Exam Leaks 2025-2026 — Topic-to-Lecture Map with Predicted Question Types

Known questions from leaks + predicted question types based on actual lecture content and past UAS papers.

Sources: FAD1022 Final Exam Scope — Complete Guide, FAD1014 — Final Exam Scope 2025-2026, FAD1022 Exam Leaks 2025-2026, FAD1015 Exam Leaks 2025-2026, FAD1014 Exam Leaks 2025-2026, FAD1018 Exam Leaks 2025-2026, FAC1003 Exam Leaks 2025-2026, FAD1022 Exam Tips — WhatsApp Voice Notes

Each section includes: known leak → lecture-exact problem patterns → predicted question type → key formulas from lectures → specific lecture examples to review.

FAD1022 — Basic Physics II

Section A — Structured Questions (15 × 3 = 45 marks)

Technique (from lecturer voice notes): 1 formula → 1 substitution → 1 answer WITH correct unit. For explanations: "E must equal to work function, 3 factors, must be metal."

Known from Coordinator Leak

A1: RC Charging/Discharging

  • Source: L7-L9 Capacitors (Dr Siti Nabila Aidit) — RC circuit section
  • Lecture formula: $\tau = RC$, $q(t) = CV(1 - e^{-t/RC})$ (charging), $q(t) = Q_0 e^{-t/RC}$ (discharging)
  • Lecture example: L7 Quick Quiz — capacitor marked 35V 1000μF, find Q when connected to 30V ($Q = CV = 0.03$ C)
  • Predicted question type: "A $10\ \mu\text{F}$ capacitor charges through $R = 5\ \text{k}\Omega$. Find the time constant." ($\tau = (5000)(10\times10^{-6}) = 0.05$ s)
  • Watch for: Distinguishing charging vs discharging formula

A2: Kirchhoff's Current Law (KCL)

  • Source: FAD1022 L11 — Kirchhoff's Rules (Theory) — Section 11.2
  • Lecture formula: $\sum I_{\text{in}} = \sum I_{\text{out}}$ (charge conservation)
  • Predicted question type: "At a junction, $I_1 = 2$ A enters, $I_2 = 0.5$ A enters, $I_3 = 1$ A leaves. Find $I_4$ leaving." → $2 + 0.5 = 1 + I_4 \Rightarrow I_4 = 1.5$ A
  • Note from coordinator: KCL only (node analysis), NOT KVL for Section A

A3: Op-Amp Formula

  • Source: L37-L38 Op-Amp (Dr Zainal)
  • Lecture formulas:
    • Inverting: $V_{\text{out}} = -\frac{R_f}{R_i} V_{\text{in}}$ (L37)
    • Non-inverting: $V_{\text{out}} = \left(1 + \frac{R_f}{R_i}\right) V_{\text{in}}$ (L38)
  • Lecture example (L37): $R_1 = 100\ \text{k}\Omega$, $R_f = 500\ \text{k}\Omega$, find $V_{\text{in}}$ to get $V_{\text{out}} = -10$ V → $V_{\text{in}} = 2$ V
  • Predicted question type: "Given $R_f = 10\ \text{k}\Omega$, $R_i = 2\ \text{k}\Omega$, $V_{\text{in}} = 1$ V. Find $V_{\text{out}}$ for inverting op-amp." → $V_{\text{out}} = -(10/2)(1) = -5$ V

A4: Ampere's Law — Wire (Inside/Outside)

  • Source: FAD1022 L22-L26 — Magnetism
  • Lecture formulas:
    • Inside wire ($r < R$): $B = \frac{\mu_0 I r}{2\pi R^2}$
    • Outside wire ($r > R$): $B = \frac{\mu_0 I}{2\pi r}$
  • Predicted question type: "A wire of radius $R = 2$ mm carries $I = 5$ A. Find $B$ at $r = 1$ mm." → $B = \frac{(4\pi\times10^{-7})(5)(0.001)}{2\pi(0.002)^2} = 2.5 \times 10^{-4}$ T

Section B — Structured Questions (Pick 3 of 4, 12 marks each)

B1: Electrostatics — E-field Vector + Projectile Motion

Leak says: E-field and surface / gauss law with spherical charge distributions. Marked "sng" (senang/easy).

Source lecture: FAD1022 L1-L3 — Electrostatics

From L1-L3 lectures (Coulomb's Law, E-field):

  • $F = k\frac{Qq}{r^2}$, $E = \frac{F}{q} = k\frac{Q}{r^2}$
  • Net E-field via vector superposition: $\vec{E}_{\text{net}} = \sum \vec{E}_i$
  • $F = q\vec{E}$ for test charge in E-field
  • Projectile in uniform E-field: $a_y = \frac{qE}{m}$, $y = \frac12 a_y t^2$

Predicted question pattern (from past UAS):

  • (a) Find net E-field at a point between/above two point charges (4 marks). Common setup: charges at $(-d,0)$ and $(+d,0)$, find E at $(0,y)$ or on x-axis.
  • (b) Place test charge $q_0$, find force magnitude and direction (3 marks)
  • (c) Charged particle enters uniform E-field of parallel plates: find acceleration, deflection at exit, exit angle (5 marks)

Lecture examples to review:

  • L1-L3 worked examples: Coulomb's law problems, E-field of point charges
  • L4-L5: Gauss's law applications, spherical charge distributions, electric potential

Key formulas to memorise:

  • $E = kQ/r^2 = Q/(4\pi\varepsilon_0 r^2)$
  • $\vec{E}_{\text{net}} = \vec{E}_1 + \vec{E}_2 + \dots$
  • $F = qE$
  • $a_y = qE/m$
  • $y = \frac12 a_y (x/v_0)^2 = \frac12 \frac{qE}{m} \left(\frac{L}{v_0}\right)^2$
  • $\theta = \tan^{-1}(v_y/v_x)$

B2: Capacitor + Dielectric + DC Voltage Divider

Leak says: Capacitor + dielectric, DC circuits, voltage divider (loaded and unloaded). Marked "sng."

