Can you solve three high-school Math problems?

Figure 1: Math curriculum in Year 11 and 12 of NSW, Australia. Source (Page 13 of this PDF)

New South Wales (NSW, Australia) has an HSC (higher school certificate) math curriculum as shown in Figure 1. Year 12 Mathematics Extension 2 is the hardest math class taught at high-school there.

Let’s look at three problems from the Year 12 Mathematics Extension 2 HSC exam from several different years that became news stories and were considered hard.

Answering these questions requires prerequisite knowledge and awareness of the following math concepts:

• complex numbers,
• the complex plane,
• Euler’s identity,
• properties of circles,
• properties of triangles,
• properties of parallelograms,
• triangle similarity criteria,
• Vieta’s formulas,
• roots of polynomials etc.

Problem 1

The state's top maths student shows us how to answer the hardest HSC question