All solutions here are SUGGESTED. Mr. Teng will hold no liability for any errors. Comments are entirely personal opinions.
Numerical Answers (click the questions for workings/explanation)
Question 4: 1277cm, 3400cm
Question 5: is a maximum, 20
Let and be the circumference and area of the ink-blot at time respectively.
When , .
At point of intersection, (3 d.p.)
Let be the maximum height of the ball after the first bounce.
Least . Thus, the required number of bounces is 85.
At turning point, .
Using GC, when , we have that .
Thus the turning point at is a maximum.
Thus is parallel to since is a nonzero vector and is also a nonzero vector.
The set is a line passing through the position vector and parallel to the direction vector , where is a scalar parameter.
At A, .
At B, .
Thus length of depends only on .
At , for some .
Let be the reflection of on .
Let be the common point of and .
We observe that in the long run, the area will increase toward .
The specimen paper 1 was useful to provide us with a glimpse of what is to be expected of the upcoming syllabus. The last two questions, in particular, showed us the extent of applications. It is definitely different from the old 9740 H2 Mathematics Syllabus as the questions are more intuitive and seek to push students’ imaginations more.
In this paper, Question 9 and Question 11 serve to be the application questions. Question 4 is a contextual/ application question that involves modelling solution. Question 8 test students on application of Mathematics and generally involves a brief statement to test the application.