Source lectures: FAD1022 L7-L9 — Capacitors, FAD1022 L13 — Wheatstone Bridge and Voltage Divider

From L7-L9 (Capacitors):

  • Parallel plate: $C = \frac{\varepsilon_0 A}{d}$
  • With dielectric: $C = \kappa C_0$
  • Energy stored: $U = \frac12 CV^2 = \frac{Q^2}{2C} = \frac12 QV$
  • L7 Example 2 (the "dielectric problem"): Vacuum-filled parallel plate $A = 150\ \text{cm}^2$, $d = 2\ \text{mm}$, $V = 2000$ V. Battery disconnected, dielectric inserted, $V$ drops to 500 V. Find $C_0$, $Q$, $C$, $\kappa$, $\varepsilon$, $E_0$, $E$.
  • RC: $q(t) = CV(1 - e^{-t/\tau})$, $\tau = RC$

From L13 (Voltage Divider):

  • Unloaded: $V_{\text{out}} = V_{\text{in}} \times \frac{R_2}{R_1 + R_2}$
  • Loaded: $R_p = \frac{R_2 R_L}{R_2 + R_L}$, $V_{\text{out}} = V_{\text{in}} \times \frac{R_p}{R_1 + R_p}$
  • L13 Problem 13.1: $V_{\text{in}} = 100$ V, $R_1 = 25$ kΩ, $R_2 = 47$ kΩ → $V_{\text{out}} = 65.28$ V
  • L13 Problem 13.2: Loaded voltage divider — adding load $R_L$ reduces $V_{\text{out}}$ because $R_p < R_2$, so voltage drop across $R_1$ increases

Predicted question pattern:

  • (a) Find capacitance of parallel plate with dielectric: $C = \kappa\varepsilon_0 A/d$ (3 marks)
  • (b) Find energy stored: $U = \frac12 CV^2$ or charge $Q = CV$ (3 marks)
  • (c) Voltage divider: either loaded or unloaded, find $V_{\text{out}}$ OR RC charging problem (6 marks)

B3: AC — Phasor Diagram, PRC/PLC/PCC, Power

Leak says: AC analysis, phasor diagram drawing, 90° phase relationships, PRC/PLC/PCC. Marked "sng."

Source lectures: FAD1022 L14-L16 — AC Analysis (Nurul Izzati), FAD1022 L17-L21 — AC Series Circuits (Mohd Fahmi Azman)

From L14 (AC Fundamentals):

  • $I(t) = I_0\sin(\omega t)$, $V(t) = V_0\sin(\omega t)$
  • $\omega = 2\pi/T = 2\pi f$
  • RMS: $I_{\text{rms}} = I_0/\sqrt{2}$, $V_{\text{rms}} = V_0/\sqrt{2}$

From L15 (Phasor Diagrams):

  • Phasor = vector rotating anticlockwise at $\omega$
  • Leading: signal peaks earlier than reference ($+\phi$)
  • Lagging: signal peaks later than reference ($-\phi$)
  • Past year (22/23): Sketch sinusoidal waves from a given phasor diagram at $t=0$ and state which signal leads

From L16 (Reactance/Phase):

  • PRC ($0^\circ$): $V$ and $I$ in phase, $Z = R$
  • PLC ($+90^\circ$): $V$ leads $I$ by $90^\circ$, $X_L = 2\pi fL$
  • PCC ($-90^\circ$): $I$ leads $V$ by $90^\circ$, $X_C = 1/(2\pi fC)$
  • CIVIL mnemonic: C (Capacitor) → I leads V; Inductor → V leads I (or I lags V)
  • Past year (23/24 A5): $X_C = 69.2\ \Omega$, $V(t) = 200\sin(120\pi t)$. Find $C$.
  • Past year (23/24 c): At $f = 30$ Hz, $X_L = 1.5\ \Omega$. Find $X_L$ at $90$ Hz → $X_L \propto f$, so $X_L = 4.5\ \Omega$

From L21 (Power & Power Factor):

  • Average (real) power: $P_{\text{ave}} = I_{\text{rms}}^2 R = V_{\text{rms}}I_{\text{rms}}\cos\phi$
  • Reactive power: $P_R = I_{\text{rms}}^2 X$
  • Apparent power: $P_A = I_{\text{rms}}^2 Z$
  • Power triangle: $P_A^2 = P_{\text{ave}}^2 + P_R^2$
  • Power factor: $\text{PF} = \cos\phi = R/Z = P_{\text{ave}}/P_A$
  • L21 Example 1 (RL): $R = 30\ \Omega$, $L = 80$ mH, $120$ V, $50$ Hz — find PF and $\phi$
  • L21 Example 2: $L = 63$ mH, $R = 248\ \Omega$, $V_{\text{peak}} = 240$ V, $f = 200$ Hz — find $X_L$, $Z$, PF, $V_{\text{rms}}$, $P_{\text{ave}}$

Predicted question pattern (from past UAS + leak):

  • (a) Given $V(t) = V_m\sin(\omega t)$, $I(t) = I_m\sin(\omega t \pm \phi)$ — draw phasor diagram showing phase relationship (4 marks)
  • (b) Identify circuit type from phasor: PRC (in phase), PLC (V leads I), PCC (I leads V) — calculate $X_L$ or $X_C$ (4 marks)
  • (c) Calculate $P_{\text{ave}}$, $P_R$, $P_A$, and $\cos\phi$ for the circuit (4 marks)

B4: AC — RLC + Resonance + Claims

Leak says: AC + diode, given statement with 2 false / 2 correct, RLC (power factor, resonance). Hard — Sir Hafizul suggests skipping unless confident.

