Here’s one of two* topics that strike fear in the majority of maths A Level students. Trigonometry. According to Wikipedia, trigonometry is a “branch of mathematics that studies triangles”. Now, how many A/L students can define trigonometry this way? Very few. Most students would just mutter “triangles and formulas and stuff” (note the incorrect spelling of formulae). They know the subject matter given in the syllabus, and that’s it. It’s OK if you don’t have the slightest idea of what you are learning, as long as you can vomit it all out during the exam. I’m sure some students don’t even know what “trigonometry” is, but can readily identify “sin x/cos x = tan x”.
Trigonometry involves trig. functions sine, cosine and tangent, as well as secant, cosecant and cotangent. There are certain trig. identies such as the one at the end of the last paragraph. Actually there are a lot of identities, and many of them are in the maths syllabus. Double angle formulae, addition formulae, blah blah blah. Students mostly complain about the difficulty of studying these identities, and also about the greater difficulty of applying these identities correctly to questions. And also, you have to know how to draw graphs of trig. functions and their inverses.
Fortunately for London A/L students, the trigonometry is spread over two or three units. But local syllabus students are forced to learn it all at once (and vomit it all out at only one super-exam). But this does not comfort many students who hate trigonometry and anything associated with it. Sadly, most of A/L maths and further maths are associated with trigonometry, so this is a very bad attitude going into the exam.
I don’t hate trigonometry at all. I think it’s interesting and challenging. And I know I have to learn this stuff very well if I want to succeed at my exams. I wish most of my friends thought the same.
*The second topic is Calculus.