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Formulas, dates, tables and the points examiners ask about, for every Class 9 and Class 10 chapter. Pick a course and try a few.

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CBSE Class 9 · Social Science

Cheat sheet

History · Chapter 1The French Revolution

Liberty, Equality, Fraternity.

1. Causes

Louis XVI (Bourbon) took the throne in 1774; empty treasury after wars (incl. helping American independence)
Three Estates: 1st – clergy, 2nd – nobility (exempt from taxes); 3rd – everyone else, paid taille (direct tax) and tithes (to church)
Subsistence crisis: population grew, bread prices rose
Growing middle class; ideas of Locke (Two Treatises), Rousseau (Social Contract), Montesquieu (The Spirit of the Laws – separation of powers)

2. Outbreak (1789)

Date	Event
5 May 1789	Estates General met; 3rd Estate demanded one vote per member
20 June 1789	Tennis Court Oath – National Assembly (Mirabeau, Abbé Sieyès)
14 July 1789	Storming of the Bastille
Aug 1789	Feudal privileges abolished; Declaration of the Rights of Man and Citizen
1791	Constitution: constitutional monarchy; only "active citizens" (tax payers, men 25+) voted

3. France Becomes a Republic

Jacobin Club (Robespierre); sans-culottes
1792: Convention; France a Republic; Louis XVI executed (Jan 1793)
Reign of Terror (1793–94): Robespierre's harsh rule; guillotine; he was executed in 1794
Directory (five-member executive) → Napoleon Bonaparte (1804 emperor; defeated at Waterloo 1815)

4. Legacy

Women's clubs – Olympe de Gouges; women got the vote only in 1946
Slavery abolished 1794, reintroduced by Napoleon, finally abolished 1848
Censorship abolished (1789); spread of ideas of liberty and democratic rights
Inspired Tipu Sultan and Rammohun Roy

5. Key Points to Remember

14 July 1789 – Bastille stormed.
Third Estate paid all taxes.
Tennis Court Oath formed the National Assembly.
1792 – France a republic.
Reign of Terror under Robespierre.
Napoleon crowned emperor in 1804.

Remember: 1774 · 1789 · 1791 · 1792 · 1793–94 · 1804

CBSE Class 9 · Mathematics

Cheat sheet

Chapter 2Polynomials

Factor Theorem: x − a is a factor if p(a) = 0.

1. Basics

Polynomial: $a_nx^n + \cdots + a_1x + a_0$ with whole-number powers.

By terms	By degree
Monomial – 1 term (3x)	Constant – 0 (e.g. 5); zero polynomial – not defined
Binomial – 2 terms (x + 1)	Linear – 1; Quadratic – 2
Trinomial – 3 terms	Cubic – 3

Zero of $p(x)$ : value $c$ where $p(c) = 0$ . A linear polynomial $ax + b$ has one zero, $-\dfrac{b}{a}$ .

2. Remainder & Factor Theorem

Remainder Theorem (not in rationalised syllabus, useful): remainder when $p(x)$ is divided by $x - a$ is $p(a)$ .

Factor Theorem: $x - a$ is a factor of $p(x)$ ⇔ $p(a) = 0$ .

$x^3 - 23x^2 + 142x - 120$ : $p(1) = 0$ ⇒ $(x - 1)$ is a factor → $(x - 1)(x - 10)(x - 12)$

Splitting the middle term

$ax^2 + bx + c$ : find $p, q$ with $p + q = b$ , $pq = ac$ . e.g. $6x^2 + 17x + 5 = (2x + 5)(3x + 1)$

3. Algebraic Identities

(x + y)^2 = x^2 + 2xy + y^2

(x - y)^2 = x^2 - 2xy + y^2

x^2 - y^2 = (x + y)(x - y)

(x + a)(x + b) = x^2 + (a + b)x + ab

(x + y + z)^2 = x^2 + y^2 + z^2 + 2xy + 2yz + 2zx

(x \pm y)^3 = x^3 \pm y^3 \pm 3xy(x \pm y)

x^3 + y^3 = (x + y)(x^2 - xy + y^2)

x^3 - y^3 = (x - y)(x^2 + xy + y^2)

x^3 + y^3 + z^3 - 3xyz = (x + y + z)(x^2 + y^2 + z^2 - xy - yz - zx)

So if $x + y + z = 0$ , then $x^3 + y^3 + z^3 = 3xyz$ .

4. Key Points to Remember

Degree = highest power of the variable.
Constant polynomial has degree 0.
x − a is a factor ⇔ p(a) = 0.
Use identities to expand or factorise quickly.
If x + y + z = 0 then x³ + y³ + z³ = 3xyz.
A polynomial of degree n has at most n zeroes.

Remember: Factor Theorem | Split the middle term | Learn the 8 identities

CBSE Class 10 · Social Science

Cheat sheet

History · Chapter 2Nationalism in India

Satyagraha: the power of truth, not force.

