Resources · Science Sage

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Physics · Mechanics Gr 10–12

Kinematics & Motion

Equations of motion for uniform acceleration — 1D and vertical projectiles.

Final velocity

v = u + at

Displacement

s = ut + ½at²

Velocity–displacement

v² = u² + 2as

Average velocity

v̄ = (u + v) / 2

Vertical projectile (up positive, g = 9.8 m·s⁻²)

a = −g = −9.8 m·s⁻²

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Physics · Mechanics Gr 10–11

Forces & Newton's Laws

Newton's three laws, friction, and the weight–mass relationship.

Newton's 2nd Law (net force)

F_net = ma

Weight

F_g = mg

Friction

f = μN

Newton's Law of Gravitation

F = Gm₁m₂ / r²

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Physics · Mechanics Gr 11

Momentum & Impulse

Linear momentum, impulse, and conservation of momentum in collisions.

Momentum

p = mv

Impulse

J = FΔt = Δp

Conservation of momentum

Σp_before = Σp_after

Elastic collision (KE conserved)

ΣKE_before = ΣKE_after

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Physics · Energy Gr 10–11

Work, Energy & Power

Mechanical energy, work-energy theorem, and power calculations.

Work done

W = FΔx·cosθ

Power

P = W/t = Fv

Kinetic energy

KE = ½mv²

Gravitational PE

PE = mgh

Work-energy theorem

W_net = ΔKE = KE_f − KE_i

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Physics · Waves Gr 10–12

Waves & Sound

Wave equation, Doppler effect, and the electromagnetic spectrum.

Wave equation

v = fλ

Period & frequency

T = 1/f

Doppler effect (source moving)

f_L = f_s · (v ± v_L) / (v ∓ v_s)

Speed of light / EM waves

c = 3.0 × 10⁸ m·s⁻¹

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Physics · Electricity Gr 10–12

Electric Circuits

Ohm's Law, series/parallel rules, power, and internal resistance.

Ohm's Law

V = IR

Power

P = VI = I²R = V²/R

Series resistors

R_T = R₁+R₂+…

Parallel resistors

1/R_T = 1/R₁+1/R₂

EMF with internal resistance

ε = I(R + r) → V_terminal = ε − Ir

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Physics · Electrostatics Gr 10–11

Electrostatics

Coulomb's Law, electric field strength, and charge quantisation.

Coulomb's Law

F = kQ₁Q₂ / r² (k = 9×10⁹ N·m²·C⁻²)

Electric field strength

E = F/q = kQ/r²

Charge quantisation

Q = ne (e = 1.6×10⁻¹⁹ C)

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Physics · Modern Gr 12

Photoelectric Effect

Photon energy, work function, and threshold frequency relationships.

Photon energy

E = hf = hc/λ

Threshold freq.

f₀ = W/h

Einstein's photoelectric equation

E_k(max) = hf − W

Planck's constant

h = 6.63 × 10⁻³⁴ J·s

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Chemistry · Stoichiometry Gr 10–12

Moles & Stoichiometry

The mole concept, molar mass, concentration, and gas volumes.

Amount (moles)

n = m / M

Concentration

c = n / V

Gas at STP

V = n × 22.4 L

Avogadro

N = n × Nₐ

Nₐ = 6.022 × 10²³ mol⁻¹ | STP: 0 °C, 101.3 kPa

Molar volume at STP = 22.4 dm³·mol⁻¹

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Chemistry · Acids & Bases Gr 11–12

Acids, Bases & pH

Arrhenius and Brønsted–Lowry definitions, pH calculations, and titrations.

pH definition

pH = −log[H₃O⁺]

pOH

pOH = −log[OH⁻]

Water dissociation

pH + pOH = 14 | Kw = 1×10⁻¹⁴

Titration formula

c₁V₁/n₁ = c₂V₂/n₂

Acid dissociation constant

Ka = [H⁺][A⁻] / [HA]

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Chemistry · Equilibrium Gr 11

Chemical Equilibrium

Equilibrium constant expressions and Le Chatelier's principle.

For aA + bB ⇌ cC + dD

Kc = [C]ᶜ[D]ᵈ / [A]ᵃ[B]ᵇ

Reaction quotient (Q vs K)

Q < K → forward | Q > K → reverse

Le Chatelier's principle

System shifts to oppose any change imposed on it

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Chemistry · Thermochem Gr 11

Energy & Chemical Change

Enthalpy changes, activation energy, and Hess's Law.

Heat transfer

q = mcΔT

Enthalpy change

ΔH = H_products − H_reactants

Exothermic (ΔH < 0) vs Endothermic (ΔH > 0)

Hess's Law: ΔH_rxn = Σ ΔH_f(products) − Σ ΔH_f(reactants)

Specific heat of water

c = 4.18 J·g⁻¹·°C⁻¹

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Chemistry · Electrochemistry Gr 12

Electrochemistry

Galvanic cells, EMF calculations, and electrolysis basics.

