Key points, formulas and digest answers for Science & Commerce streams
⚡
Physics
Chapter 2 — Units and Measurements
📌 Key Points
SI Units: Length — metre (m), Mass — kilogram (kg), Time — second (s), Temperature — Kelvin (K), Current — Ampere (A), Luminous intensity — Candela (cd), Amount of substance — Mole (mol)
Dimensional formula: expression showing how physical quantity depends on fundamental quantities
Force = [MLT⁻²], Energy = [ML²T⁻²], Power = [ML²T⁻³]
Significant figures: all certain digits + one uncertain digit in a measurement
Least count: smallest value measurable by instrument
Absolute error: difference between measured and true value
Relative error: absolute error / true value
Percentage error: relative error × 100
✅ Digest Answers
Q. Find dimensional formula of Pressure.
Pressure = Force/Area = [MLT⁻²]/[L²] = [ML⁻¹T⁻²]
Q. What are the uses of dimensional analysis?
1) To check correctness of equations. 2) To derive relationships between physical quantities. 3) To convert units from one system to another.
🏃
Physics
Chapter 3 — Motion in a Straight Line
📌 Key Formulas
Displacement: change in position (vector quantity)
Q. A car starts from rest and accelerates at 4 m/s². Find velocity after 5 seconds.
u = 0, a = 4, t = 5. v = u + at = 0 + 4×5 = 20 m/s
Q. Difference between distance and displacement?
Distance is the total path length covered (scalar, always positive). Displacement is the shortest distance from initial to final position (vector, can be zero or negative). Example: running around a 400m track and returning — distance = 400m, displacement = 0.
⚗️
Chemistry
Chapter 1 — Some Basic Concepts of Chemistry
📌 Key Points
Atomic mass unit (amu): 1/12th of mass of Carbon-12 atom
Molar mass: mass of one mole of substance in grams
Molarity M = moles of solute / volume of solution in litres
Empirical formula: simplest whole number ratio of atoms
Molecular formula: actual number of atoms in molecule
Limiting reagent: reactant that is completely consumed first in a reaction
% composition = (mass of element / molar mass of compound) × 100
✅ Digest Answers
Q. What is a mole? What is Avogadro's number?
A mole is the amount of substance that contains as many particles as there are atoms in 12g of Carbon-12. This number is 6.022 × 10²³ and is called Avogadro's number (Nₐ).
Q. Find number of moles in 36g of water (H₂O).
Molar mass of H₂O = 2(1) + 16 = 18 g/mol. Moles = 36/18 = 2 moles
🧪
Chemistry
Chapter 2 — Structure of Atom
📌 Key Points
Electron: charge −1, mass = 9.1 × 10⁻³¹ kg (J.J. Thomson)
Proton: charge +1, mass = 1.67 × 10⁻²⁷ kg (Goldstein)
Neutron: charge 0, mass ≈ proton mass (James Chadwick)
Atomic number (Z): number of protons
Mass number (A): protons + neutrons
Isotopes: same atomic number, different mass number. Example: ¹²C and ¹⁴C
Bohr's model: electrons revolve in fixed circular orbits (shells) without radiating energy
Max electrons in shell n = 2n²
Aufbau principle: electrons fill lowest energy orbitals first
Pauli's exclusion principle: no two electrons can have same set of 4 quantum numbers
Hund's rule: electrons fill each orbital singly before pairing
✅ Digest Answers
Q. What are isotopes? Give two examples.
Atoms of same element with same atomic number but different mass numbers (different neutrons). Examples: 1) Hydrogen isotopes: ¹H (protium), ²H (deuterium), ³H (tritium). 2) Carbon isotopes: ¹²C and ¹⁴C (used in carbon dating).
Q. Write electron configuration of Sodium (Na, Z=11).
Na (11 electrons): 1s² 2s² 2p⁶ 3s¹ or shell-wise: 2, 8, 1
📐
Mathematics
Chapter 1 — Sets
📌 Key Points
Set: well-defined collection of distinct objects
Roster form: listing all elements. Example: {1, 2, 3, 4}
Set builder form: {x : x is a natural number less than 5}
Empty set (∅): set with no elements
Universal set (U): set containing all elements under consideration
Subset: A ⊆ B if every element of A is in B
Union A ∪ B: all elements in A or B or both
Intersection A ∩ B: elements common to both A and B
Complement A': elements in U but not in A
n(A ∪ B) = n(A) + n(B) − n(A ∩ B)
✅ Digest Answers
Q. If n(A)=20, n(B)=15, n(A∩B)=8, find n(A∪B).
n(A∪B) = n(A) + n(B) − n(A∩B) = 20 + 15 − 8 = 27
Q. What is the difference between ∅ and {0}?
∅ (empty set) has no elements. {0} is a set with one element which is zero. So {0} is NOT an empty set — it has one element.
📊
Accounts — Commerce
Chapter 1 — Introduction to Accounting
📌 Key Points
Accounting: process of recording, classifying and summarising financial transactions
Book-keeping: recording day-to-day financial transactions in books
Assets: resources owned by business. Current assets (cash, stock), Fixed assets (land, machinery)
Liabilities: amounts owed by business. Current (short-term), Long-term
Capital: owner's investment in business. Capital = Assets − Liabilities
Revenue: income earned from main business activity
Expenses: costs incurred to earn revenue
Accounting equation: Assets = Liabilities + Capital
Double entry system: every transaction has two aspects — debit and credit
Golden rules: Personal a/c — Dr the receiver, Cr the giver. Real a/c — Dr what comes in, Cr what goes out. Nominal a/c — Dr all expenses, Cr all incomes
✅ Digest Answers
Q. What are the golden rules of accounting?
1. Personal Account: Debit the receiver, Credit the giver. 2. Real Account: Debit what comes in, Credit what goes out. 3. Nominal Account: Debit all expenses and losses, Credit all incomes and gains.
Q. Difference between book-keeping and accounting?
Book-keeping is recording day-to-day transactions systematically. Accounting is broader — it includes recording, classifying, summarising, interpreting and communicating financial data. Book-keeping is part of accounting.