Source lecture: FAD1022 L17-L21 — AC Series Circuits

From L19 (RLC Series Circuit):

  • Total voltage: $V_T = \sqrt{V_R^2 + (V_L - V_C)^2}$
  • Impedance: $Z = \sqrt{R^2 + (X_L - X_C)^2}$
  • Phase angle: $\theta = \tan^{-1}\left(\frac{X_L - X_C}{R}\right)$
  • Inductive ($X_L > X_C$): V leads I, $\theta$ positive
  • Capacitive ($X_C > X_L$): I leads V, $\theta$ negative

From L20 (Resonance):

  • Condition: $X_L = X_C$
  • $2\pi f_0 L = \frac{1}{2\pi f_0 C}$ → $f_0 = \frac{1}{2\pi\sqrt{LC}}$
  • At resonance: $Z = R$ (minimum), $I$ max, $\phi = 0^\circ$, PF = 1
  • L20 Example 1: RLC to 220 V, 60 Hz, $X_C = 53.1\ \Omega$, $X_L = 113\ \Omega$, $R = 25\ \Omega$. Find $I$, $I$ at resonance, $f_0$.
  • Past year (24/25 A6): Find $C$ in series with $L = 2.0$ H to make current in phase with 240 V, 50 Hz. → $C = 1/(4\pi^2 f^2 L) = 5.07\ \mu\text{F}$
  • Past year (24/25 B5a): Two conditions for PF = 1: $X_L = X_C$, and therefore $Z = R$ and $\phi = 0^\circ$

Predicted question pattern:

  • (a) Four claims about AC/RLC — identify 2 false and rewrite correctly (6 marks). Likely claims about phase relationships, power factor, resonance conditions.
  • (b) RLC circuit at given $f$ — determine if inductive or capacitive, find $Z$, $\phi$ (3 marks)
  • (c) Explain how to achieve resonance / effect of changing $L$ or $C$ (3 marks)

Section C — Structured Questions (Pick 4 of 6, 12 marks each)

C1: Magnetism — Gauss & Ampere Derivation

Leak says: Magnetism concepts. "Past year" pattern.

Source lecture: FAD1022 L22-L26 — Magnetism

Key content from lectures:

  • Gauss's Law for magnetism: $\oint \vec{B} \cdot d\vec{A} = 0$ (no magnetic monopoles)
  • Ampere's Law: $\oint \vec{B} \cdot d\vec{l} = \mu_0 I_{\text{enc}}$
  • $B$ inside wire ($r<R$): $B = \frac{\mu_0 I r}{2\pi R^2}$
  • $B$ outside wire ($r>R$): $B = \frac{\mu_0 I}{2\pi r}$
  • Solenoid: $B = \mu_0 nI$ where $n = N/l$
  • Force between parallel wires, torque on current loop: $\tau = NIAB\sin\theta$

Predicted question pattern (from past UAS):

  • (a) State Gauss's Law for magnetism / Ampere's Law (2 marks)
  • (b) Derive $B$ field for a specific geometry — Ampere's law derivation, showing all steps (6 marks). Common: inside wire, outside wire, or solenoid.
  • (c) 4-wire square arrangement — find net B-field at centre (4 marks)

C2: EM Induction — AC Motor Torque

Leak says: EM induction (lecturer Susan), velocity selector, induced current and EMF.

Source lecture: FAD1022 L22-L26 — Magnetism, FAD1022 L31-L33 — Inductance & Transformers

Key formulas:

  • Torque on current loop: $\tau = NIAB\sin\theta$
  • Magnetic dipole moment: $\mu = NIA$
  • Motional EMF: $\varepsilon = Blv$
  • Faraday's Law: $\varepsilon = -N d\Phi_B/dt$

Predicted question pattern:

  • (a) Torque on rectangular current loop in B-field (4 marks)
  • (b) AC motor operating principle — explain how torque varies with angle (4 marks)
  • (c) Velocity selector: $v = E/B$ OR motional EMF problem (4 marks)

C3: Transformer — Self & Mutual Induction

Leak says: Self inductance + transformer (marked together), mutual inductance. Marked "sng."

Source lecture: FAD1022 L31-L33 — Inductance & Transformers (Amirul Hakimi)

From L31 (Self Inductance):

  • Self-induced EMF: $\varepsilon = -L,dI/dt$
  • Solenoid inductance: $L = \frac{\mu_0 N^2 A}{\ell}$
  • Energy stored: $U = \frac12 LI^2$
  • L31 Exercise 3: 50 cm solenoid, diameter 10 cm, 700 turns → $L = 9.67$ mH
  • L31 Exercise 5: 300 turns, $l = 25.0$ cm, $A = 4.0$ cm², $I = 0.5$ mA → $U = 2.26 \times 10^{-11}$ J

From L32-L33 (Mutual Inductance & Transformer):

  • Mutual inductance: $\varepsilon_2 = -M,dI_1/dt$, $M = \frac{\mu_0 N_p N_s A}{l}$ (coaxial solenoids)
  • Self vs Mutual comparison table: L: single coil, stores energy; M: two coils, transfers energy
  • Transformer equation: $\frac{V_s}{V_p} = \frac{N_s}{N_p}$, $\frac{I_s}{I_p} = \frac{N_p}{N_s}$
  • L32 Exercise 4: Primary $V_p = 120$ V, $I_s = 0.10$ A, $P = 60.0$ W → $V_s = 600$ V, $N_s/N_p = 5$
  • L32 Exercise 5: $N_p = 250$, $N_s = 1500$, $V_p = 170\sin\omega t$ → $V_{s,\text{rms}} = 721.25$ V
  • L32 Exercise 6: Generator 100 A at 4 kV, stepped up to $2.40 \times 10^5$ V, line 30.0 Ω → 0.021% power lost vs 75% lost without stepping up
  • Energy losses (4 types): Copper ($I^2R$), Hysteresis (use silicon steel), Flux leakage (wrap coils together), Eddy current (laminated core)

Predicted question pattern:

  • (a) Self-inductance of solenoid: $L = \mu_0 N^2 A/l$ (4 marks)
  • (b) Transformer: given $N_p$, $N_s$, $V_p$, find $V_s$ and $I_s$ (4 marks)
  • (c) Explain how to increase transformer efficiency (list 2-3 methods with reasons) (4 marks)

C4: Semiconductor & Biasing — Dr Zainal's Section

Leak says: Semiconductor + biasing, voltage divider bias, clippers with waveform diagram. Dr Zainal is "insanely strict."

