# JUPEB WEEK 1: INTEGRATED MASTER PLAN
## ⚡ PHYSICS: Physical Quantities, Dimensions & Vectors
### Core Definitions
- Fundamental Quantities: Independent primary metrics (Mass $M$, Length $L$, Time $T$, Temperature $\theta$, Current $I$).
- Dimensional Homogeneity: Structural rule stating all terms in an equation must possess matching base units.
- Vector vs Scalar: Vectors contain absolute magnitude and directional alignment; scalars express magnitude exclusively.
### Key Formulas
- Force Equation Dimensions: $[Force]=M^1L^1T^{-2}$
- Vector Dot Scalar Product: $\vec{A}\cdot\vec{B}=AB\cos\theta$
- Vector Cross Product Magnitude: $|\vec{A}\times\vec{B}|=AB\sin\theta$
### 25-Mark Theory Essay Practice
- Q: Define the principle of dimensional homogeneity and evaluate whether the kinematic function $v^2=u^2+2as$ is dimensionally stable.
- Model Points:
1. Define the homogeneity principle clearly.
2. Evaluate left-hand side: $[v^2]=(L^1T^{-1})^2=L^2T^{-2}$.
3. Evaluate right-hand side components: $[u^2]=L^2T^{-2}$ and $[2as]=1\cdot(L^1T^{-2})\cdot(L^1)=L^2T^{-2}$.
4. Compare all terms to confirm matching dimensional arrays ($L^2T^{-2}$), validating structural consistency.
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## 🧪 CHEMISTRY: Data Measurements, Atomic Structure & Layouts
### Core Definitions
- Relative Atomic Mass ($A_r$): Calculated average atomic mass evaluated against $\frac{1}{12}$ of a stable $^{12}C$ isotope.
- Orbital Mechanics Rules: Aufbau states lowest energy configurations fill first; Pauli forbids matching quantum states; Hund requires half-filling subshells before pairing.
- Measurement Variances: Systematic variations alter accuracy in single directions; random variations alter precision unpredictably.
### Key Electron Configuration Structures
- Hydrogen ($H$): $1s^1$
- Carbon ($C$): $1s^2 2s^2 2p^2$
- Oxygen ($O$): $1s^2 2s^2 2p^4$
### 25-Mark Theory Essay Practice
- Q: Describe the four quantum integers ($n,l,m,s$) utilizing electronic energy distributions to account for chromium's exceptional configuration stability.
- Model Points:
1. State $n$ (principal energy level), $l$ (orbital subshell shape), $m$ (spatial orientation), and $s$ (spin orientation).
2. Express standard chromium configuration: $[Ar]3d^5 4s^1$.
3. Detail how the symmetric, half-filled $3d^5$ subshell maximizes exchange stability over an un-stabilized $3d^4 4s^2$ layout.
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## 🧬 BIOLOGY: Scientific Inquiries & Introduction to Biomolecules
### Core Definitions
- Scientific Methodology: Empirical loop consisting of Observation $\rightarrow$ Questioning $\rightarrow$ Hypothesis Formulation $\rightarrow$ Empirical Testing $\rightarrow$ Analytical Conclusion.
- Condensation Reaction: Synthesis mechanism pairing molecular structures while dropping $H_2O$ units.
- Hydrolysis Reaction: Cleavage mechanism splitting polymer chains by introducing reactive $H_2O$ units.
### Structural Biomolecule Frameworks
- Monosaccharides: Structural base $(CH_2O)_n$ linking into polysaccharides via glycosidic bridges.
- Amino Acids: Built from a central carbon bonded to an amino group ($-NH_2$), a carboxyl group ($-COOH$), and variable side-chains ($-R$).
### 25-Mark Theory Essay Practice
- Q: Detail the structured execution of a controlled biological experiment, explaining the role of a null hypothesis ($H_0$) in validating results.
- Model Points:
1. Isolate the independent experimental variable while binding all other background constants.
2. Detail quantitative data logging to counter observational bias.
3. Define $H_0$ as a baseline assumption asserting no actual variations exist between test subjects.
4. Use statistics to reject or fail to reject $H_0$, verifying if observed variances stem from variables or simple chance.
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