Mathematics - Science Track
What the paper tests
The science-track mathematics paper is set in Khmer and is marked for method as well as answer. Recurring items are limits and asymptotes, derivative sign tables and graph sketches, definite integrals and plane areas, sequences, exponential and logarithmic equations, probability, and coordinate geometry.
Core rules
- Begin with the domain; a simplified expression can hide a hole or vertical asymptote.
- Build a sign table for f′(x). Monotonicity and local extrema come from sign changes, not from f′(x)=0 alone.
- For area, integrate upper minus lower; split at intersections. Area is positive even when the integral is negative.
- For log equations, state the domain before solving and reject extraneous roots.
Worked example
Let f(x)=x³−3x. Then f′(x)=3x²−3=3(x−1)(x+1). Critical points are x=−1 and x=1. The sign table gives f′>0 on (−∞,−1), f′<0 on (−1,1), f′>0 on (1,∞). So f increases, decreases, then increases; f(−1)=2 is a local maximum and f(1)=−2 is a local minimum. A sketch needs these turning points and the fact that f is odd.
Traps
Losing sign-table marks by writing only “max/min”; forgetting the domain of a log or square root; giving a negative area; and failing to label axes or intercepts on the graph.