Source lecture: FAD1022 L34-L38 — Semiconductors & Op-Amps (Zainal Abidin)

From L34 (Diodes):

  • Knee voltage: Si = 0.7 V, Ge = 0.3 V, GaAs = 1.5 V
  • Forward bias: p to +ve, n to -ve; ON state
  • Reverse bias: p to -ve, n to +ve; OFF state (open circuit)
  • Half-wave rectifier: $V_{\text{DC}} = 0.318(V_m - V_D)$
  • Clippers: clip portion of input signal, output taken across diode
  • Parallel diodes: lower knee voltage turns ON first, blocks the other

From L35 (Fixed & Emitter-Stabilized Bias):

  • $I_E = I_B + I_C$, $I_C = \beta I_B$
  • Fixed bias: $I_B = (V_{CC} - V_{BE})/R_B$, $V_{CE} = V_{CC} - I_C R_C$
  • Emitter-stabilized: $I_B = (V_{CC} - V_{BE})/(R_B + (\beta+1)R_E)$, $V_{CE} = V_{CC} - I_C(R_C + R_E)$
  • Comparison: fixed bias Q-point changes 100% when $\beta$ doubles; emitter-stabilized changes only ~80%

From L36 (Voltage Divider Bias) — THE KEY LECTURE:

  • Approximate analysis (when $\beta R_E \geq 10 R_{B2}$):
    1. $V_B = \frac{R_{B2}}{R_{B1} + R_{B2}} V_{CC}$
    2. $V_E = V_B - V_{BE}$
    3. $I_C \approx I_E = V_E/R_E$
    4. $V_{CE} = V_{CC} - I_C(R_C + R_E)$
  • Key insight: $I_B$ formula does NOT depend on $\beta$ → far more stable
  • L36 Worked example: $V_{CC} = 22$ V, $R_{B1} = 39$ kΩ, $R_{B2} = 3.9$ kΩ, $R_C = 10$ kΩ, $R_E = 1.5$ kΩ, $\beta = 140$ → $V_B = 2$ V, $V_E = 1.3$ V, $I_C = 0.867$ mA, $V_{CE} = 12.03$ V

Bias Type Comparison (from L35-L36):

Quantity Fixed Bias Emitter-Stabilized Voltage Divider
$I_B$ $\frac{V_{CC} - V_{BE}}{R_B}$ $\frac{V_{CC} - V_{BE}}{R_B + (\beta+1)R_E}$ Divider (indirect)
$I_C$ $\beta I_B$ $\beta I_B$ $\cong I_E = \frac{V_B - V_{BE}}{R_E}$
$V_{CE}$ $V_{CC} - I_C R_C$ $V_{CC} - I_C(R_C+R_E)$ $V_{CC} - I_C(R_C+R_E)$
$\beta$ sensitivity 100% change ~80% change Minimal

Dr Zainal's rules (from voice notes):

  1. Follow lecture notes word-for-word, one-to-one
  2. Write direction of current on ALL circuit diagrams — mandatory
  3. Q-point "storyline" required — "The transistor is BARELY ON. $I_S$ is very small — 0.093 mA — and most of the voltage $V_{CC}$ (14.5 V out of 16 V) is still across the transistor itself. This means it is sitting in the active region, ready to amplify a signal."
  4. Study Tuto 12 (graphs) and Tuto 13 (explanations)

Predicted question pattern:

  • (a) Clipper/rectifier output waveform — draw input and output side by side (4 marks)
  • (b) Voltage divider bias circuit — find $V_B$, $V_E$, $I_C$, $V_{CE}$, Q-point using approximate analysis (5 marks)
  • (c) Compare fixed bias vs voltage divider bias — explain why voltage divider is more stable (3 marks)

C5: Atomic Physics — Bohr Radius Derivation

Leak says: Atomic physics, Bohr radius derivation. Must show full derivation (Hafizul's rule).

Source lecture: FAD1022 L39-L42 — Atomic & Nuclear Physics (Hafizul Mat)

From L39 (Atomic Physics) — THE DERIVATION:

The full derivation sequence (memorise this):

  1. Coulomb force = centripetal force: $$\frac{e^2}{4\pi\varepsilon_0 r^2} = \frac{mv^2}{r}$$

  2. Angular momentum quantization (Bohr's postulate): $$mvr = n\frac{h}{2\pi} = n\hbar$$

  3. Eliminate $v$: From step 2, $v = \frac{n\hbar}{mr}$. Substitute into step 1: $$\frac{e^2}{4\pi\varepsilon_0 r^2} = \frac{m}{r}\left(\frac{n\hbar}{mr}\right)^2 = \frac{n^2\hbar^2}{mr^3}$$

  4. Solve for $r_n$: $$r_n = \frac{4\pi\varepsilon_0 \hbar^2}{me^2} \cdot n^2 = \left(\frac{\varepsilon_0 h^2}{\pi m e^2}\right)n^2$$

  5. Substitute constants: $$r_n = (5.29 \times 10^{-11}\ \text{m}),n^2 = n^2 a_0$$ where $a_0 = 0.529\ \text{Å}$ is the Bohr radius.

  6. Energy levels: $E_n = -\frac{ke^2}{2r_n} = -\frac{13.6}{n^2}\ \text{eV}$

L39 Example: Electron drops from unknown $n$ to ground state, emits photon with $E = 2.089 \times 10^{-18}$ J = 13.056 eV → $n \approx 5$, $f = 3.15 \times 10^{15}$ Hz

Predicted question pattern:

  • (a) Derive Bohr radius $r_n$ using Coulomb force = centripetal force + angular momentum quantization (6 marks)
  • (b) Calculate $r_n$ for a given $n$ (e.g. $n=3$: $r_3 = 9a_0 = 4.76 \times 10^{-10}$ m) (3 marks)
  • (c) Energy level calculation: $E_n = -13.6/n^2$ eV, find $\Delta E$ for transition, $f = \Delta E/h$ (3 marks)

C6: Photoelectric Effect — Nurul Izzati's Section

Leak says: Photoelectric effect ("past year" pattern). Miss Nurul Izzati also tests photon momentum.

