Add 'docs/cie3mz.md'

Reviewed-on: https://git.eggworld.tk/eggy/eifueo/pulls/6

docs/cie3mz.md

@@ -0,0 +1,2 @@
+
+## Introduction

docs/eng3uz.md

@@ -133,3 +133,7 @@ The course code for this page is **ENG3UZ**.
 	- e.g., *"I don't want to! That candy is MINE, and no one is going to take it from ME! Mine, mine, MINE!"*
  - Theme: The "main idea" or underlying meaning of a literary work, which can be given directly or indirectly.
 	- e.g., *"Never forget that* you are royalty, *and that hundreds of thousands of souls have suffered and perished so you could become what you are. By their sacrifices, you have been given the comforts you take for granted. Always remember them, so that their sacrifices shall never be without meaning."* (*Eon Fable*, ScytheRider)
+
+## Resources
+
+ - [Analysis of a Poem](/resources/g11/central-asserion-1.pdf)

docs/index.md

@@ -15,3 +15,7 @@ If you would like to contribute by submitting fixes, requesting pages, and/or co
 ## Source
 
 The source for Eifueo is available [here](https://git.eggworld.tk/eggy/eifueo).
+
+## Acknowledgements
+
+Thanks to James Su, Lakshy Gupta, and Vincent Guo for providing supplementary data for accuracy and conciseness.

docs/sph3u7.md

@@ -18,6 +18,10 @@ Every other SI unit is derived from the fundamental SI units. Memorise these!
 | Amount of substance | Mole | mol |
 | Luminous intensity | Candela | cd |
 
+!!! info "Reminder"
+    Note that on an assesment, you are expected to derive the SI unit expression given the equation of unit.
+    For example Force = mass x acceleration = mass x distance / time / time = $kg \times m \times s^{-2}$. 
+
 ### Metric prefixes
 
 Every SI unit can be expanded with metric prefixes.
@@ -36,6 +40,9 @@ Every SI unit can be expanded with metric prefixes.
 | peta- | P | $10^{15}$ | f | femto- |
 | exa- | E | $10^{18}$ | a | atto- |
 
+!!! note
+    For easier memorization, notice that most of these prefixes are in multiples of $3$. 
+
 ### Significant figures
 
  - The leftmost non-zero digit is the **most significant digit**.
@@ -112,7 +119,7 @@ Uncertainties are stated in the form of [value] ± [uncertainty]. A value is onl
 To determine a measurement's absolute uncertainty, if:
 
  - the instrument states its uncertainty, use that.
- - an analog instrument is used, the last digit is estimated and appended to the end of the reported value. The estimated digit is uncertain by 5 at its order of magnitude.
+ - an analog instrument is used, the uncertainty is half of the smallest scale.
  - a digital instrument is used, the last reported digit is uncertain by 1 at its order of magnitude.
 
 !!! example
@@ -133,8 +140,8 @@ Error bars represent the uncertainty of the data, typically representing that da
 ### Uncertainty of gradient and intercepts
 
 !!! note "Definition"
-    - The **line of best fit** is the line that passes through **all error bars** while passing as closely as possible to all data points.
-    - The **minimum and maximum lines** are lines that minimise/maximise their slopes while still passing through **all error bars.**
+    - The **line of best fit** is the line that passes through **as many error bars as possible** while passing as closely as possible to all data points.
+    - The **minimum and maximum lines** are lines that minimise/maximise their slopes while passing through the first and last **error bars**.
 
 !!! warning
     - Use solid lines for lines representing **continuous data** and dotted lines for **discrete data**.
@@ -142,13 +149,134 @@ Error bars represent the uncertainty of the data, typically representing that da
 <img src="/resources/images/error-slopes.png" width=700>(Source: Kognity)</img>
 
 The uncertainty of the **slope** of the line of best fit is the difference between the maximum and minimum slopes.
-$$m_{best fit} ± m_{max}-m_{min}$$
+$$m_{\text{best fit}} ± \frac{m_{\max}-m_{\min}}{2}$$
 The uncertainty of the **intercepts** is the difference between the intercepts of the maximum and minimum lines.
-$$intercept_{best fit} ± intercept_{max} - intercept_{min}$$
+$$\text{intercept}_{\text{best fit}} ± \frac{\text{intercept}_{\max} - \text{intercept} _{\min}}{2}$$
 
