CAPE Physics Unit 1 and 2 Definitive Syllabus for 2008 Exam

Caribbean Advanced Proficiency Examination (CAPE) Physics Overview

• The Caribbean Advanced Proficiency Examination (CAPE) is a certification of academic, vocational, and technical achievement for students in the Caribbean who have completed a minimum of five years of secondary education.
• Certification Types:     - CAPE Unit Certificate: Awarded for each individual Unit completed.     - CAPE Diploma: Awarded for passing at least six Units, including Caribbean Studies.     - CAPE Associate Degree: Awarded for completing a prescribed cluster of seven Units, including Caribbean Studies and Communication Studies, within a maximum five-year period.
• Syllabus Structure: Organized into two Units, each consisting of three Modules. Each Unit is designed to be covered in approximately $150\,hours$.     - Unit 1: Mechanics, Waves, and Properties of Matter.     - Unit 2: Electricity and Magnetism, A.C. Theory and Electronics, and Atomic and Nuclear Physics.
• Rationale: Physics is considered the most fundamental scientific discipline, essential for explaining the physical environment and driving the technological conveniences of the Caribbean.

Skills and Abilities to be Assessed

• Knowledge and Comprehension (KC):     - Knowledge: The ability to identify, remember, and grasp the basic facts, concepts, and principles.     - Comprehension: The ability to select appropriate ideas, match, compare, and cite examples of facts and principles in familiar situations.
• Use of Knowledge (UK):     - Application: Using facts and procedures in familiar and novel situations; transforming data; using formulae for computation.     - Analysis and Interpretation: Identifying component parts; recognizing interactions and causal factors; inferring, predicting, and drawing conclusions; recognizing limitations and assumptions of data.     - Synthesis: Combining parts to form a new whole; solving problems.     - Evaluation: Making reasoned judgments; assessing the validity of scientific statements, experiments, and results.
• Experimental Skills (XS):     - Observation, Recording and Reporting: Selecting relevant observations; minimizing experimental errors; recording measurement with due regard for precision, accuracy, and units; reporting clearly and logically using scientific terminology.     - Manipulation and Measurement: Following detailed instructions; using apparatus safely and effectively; prioritizing accuracy in measurement.     - Planning and Designing: Developing hypotheses; devising means of testing them; using experimental controls; modifying plans as needed; identifying sources of error and danger.

Unit 1 Module 1: Mechanics

• Physical Quantities:     - Quantities are expressed as a numerical magnitude and a unit. Some quantities are dimensionless (e.g., refractive index, relative density).     - Scalars vs. Vectors: Distinction must be made between quantities that have magnitude only (scalars) and those with both magnitude and direction (vectors). Vectors are combined and resolved graphically and via calculation (using components).     - Precision vs. Accuracy: Precision relates to the reproducibility of measurement, while accuracy relates to how close a measurement is to the true value.     - Uncertainties: Estimation of uncertainty in derived quantities is required using actual, fractional, or percentage uncertainties.
• SI Units:     - Base Quantities: Mass ($kg$), length ($m$), time ($s$), temperature ($K$), current ($A$), luminous intensity ($cd$), and amount of substance ($mol$).     - Prefixes: Ranges from $10^{9}$ (giga) down to $10^{-12}$ (pico).     - Avogadro Constant ($N_A$): The number of atoms in $0.012\,kg$ of the C-12 isotope ($6.02 \times 10^{23}\,mol^{-1}$).     - Homogeneity: Base units are used to check if physical equations are dimensionally consistent.
• Motion:     - Linear Motion: Displacement ($s$), speed, velocity ($v$), and acceleration ($a$) in a single dimension.     - Equations for Uniformly Accelerated Motion:         - $v = u + at$         - $v^2 = u^2 + 2as$         - $s = \frac{u + v}{2} \times t$         - $s = ut + \frac{1}{2}at^2$         - $s = vt - \frac{1}{2}at^2$     - Projectile Motion: Non-calculus approach; motion is shown to be parabolic.     - Newton’s Laws of Motion: Includes the requirement of an unbalanced external force to change velocity.     - Linear Momentum ($p$): Product of mass and velocity; the principle of conservation of linear momentum applies in one and two dimensions.     - Impulse: Change in momentum; interpreted via Force-time ($F-t$) graphs.
• Circular Motion and Gravitation:     - Angular displacement is expressed in radians ($rad$).     - Angular velocity ($\omega$): $\omega = \frac{2\pi}{T} = 2\pi f$.     - Centripetal Acceleration: $a = v^2/r = r\omega^2$.     - Centripetal Force: $F = mv^2/r = mr\omega^2$.     - Newton’s Law of Universal Gravitation: $F = G\frac{m_1 m_2}{r^2}$.     - Gravitational Field Strength ($g$): Defined at or above Earth's surface in $N\,kg^{-1}$.     - Geostationary Satellites: Discussion includes comparison with Global Positioning System (GPS) satellites.
• Effects of Forces:     - Upthrust: Originates from pressure difference in a fluid. Solving problems involving bodies wholly or partially immersed (Archimedes' Principle).     - Resistive Forces: Includes drag forces in fluids and frictional forces.     - Terminal Velocity: The constant speed reached when resistive forces balance driving forces.     - Equilibrium: Static and dynamic; sum of forces and sum of torques (moments) both equal zero.
• Conservation of Energy:     - Work ($W$): $W = Fx$.     - Kinetic Energy ($E_k$): $E_k = \frac{1}{2}mv^2$.     - Potential Energy ($E_p$): Includes gravitational ($\Delta E_p = mgh$ near Earth's surface), electrical, elastic, and strain energy.     - Power ($P$): $P = W/t$ and $P = Fv$.     - Energy Conversion in the Caribbean: Focus on non-traditional and renewable sources: biofuels/ethanol, geothermal, solar, wind, and hydro.

