One Page Formula Sheets

Use this for the final 6 hours.

Quant formulas

Percentage

x% of y = xy/100
Increase % = (increase/original) × 100
Decrease % = (decrease/original) × 100

Successive change:

a + b + ab/100

If one increase and one decrease:

a - b - ab/100

Profit/loss

Profit = SP - CP
Loss = CP - SP
Profit% = Profit/CP × 100
Loss% = Loss/CP × 100
Discount% = Discount/MP × 100

Interest

SI = PRT/100
A = P(1 + R/100)^T
CI = A - P

Average

Average = Sum / Count
Sum = Average × Count

Ratio

a:b => ax:bx
share = total × part/sum_of_parts

Time and work

1 day's work = 1/days
Together = xy/(x+y)

Speed

Speed = Distance/Time
km/h to m/s = ×5/18
m/s to km/h = ×18/5

LCM/HCF

Product of two numbers = LCM × HCF

Technical one-page sheet

Data Structures

• Stack: LIFO
• Queue: FIFO
• BFS: Queue
• DFS: Stack/recursion
• Array access: O(1)
• Linked list search: O(n)
• Binary search: O(log n), sorted array required
• Hashing average search: O(1)
• Heap: priority queue

Sorting

Sort	Worst
Bubble	O(n²)
Selection	O(n²)
Insertion	O(n²)
Merge	O(n log n)
Quick	O(n²)
Heap	O(n log n)

OS

• Process: program in execution
• Thread: lightweight, shares process memory
• Round Robin: time quantum
• Deadlock: mutual exclusion, hold and wait, no preemption, circular wait
• Paging: fixed-size
• Segmentation: variable-size
• Page fault: page not in RAM
• Thrashing: too many page faults

Networking

• TCP: reliable, connection-oriented
• UDP: connectionless, faster
• DNS: 53
• HTTP: 80
• HTTPS: 443
• SSH: 22
• Switch: MAC
• Router: IP
• ARP: IP to MAC
• DHCP: automatic IP

Embedded

• Microcontroller: CPU + memory + I/O
• Microprocessor: CPU only
• ADC: analog to digital
• DAC: digital to analog
• Polling: CPU repeatedly checks
• Interrupt: device/event notifies CPU
• UART: async serial
• SPI: MOSI/MISO/SCLK/SS
• I2C: SDA/SCL
• Watchdog: resets hung system

QA

• Verification: building product right
• Validation: building right product
• Unit: individual module
• Integration: module interaction
• System: complete system
• Smoke: basic build check
• Regression: old features after change
• Severity: impact
• Priority: urgency
• Selenium: web automation
• Postman: API testing
• JMeter: load/performance

Pseudocode sheet

• WHILE: condition checked first
• REPEAT UNTIL: runs at least once
• Integer division drops decimal
• % gives remainder
• Nested loop total = outer × inner if fixed
• Print before recursion = descending style
• Print after recursion = ascending style
• Always trace variable update order

Coding sheet

Memorize:

• prime check up to sqrt(n)
• GCD Euclid algorithm
• frequency map
• two pointers
• second largest
• palindrome
• anagram
• Kadane’s algorithm