The 2012 NJC Prelim is renowned among tutors and students for highlighting specific, recurring pitfalls. Chief among these was the treatment of "hence" questions, where a previous result (e.g., a partial fraction or a reduction formula) must be used to solve a new problem. Many students, pressed for time, re-derived results from scratch, wasting precious minutes. The paper also featured a notorious question on complex numbers involving the condition for a set of points to form a circle. Students who relied on rote memorisation of the locus "|z - a| = r" could not adapt when the condition was presented as "arg((z - z1)/(z - z2)) = π/2". This required the insight that such an argument condition implies that the chord subtends a right angle at the circumference, leading to Thales’ theorem and the equation of a circle with the chord as diameter. Without this geometric insight, purely algebraic manipulation led to a dead end.
X = sum of two dice. Find ( E(X^2) ). Use ( E(X)=7, Var(X)=35/6 ), so ( E(X^2)=Var+[E(X)]^2 ). 2012 njc prelim h2 math
We need the area bounded by: