ib: add cas info

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

docs/eng3uz.md

@@ -1,4 +1,4 @@
-# Grade 11 HL English
+# HL English - A
 
 The course code for this page is **ENG3UZ**.
 
@@ -8,29 +8,33 @@ The course code for this page is **ENG3UZ**.
 
  - Allusion: A brief and indirect reference to a thing or idea of significance.
 	- e.g., *"Look at Einstein over there, thinking he's so smart."*
- - Anecdote: A short and interesting story or event used to support a point.
+ - Anecdote: A short and usually personal story used to support a point.
-	- e.g., *"You should all be grateful! When I was a young lad, we didn't have these fancy phones! We had to *talk* to people's *faces!"
+	- e.g., *"You should all be grateful! When I was a young lad, there was this girl that I liked, so what did I do about it? I went straight-up told to her face that I loved her! Of course, she smacked me away as if I were a stray dog, but if I was able to stand up to someone like her, you young'uns should be able to send a simple text message!"*
  - Hyperbole: An exaggeration for the purpose of emphasis.
 	- e.g., *"If you null pointer me one more time I am going to crush you into two billion pieces!"*
- - Imagery: The usage of figurative language to describe concepts in a way that invokes the **senses**.
+ - Imagery: The use of words to describe concepts in a way that involves the five senses.
 	- e.g., *"My mother…how sweet and juicy her tender limbs are."*
- - Metaphor: An implicit comparison between two unlike things without the use of "like" or "as".
+ - Metaphor: An implicit comparison between two unlike things without the use of "like" or "as", used especially to describe abstract ideas indirectly.
 	- e.g., *"My computer is an absolute potato."*
- - Simile: An explicit comparison between two unlike things *with* the use of "like" or "as".
+ - Simile: An explicit comparison between two unlike things *with* the use of "like" or "as", used especially to describe abstract ideas indirectly.
 	- e.g., *"She's as stupid as an elephant!"*
- - Litotes: An understatement by negating a positive or negative expression.
+ - Litotes: An understatement by negating a very positive or negative expression.
 	- e.g., *"My marks aren't the best in the world."*
  - Personification: The application of human concepts to non-humans, such as human-like speech. This is a common example of a metaphor.
 	- e.g., *The rock blinked at me with a cute face unlike any other I had seen before. "…Owo. Uwu?"*
- - Adjectives and adverbs: Words that describe and modify nouns and verbs, respectively.
+ - Adjectives and adverbs: Words that directly describe and modify nouns and verbs, respectively.
 	- e.g., *The traitorous man died painfully.*
 
