Random Questions from 2017 Prelims #3

Random Questions from 2017 Prelims #3

JC Mathematics

Here is another question that is from CJC H2 Mathematics 9758 Prelim Paper 1. Its a question on differentiation. I think it is simple enough and tests student on their thinking comprehension skills. This is question 6.

A straight line passes through the point with coordinates (4, 3) cuts the positive x-axis at point P and positive y-axis at point Q. It is given that \angle PQO = \theta, where 0 < \theta < \frac{\pi}{2} and O is the origin.

(i) Show that equation of line PQ is given by y = (4-x) \text{cot} \theta +3.

(ii) By finding an expression for OP + OQ, show that as \theta varies, the stationary value of OP + OQ is a + b \sqrt{3}, where a and b are constants to be determined.

A little reminder to students doing Calculus now

A little reminder to students doing Calculus now

JC Mathematics

When \frac{dy}{dx} = 0 , it implies we have a stationary point.

To determine the nature of the stationary point, we can do either the first derivative test or the second derivative.

The first derivative test:

First Derivative Test

Students should write the actual values of \alpha^-, \alpha, \alpha^+ and \frac{dy}{dx} in the table.

We use this under these two situations:
1. \frac{d^2y}{dx^2} is difficult to solve for, that is, \frac{dy}{dx} is tough to be differentiated
2. \frac{d^2y}{dx^2} = 0

The second derivative test:

Second Derivative Test

Other things students should take note is concavity and drawing of the derivative graph.

Random Questions from 2016 Prelims #4

Random Questions from 2016 Prelims #4

JC Mathematics

VJC P1 Q6

vjc p1q6

A curve has equation y^2=4x and a line l has equation 2x-y+1=0 as shown above.

B(b, 2\sqrt{b}) is a fixed point on C and A is an arbitrary point on l. State the geometrical relationship between the line segment AB and l is the distance from B to A is the least.

Taking the coordinates of A as (a, 2a+1), find an equation relating a and b for which AB is the least.

Deduce that when AB is the least, (AB)^2 = m (2b - 2\sqrt{b} +1)^2 where m is a constant to be found. Hence or otherwise, find the coordinates of the point on C that is nearest on l.