 
 ## 1.3 - Vectors and scalars
 
+!!! note "Definition"
+    - **Scalar:** A physical quantity with a numerical value (magnitude) and a unit.
+    - **Vector:** A physical quantity with a numerical value (magnitude), a unit, and a **direction.**
+        - The **minimum magnitude** for any vector must be $`\ge 0`$
+
+??? example
+    - Scalar quantities include speed, distance, mass, temperature, pressure, time, frequency, current, voltage, and more.
+    - Vector quantities include velocity, displacement, acceleration, force (e.g., weight), momentum, impulse, and more.
+
+Vectors are drawn as arrows whose length represents their scale/magnitude and their orientation refer to their direction. A variable representing a vector is written with a right-pointing arrow above it.
+
+ - The **standard form** of a vector is expressed as its magnitude followed by its unit followed by its direction in square brackets.
+$$\vec{a} = 1\text{ m }[N 45° E]$$
+ - The **component form** of a vector is expressed as the location of its head on a cartesian plane if its tail were at $(0, 0)$.
+$$\vec{a} = (1, 1)$$
+ - The **magnitude** of a vector can be expressed as the absolute value of a vector.
+$$|\vec{a}| = 1 \text{ m}$$
+
+
+### Adding/subtracting vectors diagrammatically
+
+1. Draw the first vector.
+2. Draw the second vector with its *tail* at the *head* of the first vector.
+3. Repeat step 2 as necessary for as many vectors as you want by attaching them to the *head* of the last vector.
+4. Draw a new (**resultant**) vector from the *tail* of the first vector to the *head* of the last vector.
+
+<img src="/resources/images/vector-add-direction.png" width=700>(Source: Kognity)</img>
+
+When subtracting a vector, **negate** the vector being subtracted by giving it an opposite direction and then add the vectors.
+
+<img src="/resources/images/vector-subtract-direction.png" width=700>(Source: Kognity)</img>
+
+!!! note
+    Notice that when we are subtracting vectors ($\vec{a} - \vec{b}$), we have **tail** to **tail** and the difference vector has a direction from ($\vec{b} to \vec{a}$)
+
+### Adding/subtracting vectors algebraically
+
+Vectors can be broken up into two vectors (**"components"**) laying on the x- and y-axes via trigonometry such that the resultant of the two components is the original vector. This is especially helpful when adding larger (3+) numbers of vectors.
+$$\vec{F}_x + \vec{F}_y = \vec{F}$$
+
+!!! info "Reminder"
+    The **component form** of a vector is expressed as $(|\vec{a}_x|, |\vec{a}_y|)$
+
+<img src="/resources/images/vector-simple-adding.png" width=700>(Source: Kognity)</img>
+
+By using the primary trignometric identities:
+$$
+|\vec{a}_{x}| = |\vec{a}|\cos\theta_{a} \\
+|\vec{a}_{y}| = |\vec{a}|\sin\theta_{a}
+$$
+
+<img src="/resources/images/vector-decomposition.png" width=700>(Source: Kognity)</img>
+
+Using their component forms, to:
+
+ - add two vectors, add their x- and y-coordinates together.
+ - subtract two vectors, subtract their x- and y-coordinates together.
+
+$$
+(a_{x}, a_{y}) + (b_{x}, b_{y}) = (a_{x} + b_{x}, a_{y} + b_{y}) \\
+(a_{x}, a_{y}) - (b_{x}, b_{y}) = (a_{x} - b_{x}, a_{y} - b_{y})
+$$
+
+The length of resultant vector can then be found using the Pythagorean theorem.
+
+$$
+|\vec{c}|=\sqrt{c_{x}^2 + c_{y}^2}
+$$
+
+To find the resultant direction, use inverse tan to calculate the angle of the vector using the lengths of its components.
+
+$$
+\theta_{c} = \tan^{-1}(\frac{c_y}{c_x})
+$$
+
+### Multiplying vectors and scalars
+
+The product of a vector multiplied by a scalar is a vector with a magnitude of the vector multiplied by the scalar with the same direction as the original vector.
+
+$$\vec{v} × s = (|\vec{v}|×s)[\theta_{v}]$$
+
+!!! example
+    $$3 \text{ m} · 47 \text{ ms}^{-1}[N20°E] = 141 \text{ ms}^{-1}[N20°E]$$
+
+## 2.1 - Motion
+
+### Models
+
+A **scientific model** is a simplification of a system based on assumptions used to explain or make predictions for that system.
+
+!!! note "Definition"
+    - **System**: An object or a connected group of objects.
+    - **Point particle assumption**: An assumption that models a system as a blob of matter. It is more reliable if the size and shape of the object(s) do not matter much.
+    - **Uniform motion**: The type of motion in which the speed of an object is constant.
+
+### Displaying motion
+
+Motion can be expressed visually using a **motion diagram** or a **position-time graph**.
+
+// TODO: insert motion diagram here because kognity bad
+
+A **position-time graph** expands on the motion diagram by specifying a precise **position** value on the vertical axis in addition to time on the horizontal axis. The line of best fit indicates the object's speed, as well as if it is accelerating or decelerating.
+
+<img src="/resources/images/position-time-graph.png" width=700>(Source: Kognity)</img>
+
+When the slope is:
+
+ - linear, the object is moving at a constant speed.
+ - exponential, the object is accelerating.
+ - logarithmic, the object is decelerating.
+
+## 2.2 - Forces
+
+## 2.3 - Work, energy, and power
+
+## 2.4 - Momentum and impulse
+
+## 3.1 - Thermal concepts
+
+## 3.2 - Modelling a gas
+
 ## Resources
 
  - [IB Physics Data Booklet](/resources/g11/ib-physics-data-booklet.pdf)