ExamMaster — Quickfire Lessons

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PHY 102 — General Physics II

Electricity & Magnetism · Circuits · Electromagnetic Induction · Waves
8 Topics · Coulomb to Maxwell

🔋 Electric Charge & Matter

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Matter is made of atoms. Charge exists as positive (protons) and negative (electrons). Like charges repel, opposite charges attract. Charge is conserved — it cannot be created or destroyed, only transferred.

Key Points

Conductors allow free electron flow (metals). Insulators resist it (rubber, glass).

Semiconductors (silicon, germanium) conduct under certain conditions.

Charge unit: Coulomb (C). Electron charge = 1.6 × 10⁻¹⁹ C.

Charging methods: friction, conduction, induction.

⚡ Exam Tips

CBT Favourite: "Which is a semiconductor?" — Answer: Silicon or Germanium.

Watch out: Charge conservation questions — total charge before = total charge after.

⚖️ Coulomb's Law

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The electrostatic force between two point charges is directly proportional to the product of charges and inversely proportional to the square of distance between them.

Formulas

F = kq₁q₂ / r²

k = 9×10⁹ N·m²/C² | q in Coulombs | r in metres

k = 1 / (4πε₀) | ε₀ = 8.85×10⁻¹² C²/N·m²

🚀 Shortcuts

ALWAYS convert μC to C: divide by 10⁶. e.g. 3μC = 3×10⁻⁶ C

r² trick: if distance doubles, force becomes ¼. If distance halves, force becomes 4×.

⚡ Exam Tips

Most common mistake: Forgetting to square the distance. Always write r² not r.

Unilorin loves: Numerical questions with μC charges — practice converting first.

🌐 Electric Field

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Electric field E is the force per unit charge at a point in space. Field lines point from positive to negative charges. Where lines are dense, field is stronger.

Formulas

E = F / q

Unit: N/C or V/m

E = kQ / r²

Field due to point charge Q at distance r

🚀 Shortcuts

Inside conductor: E = 0 always. Free charges redistribute to cancel internal field.

Direction rule: Field lines leave (+) and arrive at (−). Never cross each other.

⚡ Exam Tips

CBT Trap: "E inside a conductor" — always ZERO. Don't overthink it.

Superposition: For multiple charges, calculate E from each and add as vectors.

🔵 Gauss's Law

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The total electric flux through any closed surface equals the total enclosed charge divided by ε₀. The shape of the surface doesn't matter — only what's inside counts.

Formulas

Φ_E = Q_enc / ε₀

Φ = Electric flux | Q_enc = total charge inside surface

Φ_E = ∮ E · dA = Q_enc / ε₀

🚀 Shortcuts

Key insight: If Q_enc = 0 (empty Gaussian surface), then E = 0 inside. This is why conductors have zero internal field.

Sphere rule: Outside sphere → E = kQ/r². Inside hollow sphere → E = 0.

⚡ Exam Tips

Most tested: "What is E inside a conducting sphere?" — ZERO. "What is E outside?" — kQ/r².

🔌 DC Circuits & Ohm's Law

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Direct current flows in one direction. Ohm's Law relates voltage, current and resistance. Resistors in series add up; in parallel, the reciprocals add.

Formulas

V = IR

V=Voltage(V) | I=Current(A) | R=Resistance(Ω)

Series: R_total = R₁ + R₂ + R₃

Parallel: 1/R_total = 1/R₁ + 1/R₂ + 1/R₃

P = IV = I²R = V²/R

P = Power (Watts)

🚀 Shortcuts

Series: Same current everywhere. Voltage splits across resistors.

Parallel: Same voltage across all. Current splits into branches.

Two parallel resistors: R = (R₁ × R₂) / (R₁ + R₂)

⚡ Exam Tips

Kirchhoff's Laws: KCL — current into node = current out. KVL — sum of voltages in loop = 0.

🧲 Magnetic Fields & Lorentz Force

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Moving charges create magnetic fields. A charge moving in a magnetic field experiences the Lorentz force. Magnetic field lines form closed loops — no monopoles exist.

