The following question is from the 2019 ATAR Mathematics Applications Paper – Calculator Free Question 3.
Monthly Archives: August 2024
Using the Hungarian Algorithm for an Assignment Problem
Filed under Networks, Year 12 Mathematics Applications
Sketching in the Complex Plane Using a TI-nspire CX 11
Let 
be the region of the complex plane where the inequalities 
and 
hold simultaneously.
First find the Cartesian equations.
Finding the symbols The  is found underMenu – Number – Complex Number Tools – Complex Conjugate  |
Second, sketch each of the functions.
The section that is shaded twice is our region.
Determine the minimum value of 
in .
We can find the point of intersection between the circle and the line.
Or if you want exact values
Use the Solve Systems of Equations tool – Menu – Algebra – Solve Systems of Equations – Solve Systems of Equations.
Pythagoras Question
This was a question one of my year 9s had to tackle:
A hemisphere of radius length 5cm is partially filled with water. The top of the hemisphere is horizontal and the surface of the water is a circle of radius 4cm. Find the depth of the water.
ICE-EM Mathematics 9, page 70, question 2
Below is a cross section of the hemisphere
The depth of the water is 
We can find 
using the Pythagorean theorem
(it’s the classic 3-4-5 triangle)
Hence the depth of the water is 2cm.
Filed under Pythagoras