Source lectures: FAD1022 L44 — Photons and Photoelectric Effect, FAD1022 L45 — Introduction to Quantum Mechanics (Nurul Izzati)

From L44 (Photoelectric Effect):

  • Photon energy: $E = hf = hc/\lambda$
  • Work function $\phi$ = minimum energy to eject electron
  • Threshold frequency: $f_0 = \phi/h$
  • Einstein's equation: $KE_{\text{max}} = hf - \phi$
  • Stopping potential: $KE_{\text{max}} = eV_s$
  • $V_s$ vs $f$ graph: slope $= h/e$, intercept $= -\phi/e$
  • Three cases (from voice notes):
    1. $hf < \phi$: no electrons
    2. $hf = \phi$: electron escapes with $KE = 0$
    3. $hf > \phi$: electron emitted with $KE = hf - \phi$
  • L44 Example 3: $v_{\text{max}} = 4.6 \times 10^5$ m/s, $\lambda = 625$ nm. Find $\phi$ and $f_c$.
  • L44 Example 4: $\lambda = 350$ nm on potassium, $KE_{\text{max}} = 1.31$ eV. Find $\phi$, $\lambda_c$, $f_c$.

From L45 (Quantum Mechanics):

  • De Broglie: $\lambda = h/p = h/(mv)$
  • Heisenberg: $\Delta x \cdot \Delta p \geq \hbar/2$
  • L45 example: Electron at $v = 2.0 \times 10^6$ m/s → $\lambda = 3.63 \times 10^{-10}$ m
  • L45 example: e- with KE = 150 eV → $\lambda = 0.1$ nm
  • L45 Heisenberg example: Baseball ($m = 0.1$ kg, $v = 40$ m/s, 1% accuracy) → $\Delta x \geq 1.3 \times 10^{-33}$ m
  • L45 Heisenberg example: Electron ($v = 4 \times 10^6$ m/s, 1% accuracy) → $\Delta x \geq 1.4 \times 10^{-4}$ m

Predicted question pattern:

  • (a) Photoelectric effect: state conditions for emission, explain work function (3 marks)
  • (b) Given two $(f, V_s)$ data pairs — find $\phi$ and $h$ (exam favorite, appears every year) (5 marks)
  • (c) Photon momentum $p = E/c$ OR de Broglie wavelength $\lambda = h/p$ OR Heisenberg minimum $\Delta x$ (4 marks)

FAD1015 — Mathematics III

Part A — Known Questions (Directly from Leak)

Q1 (a-c): Binomial Distribution

Leak says: Definition, characteristic, determine type, identify parameter or statistics.

Source: FAD1015 L13 — Binomial Distribution

From L13 lecture:

  • Definition: A binomial experiment counts the number of successes in $n$ identical, independent trials with two outcomes (success/failure) and constant probability $p$.
  • 4 characteristics (from L13):
    1. Fixed number of trials $n$
    2. Two possible outcomes per trial (success/failure)
    3. Independent trials
    4. Constant probability $p$ for every trial
  • Formula: $P(X=x) = \binom{n}{x}p^x(1-p)^{n-x}$
  • Mean: $\mu = np$, Variance: $\sigma^2 = npq$, SD: $\sigma = \sqrt{npq}$
  • Table usage (L13): $P(X \geq x)$ from table, convert others:
    • $P(X \leq x) = 1 - P(X \geq x+1)$
    • $P(X = x) = P(X \geq x) - P(X \geq x+1)$
    • $P(X < x) = 1 - P(X \geq x)$
    • $P(X > x) = P(X \geq x+1)$

Predicted question: Given a scenario, (a) state definition, (b) list characteristics, (c) determine if binomial or identify parameter vs statistic.

Tutorial reference: Tuto 13 Q1 (specifically mentioned in leak)

Q2 (a-c): Uniform Distribution & Poisson Approximation

Leak says: Uniform distribution, syarat binomial → Poisson, Tuto 13 soalan 1.

Sources: FAD1015 L17-L18 — Uniform & Exponential Distributions + R Intro, FAD1015 L14 — Poisson Distribution

From Poisson lecture (L14):

  • Poisson approximation to Binomial: When $n$ is large, $p$ is small, and $\lambda = np$ stays constant
  • Rule of thumb: $n > 20$ and $np < 5$ (or $nq < 5$)
  • Poisson PMF: $P(X=x) = \frac{\lambda^x e^{-\lambda}}{x!}$, $\lambda > 0$
  • Key difference: Binomial has upper limit $n$; Poisson has no upper limit
  • Mean = Variance = $\lambda$ for Poisson

Predicted question: (a) Uniform distribution probability calculation, (b) Explain when binomial→Poisson approximation is valid, (c) Tuto 13 Q1 style problem.

Part B — Known Questions (Directly from Leak)

Q3 (a-b): CDF & Poisson Calculations

Leak says: Cumulative distribution function, Poisson distribution calculations.

Source: FAD1015 L14 — Poisson Distribution

From L14:

  • $P(X = x) = \lambda^x e^{-\lambda}/x!$
  • Cumulative: $P(X \leq k) = \sum_{x=0}^{k} \lambda^x e^{-\lambda}/x!$ (or use Poisson table)
  • L14 Example 1: Car breaks down avg 3/month. Find $P(X=2)$ and $P(X \leq 1)$.
  • L14 Example 4 (LAZADA): 2 of 10 returned. Find probability for 40 products.

Predicted question: Given PDF, find CDF. Then Poisson calculation: $P(X=k)$ and $P(X \leq k)$.

Q4 (a-b): Continuous/Discrete, Probability Intervals, Mean & SD

Source: FAD1015 Week 6 — Continuous Random Variables, FAD1015 Week 5 — Mean & Variance

Predicted question: (a) Identify continuous vs discrete variable. (b) Find smallest/biggest $n$ meeting condition, $P(a < X < b)$, or mean and SD.

