Competition 1 (C1) Course
- Lessons: 20
- Fee: $1,100 AUD
- Current Time: Tue 14:15–16:15
- Workload: 3–5 hours
There will be 2 hours of teaching per week every over 20 weeks, and I expect students to spend about 3–5 hours per week reviewing the material and doing homework. The total time spent in this course should be around 100–150 hours over 2 terms. The content focuses on numerical or multichoice questions which feature on competitions like the AMCs, AIME, Mathex, ICAS, Otago Junior Maths Challenge, and so on. However, students will encounter proofs occasionally in anticipation of the Olympiad courses, which come after this one.
Classes
| Name | Time | Students | Duration | Status |
|---|---|---|---|---|
| 2025-07-C1 | 3 | – | Active |
Syllabus
- Problem-Solving Strategies (4 weeks): try small cases, case bashing, extremal principle, pigeonhole principle, representation and visualisation techniques.
- Combinatorics (4 weeks): permutations and combinations, supermarket principle, combinatorial identities, Pascal’s triangle, binomial theorem, double counting and bijections, introduction to probability, probability states.
- Number Theory (4 weeks): prime factorisations, divisibility, Euclidean algorithm, Bézout’s identity, base-n arithmetic, modular arithmetic, modular inverses, Fermat’s little theorem, Euler’s theorem, Chinese remainder theorem.
- Algebra (4 weeks): simultaneous equations, statistics fundamentals, rate problems, graphing, arithmetic and geometric sequences and series, telescoping sums, recurrence relations, exponents and logarithms, polynomials, Vieta’s formulas, quadratics, complex numbers and applications.
- Geometry (4 weeks): angle chasing in parallel lines and circles, similar triangles, length chasing, mass points, area formulas, basic triangle centres, coordinate bashing, trig bashing.
Learning Outcomes
- Be able to use a variety of soft and hard techniques in problem-solving.
- Be able to use permutations and combinations, combinatorial identities, and bijection arguments in counting problems.
- Be able to manipulate probabilities and conditional probabilities, and understand how to apply states in calculating probabilities.
- Be able to utilise prime factorisations and modular arithmetic techniques in Number Theory.
- Be able to solve simultaneous equations and quadratics.
- Be able to calculate and manipulate various types of statistics metrics, exponents, logarithms, series, and recurrence relations.
- Understand the relationship between the roots, coefficients, and graphs of polynomials
- Be able to manipulate complex numbers and know when to use them in problems which don’t mention them.
- Be able to chase and translate between various angle, length, and area conditions to solve geometry problems.
- Understand the concept of bashing in geometry and be able to perform coordinate bashes and utilise the law of sines and cosines to solve geometry problems.
Prerequisites
Before starting this course, students should be at Years 10 to 11 of the New Zealand mathematics curriculum. In particular, students should:
- be very comfortable with algebraic manipulation, including routine factorisations,
- understand sets and set notation,
- be familiar with the long division algorithm,
- be familiar with negative and rational exponents,
- understand what prime numbers, GCDs, and LCMs are, and be able to use odd and even arguments to solve basic number theory problems,
- know what functions and polynomials are,
- understand how translations and stretching of the graph of a function corresponds with changes in the functions itself, and
- be familiar with basic geometry, such as angles, lengths, areas, triangles, and various geometric terminology (e.g. right angle, perimeter, radius, isosceles triangle, polygon, parallel).