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Various notes for NCEA/NZ Scholarship

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# NCEA/Scholarship Notes
These notes pertain to several NZ NCEA/Scholarship standards. I have split them into folders per subject, and the original
LaTeX code is available for most. Any errata/feedback encouraged either via email or the issue tracker.

Hopefully the folder structure is relatively straightforward.

## University Mathematics Book Reviews/Bibliography
See [this page](unibooks.md). Very work-in-progress; please note the disclaimer.

## Mathematics
### Level One
I am not currently tutoring L1, there is not much I have to add in the way of notes as most of the material
is either revision from Y9/10 or simple calculations.
 * Algebra (91027) and Tables, Equations and Graphs (91028): [weekly exercises](L1%20Maths/Algebra/algebra.pdf)
 * Trigonometry (91032): [worksheet](L1%20Maths/Trigonometry/level_1_trig.pdf), [homework](L1%20Maths/Trigonometry/level_1_trig1_hw.pdf).
 * Practice exams: [Algebra](L1%20Maths/Algebra/algebra_paper1.pdf)

In addition, I have some questions on [numeracy and basic skills](L1%20Maths/Numeracy/numeracy.pdf).

### Level Two
My new Level Two Mathematics notes are available [here](L2%20Maths/bookform.pdf). The sheets include:
 1. (2.1) 			Coordinate Geometry
 2. (2.4)			Arcs and Sectors of Circles
 3. (2.4) 			Trigonometry
 4. (2.2) 			Functions
 5. (2.2/2.6) 		Quadratic Modelling
 6. (2.6/2.14) 		Simultaneous Equations
 7. (2.6/2.14) 		Linear Inequations
 8. (2.6) 			The Quadratic Formula
 9. (2.2/2.6)		Exponential and Logarithmic Functions
 10. (2.2/2.6) 		Negative and Fractional Powers
 11. (2.7) 			Slopes and Differentiation
 12. (2.7) 			Tangent Lines and Approximation
 13. (2.7) 			Turning Points Optimisation
 14. (2.7) 			Anti-differentiation
 15. (2.7) 			Kinematics and Rates of Change
 16. (Stats?)		Counting and Combinatorics
 17. (2.3) 			Number Sequences and Fractals
 18. (2.5) 			Graphs and Networks
 19. (2.10/2.11)	The statistical enquiry process
 20. (2.9/2.11)		Sampling
 21. (2.9)			Statistical inference
 22. (2.12/2.13)	Probability and risk
 23. (2.12)			Probability distributions

There is also a [sheet](L3%20Maths/Foundations/diagn.pdf) of diagnostic questions that assess the bare minimum of skills and knowledge required for the transition to L3.

### Level Three and Scholarship Calculus
I have almost completed the process of reworking and reorganising my L3/Scholarship maths notes; I have written the following sets of notes, designed
to be used broadly in the given logical order and aligned with the L2 notes above.

1. _Down the River: Foundations for Scholarship_. a [set of notes](L3%20Maths/Foundations/foundations.pdf) covering basic set theory, combinatorics,
   and number theory, with proof writing and induction.
2. Linear programming (91574) and simultaneous equations (91587). a [set of notes](L3%20Maths/Linear/linear.pdf) from a proof-based
   perspective, although most non-easy proofs are clearly marked and optional. Some exercises are included.
3. Trigonometry (91575). a [set of notes](L3%20Maths/Trigonometry/trigonometry.pdf) which covers the definition of the trigonometric functions
   and proves various identities, with a view towards mix of geometric and analytical thinking. (Problem sets: [1](L3%20Maths/Trigonometry/exercises-1.pdf), [2](L3%20Maths/Trigonometry/exercises-2.pdf), [3](L3%20Maths/Trigonometry/exercises-3.pdf), [4](L3%20Maths/Trigonometry/exercises-4.pdf), [5](L3%20Maths/Trigonometry/exercises-5.pdf), [6](L3%20Maths/Trigonometry/exercises-6.pdf), [7](L3%20Maths/Trigonometry/exercises-7.pdf), [8](L3%20Maths/Trigonometry/exercises-8.pdf))
4. Calculus (91578 and 91579). a [set of notes](L3%20Maths/Calculus/bookform.pdf) containing both tutorial session material and homeworks
   with material ranging in difficulty from achieved to outstanding scholarship.
5. Algebra (91577). a set of notes entitled [_Solutions_](L3%20Maths/Algebra/solutions.pdf) designed for self-study for scholarship students
   (with [full answers to exercises](L3%20Maths/Algebra/solutions2.pdf)). There are a number of sections for further reading beyond the required
   material, and a great deal of geometry.
6. Conic sections (91573). a [set of notes](L3%20Maths/Geometry/geometry.pdf) in the form of a sequence of exercises. Solutions can be
   found [here](L3%20Maths/Geometry/geometry_with_solutions.pdf). This is currently a work in progress.

