Hardest Questions in Additional Mathematics (A Math)

Additional Mathematics questions can range from standard all the way to super challenging among the secondary schools in Singapore.

Certain schools (such as IP schools), and also some schools such as Anderson, Chung Cheng High School, are well known for setting hard A Math papers.

Note that even though top schools set hard A Math papers, it is not often the case that top schools teach or prepare well their students for the tests! Often, the teachers in school teach at a basic level (due to time constraints or other factors), but still test at an advanced level. Hence, many students in top IP schools are not well prepared for their school’s tests (unless they have excellent self study skills or have a parent or tutor to guide them). It is not uncommon for a student in a top IP school to be failing his/her math tests due to the above phenomena (difficult tests which do not match what is taught in school).

Some of the more difficult types of questions in the A Math syllabus are listed below.

Algebra

1. Conditions for ax^2 + bx + c to be always positive (or always negative).
   This type of question has potential to be very tricky. Somehow, many students will assume wrongly that b^2-4ac is always positive as well (where it should be the opposite).
2. Partial Fractions with Improper Fractions.
   Only top schools tend to test improper partial fractions. Many students will miss out long division or make mistakes along the way.
3. Binomial Theorem.
   Many students have serious problems with this topic. Also, not many seem to know that .

Logarithm

• Check out this O Level Logarithm Question (Challenging) question. Would be quite tough for most students, even those in top IP schools.

Trigonometry

• Sketching of Tangent graphs.
  90% of all sketching questions are on Sine or Cosine. Only top schools will set tangent sketching questions, and many students will be caught unaware.
• Half-angle formula sin(x/2) or Quadruple angle formula sin(4x)
  Top schools like to test half-angle formula, many students who have not seen such questions will be stuck.

Integration

• Finding area to the left of the curve, i.e. .
  Most schools kind of brush off this type of questions during teaching. But it is a hot topic for testing among top schools. Hence, students will have a hard time solving it if they lack practice for this type of questions.