 ### Sound
 
- - Alliteration: A number of words with the same beginning consonant sound that appear close together in sequence.
+ - Alliteration: A number of words with the same beginning sound that appear close together.
 	- e.g., *The dancing damsel dazzled the crowd.*
- - Assonance: A repetition of similar vowel sounds in words close to each other in a sentence.
+ - Assonance: A number of words with the same vowel sound, not at the beginning, that appear close together.
-	- e.g., *"Oh, please let her go."*
+	- e.g., *The cat in the hat knows a lot about that!*
+ - Cacophony: The use of words and phrases that are harsh to the ear by using consonants that require pressure to to say (e.g., p, b, d, g, k, ch-, sh-).
+	- e.g., *How much wood could a woodchuck chuck if a woodchuck could chuck wood?*
+ - Consonance: A number of words with the same consonant sound, not at the beginning, that appear close together.
+	- e.g., *Shelley sells shells by the seashore.*
  - Dialect: A regional variety of language with spelling, grammar, and pronunciation that differentiates a population from others around them.
 	- e.g., *"There's five of them dirty ducks flappin' out and about, sir!"*
  - Euphony: The use of words and phrases that are pleasing to the ear by using long vowel sounds, harmonious constants (l, m, n, r, f, v), and soft consonants or semi-vowels (w, s, y, th, wh).
@@ -46,25 +50,25 @@ The course code for this page is **ENG3UZ**.
  - Rhyme scheme: The rhyming pattern or structure at the end of each line of poetry.
 	- e.g., the above poem uses ABAB as its rhyme scheme.
  - Rhythm: The usage of stressed and unstressed syllables to demonstrate patterns, especially in verses.
-	- Anapest: Three syllables, in which the first two are unstressed while the last is stressed.
+	- Anapest: Two unstressed syllables followed by a stressed syllable (uu/).
-		- e.g., *"'Twas the* ***night*** *before* ***Christ****mas and* ***all*** *through the* ***house****"*
+		- e.g., *"Understand?"*
-	- Dactyl: Three syllables, in which the first is stressed while the rest are unstressed.
+	- Dactyl: A stressed syllable followed by two unstressed syllables (/uu).
 		- e.g., *"Marvelous!"*
-	- Iamb: Two syllables, in which the first is unstressed while the second is stressed.
+	- Iamb: An unstressed syllable followed by a stressed syllable (u/).
-		- e.g., *"You* ***stu****pid* ***id****iot."*
+		- e.g., *To be, or not to be, that is the question.*
-	- Spondee: Two syllables, both of which are stressed.
+	- Spondee: A stressed syllable followed by another stressed syllable (//).
-		- e.g., *"Rage, rage against the dying of the light"* (Dylan Thomas)
+		- e.g., *"Rage, rage against the dying of the light."* ("Do not go gentle into that good night", Dylan Thomas)
-	- Trochee: Two syllables, in which the first is stressed while the second is unstressed.
+	- Trochee: A stressed syllable followed an unstressed syllable (/u).
-		- e.g., *Double, double, toil and trouble* (William Shakespeare)
+		- e.g., *Double, double, toil and trouble* (*Macbeth*, William Shakespeare)
 