Unit 1 Module 2: Oscillations and Waves

• Harmonic Motion:     - Simple Harmonic Motion (SHM): Conditions for SHM; equations for displacement ($x = A \sin(\omega t)$ or $x = A \cos(\omega t)$) and velocity ($v = v_0 \cos(\omega t)$ where $v_0 = \omega A$).     - Periods ($T$):         - Simple Pendulum: $T = 2\pi\sqrt{\frac{l}{g}}$         - Mass on a Spring: $T = 2\pi\sqrt{\frac{m}{k}}$ (includes series and parallel configurations).     - Damping and Resonance: Damping (e.g., vehicle suspension); forced oscillations; resonance applications and hazards.
• Properties of Waves:     - Terms: Amplitude, period, frequency, velocity ($v = f\lambda$).     - Wave Types: Longitudinal vs. Transverse (differentiation based on particle movement and energy propagation).     - Polarisation: Only transverse waves can be polarized.     - Intensity: $\text{Intensity} \propto (\text{amplitude})^2$.     - Stationary vs. Progressive Waves: Graphical representation; nodes and antinodes.     - Applications of Sound: Sonar (depth gauging), medicine (foetal imaging), and musical instruments (steel pan, flute, guitar).     - Reflection and Refraction: Laws of reflection and Snell’s law ($n_1 \sin(\theta_1) = n_2 \sin(\theta_2)$).     - Interference and Diffraction:         - Two-source interference: Young’s slits; $\lambda = \frac{ax}{D}$.         - Diffraction grating: $n\lambda = d \sin(\theta)$.     - Total Internal Reflection: Critical angle calculation; applications in fiber optic cables.
• Physics of the Ear and Eye:     - Ear: Sensitivity, frequency response, threshold of hearing, intensity level in decibels ($\text{intensity level in dB} = 10 \log_{10}(\frac{I}{I_0})$).     - Eye: Lens formula ($\frac{1}{u} + \frac{1}{v} = \frac{1}{f}$; Power in dioptres = $1/f$ in meters).     - Defects: Long sight, short sight, astigmatism, cataracts, and their correction.

