Topic Drills
One exam topic per page: the method, real exam questions taken apart, the common mistakes, and a mastery check to confirm you have it.
This page is written in Chinese and English (the two CSCA exam languages); you are reading the English version.
Trig Reduction (Induction) Formulas
Stop memorising six formula groups: see the symmetry on the unit circle and derive "odd multiple: swap the name; sign from the quadrant" yourself. With CSCA exam examples, the three most common mistakes and a 5-question mastery check.
About 15 minutes · Tested in all 5 recent real CSCA papers (7 questions) · 30 exam and mock questions
Quadratic and Rational Inequalities
A quadratic inequality asks which side of the x-axis a parabola is on. See why "greater than: outside, less than: inside" works, then handle a<0, double roots, no real roots and rational inequalities — with CSCA exam examples, the most common mistakes and a mastery check.
About 15 minutes · Tested in all 5 recent real CSCA papers (10 questions) · 30 exam and mock questions
Odd and Even Functions
Parity is just symmetry: about the y-axis it is even, about the origin it is odd. See it on a graph, then learn the two-step test — check the domain, then compute f(−x). With CSCA exam examples, the four most common mistakes and a 5-question mastery check.
About 15 minutes · Tested in all 5 recent real CSCA papers (6 questions) · 28 exam and mock questions
Trig Values from a Point on the Terminal Side
Nothing to memorise: with a point P(x,y) on the terminal side, find r and the three ratios y/r, x/r, y/x are sin, cos, tan. See how r pulls the point back onto the unit circle, then learn to fix the quadrant and the signs. With CSCA exam examples, the three most common mistakes and a 5-question mastery check.
About 15 minutes · Tested in 4 of the last 5 real CSCA papers (4 questions) · 23 exam and mock questions
Focus and Directrix of a Parabola
The focus and the directrix sit on opposite sides of the vertex, both p/2 away. See the four standard forms on a graph, then learn the routine: put it in standard form, read p, write the focus and directrix, and turn a distance to the focus into a distance to the directrix. With CSCA exam examples, the two most common mistakes and a 5-question mastery check.
About 15 minutes · Tested in all 5 recent real CSCA papers (8 questions) · 26 exam and mock questions