From: Andrew Lorimer <andrew@lorimer.id.au>
Date: Thu, 3 Jan 2019 02:56:05 +0000 (+1100)
Subject: Merge branch 'master' of ssh://charles/tank/andrew/school/notes
X-Git-Tag: yr12~288
X-Git-Url: https://git.lorimer.id.au/notes.git/diff_plain/3817bcdc33d972532ed8fabb75aed04c11421235?hp=37d8feb5693765d6396de584887203acbde4174f

Merge branch 'master' of ssh://charles/tank/andrew/school/notes
---

diff --git a/chem/energy.md b/chem/energy.md
new file mode 100644
index 0000000..c532be1
--- /dev/null
+++ b/chem/energy.md
@@ -0,0 +1,16 @@
+# Chemical energy
+
+Chemical energy = heat content = enthalpy
+
+$$\Delta H = H_{\text{products}} - H_{\text{reactants}}$$
+
+**Exothermic** - energy released from system  
+**Endothermic** - energy absorbed by system
+
+Must specify states (latent heat)
+
+## Calorimetry
+
+$$E = mc \Delta T$$
+
+$$\text{calibration factor} = {E \over \Delta T} = {VIt \over \Delta T} \quad \text{J/K}$$
\ No newline at end of file
diff --git a/english/cold-blood.md b/english/cold-blood.md
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index 0000000..de5d479
--- /dev/null
+++ b/english/cold-blood.md
@@ -0,0 +1,73 @@
+# *In Cold Blood* - Truman Capote
+
+## Setting
+
+**What does the setting of the text include?**
+
+- cultural information - America, small isolated community, agricultural economy, 1959
+- explicit mention of dates to set period (Nov 14, 1959)
+- Holcomb, Kansas - small town, "not a place that strangers come upon by chance"
+- introduction to characters - family interactions/relationships
+- integration of events & people to describe culture/period/location
+- "hip-high, sheep-slaughtering snows" - harsh weather
+- description of clothing - "narrow frontier trousers, Stevensons, and high heeled boots"
+- description of accent - "the local accent is barbed with a prairie twang"
+- landscape - dusty, dry flat, vast
+- low population
+- "few Americans [..] had ever heard of Holcomb"
+- dilapidated buildings, uniform through town
+
+**How do the setting and events work together?**
+
+**Foreshadowing**
+
+p 25, 41, 52, 63, 67
+
+- chapter titles - "the last to see them alive" etc
+- not going to church
+- ambiguous implications
+- “Chinese elms had turned into a tunnel of darkening green” (leading up to Clutters' house)
+- “until one morning in mid-November of 1959, few Americans [..] had ever heard of Holcomb”
+- Herbert “headed for home and the day’s work, unaware that it would be his last”
+- “if Dick had not hammered home the every-minute importance of the next twenty-four hours” - Dick and Perry planning
+- “the only sure thing is every one of them has got to go” - Dick
+- “four shotgun blasts that, all told, ended six human lives”
+- “Only now when I think back, I think somebody must have been hiding there. Maybe down among the trees. Somebody just waiting for me to leave”
+- dual narrative in chronological order approaching murder
+- - create a sense that the narrative will "collide"
+- - different settings, same time
+
+
+## Characters
+
+### Herbert Clutter
+
+- owns River Valley Farm
+- four children - two daughters + Nancy + Kenyon
+- successful - owns large property
+- "I'm not as poor as I look"
+
+### Nancy Clutter
+
+
+### Kenyon Clutter
+- 15
+- builds stuff
+
+
+### Dick Hickock
+
+- murders Clutter with Perry Smith
+- "Dick, the practical Dick"
+
+### Perry Smith
+
+- murders Clutter with Dick Hickock
+- breakfast - "three aspirin, cold root beer and a chain of Paul Mall cigarettes"
+- self-centred/egotistical - “Every time you see a mirror you go into a trance”
+- more open/prominent in text than Dick
+- 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
+- "never drank coffeemy name sluger lolol"
\ No newline at end of file
diff --git a/methods/polynomials.md b/methods/polynomials.md
index 0542afc..b80ea63 100644
--- a/methods/polynomials.md
+++ b/methods/polynomials.md
@@ -8,9 +8,43 @@
 **Perfect squares:** $a^2 \pm 2ab + b^2 = (a \pm b^2)$  
 **Completing the square (monic):** $x^2+bx+c=(x+{b\over2})^2+c-{b^2\over4}$  
 **Completing the square (non-monic):** $ax^2+bx+c=a(x-{b\over2a})^2+c-{b^2\over4a}$  
-**Quadratic formula:** $x={{-b\pm\sqrt{b^2-4ac}}\over2a}$ where $\Delta=b^2-4ac$
+**Quadratic formula:** $x={{-b\pm\sqrt{b^2-4ac}}\over2a}$ where $\Delta=b^2-4ac$ (if $\Delta$ is a perfect square, rational roots)
 