Formulas

F = qv × B = qvB sinθ

q=charge | v=velocity | B=magnetic field (Tesla)

F = IL × B = BIL sinθ

Force on current-carrying conductor

🚀 Shortcuts

Right-hand rule: Point fingers in direction of v (or I), curl toward B — thumb points in direction of force.

Maximum force: when θ = 90° (v ⊥ B). Zero force when θ = 0° (v parallel to B).

⚡ Exam Tips

Unit of B: Tesla (T) = kg/(A·s²). Don't confuse with Electric field unit N/C.

⚡ Faraday's & Lenz's Laws

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A changing magnetic flux induces an EMF in a conductor. Lenz's Law says the induced current opposes the change that caused it — nature resisting change!

Formulas

EMF = -dΦ/dt

EMF induced = rate of change of magnetic flux

Φ = BA cosθ

Magnetic flux = B × Area × cos(angle)

EMF = -N × dΦ/dt

For N-turn coil

🚀 Shortcuts

Lenz's Law memory trick: "Induced current always FIGHTS the change." If flux increases, induced current creates opposing field.

Transformer ratio: V₁/V₂ = N₁/N₂ = I₂/I₁

⚡ Exam Tips

The negative sign in EMF = -dΦ/dt is Lenz's Law in math form. Always explain its meaning.

📡 AC Circuits & EM Waves

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AC current alternates direction. Capacitors and inductors oppose AC differently. Electromagnetic waves are transverse and travel at speed of light — they need no medium.

Formulas

X_C = 1/(2πfC)

Capacitive reactance (Ω) — opposes AC

X_L = 2πfL

Inductive reactance (Ω)

Z = √(R² + (X_L - X_C)²)

Impedance of RLC circuit

c = λf = 3×10⁸ m/s

Speed of EM waves in vacuum

🚀 Shortcuts

Resonance: occurs when X_L = X_C. At resonance, Z = R (minimum impedance, maximum current).

EM spectrum order: Radio → Microwave → Infrared → Visible → UV → X-ray → Gamma

📐

MTH 102 — Elementary Mathematics II

Calculus · Differentiation · Integration · Applications
6 Topics · Functions to Volumes

📈 Functions, Limits & Continuity

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A function maps inputs to unique outputs. A limit describes what a function approaches as x approaches a value. Continuity means no breaks, holes, or jumps in the graph.

Key Points

lim(x→a) f(x) = L means f(x) gets arbitrarily close to L as x approaches a.

A function is continuous at x=a if: f(a) exists, limit exists, and they are equal.

Left-hand limit = Right-hand limit → limit exists.

Formulas

lim(x→0) sinx/x = 1

Standard limit — memorise this!

lim(x→∞) (1 + 1/n)ⁿ = e ≈ 2.718

⚡ Exam Tips

0/0 form: Try L'Hôpital's rule — differentiate top and bottom separately.

Continuity check: Always verify all 3 conditions. Missing one = discontinuous.

📉 Differentiation

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The derivative measures the rate of change of a function. It gives the slope of the tangent line at any point. Differentiation is the core skill of calculus.

Formulas

d/dx(xⁿ) = nxⁿ⁻¹

Power rule — most used rule

d/dx(uv) = u'v + uv'

Product rule

d/dx(u/v) = (u'v - uv') / v²

Quotient rule

d/dx[f(g(x))] = f'(g(x)) × g'(x)

Chain rule

d/dx(sinx) = cosx | d/dx(cosx) = -sinx

d/dx(eˣ) = eˣ | d/dx(ln x) = 1/x

🚀 Shortcuts

Power rule memory: "Bring down the power, reduce by 1." d/dx(x⁵) = 5x⁴

Chain rule trigger: Any function inside another function needs chain rule.

⚡ Exam Tips

Implicit differentiation: When y is not isolated — differentiate both sides and collect dy/dx terms.

📊 Maxima, Minima & Curve Sketching

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Critical points occur where f'(x) = 0 or undefined. The second derivative test tells you if it's a maximum, minimum, or inflection point. Curve sketching combines all of this.

Formulas

f'(x) = 0 → Critical point

f''(x) < 0 → Maximum (curve bends down ⌢)

f''(x) > 0 → Minimum (curve bends up ⌣)

f''(x) = 0 → Possible inflection point

🚀 Shortcuts

Steps to find extrema: 1) Find f'(x). 2) Set = 0. 3) Solve for x. 4) Use f''(x) to classify.

