ib: add basic presentation information unorganised

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

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/ib.md

@@ -0,0 +1,57 @@
+# International Baccalaureate Diploma Program
+
+## Theory of Knowledge
+
+ - Presentation
+ - Essay
+
+ - Is a course
+
+## Extended Essay
+
+ - 4 000 word essays
+ - Letter grade
+ - 
+
+### Steps
+
+1. Select a topic
+2. Get matched with a mentor
+	- Mentor helps you out
+	- Mentor may be knowledgeable in the topic
+3. Formulate a research question
+4. Conduct research
+5. Write the paper
+
+### Timeline
+
+ - G11
+ - Feb/Mar
+	- Intro to EE presentation
+	- Declare topic and research question
+ - Apr/May
+
+ - Summer
+	- Write first full draft or extremely detailed outline
+
+- G12
+ - Oct-Nov
+	- Submit draft to mentor and edit draft
+ - Nov-Dec
+	- Final work due
+
+## CAS
+
+ - CAS committee is a thing
+
+## ManageBac
+
+ - Submit documents here
+ - Track CAS progress
+	- Supervisor review, evidence of experiences, and personal reflections
+ - Track EE progress
+ - Communicate with IB staff
+	- CAS advisors
+	- EE supervisors
+	- Teachers
+	- IB Coordinators

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

@@ -133,8 +133,8 @@ 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 **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 still passing through **all error bars.**
+    - 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**.
@@ -149,6 +149,85 @@ $$intercept_{best fit} ± intercept_{max} - intercept_{min}$$
 
 ## 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.**
+
+??? 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>
+
+### 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.
+
+$$
+\vec{c}_{direction} = \tan^{-1} \frac{c_y}{c_x}
+$$
+
+### 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
+    $$3 \text{ m} · 47 \text{ ms}^{-1}[N20°E] = 141 \text{ ms}^{-1}[N20°E]$$
+
 ## Resources
 
  - [IB Physics Data Booklet](/resources/g11/ib-physics-data-booklet.pdf)