2012 Njc Prelim - H2 Math

Some questions are overly convoluted. Focus on:

Let’s briefly walk through the Vector Question 11 solution to illustrate the mental rigor required:

Given plane $p: r \cdot (2, -1, 2) = 5$ and point $A(3, 2, 1)$ not on the plane. A light ray from $A$ meets the plane at $B$ such that the angle between the ray and the normal is $30^\circ$. Find the position vector of $B$.

Solution Logic:

Even reading the solution requires focus. That is the 2012 NJC effect.

The first paper in the 2012 NJC Prelim focused heavily on Pure Math. Let’s break down the sections that caused the most distress.

Likely: Implicit differentiation, parametric, rates of change, small increments. 2012 njc prelim h2 math

Example (NJC style): A cone has radius increasing at 2 cm/s and height decreasing at 1 cm/s. Find rate of change of volume when ( r=3, h=5 ).

Likely: Mixed progression (AP+GP) word problem, or summation of ( r^2, r(r+1) ) etc.

NJC Favorite: Summation of ( \frac1r(r+1)(r+2) ) using partial fractions. Some questions are overly convoluted

Example: [ \frac1r(r+1)(r+2) = \fracAr + \fracBr+1 + \fracCr+2 ] Solve: ( A=1/2, B=-1, C=1/2 ). Then telescoping sum.

Paper 2 of the 2012 NJC Prelim is where the school earned its reputation for "killer" application questions.

Do not review the paper linearly. Cluster your mistakes: Given plane $p: r \cdot (2, -1, 2)