 ### Organisation and Pace
 
  - Blank verse: An non-rhyming verse with a regular rhythmic structure, most commonly iambic pentameter (10 syllables/line, unstressed-to-stressed pattern)
-	- e.g., *But, woe is me, you are so sick of late, / So far from cheer and from your former state* (William Shakespeare)
+	- e.g., *But, woe is me, you are so sick of late, / So far from cheer and from your former state.* (*Hamlet*, William Shakespeare)
  - Enjambment: A single thought in a line of poetry using two lines.
-	- e.g., *If I were a potato / The world would be a tomato.*
+	- e.g., *The world / is a tomato.*
- - Caesura: A pause, represented by two vertical lines ("||"), most commonly found in the middle of a line. Masculine caesurae follow stressed syllables while feminine caesurae follow ununstressed ones. They are also distinguished by their location in the line: Caesurae near the beginning, middle, or end of a line are referred to as initial, medial, and terminal caesurae, respectively.
+ - Caesura: A pause in a poem used to emphasise a phrase.
-	- e.g., *You're stupid! || But so am I.*
+	- e.g., *I, am intellectual, make no speling errors whatsoever.*
  - Form:
 	- Ballad: A poetic story set to music relying on simple language, commonly containing romance and tragedy.
 	- Concrete poem: A poem written, arranged, or "drawn" in a way that its visual appearance is most important in conveying meaning.
@@ -79,7 +83,8 @@ The course code for this page is **ENG3UZ**.
  - Genre: A work classified by its form, content, and style. Poetry, fiction, drama, and non-fiction are the four main genres of literature.
  - Line: A typically straight sequence of characters that ends at the last character before a newline.
  - Meter: The pattern of stressed and unstressed syllables in a verse or poem.
- - Stanza: A collection of four or more lines of poetry with with a fixed length, meter, or rhyme scheme, similar to a paragraph in prose.
+ - Point of view: The perspective that a literary work is written from. First person usually focuses more on characters while third person perspectives focus more on plot.
+ - Stanza: A collection of four or more lines of poetry with with a fixed length, meter, or rhyme scheme, similar to a paragraph in prose. However, it is not paragraph.
  - Sentence types: The use of simple, compound, complex, and compound-complex sentences.
  - Sentence lengths: The number of characters or words present in a sentence.
  - Syntax: A set of rules in a language regarding the order of words.
@@ -92,7 +97,7 @@ The course code for this page is **ENG3UZ**.
 	- e.g., *She was beautiful.*
  - Allegory: The use of characters and events to describe an abstract idea to teach a moral lesson.
 	- e.g., *Animal Farm* by George Orwell, which uses farm animals and their actions to describe the Russian Revolution.
- - Ambiguity: A statement or phrase whose meaning is unclear. This can usually be resolved via context.
+ - Ambiguity: A statement or phrase whose meaning is unclear or can have multiple different meanings. This can usually be resolved via context. Strongly recommended to be used in poetry analysis.
 	- e.g., *Nintendo sold 22 million of them.*
  - Colloquialism: The use of informal phrases or slang in writing.
 	- e.g., *"Pog!"*
@@ -101,13 +106,13 @@ The course code for this page is **ENG3UZ**.
  - Connotation: An implied meaning from a phrase that differs from its explicit and direct meaning.
 	- e.g., *I carried him for the entire assignment.*
  - Contrast/Juxtaposition: A comparison between multiple ideas or things by placing them side by side.
-	- e.g., *It was the best of times, it was the worst of times…* (Charles Dickens)
+	- e.g., *It was the best of times, it was the worst of times…* (*A Tale of Two Cities*, Charles Dickens)
  - Denotation: The literal meaning of a word.
 	- e.g., *"My old computer no longer functions."*
  - Diction: The word choice used by a speaker or writer to create an effect.
 	- e.g., *"I shall take Her Majesty back to the carriage."*
  - Epigram: A brief, interesting, memorable, and sometimes surprising or satirical statement.
-	- e.g., *"No one can make you efel inferior without your consent."* (Eleanor Roosevelt)
+	- e.g., *"No one can make you feel inferior without your consent."* (Eleanor Roosevelt)
  - Irony: An unexpected event or statement revealing what was believed to be true was false.
 	- e.g., *Thunder boomed as rain poured down all around the classroom. "Nice weather we're having today."* (Verbal)
 	- e.g., *The fire station burned down.* (Situational)
@@ -115,11 +120,11 @@ The course code for this page is **ENG3UZ**.
  - Jargon: Specialised terms that use actual words, which are usually unfamiliar to the layman.
 	- e.g., *p53 is responsible for holding the cell cycle at the G1/S checkpoint and will induce apoptosis if damage to the cell's deoxyribonucleic acid is too great.*
  - Motif: An recurring object or idea used to explain the theme.
-	- e.g., The usage of life in Maycomb to show goodness and recurring images of gloomy areas supports the central idea of co-existence of good and evil.
+	- e.g., In *To Kill a Mockingbird* by Harper Lee, The usage of life in Maycomb to show goodness and recurring images of gloomy areas supports the central idea of co-existence of good and evil.
  - Oxymoron: The pairing of two opposing or contradictory words.
 	- e.g., *It was her only choice.*
  - Paradox: A statement that appears to be self-contradictory at first glance, typically used to allow the reader to think over an idea differently.
-	- e.g., *All animals are equal, but some are more equal than others.* (George Orwell)
+	- e.g., *All animals are equal, but some are more equal than others.* (*Animal Farm*, George Orwell)
  - Pathetic fallacy: A form of personification in which inanimate objects in nature are given emotions.
 	- e.g., *The wind roared as the earth shook in fury at our insolence.*
  - Symbol: The use of objects to represent an abstract idea.
@@ -127,4 +132,8 @@ The course code for this page is **ENG3UZ**.
  - Tone: The attitude of a writer or character toward a subject or audience, typically through word choice.
 	- 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.* (ScytheRider)
+	- 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 +1,121 @@
+# 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
+
+ - Expanded to Creativity, Activity, and Service
+ - Completion is requirement for IB Diploma
+ - CAS committee is a thing
+ - **All activities must be confirmed by a supervisor**
+
+### Learning outcomes
+
+Each of the following must be completed at least once:
+
+ - Increased **awareness** of strengths and areas for growth
+ - Undertaking **new challenges** and developing **new skills**
+ - **Plan and initiate** a CAS experience
+ - Showing **perseverance** and **commitment**
+ - **Working collaboratively** with others
+ - Engaged with issues of **global importance**
+ - Consideration of **ethical implications**
+ - Takes place over at least 1 month
+
+### Creativity
+
+ - Any art or experience that involves creative thinking that ends in a sharable product
+	- Organising a club
+	- Music
+	- School play/drama club
+	- Lessons in the arts
+	- Cooking classes
+	- Martial arts
+	- Creative writing
+ - Must be heavily supported by evidence
+
+### Activity
+
+ - Physical exertion contributing to a healthy lifestyle with an end goal
+	- School teams
+	- Intermural sports
+	- Community sporting events
+	- Outdoor recreations
+	- Classes
+ - **Personal goals must be set**
+
+### Service
+
+ - Unpaid voluntary experience that has a learning benefit
+	- Volunteering at camps, hospitals, seniors' homes
+	- Fundraising
+	- Homework clubs/volunteer tutoring
+	- Online volunteering
+	- Student Council
+	- Red Cross, Cancer Society, etc.
+
+### Activity requirements
+
+ - 1 CAS project (at least 1 C/A or /S spanning at least one month)
+ - 1 primary commitment of each C/A and /S each year
+ - 2 or 3 additional shorter secondary activities in C/A or /S as available
+
+### ManageBac and CAS
+
+ - Propose an experience
+	- What do I plan to do and what do I hope to achieve?
+ - Engage in the experience
+ - Reflect on the experience
+	- What evidence is there that I achieved my goals?
+ - Once the experience is finished, request a supervisor review via ManageBac
+
+## ManageBac
+
+ - Submit documents here
+ - Track CAS progress
+	- Supervisor review, evidence of experiences, and personal reflections
+	- Activities must be reviewed here before it begins
+ - 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/mhf4u7.md