1. First World War & Khilafat

WWI → higher defence spending, taxes, prices; forced recruitment; crop failures, influenza
Satyagraha (Gandhi returned Jan 1915): Champaran 1917 (indigo), Kheda 1917 (peasants), Ahmedabad 1918 (mill workers)
Rowlatt Act 1919: detention without trial → hartal
Jallianwala Bagh, 13 April 1919 – General Dyer fired on crowd
Khilafat movement: Ali brothers (Muhammad Ali, Shaukat Ali); Calcutta Congress Sept 1920 agreed on Non-Cooperation

2. Non-Cooperation Movement (1920–22)

Accepted at Nagpur session, Dec 1920. Based on Gandhi's book Hind Swaraj (1909).

Group	Participation
Towns (middle class)	Boycott of foreign cloth, schools, courts; khadi
Awadh peasants	Baba Ramchandra vs talukdars; Oudh Kisan Sabha
Gudem hills (Andhra)	Tribals under Alluri Sitaram Raju – guerrilla war
Assam plantations	Workers left (Inland Emigration Act 1859 restricted movement)

Called off after Chauri Chaura (Feb 1922) violence.

3. Towards Civil Disobedience

Swaraj Party (C.R. Das, Motilal Nehru) – council elections
Simon Commission 1928: no Indian member → "Go back Simon"
Lahore Congress Dec 1929 (Nehru): Purna Swaraj; 26 Jan 1930 Independence Day
Gandhi's 11 demands; Salt March Sabarmati → Dandi, 12 Mar – 6 Apr 1930

4. Civil Disobedience (1930–34)

Break salt law, boycott foreign cloth, refuse taxes, forest law violations
Gandhi–Irwin Pact (5 Mar 1931) → Second Round Table Conference, London – failed
Rich peasants (Patidars, Jats), poor peasants (rent), business (FICCI, Purshottamdas Thakurdas, G.D. Birla), industrial workers (Nagpur), women
Limited Dalit participation – Dr B.R. Ambedkar, Depressed Classes Association (1930); separate electorates → Poona Pact, Sept 1932 (reserved seats)
Muslim alienation – Muhammad Iqbal 1930 (separate electorates)

5. Sense of Collective Belonging

Bharat Mata

Bankim Chandra's Vande Mataram (Anandamath); painting by Abanindranath Tagore

Folklore

Rabindranath Tagore, Natesa Sastri (Folklore of Southern India)

Flag

Swadeshi flag (1905, Bengal) – 8 lotuses, crescent; Gandhi's tricolour 1921 with spinning wheel

History

Reinterpreting India's past glory

6. Key Points to Remember

1917–18: Champaran, Kheda, Ahmedabad satyagrahas.
1919: Rowlatt Act and Jallianwala Bagh.
1920: Non-Cooperation begins (Nagpur).
1922: Chauri Chaura – NCM withdrawn.
1930: Dandi March starts Civil Disobedience.
1932: Poona Pact (Gandhi–Ambedkar).

Remember: 1915 · 1917 · 1919 · 1920 · 1922 · 1928 · 1929 · 1930 · 1931 · 1932

CBSE Class 10 · Mathematics

Cheat sheet

Chapter 8Introduction to Trigonometry

Some People Have Curly Brown Hair Through Proper Brushing.

1. Trigonometric Ratios

In right $\triangle ABC$ (right angle at B), for angle $A$ :

\sin A = \dfrac{P}{H}

\cos A = \dfrac{B}{H}

\tan A = \dfrac{P}{B}

\operatorname{cosec} A = \dfrac{1}{\sin A}

\sec A = \dfrac{1}{\cos A}

\cot A = \dfrac{1}{\tan A}

\tan A = \dfrac{\sin A}{\cos A}

\cot A = \dfrac{\cos A}{\sin A}

P = perpendicular (opposite), B = base (adjacent), H = hypotenuse. Ratios depend only on the angle, not the triangle size.

2. Identities

\sin^2 A + \cos^2 A = 1

1 + \tan^2 A = \sec^2 A

(0^\circ \le A < 90^\circ)

1 + \cot^2 A = \operatorname{cosec}^2 A

(0^\circ < A \le 90^\circ)

Proof tips

Convert everything to sin and cos
Start from the more complicated side
Use $a^2 - b^2 = (a - b)(a + b)$ and rationalise

3. Standard Values

Ratio	0°	30°	45°	60°	90°
sin	0	$\dfrac{1}{2}$	$\dfrac{1}{\sqrt{2}}$	$\dfrac{\sqrt{3}}{2}$	1
cos	1	$\dfrac{\sqrt{3}}{2}$	$\dfrac{1}{\sqrt{2}}$	$\dfrac{1}{2}$	0
tan	0	$\dfrac{1}{\sqrt{3}}$	1	$\sqrt{3}$	not defined
cosec	not defined	2	$\sqrt{2}$	$\dfrac{2}{\sqrt{3}}$	1
sec	1	$\dfrac{2}{\sqrt{3}}$	$\sqrt{2}$	2	not defined
cot	not defined	$\sqrt{3}$	1	$\dfrac{1}{\sqrt{3}}$	0

Trick: sin values = $\sqrt{\frac{0}{4}}, \sqrt{\frac{1}{4}}, \sqrt{\frac{2}{4}}, \sqrt{\frac{3}{4}}, \sqrt{\frac{4}{4}}$ ; cos is the reverse.

