List of publications

This page outlines a list of publications, often mathematical, written by Jonathan Lam (JL) and/or Johnny Bui (JB). In more recent times, Vincent Tran (VT) has also contributed to this works catalogue. Where other authors contributed to a work, acknowledgement is made in the notes.


Certain publications are available by request (contact publications@jonathanlamao.com) for people with a legitimate purpose (students, teachers). Certain publications are not for public release as they are used for internal training programmes.
As a general guide, the less likely something is in the syllabus, the more likely I am able to give this out.

Junior Maths

JJWC Number Name of publication Description Notes
J1 Finding Patterns (year 7 and above) A systematic way to finding patterns between two sequences JL
J2 Extreme Value (Distance Formula - year 8 and above) A class of questions involving insight on the distance formula (year 8) to solve seemingly hard questions JL
J3 Areas of related figures (year 7 and above) A class of questions involving areas of related figures JL
J4 Dealing with Digits (year 7 and above) Techniques on working with questions involving digits of a number JL
J5 Factorials (year 7 and above) Approaching questions involving factorials and their properties. JL
J6 Simultaneous Equations (year 9 and above) Various questions on simultaneous equations. These are often non-linear and in 3 variables. JL
J7 Folding Paper (year 7 and above) Geometrical questions involving a piece of paper being folded. Students should note properties such as reflection. JL

Senior Maths

Due to the large amount of publications in this section, I have attempted to group them my topic, as well as difficulty. Some publications are aimed at intermediate students/normal students, while some are aimed at more advanced students. Some are even higher up and aimed at students with olympiad experience or are just interested in maths in general.

Calculus
S1 Integration Add 1 Subtract 1 (4u) A class of questions on Reduction Formulae where this particular insight is required JL
S2 Integration - Sin/Cos swapping (4u) A class of questions in integration where a transformuation swaps the sin and cos JL
S3 Integration - Putnam Variation (4u) Variations on a famous integral from the Putnam JL
S4 Calculus FTC (4u) A class of questions involving the Fundamental Theorem of Calculus that has been appearing in recent trial exams JL
S5 Differential Equations A formal introduction to differential equations, various approaches to solving them, and example questions from past HSC and Trials JL
S6 Inequalities involving Definite Integrals Proving inequalities involving integrals by considering areas. Also includes ideas like Stirling's formula and proofs for famous results JL
Geometry
S11 Triangle Centres Introducing the 4 main triangle centres, and their properties JL
S12 Triangle Areas Introducing new formulae for area of a triangle under different contexts, with questions demonstrating when certain formulae will be more beneficial JL
S13 Other Triangle Theorems Introducing other theorems and proofs relating to triangles (e.g. Simson's, 9 point circle, extended sine law, Ceva, Menalaus, Stewarts) JL
S14 Lemmas in Geometry Some common configurations in geometry. Not quite theorems, but "worth" knowing. JL
S15 Configurations in Geometry Some common configurations in geometry. Some are theorems; some don't have names. This is a more accessible version of S14. JL
Algebra, Mechanics, Combinatorics, Number theory, and Other topics
S21 Series and Sequences (4u) Various techniques on evaluating series JL
S22 Factorisations Various techniques on factorising seemingly difficult polynomials or expressions JL
S23 Counting Roots using curve sketching (4u) Applications of curve sketching to counting roots JL
S24 Supersums of square weights (4u+) Advanced Inequalities Techniques JL
S25 Summations Techniques on evaluating sums JL
S26 Powers of Two (4u) Various questions relating to a trick on the powers of two JL
S31 Floor and Ceiling Functions (4u) Various techniques and questions on dealing with the floor/ceiling function JL
S27 Telescoping Sums (4u) Various techniques on evaluating telescoping sums JL
S28 Inequalities - Isolated Fudging (4u) A technique to solve inequalities JL
S29 Combinatorial Reciprocal Principle A theorem in combinatorics and set theory that isn't really a theorem and is more like a cool trick JL
S30 Locus with Rectangular Hyperbola - Strategies, Restrictions, Variations Techniques on approaching locus questions in conics (and in general), strategies on finding restrictions in loci, as well as a theme and (10) variations on a class of one locus question JL
S32 Definitions of e The definitions of e, such as factorial and limit definitions. Questions from past HSC and trials involving these definitions and properties, with solutions. JL
S33 Advanced Perms and Combs Covering techniques such as stars and bars, path walking, Catalan numbers, derangements, etc JL
S34 Fibonacci Numbers Properties and Identities of Fibonacci numbers and various exercises JL
S35 Resisted Motion - Strategies and Techniques For rectilinear motion with resistance JL
S36 Circular Motion - Strategies and Techniques For circular motion, including banked track, trains and cars, conical pendulum JL

