Random Questions from 2016 Prelims #7

Random Questions from 2016 Prelims #7

JC Mathematics

VJC P1 Q9

(i) Sketch the graph with equation x^2 +(y-r)^2 = r^2, where r >0 and y \le r

A hemispherical bowl of fixed radius r cm is filled with water. Water drains out from a hole at the bottom of the bowl at a constant rate. When the depth of water if h cm (where h \le r).

(ii) Use your graph in (i) to show that the volume of water in the bowl is given by V = \frac{\pi h^2}{3} (3r-h).

(iii) Find the rate of decrease of the depth of water in the bowl, given that a full bowl of water would become empty in 24 s,

(iv) without any differentiation, determine the slowest rate at which the depth of water is decreasing.

Random Questions from 2016 Prelims #5

Random Questions from 2016 Prelims #5

JC Mathematics

NYJC P1 Q4

Referred to the origin , the points A and B have position vectors a and b respectively. A point C is such that OACB forms a parallelogram. Given that M is the mid-point of AC, find the position vector of point N if M lies on ON produced such that OM:ON is in ratio 3:2. Hence show that A, B, and N are collinear.

Point P is on AB such that MP is perpendicular to AB. Given that angle AOB is 60^{\circ}, |a|=2 \text{~and~} |b|=3, find the position vector of P in terms of a and b.

Challenging A’levels Questions

JC Mathematics

Below is a list of questions that students should take note of! The questions are not there due to copyright issues. But linked are the suggested solutions by KS. 🙂

2015 P1: 3, 9

2015 P2: 9, 11

2014 P1: 3, 7, 9

2014 P2: 1, 4, 6, 9

2013 P1: 5, 6

2013 P2: 1, 4, 8, 11

2012 P1: 5, 6, 7, 9, 11

2012 P2: 4, 6, 7, 10

2011 P1: 3, 4, 5, 6, 7

2011 P2: 11

2010 P1: None

2010 P2: 7, 8, 11

2009 P1: 2, 10 iii, 11 iv

2009 P2: 2 iii, 2 iv, 3, 7 ii, 8, 9

2008 P1: 1, 4 iii, 5 ii, 6a, 8, 9, 11

2008 P2: 1 iv, 2 ii, 3a, 3b ii, 7, 10, 11 last part

2007 P1: 7 iii, 9, 11

2007 P2: 8 iv, 9, 10