--- /dev/null
+# Gases
+
+## Comibned gas equation
+
+$${P_1 V_1 \over T_1} = {P_2 V_2 \over T_2}$$
+
+## Perfect gas equation
+
+$$PV=nRT$$
+
+where
+$R =$ universal gas constant $= 8.31 \text{ J K}^{-1} \text{mol}^{-1}$
+$P$ is measured in kPa
+$V$ is measured in L
+$T$ is measured in K
+$n$ is no of mol of gas
+
+
+- **Standard temperature and pressure (STP)** - standard temperature is 0 $^\circ$ C or 273 K. Standar dpressure is 100.0 kPa
+- **Standard laboratory conditions (SLC)** - temperature 25 $^\circ$ C (298K), pressure 100.0 kPa
+
+## Molar gas volume
+
+> Equal volumes of all gases measured at the same temperature and pressure contain the same number of gas particles
+
+$\therefore$ 1 mole of any gas at SLC occupies 24.8L - **molar gas volume**
+
+$$n={V \over V_M}$$
+
+where $n$ = number of mol
+$V$ = actual volume (in litres)
+$V_m$ = molar volume of gas
+
+$$\therefore n_{SLC} = {V \over 24.8}$$
+
+## Molar volume
+
+Volume of a mole of a gas - depends on pressure & temperature
+Molar gas volume = $V_M = 24.8 \text{ L mol}^{-1}$ at SLC
+Use $n = {V \over V_m}$ like $n={m \over M}$
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- egotistical - e.g. tattoos (contrasting themes) etc
- moderately high IQ
- diction - indicates uneducation
+- charistmatic (e.g. cheques)
+- "honey"
+- family believes he is more innocent
+- diverts blame to others, justifies behaviour
+- desire for "American Dream"
+- assumes power over Perry
+- views himself as a victim of society
+- food
+- cautious of Perry due to tendency to suddenly take control
+
+
*Perry and Dick appear less genuinely criminal at the beginning of the novel*
- messy/materialistic - “Christ, Perry. You carry that junk everywhere?”
- "know the ins and outs of hunting gold"
- has trouble meeting deadlines - "if Dick had not hammered home the every-minute importance of the next twenty-four hours"
-- criminal past
+- criminal past
- "never drank coffeemy name sluger lolol"
- personal account of boyhood while in Mexico
- parents were rodeo riders
- two siblings and one inlaw committed suicide
- tattoos - more delicate / meaningful than Dick's (juxtaposition). contrasting themes
+- legs
+- snake in dreams
+- yellow parrot
+- tiger
+- guitar
+- family issues
+- childish
+- hymns/music
+- correcting grammar
+- premonition
+- idolises Willie-Jay
+- relationship with Dick as a substitute for Willie-Jay
+- motivated to murder so that he can be associated with Dick
+- idealistic
### Willie-Jay
- assistant to prison chaplain
- detail
- imagery
- mixed perspective
+
+## Creative response analysis
+
+- knowledge of other parts of text
+- minor characters
+- descriptive imagery
+- linking motif in scene transitions
+- long sentences
+- include obscure plot details
+- implicit explanation of people & emotions
+- contrasting voice of dialogue & narrations
+- use obvious/explicit motifs sparingly
+- past tense consistently
+- don't replicate events from original
+
+### Statement of intention
+
+- explore purpose & style
+- explain themes & symobls
--- /dev/null
+After Nancy's performance the previous night, she was clearly dilapidated and "barely looked fit to leave the house", according to her friend Susan Kidwell whom she met at the movies. boy, however, was as loud and expressive as ever - a quality that he could always be trusted for. As a basketball player, he had been taught to speak so that he was heard, and frequently translated his dominant behaviour into everyday life, much to the amusement of Nancy and her friend Sue Kidwell. The cinema was packed, despite the scorching squals of Holcomb, which even the locals struggled to become accustomed to.
+
+The weather of Mexico was of little concern to Dick and Perry, particularly Dick who was "as well-travelled as a politician" and boasted that he could cope with any living conditions. Perry, however, enforced that all they needed was an anonymous excursion until they were safe from the law. As Perry swallowed three aspirin tablets, one by one, he daydreamed of the riches they could accrue in these exotic destinations.
+
+---
+
+Dick woke up in a start, surpirsed to see the couch beneath him, and his mother standing in front of him in the doorway of the living room. It was a smally, musty space, and despite the sun streaming in from the bay windows, the room still felt dingy - partly owing to the dispersing layer of cigarette smoke from the previous night.
+
+Dick's stagnant body eventually came to its senses, as he recalled the events of the previous 36 hours. He was well-prepared for the exhaustion that would follow, but his family were utterly surprised to see him sleeping in so late. Dick stretched his arms and dragged himself off the couch at the request of his mother, then eh started cooking his breakfast - 4 eggs, several rashes of bacon, toast, scrolls, and strong coffee to wash it down.
+
+This was not a breakfast that Perry would approve of, but thankfully, for Dick, the pair had returned to their respective families. Perry's family was more suspicious of his absence than Dick's, but Perry was experienced in the art of convincing, and had no trouble dispelling his father's assumptions. However, even Perry was still uncomfortable to be in the vicinity of his family, particularly his sister who he had observed to be distant and ignorant of him lately.
