opp: S₁+S₂
• Train crossing pole: L=vt; platform: L+plat=vt

Boats

• Downstream b+s; upstream b-s
• If t↓,t↑ given, still water time=2t↓t↑/(t↓+t↑)

Work

• M₁D₁H₁/W₁ = M₂D₂H₂/W₂
• Combined work 1/t = 1/t₁+1/t₂

Pipe-Cistern

• Net part filled in 1 h = 1/x-1/y (x=inlet,y=outlet)

Average

• New avg = old avg + (increase×no.of items)/total items

Mixture

• Alligation: (d-m)/(m-c)=qtyI/qtyII

Ratio

• If A:B=C:D then A/B=C/D → AD=BC

Algebra

• (a+b)²=a²+2ab+b²
• a³+b³+c³-3abc=(a+b+c)(a²+b²+c²-ab-bc-ca)
• If a+b+c=0 → a³+b³+c³=3abc

Progressions

• AP nth term a+(n-1)d; sum n/2[2a+(n-1)d]
• GP nth term arⁿ⁻¹; sum a(rⁿ-1)/(r-1)

Geometry

• △ area ½bh, ½ab sinC, √[s(s-a)(s-b)(s-c)]
• Circle area πr², circ 2πr, sector=(θ/360)πr²
• Sphere vol 4/3πr³, surface 4πr²
• Cylinder vol πr²h, TSA 2πr(r+h)
• Cone vol ⅓πr²h, l=√(r²+h²)

Mensuration short

• For same surface, sphere has max vol
• Cyclic quad: opp angles=180°

Trigonometry

• 0° 30° 45° 60° 90° sin row: 0 ½ 1/√2 √3/2 1
• cos reverse; tan=sin/cos
• Height shadow: h/x=tanθ

Statistics

• Mean=Σx/n, Median: (n+1)/2 th term (odd)
• Mode=max freq
• SD(ungrouped)=√[Σ(x-x̅)²/n]

Probability

• P(E)=n(E)/n(S)
• At least one = 1-P(none)

SECTION-6 : COMMON CONFUSIONS CLEARED (1 min) Often Confused → Correct Fact
% increase & % of → “increase by 20%” = ×1.2; “20% of” = ×0.2
CI half-yearly → rate halved, time doubled
Average speed vs avg of speeds → Same distance: HM; diff distance: total dist/total time
Profit on SP vs CP → Always on CP unless stated
0 even or odd → Even
1 prime? → No
HCF can be 0? → No, HCF≥1
π rational? → Irrational
Discount successive vs single → Successive multiply factors
log 100 = 2 (base 10) not 10

SECTION-1 : TOP-30 CORE CONCEPTS (2 min glance) 1 Number system: Divis, rem, unit digit cycle
2 HCF-LCM: Factor-tree & division method
3 Simplification: BODMAS + fraction tricks
4 Percentage: Base shift & fractional eq
5 Profit-Loss: Dishonest dealer, no-weighing
6 SI-CI: Compounding half-yrly, quarterly
7 Ratio-Proportion: Chain & compounding
8 Mixture-Allegation: Cross-line 10 sec
9 Partnership: Time-weighted cap
10 Average: Age, replacement, surplus-deficit
11 Time-Distance: Train-bridge, stoppage, circular
12 Boat-Stream: Same-dist up-down shortcut
13 Time-Work: Efficiency %, work-leave
14 Pipe-Cistern: Net rate negative
15 Mensuration: 2-D area, 3-D vol+TSA
16 Geometry: Triangle congruency-similarity
17 Circle: Tangent-chord theorem, angle in segment
18 Trigonometry: Height-distance, angle elevation
19 Coordinate: Distance, section, slope
20 Linear Equation: Substitution-elimination
21 Quadratic: Nature of roots, graph
22 Polynomials: Remainder-factor theorem
23 Indices-Surds: Rationalise, square root trick
24 Logarithms: Basic identities, change base
25 AP-GP: nth term, sum, insert mean
26 Permutation-Combination: nPr, nCr, circular
27 Probability: Independent, Bayes (basic)
28 Statistics: Mean-Median-Mode, SD shortcut
29 Data Interpretation: Table-bar-pie, % diff
30 Number Series: Diff-ratio mixed, wrong no.

SECTION-4 : PREVIOUS-YEAR TREND (10 sec) RRB NTPC CBT-1 ( maths 30q)

• Arithmetic(%) 8-9
• SI-CI 2
• Ratio-mixture 3
• TSD-work 4
• Mensuration 3
• Trigo-height 2
• DI 5
• Simplification 3
  Average difficulty Easy-Mod; calc-heavy; options gap ≥5%

RRB Group-D ( maths 25q)
Simplification+number sys 8
TSD-work 4
Mensuration 3
Trigo 2
DI 3
Rest arithmetic 5

ALP Stage-I ( maths 20q)
Similar to NTPC but 2 extra coordinate geometry & 1 logarithm

SECTION-7 : MEMORY TRICKS (30 sec)

• % fraction: “Triple your 1” 1/3→33, 1/6→16, 1/9→11
• CI 2-yr diff: “Rate-square Principle” → P(r%)²
• sin 0-90 row: “O H A H O” (0,1/2,1/√2,√3/2,1)
• Complimentary pairs: “S C T” (sin↔cos, tan↔cot)
• HCF-LCM big nos: “Divide till co-prime, multiply left & around”
• π decimals: “May I have a large container coffee” 3.1415926 (words-length)
• Boat same distance up-down time: “2ab/(a+b)” remember Harmonic mean

REVISION TIMETABLE (60 min total)
0-7 min: Sec-8 + Sec-5
7-10 min: Sec-3
10-15 min: Sec-2 (only starred formulas)
15-16 min: Sec-6
16-18 min: Sec-1 (heading scan)
18-20 min: Sec-7 + quick self-quiz (close sheet, recall 20 facts)

Carry ONLY this sheet inside exam hall—read Sec-8 just before gate.