Unit 1 Module 3: Thermal and Mechanical Properties of Matter

• Thermometers:     - Use of physical properties (linear and non-linear) to measure temperature.     - Types: Liquid-in-glass, resistance (thermistor), thermocouple, and constant volume gas thermometer.     - Scales: Kelvin scale ($T = 273.16\,K$ at the triple point of water); relations between Celsius and Kelvin ($T/^{\circ}C = T/K - 273.15$).
• Thermal Properties:     - Internal Energy: Sum of kinetic and potential energies of molecules.     - Specific Heat Capacity ($c$): $E_H = mc\Delta\theta$.     - Specific Latent Heat ($L$): $E_H = mL$. Covers latent heat of fusion and vaporization.     - Evaporation: Theoretical cooling explained via the escape of high kinetic energy molecules.
• Heat Transfer:     - Conduction: Thermal conductivity equation $\frac{Q}{t} = kA\frac{\Delta\theta}{x}$.     - Convection: Result of density changes; explanation for ocean currents and winds.     - Radiation: Stefan-Boltzmann Law for a black body ($P = A\sigma T^4$). Greenhouse effect and solar water heaters.
• Kinetic Theory of Gases:     - Ideal Gas Equation: $pV = nRT$ and $pV = NkT$.     - Assumptions: Basic kinetic theory assumptions (e.g., negligible volume of molecules, elastic collisions).     - Pressure of a Gas: $p = \frac{1}{3}\rho \langle c^2 \rangle$.     - Average Kinetic Energy: Translation energy of monatomic molecules: $\frac{1}{2}m \langle c^2 \rangle = \frac{3}{2}kT$.
• First Law of Thermodynamics:     - Internal Energy Change: $\Delta U = Q + W$ (where $Q$ is heat supplied and $W$ is work done on the system).     - Molar Heat Capacity: Distinction between $C_p$ (constant pressure) and $C_v$ (constant volume); $C_p = C_v + R$.     - Work Done: $W = p\Delta V$.
• Mechanical Properties of Materials:     - Density and Pressure: $\rho = M/V$; $p = F/A$; $\Delta p = \rho g \Delta h$.     - Structures: Crystalline vs. non-crystalline solids (metals, polymers, glasses).     - Hooke’s Law: Stretching of springs and wires; force-extension graphs.     - Young Modulus ($E$): $E = \frac{\text{stress}}{\text{strain}}$.     - Strain Energy: Energy stored in deformed material, deduced from the area under a force-extension graph.

Unit 2 Module 1: Electricity and Magnetism

• Electrical Quantities:     - Current: $Q = It$. Coulomb is defined.     - Potential Difference: Volt is defined; $V = W/Q$ and $V = IR$.     - Power: $P = IV$, $P = I^2 R$, $P = V^2/R$.     - Resistivity ($\rho$): $R = \rho L/A$.     - EMF vs PD: EMF is associated with sources/active devices; PD is associated with electric fields/passive devices.     - Drift Velocity ($v$): $I = nevA$ (where $n$ = charge density).
• Electrical Circuits:     - I-V Characteristics: Metallic conductors, semiconductor diodes, filament lamps.     - Kirchhoff’s Laws: First Law (conservation of charge), Second Law (conservation of energy).     - Resistors: Series ($R = R_1 + R_2 + ...$) and Parallel ($1/R = 1/R_1 + 1/R_2 + ...$).     - Potential Divider: Used as a source of variable or fixed voltage.     - Wheatstone Bridge: Used to compare resistances.
• Electric Fields:     - Coulomb’s Law: Force between charges in free space ($F = \frac{Q_1 Q_2}{4\pi\varepsilon_0 r^2}$).     - Electric Field Intensity ($E$): $E = \frac{Q}{4\pi\varepsilon_0 r^2}$. For parallel plates, $E = V/d$.     - Potential ($V$): $V = \frac{Q}{4\pi\varepsilon_0 r}$. Field strength is numerically equal to the potential gradient ($E = -dV/dx$).
• Capacitors:     - Capacitance ($C$): $C = Q/V$. Measured in Farads ($F$).     - Parallel Plate Capacitor: $C = \frac{\varepsilon_0 \varepsilon_r A}{d}$.     - Energy Stored: $W = \frac{1}{2}QV = \frac{1}{2}CV^2 = \frac{Q^2}{2C}$.     - Discharge: $Q = Q_0 \exp(-\frac{t}{RC})$. The term $RC$ is the time constant.
• Magnetic Fields and Forces:     - Flux Density ($B$): Pattern sketches for straight wires, coils, and solenoids. Units: Tesla ($T$).     - Force on Conductor: Fleming’s Left-Hand Rule; $F = BIL \sin(\theta)$.     - Force on Moving Charge: $F = BQv \sin(\theta)$. Trapping of particles in Earth's magnetic field (Van Allen radiation belt).     - Hall Effect: Used to measure magnetic flux density ($B$).
• Electromagnetic Induction:     - Magnetic Flux ($\Phi$): $\Phi = BA$. Units: Weber ($Wb$).     - Faraday’s Law: Induced EMF equals the rate of change of magnetic flux linkage.     - Lenz’s Law: Direction of induced EMF; consistent with conservation of energy.     - Transformers: $\frac{V_s}{V_p} = \frac{N_s}{N_p} = \frac{I_p}{I_s}$.