@@ -1,8 +1,24 @@
-# Grade 11 Math - Advanced Functions
+# SL Math - Analysis and Approaches - A
 
 The course code for this page is **MHF4U7**.
 
+## 4 - Statistics and probability
+
+!!! note "Definition"
+    - **Descriptive statistics:** The use of methods to organise, display, and describe data by using various charts and summary methods to reduce data to a manageable size.
+    - **Inferential statistics:** The use of samples to make judgements about a population.
+    - **Data set:** A collection of data with elements and observations, typically in the form of a table. It is similar to a map or dictionary in programming.
+    - **Element:** The name of an observation(s), similar to a key to a map/dictionary in programming.
+    - **Observation:** The collected data linked to an element, similar to a value to a map/dictionary in programming.
+    - **Raw data:** Data collected prior to processing or ranking.
+
+### Frequency distribution
+
+
+
 ## Resources
 
+ - [IB Math Analysis and Approaches Syllabus](/resources/g11/ib-math-syllabus.pdf)
+ - [IB Math Analysis and Approaches Formula Booklet](/resources/g11/ib-math-data-booklet.pdf)
  - [Calculus and Vectors 12 Textbook](/resources/g11/calculus-vectors-textbook.pdf)
  - [Course Pack Unit 1: Descriptive Statistics](/resources/g11/s1cp1.pdf)

docs/sch3uz.md

@@ -1,12 +1,24 @@
-# Grade 11 HL Chemistry
+# HL Chemistry - A
 
 The course code for this page is **SCH3UZ**.
 
