free graphing technology-1
The decision by teacher and student on which graphing technology to use is a very important one. In some schools a teacher will have full control of the graphing technology used both by themselves in...
Yang Hui's triangle
Perhaps the most well-known two-dimensional number pattern is the triangular array of binomial coefficients most commonly referred to as Pascal's triangle. However, the pattern had been known and studied...
GDC solution times - Specimen P2 question
There has been quite of bit of interesting discussion going on recently in the Maths HL forum on the Online Curriculum Centre (OCC) with regard Question 5, part (b) on the most recent HL Specimen Paper...
cosine of pi/5
An interesting exercise for HL students is to prove that the cosine of (36 degrees) is exactly one-half of the golden ratio (phi). Students are aware of 'special' angles, such as and , for which they...
Conditional Probability Brainteaser
You have two coins in your pocket. One of them is double-headed and the other is a fair coin (head-tail). You randomly choose one of the coins from your pocket. You look at one side of it. Given that...
Unfamiliar Questions
A common comment from examiners that appears on Maths HL Subject Reports is that teachers are strongly encouraged to take measures to develop their students' problem solving skills and their ability to...
Counting by Twelves
There are some very thought-provoking questions that can arise while discussing mathematical ideas with students. Some intriguing questions that have emerged at different times (some repeatedly) in my...
Drawing a Line with Circles
I've always been fascinated with cycloids. It's a shape that is best illustrated not by a formula but by a particular type of motion. A cycloid is the shape that is traced out by a fixed point on a...
Do not completely trust your GDC
For a recent review lesson, I composed a question which I thought would nicely review using definite integrals to find areas and volumes and to illustrate the significant difference that could occur between...
What About Computer Algebra Systems (CAS)?
I remember well the first time I saw a computer algebra system (CAS) in action. It was 1984 and I was in my first year of teaching. The head of the mathematics department at my school was excited (he...