 #### Cubics
 **Difference of cubes:** $a^3 - b^3 = (a-b)(a^2 + ab + b^2)$  
 **Sum of cubes:** $a^3 + b^3 = (a+b)(a^2 - ab + b^2)$  
 **Perfect cubes:** $a^3 \pm 3a^2b + 3ab^2 \pm b^3 = (a \pm b)^3$  
+
+## Linear and quadratic graphs
+
+$$y=mx+c, \quad {x \over a} + {y \over b}=1$$
+
+Parallel lines - $m_1 = m_2$  
+Perpendicular lines - $m_1 \times m_2 = -1$
+
+
+## Cubic graphs
+
+$$y=a(x-b)^3 + c$$
+
+- $m=0$ at *stationary point of inflection*
+- in form $y=(x-a)^2(x-b)$, local max at $x=a$, local min at $x=b$
+- in form $y=a(x-b)(x-c)(x-d)$: $x$-intercepts at $b, c, d$
+
+
+## Quartic graphs
+
+$$y=ax^4$$
+
+$$=a(x-b)(x-c)(x-d)(x-e)$$
+
+$$=ax^4+cd^2 (c \ge 0)$$
+
+$$=ax^2(x-b)(x-c)$$
+
+$$=a(x-b)^2(x-c)^2$$
+
+$$=a(x-b)(x-c)^3$$
+
+where
+- $x$-intercepts at $x=b,c,d,e$
diff --git a/spec/prelim.md b/spec/prelim.md
index 586fc59..d158bbb 100644
--- a/spec/prelim.md
+++ b/spec/prelim.md
@@ -2,6 +2,9 @@
 
 ## Circular functions
 
+![](../methods/graphics/exact-values-1.png){#id .class height=150px}
+![](../methods/graphics/exact-values-2.png){#id .class height=150px}
+
 $\sin \theta$ - $y$-coord on unit circle  
 $\cos \theta$ - $x$-coord on unit circle  
 $\tan \theta = {\sin \theta \over \cos \theta}$
@@ -47,14 +50,31 @@ Sum of interior angles of $n$-sided polygon is $(n-2) \times 180^\circ$
 - ![](graphics/segment-angles.png){#id .class width=40%} angles in the same segment of a circle are equal
 - ![]()
 
+## Circles, ellipses and hyperbolas
+
+Standard form is $Ax^2+By^2+Cx+Dy=0$
+
+- if $A+B$ then circle
+- if $A>0$ and $B>0$ and $A\ne B$ then ellipse
+- if $A<0<B$ or $B<0<A$ then hyperbola
 
-## Ellipses and hyperbolas
+### Circles
 
-#### Ellipses
+$$(x-h)^2 + (y-k)^2 = r^2$$
+
+- centre $(h,k)$
+- radius $r$
+
+### Ellipses
 
 $${(x-h)^2 \over a^2}+{(y-k)^2 \over b^2} = 1$$
 
-#### Hyperbolas
+- centre $(h, k)$
+- $x$-radius $a$
+- $y$-radius $b$
+- $\therefore \text{width}=2a, \quad \text{height}=2b$
+
+### Hyperbolas
 
 $${(x-h)^2 \over a^2} - {(y-k)^2 \over b^2} = 1$$
 
@@ -63,3 +83,20 @@ $${(x-h)^2 \over a^2} - {(y-k)^2 \over b^2} = 1$$
 
 ${(x-h)^2 \over a^2} - {(y-k)^2 \over b^2} = 1$ and ${(y-k)^2 \over b^2} - {(x-h)^2 \over a^2} = 1$ are **conjugate hyperbolas**
 
+## Modulus function
+
+$$|x|=\sqrt{x^2}$$
+
+## Parametric equations
+
+### Circles
+$$\[\begin{cases}
+        x=a\cos t\\
+        y=a\sin t
+    \end{cases}
+\text{where radius} =a$$
+
+To convert to cartesian, factorise and use $\cos^2 x + \sin^2 x=1$
+
+$\cos^2 t + \sin^2 t = 1$  
+$\implies {\cos^2 \over \sin^2 t} + {\sin^2 t \over sin^2 t} = {1 \over \sin^2 t} \implies \csc^2 t - \cot^2 t$
diff --git a/spec/sampling.md b/spec/sampling.md
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+++ b/spec/sampling.md
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+# Sampling and Distributions
+
+**Population** - set of all eligible members  
+**Sample** - subset of population, may be representative of population  
+**Random sample** - every element of population has equal chance of selection  
+**Population proportion $p$** - proportion of individuals in population with an attribute  
+**Sample proportion $\^p$** -
+**Discrete random variable** - countable number of distinct values
+
+$$\sum \Pr(n)=1$$
+
+### Hypergeometric distribution
+
+$$\Pr(X=x) = {{{\begin{Bmatrix}
+  D \\
+  x \\
+  \end{Bmatrix}}\begin{Bmatrix} {N-D} \\ {n-x} \end{Bmatrix} }\over\begin{Bmatrix}N \\ n \end{Bmatrix}}$$
+
+
+### Generating random numbers
+Catalog -> `rand(a,b)` generates a random number between $a$ and $b$  
+`randlist(n,a,b)` generates $n$ random numbers between $a$ and $b$
+
+### Combinations
+
+CAS: Advanced -> `nCr(n,r)` $= ^nC_r$
+
+### Binomial distributions
+
+with replacement.
+
+probability of achieving $x$ successes in $n$ trials for random variable $X$:
+
+$$\Pr(X=x)=\begin{Bmatrix} n \\ x \end{Bmatrix} p^x (1-p)^{n-x} \quad \text{for }x = 0,1,2, \dots, n$$
+
+where $p$ = probability of success on each trial
+
+#### on CAS:
+
+`randBin(sample size, p^, no of samples)`
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