+## 11.1 - Uncertainties and errors in measurement and results
+
+!!! info
+    Please see [SL Physics](/sph3u7/#12-uncertainties-and-errors) for more information.
+
+## 11.2 - Graphical techniques
+
+
+
+## 11.3 - Spectroscopic identification of organic compounds
+
 ## Resources
 
- - [IB Chemistry Data Booklet](/resources/g11/ib-chemistry-data-booklet.pdf
+ - [IB Chemistry Data Booklet](/resources/g11/ib-chemistry-data-booklet.pdf)
+ - [IB HL Chemistry Syllabus](/resources/g11/ib-chemistry-syllabus.pdf)
  - [Significant Figures/Digits](/resources/g11/chemistry-sig-figs.pdf)
- - [Error Analysis and Significant Figures (long)](/resources/g11/error-analysis-sig-figs.pdf))
+ - [Error Analysis and Significant Figures (long)](/resources/g11/error-analysis-sig-figs.pdf)
  - [General Guidelines for Writing a Formal Laboratory Report](/resources/g11/lab-report-guidelines.pdf)
  - [Designing an IB Investigation](/resources/g11/designing-investigation.pdf)
 

docs/sph3u7.md

@@ -1,8 +1,237 @@
-# Grade 11 SL Physics
+# SL Physics - A
 
 The course code for this page is **SPH3U7**.
 
