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.
See this page. Very work-in-progress; please note the disclaimer.
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
- Trigonometry (91032): worksheet, homework.
- Practice exams: Algebra
In addition, I have some questions on numeracy and basic skills.
My new Level Two Mathematics notes are available here. The sheets include:
- (2.1) Coordinate Geometry
- (2.4) Arcs and Sectors of Circles
- (2.4) Trigonometry
- (2.2) Functions
- (2.2/2.6) Quadratic Modelling
- (2.6/2.14) Simultaneous Equations
- (2.6/2.14) Linear Inequations
- (2.6) The Quadratic Formula
- (2.2/2.6) Exponential and Logarithmic Functions
- (2.2/2.6) Negative and Fractional Powers
- (2.7) Slopes and Differentiation
- (2.7) Tangent Lines and Approximation
- (2.7) Turning Points Optimisation
- (2.7) Anti-differentiation
- (2.7) Kinematics and Rates of Change
- (Stats?) Counting and Combinatorics
- (2.3) Number Sequences and Fractals
- (2.5) Graphs and Networks
- (2.10/2.11) The statistical enquiry process
- (2.9/2.11) Sampling
- (2.9) Statistical inference
- (2.12/2.13) Probability and risk
- (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.
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.
- Down the River: Foundations for Scholarship. a set of notes covering basic set theory, combinatorics, and number theory, with proof writing and induction.
- 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.
- 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)
- 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.
- 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.
- 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.
I have written a set of very terse notes.
- 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.
- Scientific Investigations and the Scientific Method
- Biology (90948): 01 - Genetics and DNA, 02 - Inheritance and Variation, 03 - Reproduction and Variation
- Chemistry (90944): Notes
- General exam advice.
- Basic reading list for a Greek focus.
- Aristophanes: practice questions and timeline.
- Alexander the Great: random notes on sources and early life.
In progress: Homeworks (and some other notes) for Alexander, general bibliography. Final plan is to have a full reading course written.
- Key concepts.
- Skills practice exams: Mahia: Questions, Resources; Chatham Islands: Questions, Resources