First derivative test: f' changes + to − → Maximum. f' changes − to + → Minimum.

∫ Integration (Antiderivatives)

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Integration is the reverse of differentiation. The indefinite integral gives a family of functions. Always add the constant of integration C for indefinite integrals.

Formulas

∫xⁿ dx = xⁿ⁺¹/(n+1) + C

Power rule for integration (n ≠ -1)

∫eˣ dx = eˣ + C

∫sinx dx = -cosx + C

∫cosx dx = sinx + C

∫(1/x) dx = ln|x| + C

🚀 Shortcuts

Integration by parts: ∫u dv = uv - ∫v du. Use LIATE to choose u: Logarithm, Inverse trig, Algebraic, Trig, Exponential.

Substitution: If you see f(g(x))·g'(x), let u = g(x).

⚡ Exam Tips

Never forget +C for indefinite integrals. Lecturers deduct marks for this.

📏 Definite Integrals

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Definite integrals have upper and lower limits. They give a specific numerical answer — no +C needed. They represent the area under a curve between two points.

Formulas

∫[a to b] f(x)dx = F(b) - F(a)

Fundamental Theorem of Calculus

🚀 Shortcuts

Steps: 1) Integrate normally. 2) Substitute upper limit. 3) Subtract lower limit substitution. 4) Simplify.

Even function: ∫[-a to a] f(x)dx = 2∫[0 to a]. Odd function: ∫[-a to a] = 0.

🏔️ Area & Volume Applications

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Integration calculates areas between curves and volumes of solids of revolution. Area between two curves = integral of (top − bottom). Volume uses the disk or shell method.

Formulas

Area = ∫[a to b] [f(x) - g(x)] dx

Area between curves f(x) above g(x)

Volume = π∫[a to b] [f(x)]² dx

Disk method — revolution about x-axis

⚡ Exam Tips

Find intersections first: Set f(x) = g(x) to find the limits a and b before integrating.

Negative areas: Area is always positive — take absolute value if curve dips below x-axis.

🧪

CHM 102 — General Chemistry II

Organic Chemistry · Functional Groups · Metals · Nomenclature
8 Topics · Alkanes to Transition Metals

📜 History & Basics of Organic Chemistry

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Organic chemistry is the study of carbon compounds. Once thought to only come from living things (vitalism), Wöhler's 1828 synthesis of urea from inorganic materials changed everything.

Key Points

Carbon forms 4 bonds — enables enormous molecular variety.

Organic compounds contain C-H bonds primarily.

Vital force theory disproved by Wöhler (1828).

Carbon hybridisation: sp³ (alkanes), sp² (alkenes), sp (alkynes).

⚡ Exam Tips

Unilorin favourite: "Who disproved vitalism?" — Friedrich Wöhler, 1828, urea synthesis.

⚽ Fullerenes & Nanostructures

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Fullerenes are the fourth allotrope of carbon (after diamond, graphite, amorphous carbon). C₆₀ (Buckminsterfullerene) looks like a football — 60 carbon atoms in pentagons and hexagons.

Key Points

4 allotropes of carbon: Diamond, Graphite, Amorphous carbon, Fullerenes.

C₆₀ = Buckminsterfullerene (Buckyball) — discovered 1985 by Curl, Smalley, Kroto.

Carbon nanotubes = rolled graphene sheets. Extremely strong, electrically conductive.

Applications: drug delivery, electronics, materials science.

⚡ Exam Tips

Very popular in Unilorin CBT: "How many atoms in Buckminsterfullerene?" — 60 carbon atoms.

Nobel Prize 1996: Curl, Smalley, Kroto — for discovering fullerenes.

🏷️ IUPAC Nomenclature

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IUPAC naming gives every organic compound a systematic, universally understood name based on structure. Master the prefixes and you can name any compound.

Key Points

Prefixes: Meth(1), Eth(2), Prop(3), But(4), Pent(5), Hex(6), Hept(7), Oct(8), Non(9), Dec(10).

