ULTIMATE MATH CHEAT SHEET: FORMULAS, TRICKS, AND TIPS TO ACE ANY EXAM!

February 23, 2025

1682

When it comes to preparing for competitive exams or refreshing our knowledge, a concise and well-organized cheat sheet can make all the difference. This cheat sheet is a quick revision guide for several important topics in mathematics and problem-solving, covering everything from percentages, areas, and volumes to algebra, statistics, and time-related concepts. Whether you’re a student gearing up for exams or someone who needs to brush up on essential formulas and tricks, this guide provides all the necessary information in one place for a streamlined review. Let’s dive in!

Table of Contents

Unit 1: Percentages

Basic Percentage Formula:
Percentage = (Part / Whole) × 100
Common Fractions as Percentages:
1. 10% = 1/10
2. 15% = 3/20
3. 20% = 1/5
4. 25% = ¼
5. 33.33% = 1/3
6. 50% = ½
7. 66.67% = 2/3
8. 75% = ¾
9. 100% = 1
Percentage Increase/Decrease:
- New Value = Old Value (1 + Inc% / 100)
- New Value = Old Value (1 – Dec% / 100)
Successive Percentage Changes:
a + b + (ab)/100
Finding the Original Value After Percentage Increase/Decrease:
- Original Value = Increased Value / (1 + Percentage Increase / 100)
- Original Value = Decreased Value / (1 – Percentage Decrease / 100)
Percentage Change Formula:
Percentage Change = [(New Value – Old Value) / Old Value] × 100

Unit 2: Problem on Ages

Age Difference Trick:
The age difference between two people does not change over time.
Sum of Ages Trick:
If you know the sum of their ages now, you can also calculate future or past sums using similar techniques.

Unit 3: Area, Shapes, and Perimeter

Area Formulas:
- Square: $s^2$
- Rectangle: $\times B$
- Triangle: $12×Base×Height\frac{1}{2} \times \text{Base} \times \text{Height}$
- Equilateral Triangle: $34×s2\frac{\sqrt{3}}{4} \times s^2$
- Parallelogram: $\times H$
- Rhombus: $12×d1×d2\frac{1}{2} \times d1 \times d2$
- Trapezium: $12×(p1+p2)×H\frac{1}{2} \times (p1 + p2) \times H$
- Circle: $πr2\pi r^2$
- Ellipse: $π×a×b\pi \times a \times b$ where a and b are the semi-major and semi-minor axes.
Volume Formulas:
- Cube: $s^3$
- Cuboid: $\times W \times H$
- Sphere: $43πr3\frac{4}{3} \pi r^3$
- Cylinder: $πr2h\pi r^2 h$
- Cone: $13πr2h\frac{1}{3} \pi r^2 h$

Unit 4: Equations

Linear Equation:
$a x + b = 0$
Quadratic Equation:
$ax^2 + bx + c = 0$
Discriminant (D) Formula:
$D = b^2 – 4ac$
Roots based on the discriminant:
- If $D > 0$ : Two distinct real roots.
- If $D = 0$ : Two equal real roots.
- If $D < 0$ : No real roots (complex roots).

Unit 5: Simplifications

BODMAS Rule:
Use the BODMAS rule (Brackets, Orders, Division, Multiplication, Addition, Subtraction) for simplifying expressions.

Unit 6: Mean, Median, Mode, Variance, and Standard Deviation

Mean: Average of a data set.
Median: Middle term when data is arranged in ascending order.
Mode: Most frequent term.
Variance and Standard Deviation: Measures of spread in the data.

Unit 7: Progressions

Geometric Progression (GP):
$an=a×rn−1a_n = a \times r^{n-1}$
Sum of first $n$ terms:
- If $\neq 1$ :
  $Sn=a(1−rn)1−rS_n = \frac{a(1 – r^n)}{1 – r}$
- If $r = 1$ :
  $Sn=n×aS_n = n \times a$
Arithmetic Progression (AP):
$an=a+(n−1)×da_n = a + (n – 1) \times d$
Sum of the first $n$ terms:
$Sn=n2×(a+l)S_n = \frac{n}{2} \times (a + l)$ where $l$ is the last term.

Unit 8: Profit and Loss

Relation Between C.P., S.P., and Profit/Loss:
$Profit=S.P.−C.P.\text{Profit} = \text{S.P.} – \text{C.P.}$
- C.P. = S.P. / (1 + Profit% / 100)
- C.P. = S.P. – Loss
- S.P. = C.P. / (1 – Loss% / 100)
Mark-up and Discounts:
Discount is always calculated on the marked price.
Successive Discounts:
$S.P.=MP×(1−D1/100)×(1−D2/100)\text{S.P.} = \text{MP} \times (1 – D_1 / 100) \times (1 – D_2 / 100)$

Unit 9: HCF and LCM

Relation Between HCF and LCM:
$HCF(a,b)×LCM(a,b)=a×b\text{HCF}(a, b) \times \text{LCM}(a, b) = a \times b$

Unit 10: Speed, Time, and Distance

Conversion:
- $Km/h\text{Km/h}$ to $m/s\text{m/s}$
- $m/s\text{m/s}$ to $Km/h\text{Km/h}$
Relative Speed:
- If two objects move towards each other: $Speed=S1+S2\text{Relative Speed} = S_1 + S_2$
- If two objects move in the same direction: $Speed=∣S1−S2∣\text{Relative Speed} = |S_1 – S_2|$

Unit 11: Boat and Streams

Speed of the Boat in Still Water (B):
Downstream Speed: $D = B + S$
Upstream Speed: $U = B - S$

Unit 12: Clocks and Calendars

Clock Problems:
- Angle between hour and minute hands:
  $∣ (30 H - 5.5 M) ∣$
- Time when hands overlap:
  $Time=H×60+15+30H11\text{Time} = H \times 60 + \frac{15 + 30H}{11}$
Calendar:
Leap year calculation: Divisible by 4, but not 100 unless divisible by 400.

Conclusion:

This cheat sheet offers a comprehensive overview of essential formulas, tricks, and concepts to help you quickly revise and solve problems in mathematics. By keeping these key formulas at your fingertips, you’ll be able to tackle a wide range of questions efficiently. Whether you’re prepping for an exam or looking to strengthen your problem-solving skills, revisiting these core concepts will ensure you’re well-prepared for whatever comes your way

TCS Free NQT 2025 for Freshers, CLICK HERE

TOP 100 TCS NQT CODING QUESTIONS, CLICK HERE

ULTIMATE MATH CHEAT SHEET, CLICK HERE

A COMPLETE GUIDE & EXAM PATTERN OVERVIEW, CLICK HERE

COMPLETE GUIDE TO CUT-OFF, PREPARATION, EXAM RULES & THINGS TO AVOI, CLICK HERE

Join Our Telegram Group (1.9 Lakhs + members):- Click Here To Join

For Experience Job Updates Follow – FLM Pro Network – Instagram Page

For All types of Job Updates (B.Tech, Degree, Walk in, Internships, Govt Jobs & Core Jobs) Follow – Frontlinesmedia JobUpdates – Instagram Page

For Healthcare Domain Related Jobs Follow – Frontlines Healthcare – Instagram Page

For Major Job Updates & Other Info Follow – Frontlinesmedia – Instagram Page