Problems Compilation

Note that I enjoy writing "troll" questions a lot (absurd, unreasonable or extremely difficult, or impossible). These questions are marked with "Troll", and are available for public distribution. The other documents are generally internal use only.
JJWC Number Name of publication Description Notes
P1 Vectors (standard) Standard high school level vector questions Various contributors
P2 Vectors (olympiad) Vectors JL
P3 Conics Variations The same geometrical property can be seen across ellipses and hyperbolas, with slight variation JL
P4 Troll Perms and Combs Various troll questions on perms and combs, often requiring an absurd or unreasonable amount of cases JL, VT
P5 Troll Inequalities A troll question on inequalities where only really basic concepts are used (e.g. 2-variable AM-GM and perfect squares) but where the insight required is unreasonable. JL
P6 Troll Collatz A troll question where the student is to solve various properties on the Collatz conjecture (doable), culminating with a proof for the conjecture (unproven result) JL, VT
P7 Troll Complex Numbers Geometry Bash A troll question where the student is to solve a geometry question using complex numbers bashing JL
P8 Troll Coordinate Geometry Bash A troll question where the student is to solve a geometry question using coordinate geometry bashing JL
P9 Troll Mango Question A parody on the 2017 English HSC Paper 1 unseen text (poem) on mangoes. JL
P10 Troll 4 unit trial The questions are technically in the syllabus, but are too unreasonable to ask in an actual exam. Features parodies of actual questions. Solutions provided. JL

HSC Solutions

These are publically available here. There are also official HSC solutions published by NESA on their website, as well as other unofficial solutions on other websites.
JJWC Number Name of publication Notes
H2 HSC 2017 Extension 1 Mathematics Solutions Various contributors
H1 HSC 2017 Extension 2 Mathematics Solutions Various contributors

Undergraduate

Main stuff from UNSW. These are available for students studying these courses. Just message or email me for access.
JJWC Number Name of publication Description Notes
U1 MATH1151 Notes Vectors, Matrices JB
U2 MATH1251 Notes Vector spaces JB
U3 ACTL3141 Notes Actuarial Models and Statistics Various contributors
U4 ACTL3151 Notes Life Contingencies Various contributors
U5 MATH1251 Quiz Compilation Various students memorised their exams to produce this compilation of quizzes (all original) Various contributors
U6 BABS1201 Essay Journal Article (HD) My assignment (task 1, tex and pdf) JL
U7 BABS1201 Enzyme Lab Report (HD) My assignment (task 2, tex and pdf format) JL
U8 BIOS1101 Final Exam Question Bank Questions that students have memorised to reproduce a question bank (original) Various contributors
U9 MICR2011 Final Exam Bank Questions that I have memorised to reproduce a question bank (original) JL
U10 MGMT1001 Essays/Reports (HD) My essay, as well as Everest report. Marker feedback and Tex source files provided. JL
U11 MGMT1001 2017 Final Sample Extended Response Questions from the final which I memorised JL
U12 COMP1511 Challenge Question Explanations Explanations (in tex and pdf format) for various COMP1511 Lab Challenge Exercises. I can also give you the full code if you're still stick/interested. JL
U13 ACTL2102 Assignment (HD) Assignment (in tex and pdf format) of assignment. It should also be available on Moodle, under Sample Reports. JL and other group members

AMC and AIMO Solutions

I have spent a considerable amount of time writing solutions for questions from the AIMO and selected questions from the AMC. Again, not all of it is available, but if you email me, I'll see what I can do to help you out.

Maths Camp Quotes and Jokes

This is a 20 page book which is a compilation of the various quotes (usually humerous) from the April and December maths camps.
Whilst this text is more comedic and less mathematical, a lot of the content makes reference to inside jokes.
Some mathematical knowledge (especially on olympiad mathematics) is required to understand some jokes.