+## 1.1 - Measurements in physics
+
+### Fundamental units
+
+Every other SI unit is derived from the fundamental SI units. Memorise these!
+
+| Quantity type | Unit | Symbol |
+| --- | --- | --- |
+| Time | Second | s |
+| Distance | Metre | m |
+| Mass | Kilogram | kg |
+| Electric current | Ampere | A |
+| Temperature | Kelvin | K |
+| Amount of substance | Mole | mol |
+| Luminous intensity | Candela | cd |
+
+### Metric prefixes
+
+Every SI unit can be expanded with metric prefixes.
+
+!!! example
+    milli + metre = millimetre ($10^{-3}$) m
+
+| Prefix | Abbreviation | Value | Inverse ($10^{-n}$) abbreviation | Inverse prefix |
+| --- | --- | --- | --- | --- |
+| deca- | da | $10^1$ | d | deci- |
+| hecto- | h | $10^2$ | c | centi- |
+| kilo- | k | $10^3$ | m | milli- |
+| mega- | M | $10^6$ | µ | micro- |
+| giga- | G | $10^9$ | n | nano- |
+| tera- | T | $10^{12}$ | p | pico- |
+| peta- | P | $10^{15}$ | f | femto- |
+| exa- | E | $10^{18}$ | a | atto- |
+
+### Significant figures
+
+ - The leftmost non-zero digit is the **most significant digit**.
+ - If there is no decimal point, the rightmost non-zero digit is the **least significant digit**.
+	- Otherwise, the right-most digit (including zeroes) is the least significant digit.
+ - All digits between the most and least significant digits are significant.
+ - Pure (discrete) numbers are unitless and have infinite significant figures.
+
+!!! example
+    In $123000$, there are 3 significant digits.<br>
+    In $0.1230$, there are 4 significant digits.
+
+ - When adding or subtracting significant figures, the answer has the **same number of decimals** as the number with the lowest number of decimal points.
+ - When multiplying or dividing significant figures, the answer has the **same number of significant figures** as the number with the lowest number of significant figures.
+ - Values of a calculated result can be **no more precise** than the least precise value used.
+
+!!! example
+    $$1.25 + 1.20 = 2.45$$
+    $$1.24 + 1.2 = 2.4$$
+    $$1.2 × 2 = 2$$
+    $$1.2 × 2.0 = 2.4$$
+
+!!! warning
+    When rounding an answer with significant figures, if the **least significant figure** is $5$, round up only if the **second-least** significant figure is **odd**.
+
+    $$1.25 + 1.2 = 2.4$$
+    $$1.35 + 1.2 = 2.6$$
+
+### Scientific notation
+
+Scientific notation is written in the form of $m×10^{n}$, where $1 \leq m < 10, n \in \mathbb{Z}$. All digits before the multiplication sign in scientific notation are significant.<br>
+
+!!! example
+    The speed of light is 300 000 000 ms<sup>-1</sup>, or $3×10^8$ ms<sup>-1</sup>.
+
+### Orders of magnitude
+
+The order of magnitude of a number can be found by converting it to scientific notation and taking its power of 10.
+
+!!! example
+    - The order of magnitude of $212000$, or $2.12×10^{5}$, is 5.
+    - The order of magnitude of $0.212$, or $2.12×10^{-1}$, is -1.
+
+## 1.2 - Uncertainties and errors
+
+### Random and systematic errors
+
+| Random error | Systematic error |
+| --- | --- |
+| Caused by imperfect measurements and is present in every measurement. | Caused by a flaw in experiment design or in the procedure. |
+| Can be reduced (but not avoided) by repeated trials or measurements. | Cannot be reduced by repeated measurements, but can be avoided completely. |
+| Error in precision. | Error in accuracy. |
+
+!!! example
+    - The failure to account for fluid evaporating at high temperatures is a systematic error, as it cannot be minimised by repeated measurements.
+    - The addition of slightly more solute due to uncertainty in instrument data is a random error, as it can be reduced by averaging the result of multiple trials.
+
+<img src="/resources/images/types-of-error.png" width=700>(Source: Kognity)</img>
+
+### Uncertainties
+
+Uncertainties are stated in the form of [value] ± [uncertainty]. A value is only as precise as its absolute uncertainty. Absolute uncertainty of **measurement** is usually represented to only 1 significant digit.
+
+!!! note
+    Variables with uncertainty use an uppercase delta for their uncertainty value: $a ± \Delta a$
+
+ - The absolute uncertainty of a number is written in the same unit as the value.
+ - The percentage uncertainty of a number is the written as a percentage of the value.
+
+!!! example
+    - Absolute uncertainty: 1.0 g ± 0.1 g
+    - Percentage uncertainty: 1.0 g ± 10%
+
+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.
+ - a digital instrument is used, the last reported digit is uncertain by 1 at its order of magnitude.
+
+!!! example
+    - A ruler has millimetre markings. A pencil placed alongside the ruler has its tip just past 14 mm but before 15 mm. The pencil is 14.5 mm ± 0.5 mm long.
+    - A digital scale reads 0.66 kg for the mass of a human body. The human body has a mass of 0.66 kg ± 0.01 kg.
+
+See [Dealing with Uncertainties](/resources/g11/physics-uncertainties.pdf) for how to perform **operations with uncertainties**.
+
+### Error bars
+
+Error bars represent the uncertainty of the data, typically representing that data point's standard deviation, and can be both horizontal or vertical.
+
+<img src="/resources/images/error-bars.png" width=600>(Source: Kognity)</img>
+
+!!! note
+    On a graph, a data point with uncertain values is written as $(x ± \Delta x, y ± \Delta y)$
+
+### Uncertainty of gradient and intercepts
+
+!!! note "Definition"
+    - 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**.
+
+<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.
+$$m_{best fit} ± m_{max}-m_{min}$$
+The uncertainty of the **intercepts** is the difference between the intercepts of the maximum and minimum lines.
+$$intercept_{best fit} ± intercept_{max} - intercept_{min}$$
+
+
+## 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)
+ - [IB SL Physics Syllabus](/resources/g11/ib-physics-syllabus.pdf)
  - [Dealing with Uncertainties](/resources/g11/physics-uncertainties.pdf)
-
+ - [Linearising Data](/resources/g11/linearising-data.pdf)
+ - [External: IB Physics Notes](https://ibphysics.org)

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-  - G11 SL Math - Advanced Functions: mhf4u7.md
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