+
+After waking from a short but deep sleep, Perry covered his previously bare tattoos with a checked shirt, then slid on some ripped blue jeans. Despite being utterly disinterested in working on Tex Smith's dilapidated property, he hoped that these jeans would be viewed favourably by his father. Perry downed his breakfast in his usual rushed and slapdash fashion, then hurriedly left the house without a word to his family. He took his guitar with him, which he was almost as attached to as his partner in crime. Admittedly, Perry had grown used to having Dick by his side, making witty jokes and showing off to Perry. However, this was a feeling that Perry knew well by now, having iterated through many "best friends".
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# Transformation
+**Order of operations:** DRT - Dilations, Reflections, Translations
+
## $f(x) = x^n$ to $f(x)=a(x-h)^n+K$##
- $|a|$ is the dilation factor of $|a|$ units parallel to $y$-axis or from $x$-axis
2. - Dilating from $y$-axis: $(x, y) \rightarrow (ax, y)$
- Replacing $x$ with $x \over a$ to obtain $y = f({x \over a})$
-For graph of $y={1 \over x}$, horizontal & vertical dilations are equivalent (symmetrical). If $y={a \over x}$, graph is contracted rather than dilated.
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+For graph of $y={1 \over x}$, horizontal & vertical dilations are equivalent (symmetrical). If $y={a \over x}$, graph is contracted rather than dilated.
+
+## Transformations from $f(x)$ to $y=Af[n(x+c)]+b$#
+
+Applies to exponential, log, trig, power, polynomial functions.
+Functions must be written in form $y=Af[n(x+c)] + b$
+
+$A$ - dilation by factor $A$ from $x$-axis (if $A<0$, reflection across $y$-axis)
+$n$ - dilation by factor $1 \over n$ from $y$-axis (if $n<0$, reflection across $x$-axis)
+$c$ - translation from $y$-axis ($x$-shift)
+$b$ - translation from $x$-axis ($y$-shift)
+
+## Power functions
+
+**Strictly increasing** on an interval where $x_2 > x_1 \implies f(x_2) > f(x_2)$ (including $x=0$)
+
+#### $n$ is odd and $n>1$:
+$f(-x)=-f(x)$
+
+#### $n$ is even and $n>1$:
+$f(-x)=f(x)$
+
+### Function $f(x)=x^{-1 \over n}$ where $n \in \mathbb{Z}^+$
+
+Mostly only on CAS.
+
+We can write $x^{-1 \over n} = {1 \over {x^{1 \over n}}} = {1 \over ^n \sqrt{x}}$n. Domain is: $\begin{cases} \mathbb{R} \setminus \{0\}\hspace{0.5em} \text{ if }n\text{ is odd} \\ \mathbb{R}^+ \hspace{2.6em}\text{if }n\text{ is even}\end{cases}$
+
+**Odd and even functions:**
+Function is even if it can be reflected across $y$-axis $\implies f(x)=f(-x)$
+If $n$ is odd, then $f$ is an odd function since $f(-x)=-f(x) \implies f(x)=-f(x)$
+
+## Combinations of functions (piecewise/hybrid)
+
+$$\text{e.g.}\quad f(x)=\begin{cases} ^3 \sqrt{x}, \hspace{2em} x \le 0 \\ 2, \hspace{3.4em} 0 < x < 2 \\ x, \hspace{3.4em} x \ge 2 \end{cases}$$
+
+Open circle - point included
+Closed circle - point not included
+
+### Sum, difference, product of functions
+| | | |
+|---|-----|-----|
+|sum|$f+g$|domain $= \text{dom}(f) \cap \text{dom}(g)$|
+|difference|$f-g$ or $g-f$|domain $=\text{dom}(f) \cap \text{dom}(g)$|
+|product|$f \times g$|domain $=\text{dom}(f) \cap \text{dom}(g)$|
+
+Addition of linear piecewise graphs - add $y$-values at key points
+
+Product functions:
+- product will equal 0 if one of the functions is equal to 0
+- turning point on one function does not equate to turning point on product
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$$\boldsymbol{u}={{\boldsymbol{a}\cdot\boldsymbol{b}}\over |\boldsymbol{b}|^2}\boldsymbol{b}=\left({\boldsymbol{a}\cdot{\boldsymbol{b} \over |\boldsymbol{b}|}}\right)\left({\boldsymbol{b} \over |\boldsymbol{b}|}\right)=(\boldsymbol{a} \cdot \hat{\boldsymbol{b}})\hat{\boldsymbol{b}}$$
+Scalar resolute of $\vec{a}$ on $\vec{b} = |\vec{u}| = \vec{a} \cdot \hat{\vec{b}}$
+
## Vector proofs
**Concurrent lines -** $\ge$ 3 lines intersect at a single point
**on CAS:** `angle([a b c], [1 0 0])` for angle between $a\vec{i} + b\vec{j} + c\vec{k}$ and $x$-axis
+## Collinearity
+
+Points $A, B, C$ are collinear iff $\vec{AC}=m\vec{AB} \text{ where } m \ne 0$