Suffixes: -ane (single), -ene (double bond), -yne (triple bond), -ol (alcohol), -al (aldehyde), -one (ketone), -oic acid (carboxylic acid).

Number the chain from the end closest to the substituent/functional group.

🚀 Shortcuts

Memory trick for prefixes: "My Enormous Purple Butterfly Pretty Happily Hops On New Doors" = Meth, Eth, Prop, But, Pent, Hex, Hept, Oct, Non, Dec

⚡ Exam Tips

Always find longest chain first. Then number from end nearest to branch/functional group.

⛓️ Alkanes, Alkenes & Alkynes

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Hydrocarbons — compounds of only carbon and hydrogen. Alkanes are saturated (single bonds only). Alkenes have double bonds. Alkynes have triple bonds. Reactivity increases with unsaturation.

Key Points

Alkanes: CₙH₂ₙ₊₂ formula. Undergo substitution reactions.

Alkenes: CₙH₂ₙ formula. Undergo addition reactions. Most reactive.

Alkynes: CₙH₂ₙ₋₂ formula. Triple bond — very reactive.

Markovnikov's rule: in addition, H adds to carbon with more H atoms.

🚀 Shortcuts

Reactivity order: Alkynes > Alkenes > Alkanes (more π bonds = more reactive)

Geometric isomerism: Only in alkenes (cis/trans) due to restricted rotation around double bond.

🍺 Alcohols, Ethers & Amines

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Functional groups define chemical behaviour. Alcohols (-OH), ethers (R-O-R), and amines (-NH₂) are key families with distinct properties and reactions.

Key Points

Alcohols: -OH group. Primary (1°), Secondary (2°), Tertiary (3°) based on how many carbons attached to C-OH.

Ethers: R-O-R'. Relatively unreactive. Diethyl ether = anaesthetic.

Amines: -NH₂ group. Basic character — accept protons.

⚡ Exam Tips

Alcohol oxidation: 1° → Aldehyde → Carboxylic acid. 2° → Ketone. 3° → Doesn't oxidise easily.

🔬 Aldehydes, Ketones & Carboxylic Acids

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Carbonyl compounds (C=O) include aldehydes, ketones, and carboxylic acids. They differ in where the C=O group sits and what's attached to it.

Key Points

Aldehyde: -CHO at end of chain. e.g. Methanal (formaldehyde), Ethanal.

Ketone: C=O in middle of chain. e.g. Propanone (acetone).

Carboxylic acid: -COOH group. Weak acids. e.g. Ethanoic acid (vinegar).

🚀 Shortcuts

Tollens test: Aldehydes give silver mirror. Ketones don't react — used to distinguish them.

Fehling's test: Aldehydes give brick-red precipitate. Ketones — no reaction.

🏗️ Group IA, IIA & IVA Elements

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Comparative chemistry of the s-block (IA, IIA) and Group IVA elements. Properties change predictably down each group.

Key Points

Group IA (Alkali metals): Li, Na, K, Rb, Cs. +1 charge. React vigorously with water.

Group IIA (Alkaline earth): Be, Mg, Ca, Sr, Ba. +2 charge. Less reactive than IA.

Group IVA: C, Si, Ge, Sn, Pb. Goes from nonmetal to metal down the group.

Down IA/IIA: Atomic radius increases, ionisation energy decreases, reactivity increases.

⚡ Exam Tips

Unilorin loves: "Which Group IA metal is least reactive?" — Lithium (Li) is least reactive in Group IA.

Flame colours: Li=red, Na=yellow, K=lilac, Ca=brick red, Ba=green.

🌀 Stereochemistry & Isomerism

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Isomers have the same molecular formula but different structures or arrangements. Stereoisomers have the same connectivity but different spatial arrangements.

Key Points

Structural isomers: different connectivity. e.g. Butane vs 2-methylpropane.

Geometric isomers (cis/trans): only in alkenes and cyclic compounds.

Optical isomers (enantiomers): mirror images, not superimposable. Have chiral centre.

Chiral carbon: carbon bonded to 4 different groups.

🚀 Shortcuts

Cis: same groups on same side of double bond. Trans: same groups on opposite sides.

R/S configuration: Arrange groups by priority (atomic number). Clockwise = R. Anticlockwise = S.

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