I also have [a document](L3%20Maths/Exams/exam-practice-qns.pdf) containing some additional exam practice questions (without solutions). Use
at your own risk.

One should note that the majority of my notes are at a slightly higher level than is strictly required. As such, students should be
guided through skipping or only lightly touching some sections (for example, the functional definition of the trig functions in my
trig notes is only of use to students that are very comfortable with the geometric definition of the functions from L2 or earlier).

The conic sections notes in particular require a significant amount of mathematical sophistication on the part of the student, and
as such I would probably only use them for scholarship students. (With the right mentoring, L3 students could probably profit from
them as well; if anyone does this, I would be intrigued to hear the results.)

**For the interested.** I am working on a revised version of my calculus notes; this is not complete yet, but what has been
done can be found [here](L3%20Maths/Calculus2/notes.pdf). There is a very definite philosophy that I am trying to convey with
these new notes, based somewhat on a mixture of numeric approximations and the treatment of elementary calculus given in
Loomis and Sternberg; my idea of the `correct' way to understand calculus has changed significantly from when I wrote my
older notes above, and I am no longer happy with them.

If the rewriting goes successfully, I will likely give a similar treatment to the algebra notes, as _Solutions_ is beginning
to bend under the weight of three or four years of constant bolting-on of new pieces of random mathematics.

### Level Three Statistics
I have written a set of very terse [notes](L3%20Statistics/stats.pdf).

## Physics
<!--### Level Two
 * Waves (91170), mechanics (91171), and electromagnetism (91172): [full set of notes](L2%20Physics/externals.pdf), including many diagrams and links to youtube videos,
   but (by design) with limited exercises. To be used with a workbook or similar set of problems.
   (Assignments: [1](L2%20Physics/problems/asst-mech-1.pdf), [2](L2%20Physics/problems/asst-mech-2.pdf), [3](L2%20Physics/problems/asst-mech-3.pdf), [4](L2%20Physics/problems/asst-mech-4.pdf))
 * Practice exams: [mechanics](L2%20Physics/Exams/mech.pdf), [electromagnetism](L2%20Physics/Exams/edyn.pdf), and [waves](L2%20Physics/Exams/waves.pdf).
 * Problem sets: [mechanics](L2%20Physics/problems/problems-mech.pdf), [waves](L2%20Physics/problems/problems-waves.pdf)

I do not intend to write modern physics notes for L2 at this point in time; my L3 notes revise this material and so can be used for this purpose.-->

### Level Three
 * Waves (91523), mechanics (91524), modern physics (91525), and electromagnetism (91526): [full set of notes](L3%20Physics/externals.pdf), much terser and much
   longer than level 2, ideal for motivated students for self-study. A large amount of interest material in modern physics is included. Recommend L2 calculus
   with concurrent L3 calculus, but not strictly required. (Very short summary of required mathematics in introductory chapter.)
 * Problem sets related to the above notes can be found [in a subfolder](L3%20Physics/sheets).

## General Science (Level One)
 * [Scientific Investigations and the Scientific Method](L1%20Science/Scientific%20Investigations.odt)
 * Biology (90948): [01 - Genetics and DNA](L1%20Science/Biology/level_1_bio_genes.pdf), [02 - Inheritance and Variation](L1%20Science/Biology/level_1_bio_inheritance.pdf), [03 - Reproduction and Variation](L1%20Science/Biology/level_1_bio_reprod.pdf)
 * Chemistry (90944): [Notes](L1%20Science/Chemistry/notes.pdf)

## Classical Studies
### Scholarship
 * [General exam advice](Scholarship%20Classics/examadvice.pdf).
 * [Basic reading list for a Greek focus](Scholarship%20Classics/reading%20lists.odt).
 * Aristophanes: [practice questions](Scholarship%20Classics/Aristophanes/aristophanes%20questions.odt) and [timeline](Scholarship%20Classics/Aristophanes/aristophanes%20timeline.odt).
 * Alexander the Great: [random notes on sources and early life](Scholarship%20Classics/Alexander%20the%20Great/sources%20and%20early%20life.odt).

**In progress:** Homeworks (and some other notes) for Alexander, general bibliography. Final plan is to have a full reading course written.

## Geography
 * [Key concepts](Geography/Key%20Concepts.odt).
 * Skills practice exams: Mahia: [Questions](Geography/L3-Skills-Mahia-qns.pdf), [Resources](Geography/L3-Skills-Mahia-res.pdf); Chatham Islands: [Questions](Geography/L3-Skills-Chathams-qns.pdf), [Resources](Geography/L3-Skills-Chathams-res.pdf)

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