Formula & Quick Fact Cheat Sheets
Numerical (Section A)
| Topic | Formula / Rule |
|---|---|
| Percentage | x% of N = (x/100)×N; A is what % of B → (A/B)×100 |
| Ratio | a:b = a/b; if a:b = m:n, divide total in m+n parts |
| Average | Sum / n |
| Profit % | (Profit/CP)×100; SP = CP×(100+P%)/100 |
| Loss % | (Loss/CP)×100; SP = CP×(100−L%)/100 |
| SI | (P×R×T)/100 |
| CI (annual) | A = P(1+R/100)^T; CI = A−P |
| Time & Work | Work = Rate×Time; 1/a + 1/b = combined rate |
| Speed | Speed = Distance/Time; Avg speed (equal dist) = 2xy/(x+y) |
| Train | Same dir: relative = |
Digital / Number systems
| Convert | Method |
|---|---|
| Decimal → Binary | Divide by 2, remainders bottom→top |
| Binary → Decimal | Sum bit×2^position |
| Hex ↔ Binary | 4 bits per hex digit |
| 2's complement | Invert bits + 1 |
| NAND/NOR | Universal gates |
Boolean quick laws
- A+0=A, A·1=A, A+A'=1, A·A'=0
- De Morgan: (A+B)'=A'B' ; (AB)'=A'+B'
- A+AB=A ; A+A'B=A+B
OS scheduling / memory
| Algorithm | Key point |
|---|---|
| FCFS | Non-preemptive; convoy effect |
| SJF | Shortest job first; may starve long jobs |
| Round Robin | Time quantum; fair |
| Priority | Starvation → aging |
| Deadlock | Mutual exclusion, hold&wait, no preemption, circular wait |
| LRU | Replace least recently used page |
DBMS keys & normal forms
| Term | Meaning |
|---|---|
| Primary key | Unique + not null identifier |
| Foreign key | References primary key of another table |
| 1NF | Atomic values |
| 2NF | 1NF + no partial dependency |
| 3NF | 2NF + no transitive dependency |
| ACID | Atomicity, Consistency, Isolation, Durability |
Networks
| Layer (TCP/IP) | Examples |
|---|---|
| Application | HTTP, FTP, SMTP, DNS |
| Transport | TCP, UDP |
| Internet | IP, ICMP |
| Network Access | Ethernet, Wi-Fi |
| Private IPv4 | 10.x, 172.16–31.x, 192.168.x |
Programming complexities (common)
| Algo | Best | Average | Worst |
|---|---|---|---|
| Binary search | O(1) | O(log n) | O(log n) |
| Bubble/Selection/Insertion | O(n)/O(n²)/O(n) | O(n²) | O(n²) |
| Merge sort | O(n log n) | O(n log n) | O(n log n) |
| Quick sort | O(n log n) | O(n log n) | O(n²) |
| Stack/Queue ops | O(1) push/pop or enqueue/dequeue |
Software Engineering
- Waterfall: linear; Agile/Scrum: iterative sprints
- Cohesion high ↑ good; Coupling low ↓ good
- Unit → Integration → System → Acceptance
Pedagogy one-liners
- Formative = during learning; Summative = end
- Bloom: Remember→Understand→Apply→Analyze→Evaluate→Create
- Inclusive education = all learners in common setting with support