4. Remember

$0 \le \sin A, \cos A \le 1$ for acute A
sin increases, cos decreases from 0° to 90°
$\sec A, \operatorname{cosec} A \ge 1$
Given one ratio, draw a triangle and use Pythagoras to find the rest

5. Key Points to Remember

sin A = P/H, cos A = B/H, tan A = P/B.
sin²A + cos²A = 1.
tan 45° = 1; tan 90° is not defined.
sin 30° = cos 60° = ½.
Reciprocal pairs: sin–cosec, cos–sec, tan–cot.
Write a value table from memory before solving.

Remember: SOH-CAH-TOA | sin² + cos² = 1 | 1 + tan² = sec²

CBSE Class 10 · Science

Cheat sheet

Chapter 11Electricity

V = IR keeps every circuit in check.

1. Current, Potential, Ohm's Law

I = \dfrac{Q}{t}

(A)

V = \dfrac{W}{Q}

(V)

V = IR

(Ω)

1 A = 1 C/s; charge of electron = $1.6 \times 10^{-19}$ C; 1 C ≈ $6 \times 10^{18}$ electrons
Conventional current flows + to −, opposite to electrons
Ammeter in series (low R); voltmeter in parallel (high R)
Ohm's law: V ∝ I at constant temperature; V–I graph is a straight line

Resistance & resistivity

R = \rho \dfrac{l}{A}

ρ in Ω m

R ∝ length, ∝ 1/area; depends on material and temperature. Alloys (nichrome) have high ρ – used in heaters. Conductors: ρ from $10^{-8}$ to $10^{-6}$ Ω m.

2. Resistors in Circuits

Series

$R_s = R_1 + R_2 + R_3$

Same current; voltage divides. One fails → all stop.

Parallel

$\dfrac{1}{R_p} = \dfrac{1}{R_1} + \dfrac{1}{R_2} + \dfrac{1}{R_3}$

Same voltage; current divides. $R_p$ < smallest R.

Homes use parallel wiring: each appliance gets full voltage and can be switched separately.

Circuit symbols to know

Cell
Battery
Resistor
Rheostat
Ammeter (A)
Voltmeter (V)

3. Heating Effect

Joule's law:

H = I^2Rt

Used in heaters, irons, toasters, bulbs (tungsten, m.p. 3380 °C, bulbs filled with N₂/Ar) and fuses (low m.p. alloy, in series).

4. Electric Power & Energy

P = VI = I^2R = \dfrac{V^2}{R}

(W)

1 kWh = 1 'unit' = $\mathbf{3.6 \times 10^{6}}$ J. Energy = P × t.

Example: 100 W bulb for 10 h = 1 kWh = 1 unit.

5. Key Points to Remember

Ammeter in series, voltmeter in parallel.
Resistance doubles if length doubles; quarters if diameter doubles.
Parallel combination gives less resistance than any single resistor.
Fuse wire melts when current is too high.
Unit of ρ is Ω m; unit of power is watt.
1 kWh = 3.6 MJ.

Remember: V = IR | R = ρl/A | H = I²Rt | P = VI

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CBSE Class 9 and Class 10, Class 11 and Class 12 Commerce, NEET PG and INI-CET. More courses are on the way, and you can request one from inside the app.

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Built for your syllabus

Class 9 · CBSE

Class 10 · CBSE

Class 11 · Commerce

Class 12 · Commerce

NEET PG

INI-CET

Everything you need to prep with purpose

Adaptive practice

Chapter-wise question bank

Live quizzes

Real progress tracking

Streaks, XP & leaderboard

AI explanations & grading

A whole chapter on one page

1. Causes

2. Outbreak (1789)

3. France Becomes a Republic

4. Legacy

5. Key Points to Remember

1. Basics

2. Remainder & Factor Theorem

Splitting the middle term

3. Algebraic Identities

4. Key Points to Remember

1. Describing Motion

2. Equations of Motion

Graphs

3. Key Points to Remember

1. First World War & Khilafat

2. Non-Cooperation Movement (1920–22)

3. Towards Civil Disobedience

4. Civil Disobedience (1930–34)

5. Sense of Collective Belonging

6. Key Points to Remember

1. Trigonometric Ratios

2. Identities

Proof tips

3. Standard Values

4. Remember

5. Key Points to Remember

1. Current, Potential, Ohm's Law

Resistance & resistivity

2. Resistors in Circuits

Circuit symbols to know

3. Heating Effect

4. Electric Power & Energy

5. Key Points to Remember

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