Q5 (a-b): Hypothesis Testing

Leak says: Critical value → p-value → compare with $\alpha$ → conclusion → confidence interval → conclusion.

Source: FAD1015 L23-L24 — Hypothesis Testing About the Mean

From L23-L24 (lecture-exact procedure):

6-step hypothesis testing procedure:

  1. State $H_0$ and $H_1$ (null/alternative)
  2. Select $\alpha$ (level of significance)
  3. Identify test statistic (Z if $n \geq 30$ or $\sigma$ known; t if $n < 30$ and $\sigma$ unknown)
  4. Identify rejection region (critical value(s))
  5. Make decision: reject $H_0$ if test statistic falls in rejection region
  6. Conclusion in context of the problem

3 Methods (all from L23-L24):

  • Traditional: $|Z_{\text{calc}}| > Z_{\text{crit}}$ → reject $H_0$
  • P-value: P-value $\leq \alpha$ → reject $H_0$
  • Confidence Interval: $\mu_0$ outside CI → reject $H_0$

L23-L24 worked examples:

  • Example 1 (Two-tailed Z): XYZ Ketchup, $n=36$, $\bar{x}=16.12$, $s=0.5$, $\mu=16$, $\alpha=0.05$. $Z=1.44$, $Z_{\text{crit}}=\pm1.96$ → do not reject
  • Example 2 (Right-tailed Z): Phone bill, $n=64$, $\bar{x}=53.1$, $s=10$, $\mu>52$, $\alpha=0.10$. $Z=0.88$, $Z_{\text{crit}}=1.28$ → do not reject
  • Example 3 (Left-tailed Z): Light bulbs, $n=100$, $\bar{x}=470$, $\sigma=25$, $\mu<480$, $\alpha=0.05$. $Z=-4.0$, $Z_{\text{crit}}=-1.645$ → reject
  • Example 4 (Two-tailed t): Hotel RM, $n=25$, $\bar{x}=172.50$, $s=15.40$, $\mu=168$, $\alpha=0.05$. $t=1.46$, $t_{\text{crit}}=\pm2.064$, df=24 → do not reject
  • Example 5 (P-value approach): Same as Example 2, P-value $=0.1894 > 0.10$ → do not reject
  • Example 6 (P-value two-tailed): Same as Example 1, P-value $=0.1498 > 0.05$ → do not reject

Predicted question (full workflow):

  1. State $H_0$ and $H_1$
  2. Find critical value from table (given $\alpha$, df)
  3. Calculate test statistic: $t = \frac{\bar{x} - \mu}{s/\sqrt{n}}$ or $Z = \frac{\bar{x} - \mu}{\sigma/\sqrt{n}}$
  4. Compare: reject or do not reject $H_0$
  5. Find p-value
  6. Make conclusion in context
  7. Construct confidence interval: $\bar{x} \pm t_{\alpha/2} \cdot \frac{s}{\sqrt{n}}$
  8. Make conclusion from CI

Q6 (a-b): Matrices in R ⭐ HIGHEST PRIORITY

Leak says: Matrix calculation (Tuto 14), given R coding find output, write R code.

Sources: FAD1015 L27-L28 — Matrices (Types & Operations), FAD1015 L29-L30 — Matrices (Inverse & Systems of Equations)

From L27-L28:

  • Matrix definition: Rectangular array of numbers, size $m \times n$
  • Types: row, column, square, zero, diagonal, identity, triangular, symmetric
  • Operations: addition (same size), scalar multiplication, multiplication (columns of A = rows of B)
  • Determinant: $2\times2$: $|A| = a_{11}a_{22} - a_{12}a_{21}$
  • Transpose: $(A^T){ij} = a{ji}$, $(AB)^T = B^T A^T$

From L29-L30:

  • Inverse (2×2): $A^{-1} = \frac{1}{|A|}\begin{pmatrix} d & -b \ -c & a \end{pmatrix}$
  • Singular if $|A| = 0$ (no inverse)
  • Adjoint: $A^{-1} = \frac{1}{|A|}\text{adj}(A)$
  • ERO: interchange rows, multiply row by scalar, add multiple of one row to another
  • Solving $AX = B$: $X = A^{-1}B$, Gauss-Jordan elimination, Cramer's Rule
  • 3 cases: $|A| \neq 0$ (unique), $|A| = 0$ and (adj A)$B = 0$ (infinite), else (no solution)

Predicted R code questions:

# Create matrices
A <- matrix(c(1,2,3,4), nrow=2)     # 2x2 matrix
B <- matrix(1:9, nrow=3, byrow=TRUE) # 3x3 matrix by row

# Bind operations
cbind(A, c(5,6))  # column bind
rbind(A, c(7,8))  # row bind

# Matrix multiplication
A %*% B

# Inverse
solve(A)

# Determinant
det(A)

# Naming
rownames(A) <- c("row1", "row2")
colnames(A) <- c("col1", "col2")

Tutorial reference: Tuto 14 (specifically mentioned in leak)

FAD1014 — Mathematics II

Integration by Substitution (Part A ✅)

Source: FAD1014 L3-L4 — Integration by Substitution

3 cases for choosing $u$ (from lecture):

  1. Quantity under a root or raised to a power
  2. Quantity in the denominator
  3. Exponent on $e$

If $du$ doesn't match exactly: multiply inside by $k$, outside by $1/k$.

Lecture examples to review:

  • L3-L4 Example 2.1.1: $\int (2x^3+1)^4 \cdot 6x^2,dx$ → $u = 2x^3+1$
  • L3-L4 Example 2.1.4: $\int \frac{x+3}{(x^2+6x)^2},dx$ → $u = x^2+6x$
  • L3-L4 Example 2.1.5: $\int \frac{x^2+1}{x^3+3x},dx$ → $u = x^3+3x$ (log result)
  • L3-L4 Example 2.3.1: $\int x\cos(3x^2),dx$ → $u = 3x^2$

Predicted: $u$-substitution with constant adjustment or definite integral with bounds change.