Unit 2 Module 2: A.C. Theory and Electronics

• Alternating Currents:     - Sinusoidal properties: $x = x_0 \sin(\omega t)$.     - RMS Values: $\text{RMS} = \text{Peak}/\sqrt{2}$. Standard for quoting A.C. voltages.
• The p-n Junction Diode:     - Process: Depletion layer formation; forward and reverse bias current flow.     - Rectification: Half-wave and full-wave (bridge rectifier with 4 diodes).     - Smoothing: Use of capacitors; significance of the time constant ($RC$).     - Transistors: Junction transistor consists of two p-n junctions.
• Transducers:     - Input: LDRs, thermistors, microphones.     - Output: LEDs (with protective resistors), buzzers, relays.
• Operational Amplifiers (Op-amps):     - Ideal Properties: Infinite input impedance, infinite open-loop gain, zero output impedance.     - Applications: Comparators (sine to square wave), Inverting amplifiers (gain $G = -R_f/R_{in}$, virtual earth concept), Non-inverting amplifiers (gain $G = 1 + R_f/R_{in}$, high input impedance), Summing amplifiers, and Voltage followers (buffers).     - Saturation: Output cannot exceed the power supply voltage.
• Logic Gates:     - Types: NOT, AND, NAND, OR, NOR, EXOR, EXNOR.     - Combinations: Truth tables for up to two inputs; re-designing circuits using only NAND or only NOR gates.     - Storage/Counting: S-R flip-flops (as latches/memory), triggered bistables (T flip-flops), and 3-bit binary counters.

Unit 2 Module 3: Atomic and Nuclear Physics

• Particulate Nature of E-M Radiation:     - Photons: $E = hf$. Photoelectric emission explained via the photon model (Einstein's equation: $hf = \Phi + \frac{1}{2}mv^2_{max}$).     - Units: The electron-volt ($eV$).     - X-rays: Production via electron acceleration; line and continuous spectra ($I = I_0 \exp(-\mu x)$). Medical imaging/radiotherapy (CAT scanners).     - Wave-Particle Duality: De Broglie wavelength $\lambda = h/p$; evidence from electron diffraction.
• Atomic Structure:     - Geiger-Marsden Experiment: Alpha particle scattering provided evidence for the nuclear model.     - Isotopes: Same proton number, different nucleon number.     - Millikan’s Oil Drop Experiment: Evidence for the quantization of charge ($e = 1.60 \times 10^{-19}\,C$).
• Nuclear Processes:     - Energy-Mass Equivalence: $\Delta E = \Delta m c^2$.     - Binding Energy: Energy required to separate a nucleus into nucleons. Plotting binding energy per nucleon versus nucleon number to explain fission and fusion.     - Conservation: Nucleon number, proton number, energy, and charge are all conserved.
• Radioactivity:     - Nature: Spontaneous and random decay of nuclei.     - Emissions: Alpha ($\alpha$), Beta ($\beta$), and Gamma ($\gamma$) properties and detection (G-M tube, cloud chamber).     - Mathematics of Decay: Activity $A = \lambda N$; Decay Law $N = N_0 \exp(-\lambda t)$.     - Half-life ($t_{1/2}$): $\lambda t_{1/2} = 0.693$ (or $\ln(2)$).     - Safety: Biohazards of background radiation and safe handling/disposal of materials.

Outline of Assessment

• External Assessment (80%):     - Paper 01 (1h 30m): 45 multiple-choice questions (15 per module). Worth 40%.     - Paper 02 (2h 30m): Section A (3 structured questions on experimental skills) and Section B (3 essay questions). Worth 40%.
• Internal Assessment (20%):     - Portfolio of practical laboratory exercises assessing Analysis & Interpretation, Manipulation & Measurement, Observation, Recording & Reporting, and Planning & Designing.     - Minimum of 2 assessments per skill across Units.
• Private Candidates: Sit Paper 03B (Alternative to Internal Assessment), consisting of two practical questions.

Physical Constants and Units

• Gravitation Constant ($G$): $6.67 \times 10^{-11}\,N\,m^2\,kg^{-2}$.
• Acceleration due to gravity ($g$): $9.80\,m\,s^{-2}$.
• Speed of light ($c$): $3.00 \times 10^8\,m\,s^{-1}$.
• Planck Constant ($h$): $6.63 \times 10^{-34}\,J\,s$.
• Boltzmann Constant ($k$): $1.38 \times 10^{-23}\,J\,K^{-1}$.
• Molar Gas Constant ($R$): $8.31\,J\,K^{-1}\,mol^{-1}$.
• Stefan-Boltzmann Constant ($\sigma$): $5.67 \times 10^{-8}\,W\,m^{-2}\,K^{-4}$.
• Electron Charge ($e$): $1.60 \times 10^{-19}\,C$.
• Electron Mass ($m_e$): $9.11 \times 10^{-31}\,kg$.
• Permittivity of free space ($\varepsilon_0$): $8.85 \times 10^{-12}\,F\,m^{-1}$.
• Permeability of free space ($\mu_0$): $4\pi \times 10^{-7}\,H\,m^{-1}$.