Cell EMF (standard conditions)

E°_cell = E°_cathode − E°_anode

Spontaneous reaction

E°_cell > 0 → spontaneous (galvanic cell)

Faraday's law of electrolysis

m = (M × I × t) / (n × F) | F = 96 485 C·mol⁻¹

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Chemistry · Organic Gr 12

Organic Functional Groups & Homologous Series

IUPAC naming suffixes and characteristic functional groups for all Gr 12 series.

Alkane

-ane

C–C single bonds; –CH₃ / –CH₂–

Alkene

-ene

C=C double bond

Alkyne

-yne

C≡C triple bond

Alcohol

-ol

–OH (hydroxyl)

Aldehyde

-al

–CHO (terminal)

Ketone

-one

–C(=O)– (internal)

Carboxylic acid

-oic acid

–COOH

Ester

-oate

–COO– linkage

Ether

-oxy-

R–O–R′

Haloalkane

halo-

–F / –Cl / –Br / –I

Amine

-amine

–NH₂

Amide

-amide

–CONH₂

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Data Sheet · Physical Sciences

Physical Constants

CAPS-listed constants for use in NSC and IEB examinations.

Speed of light	c = 3.0 × 10⁸ m·s⁻¹
Gravitational acceleration	g = 9.8 m·s⁻²
Gravitational constant	G = 6.67 × 10⁻¹¹ N·m²·kg⁻²
Planck's constant	h = 6.63 × 10⁻³⁴ J·s
Elementary charge	e = 1.6 × 10⁻¹⁹ C
Coulomb's constant	k = 9.0 × 10⁹ N·m²·C⁻²
Electron mass	mₑ = 9.11 × 10⁻³¹ kg
Proton mass	mₚ = 1.67 × 10⁻²⁷ kg
Avogadro's number	Nₐ = 6.02 × 10²³ mol⁻¹
Faraday constant	F = 96 485 C·mol⁻¹
Molar gas volume (STP)	Vm = 22.4 dm³·mol⁻¹
Specific heat of water	cw = 4.18 J·g⁻¹·°C⁻¹

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Data Sheet · Units

SI Units & Prefixes

Base units, derived units, and metric prefixes for Physical Sciences.

Length	metre (m)
Mass	kilogram (kg)
Time	second (s)
Electric current	ampere (A)
Temperature	kelvin (K) · T(K) = T(°C) + 273
Amount of substance	mole (mol)
PREFIXES
tera (T)	× 10¹²
giga (G)	× 10⁹
mega (M)	× 10⁶
kilo (k)	× 10³
centi (c)	× 10⁻²
milli (m)	× 10⁻³
micro (μ)	× 10⁻⁶
nano (n)	× 10⁻⁹
pico (p)	× 10⁻¹²

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Data Sheet · Electrochemistry Gr 12

Standard Electrode Potentials

Selected half-reactions at standard conditions (25 °C, 1 mol·dm⁻³, 101.3 kPa). More positive E° = stronger oxidising agent.

HALF-REACTION (reduction)E° (V)

F₂ + 2e⁻ → 2F⁻+2.87

Cl₂ + 2e⁻ → 2Cl⁻+1.36

Br₂ + 2e⁻ → 2Br⁻+1.07

Ag⁺ + e⁻ → Ag+0.80

Cu²⁺ + 2e⁻ → Cu+0.34

2H⁺ + 2e⁻ → H₂ 0.00

Pb²⁺ + 2e⁻ → Pb−0.13

Fe²⁺ + 2e⁻ → Fe−0.44

Zn²⁺ + 2e⁻ → Zn−0.76

Al³⁺ + 3e⁻ → Al−1.66

Mg²⁺ + 2e⁻ → Mg−2.37

Na⁺ + e⁻ → Na−2.71

K⁺ + e⁻ → K−2.93

Li⁺ + e⁻ → Li−3.04

Red = strong oxidising agent | Green = strong reducing agent
E°_cell = E°_cathode − E°_anode

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Data Sheet · Chemistry

Metal Activity Series

Metals ranked from most to least reactive. More reactive metals displace less reactive metals from solutions.

MOST REACTIVE ↑

Potassium	K
Sodium	Na
Calcium	Ca
Magnesium	Mg
Aluminium	Al
Zinc	Zn
Iron	Fe
Nickel	Ni
Tin	Sn
Lead	Pb
Hydrogen	H₂
Copper	Cu
Silver	Ag
Gold	Au

LEAST REACTIVE ↓

React with water:
K, Na, Ca (vigorously)

React with acid:
Mg → Pb (displace H₂)

No reaction with acid:
Cu, Ag, Au

Everything you need,right here.

Everything you need,
right here.