项目作者: aelzenaar

项目描述 :
Various notes for NCEA/NZ Scholarship
高级语言: TeX
项目地址: git://github.com/aelzenaar/ncea-notes.git
创建时间: 2017-11-23T20:00:52Z
项目社区:https://github.com/aelzenaar/ncea-notes

开源协议:

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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. 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.

In addition, I have some questions on numeracy and basic skills.

Level Two

My new Level Two Mathematics notes are available here. 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 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 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 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 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, 2, 3, 4, 5, 6, 7, 8)
  4. Calculus (91578 and 91579). a set of notes 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 designed for self-study for scholarship students
    (with full answers to exercises). 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 in the form of a sequence of exercises. Solutions can be
    found here. This is currently a work in progress.

I also have a document 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. 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.

Physics

Level Three

  • Waves (91523), mechanics (91524), modern physics (91525), and electromagnetism (91526): full set of notes, 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.

General Science (Level One)

Classical Studies

Scholarship

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

Geography

homework-solutions_1647074251663.pdf
notes_1647074251843.pdf
exam-practice-qns_1647074251988.pdf
diagn_1647074252028.pdf
foundations_1647074252067.pdf
geometry_1647074252140.pdf
geometry_with_solutions_1647074252288.pdf
linear_1647074252433.pdf
exercises-1-solns_1647074252763.pdf
exercises-1_1647074252827.pdf
exercises-2-solns_1647074252883.pdf
exercises-2_1647074252993.pdf
exercises-3-solns_1647074253057.pdf
exercises-3_1647074253154.pdf
exercises-4-solns_1647074253278.pdf
exercises-4_1647074253356.pdf
exercises-5-solns_1647074253397.pdf
exercises-5_1647074253464.pdf
exercises-6-solns_1647074253515.pdf
exercises-6_1647074253593.pdf
exercises-7-solns_1647074253737.pdf
exercises-7_1647074253858.pdf
exercises-8_1647074253871.pdf
trigonometry_1647074253943.pdf
externals_1647074254716.pdf
sheet1.1-1.5_1647074255672.pdf
sheet1.1-solutions_1647074255709.pdf
sheet1.1_1647074255777.pdf
sheet1.2_1647074255792.pdf
sheet1.3_1647074255877.pdf
sheet1.4_1647074255889.pdf
sheet3.1_1647074255924.pdf
stats-figure0_1647074256101.pdf
stats_1647074256127.pdf
examadvice_1647074256208.pdf
12-parametric-hw_1647074249624.pdf
12-parametric_1647074249648.pdf
13-sequences-hw_1647074249674.pdf
13-sequences_1647074249705.pdf
14-diffrev-hw_1647074249734.pdf
14-diffrev_1647074249757.pdf
14a-workedsol-cone_1647074249773.pdf
15-approximatingareas-hw_1647074249797.pdf
15-approximatingareas_1647074249824.pdf
16-antidifferentiation-hw_1647074249861.pdf
16-antidifferentiation_1647074249879.pdf
17-ftc-hw_1647074249906.pdf
17-ftc_1647074249952.pdf
18-subsn-hw_1647074249998.pdf
18-subsn_1647074250047.pdf
19-diffeqs-hw_1647074250069.pdf
19-diffeqs_1647074250086.pdf
20-parfracs-hw_1647074250105.pdf
20-parfracs_1647074250125.pdf
21-parts-hw_1647074250174.pdf
21-parts_1647074250290.pdf
22-summing-hw_1647074250316.pdf
22-summing_1647074250342.pdf
23-trigsubsn-hw_1647074250385.pdf
23-trigsubsn_1647074250420.pdf
24-kinematics-hw_1647074250448.pdf
24-kinematics_1647074250486.pdf
25-intrev-hw_1647074250523.pdf
25-intrev_1647074250561.pdf
26-moreprobs_1647074250611.pdf
EX-examadvice_1647074250643.pdf
RV-functions_1647074250665.pdf
Scholarship-Calculus-formulae-booklet_1647074250758.pdf
asst-differentiation_1647074250841.pdf
asst-integration_1647074250941.pdf
bookform_1647074251185.pdf
13-optimisation-hw_1647074246845.pdf
13-optimisation_1647074246873.pdf
14-antidifferentiation-hw_1647074246899.pdf
14-antidifferentiation_1647074246922.pdf
15-kinematics-hw_1647074246951.pdf
15-kinematics_1647074246970.pdf
16-counting-hw_1647074247010.pdf
16-counting_1647074247051.pdf
17-sequences-hw_1647074247093.pdf
17-sequences_1647074247195.pdf
18-graphs-hw_1647074247252.pdf
18-graphs_1647074247270.pdf
19-stats1-hw_1647074247368.pdf
19-stats1_1647074247407.pdf
20-stats2-hw_1647074247452.pdf
20-stats2_1647074247481.pdf
21-inference-hw_1647074247500.pdf
21-inference_1647074247520.pdf
22-prob1-hw_1647074247558.pdf
22-prob1_1647074247583.pdf
23-prob2-hw_1647074247612.pdf
23-prob2_1647074247655.pdf
98-y11diags_1647074247686.pdf
99-bibliography_1647074247709.pdf
bookform_1647074248007.pdf
ncea2-probability_1647074248581.pdf
solutions_1647074248717.pdf
solutions2_1647074248867.pdf
00-introduction_1647074248919.pdf