Integration by Parts (Part B likely)

Source: FAD1014 L5-L6 — Integration by Parts

LIPET rule for choosing $u$:

  1. Logarithmic ($\ln x$)
  2. Inverse trig ($\sin^{-1}x$, $\tan^{-1}x$)
  3. Polynomial / Algebraic ($x^n$)
  4. Exponential ($e^x$)
  5. Trigonometric ($\sin x$, $\cos x$)

Formula: $\int u,dv = uv - \int v,du$

Lecture examples to review:

  • L5-L6 Example 3.1.1: $\int x\cos x,dx$ — polynomial × trig
  • L5-L6 Example 3.1.3: $\int \ln x,dx$ — log (just $\ln x$!)
  • L5-L6 Example 3.1.4: $\int x^2 e^x,dx$ — repeated IBP
  • L5-L6 Example 3.1.5: $\int e^x \cos x,dx$ — cyclic (be consistent!)
  • L5-L6 Example 3.1.8: $\int x^2 \ln x,dx$ — polynomial × log
  • L5-L6 Example 3.1.10: $\int x^2 e^{3x},dx$ — repeated with composite exponential

Cyclic integrals require CONSISTENT $u/dv$ choices both times (L5-L6 Example 3.1.11 shows what happens when inconsistent).

Homogeneous, Inseparable & Linear DE (Part B likely)

Sources: Bernoulli DE, Non-Homogeneous DE (linearly independent), Non-Homogeneous DE (linearly dependent), FAD1014 L15-L16 — Differential Equations (Separable)

Leak says: "Homogeneous inseparable and linear"

Interpretation from existing lectures:

Homogeneous DE → Non-homogeneous DE (linearly independent case):

  • Form: $M(x,y),dx + N(x,y),dy = 0$ where $M = a_1 x + b_1 y + c_1$, $N = a_2 x + b_2 y + c_2$
  • Condition: $a_1 b_2 - a_2 b_1 \neq 0$ (coefficients NOT proportional)
  • Method: Translate coordinates — substitute $x = u + h$, $y = v + k$
  • Lecture Example 1: $(y - x - 2),dx + (4y + x - 3),dy = 0$
  • Lecture Example 2: $(x + y),dx + (x - y + 2),dy = 0$

Inseparable DE → Non-homogeneous DE (linearly dependent case):

  • Condition: $a_1 b_2 - a_2 b_1 = 0$ (coefficients ARE proportional)
  • Method: Substitute $u = a_1 x + b_1 y$ to reduce to separable
  • Lecture Example 1: $(x + y),dx + (3x + 3y - 4),dy = 0$
  • Lecture Example 4: $(x + y),dx + (x + y + 1),dy = 0$ with $y(2) = 1$

Linear DE → Bernoulli DE:

  • Form: $\frac{dy}{dx} + yP(x) = y^n Q(x)$
  • Substitute $v = y^{1-n}$ to reduce to linear
  • Solve using integrating factor $\mu = e^{\int P(x),dx}$
  • Lecture Example 1: $y(1 + xy^4),dx - dy = 0$
  • Lecture Example 3: $y,dx + x(x^2 y - 1),dy = 0$, find particular with $y(1) = 2$

Missing: I could not find a standalone "Linear DE (integrating factor)" lecture page. The Bernoulli DE lecture covers the method, but a dedicated first-order linear DE ($dy/dx + P(x)y = Q(x)$) page may exist elsewhere. Check FAD1014 Tutorial 10 — Linear First Order Differential Equations for this method.

Maclaurin Series (Part B ✅ CONFIRMED)

Source: FAD1014 L25-L26 — Power Series, Taylor & Maclaurin

From L25-L26 (En Hisham):

Maclaurin series = Taylor series at $a=0$: $$f(x) = f(0) + f'(0)x + \frac{f''(0)}{2!}x^2 + \frac{f'''(0)}{3!}x^3 + \dots$$

Standard expansions to memorise (from lecture):

  • $e^x = 1 + x + \frac{x^2}{2!} + \frac{x^3}{3!} + \dots$
  • $\sin x = x - \frac{x^3}{3!} + \frac{x^5}{5!} - \dots$
  • $\cos x = 1 - \frac{x^2}{2!} + \frac{x^4}{4!} - \dots$
  • $\ln(1+x) = x - \frac{x^2}{2} + \frac{x^3}{3} - \dots$

Lecture examples to review:

  • Example 3: Maclaurin for $f(x)=e^x$, $g(x)=\sin x$, $k(x)=\ln(1+x)$. Approximate at $x=0.01$ using 3 terms.
  • Example 4: First three nonzero terms for $f(x) = x^4 e^{-3x^2}$.
  • Example 5: Three terms for $f(x) = (\sin 3x^2)e^{2x}$.
  • Example 6: First four nonzero terms of $\int \frac{\sin x}{x},dx$ and $\int \frac{e^x}{x},dx$.

Also Taylor series (for Part B): $$f(x) = \sum_{n=0}^\infty \frac{f^{(n)}(a)}{n!}(x-a)^n$$

Predicted question: Find Maclaurin expansion up to $x^n$ terms — find derivatives at 0, write series.

Parabola (Part A ✅)

Source: FAD1014 L27-L28 — Geometry I (Circle & Parabola)

From L27-L28:

Standard parabola equations:

Orientation Equation Vertex Focus Directrix
Vertical (opens up, $a>0$) $(x-h)^2 = 4a(y-k)$ $(h,k)$ $(h, k+a)$ $y = k-a$
Vertical (opens down, $a<0$) $(x-h)^2 = 4a(y-k)$ $(h,k)$ $(h, k-a)$ $y = k+a$
Horizontal (opens right) $(y-k)^2 = 4a(x-h)$ $(h,k)$ $(h+a, k)$ $x = h-a$
Horizontal (opens left) $(y-k)^2 = 4a(x-h)$ $(h,k)$ $(h-a, k)$ $x = h+a$
  • Latus rectum length = $4a$

Lecture examples to review:

  • Example 9: Find equation given vertex and focus (4 orientations)
  • Example 10: Find vertex, focus, directrix from given equation (including completing the square)
    • c) $(x+4)^2 = -20y-20$
    • d) $y^2 + 6y + 1 + 4x = 0$
  • Example 11: Equation of parabola with axis parallel to y-axis, vertex $(2,-1)$, passing through $(3,1)$

FAD1018 — Basic Chemistry II

Brady's Reagent for Ammonia Derivatives

Leak says: "Brady's reagent only for ammonia derivatives"

Source: FAD1018 W11 — Carboxylic Acids & Derivatives, FAD1018 W12 — Amine & Amino Acids

From W11:

  • Brady's reagent = 2,4-dinitrophenylhydrazine (2,4-DNPH)
  • Reacts with aldehydes and ketones (carbonyl compounds) to form orange/yellow precipitates
  • Used to test for presence of carbonyl group (C=O)
  • Ammonia derivatives that react with carbonyls: hydroxylamine, hydrazine, semicarbazide, 2,4-DNPH
  • Key: Brady's reagent (2,4-DNPH) is specifically mentioned — must know this reagent

Reactivity order (from W11): Acyl Chloride > Acid Anhydride > Ester ~ Carboxylic Acid > Amide

Predicted question: Identifying carbonyl compounds — use Brady's reagent (2,4-DNPH) → orange precipitate confirms carbonyl. Differentiate aldehyde vs ketone using Tollens' or Fehling's.

FAC1003 — Programming II

[!warning] Verification Status No FAC1003 lecture source pages exist in this wiki. The leak claims below come entirely from the leak provider (Adian Sani, revision session slides). Tutorial 14 covers OOP (classes/objects/inheritance/polymorphism), which is NOT mentioned in the leak. The leak's priority topics are procedural C++ (pointers, functions, recursion). Without lecture source pages, none of these claims can be cross-verified against course materials.

Pointers & References — VERY IMPORTANT

Leak says: Pointers and references/call-by-reference will appear in BOTH Part A and Part B.

From leak provider:

  • Pointer: uses * (dereference operator) and & (address-of operator)
  • Reference (call by reference): uses & in parameter declarations
  • Must be able to recognize pointer vs reference code patterns

Memorize this swap function pattern:

void swap(int &x, int &y) {
    int temp = x;
    x = y;
    y = temp;
}

Pointer pattern:

int* ptr;
ptr = &var;    // address-of
*ptr = 10;     // dereference

Predicted question: Given a code snippet, identify whether it uses pointer or reference semantics. Write a function that uses reference parameters.

Functions: Void vs Non-Void, Prototypes

Leak says: Functions are "DEFINITELY COMING OUT" — emphasized for organization and code structure.

Key distinction (from leak):

Type Return Use Case
Void No return value Actions, displaying output
Non-Void Returns a value Calculations, processing

Predicted question: Fill in the blanks for a function prototype, call, and definition. Distinguish void vs non-void.

Recursion vs Iteration — MUST DIFFERENTIATE

Leak says: Most likely they'll ask to use BOTH recursion AND iteration in the SAME question.

Factorial — Recursion:

int factorial(int n) {
    if (n == 0 || n == 1) return 1;
    else return n * factorial(n - 1);
}

Factorial — Iteration:

int factorial(int n) {
    int result = 1;
    for (int i = 1; i <= n; i++) result *= i;
    return result;
}

Fibonacci — MEMORIZE:

int fibonacci(int n) {
    if (n <= 1) return n;
    return fibonacci(n - 1) + fibonacci(n - 2);
}

Predicted question: Implement the same calculation (factorial or Fibonacci) using BOTH recursion AND iteration. Show understanding of base case vs loop condition.

Scope of Variables

Leak says: Local, global, and static variable scope.

Scope Meaning Lifetime
Local Declared inside a block/function Only inside that block
Global Declared outside all functions Entire program
Static Retains value across function calls Entire program run

Predicted question: Given code with variables at different scopes, determine output or explain lifetime.

Dynamic Memory Allocation

Leak says: Uses new keyword for runtime array creation.

int* arr = new int[size];
// ... use array ...
delete[] arr;

Predicted question: Write code that dynamically allocates an array, processes it, and deallocates.

Part A Sample — TRUE/FALSE

No Statement Answer
i A function can be called multiple times from main() TRUE
ii The function prototype must include the function's body FALSE
iii The sqrt() function requires <cmath> TRUE
iv Program flow starts from called function before main() FALSE
v Prototype params must match definition in type and order TRUE

Topics NOT Coming Out

  • ❌ Searching and sorting algorithms
  • ❌ Arrays (extensively)
  • ❌ Strings (extensively)

⚠️ Missing Content Summary

Subject What I Couldn't Verify Where to Check
FAD1014 "Linear DE" standalone (integrating factor method) — only Bernoulli DE found FAD1014 Tutorial 10 — Linear First Order Differential Equations
FAD1022 Exact content of L1-L3 Electrostatics worked problems (surface-level only) Read L1-L3 lecture in full
FAD1022 Specific tutorial question numbers (Tuto 8 Q2, Tuto 12-13 graphs) Read tutorials in full
FAD1015 Tuto 13 Q1 and Tuto 14 specific problems Read Tuto 13 and Tuto 14 in full

Recommended Study Order

Phase 1: Read Quick Reference (30 min)

Phase 2: Study High-Priority Physics (3 hours)

  1. C4: Semiconductors → L34-L38 + Tuto 12-13 (Dr Zainal — strict marking, most detailed leak)
  2. C3: Transformers → L31-L33 (standard formulas, easy marks)
  3. C5: Bohr radius → L39 (derivation, must show all steps)
  4. B2: Capacitor/Voltage divider → L7-L9 + L13
  5. B3: AC phasor/Power → L14-L16 + L17-L21

Phase 3: Study Maths Priority (2 hours)

  1. FAD1015 Q6: Matrices in R → L27-L30 + Tuto 14
  2. FAD1015 Q5: Hypothesis testing → L23-L24
  3. FAD1014: Maclaurin series → L25-L26

Phase 4: Practice from Past UAS Papers

Phase 5: Review Programming Leaks (if applicable)

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