B6

let

Sub to

Thus, it is a min point.

C7

let

(NA).

There are no stationary points for this curve.

C8

Let

Evaluate with a calculator…

Cultivating Champions, Moulding Success

General Certificate of Education Advanced Level is a school leaving qualification targeting Junior College students.

B6

let

Sub to

Thus, it is a min point.

C7

let

(NA).

There are no stationary points for this curve.

C8

Let

Evaluate with a calculator…

When , 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:

Students should write the actual values of and in the table.

We use this under these two situations:

1. is difficult to solve for, that is, is tough to be differentiated

2.

The second derivative test:

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

If , where , and are all non-zero vectors, show that bisects the angle between and .

All solutions here are SUGGESTED. Casey will hold no liability for any errors. Comments are entirely personal opinions.

- B
- C
- B
- D
- D
- C
- D
- D
- B
- C
- A
- D
- D
- C
- C
- A
- D
- A
- B
- D
- Question 21 is a flawed question. When unpolarised light goes through a polarizer, the I is halved while the A is reduced by a factor of root 2. But based on the information Cambridge provides, the answer is C.
- D
- D
- C
- C
- B
- C
- A
- B
- B
- A
- C
- D
- B
- B
- B
- D
- C
- C
- C

Note to all: Casey will not respond to most of the comments as he is busy. You may contact him by **SMS** at +65 9474 5005 if you have a burning question.

Feel free to explain the answers, if you are confident. Many thanks.

HCI/1/6

A group of boys want to set up a camping tent. They lay down a rectangular tarp OABC on the horizontal ground with OA = 3 m and AB = 1.5 m and secure the points D and E vertically above O and B respectively, such that .

Assume that the tent takes the shape as shown above with 6 triangular surfaces and a rectangular base. The point O is taken as the origin and the unit vectors i, j and k are taken to be in the direction of , and respectively.

(i) Show that the line DE can be expressed as .

(ii) Find the Cartesian equation of the plane ADE.

(iii) Determine the acute angle between the planes ADE and OABC. Hence, or otherwise, find the acute angle between the planes ADE and CDE.

Note: Question can be made harder and trickier should Origin, O be placed in the center of the base OACB.

All solutions here are SUGGESTED. We will hold no liabilities for any errors. Comments are entirely personal opinions.

Read more about Pre-A’levels 2016 thoughts here.

Question 2: Assess the view that tradition buildings have no future in your society.

Question 3: ‘Longer life expectancy creates more problems than benefits.’ Discuss

Question 10: Assess the view that most natural disasters are the result of human activity.

So these past months, I have been focusing on harnessing students’ abilities to interpret questions properly. Every line in a question is there for a reason and hold little pieces of information. As a student, you need to piece these information together.

Take the following question as an example:

We have a, b and c=a+2b.

Given further that M is on OC, and point A, B, and M are collinear. Find the ratio of OM:OC.

Now this question looks rather short. Many students will first start by drawing to help them see. To be honest, I was tell students that drawing out vectors is not necessary since it doesn’t yield any marks and we spend 10 minutes trying to figure out how it is supposed to look. We are better learning how to read questions.

Let’s start dissecting

M is on OC tells us that .

A, B, and M are collinear tells us that the points are parallel with a common point. NOTE: Collinear is different from parallel. The former is a proper subset of the latter actually.

This tells us that

Students should have no trouble continuing to solve for and .

So this little exercise is to simply illustrate the importance of learning how to read questions and of course, writing it out.

All solutions here are SUGGESTED. Mr. Teng will hold no liability for any errors. Comments are entirely personal opinions.

(i)

Let X and Y denote the mass of a apple and pear in grams respectively.

(3 SF)

(ii)

(3 SF)

(iii)

Let A and B denote the mass of a peeled apple and peeled pear in grams respectively.

(3 SF)

All solutions here are SUGGESTED. Mr. Teng will hold no liability for any errors. Comments are entirely personal opinions.

(i)

Number of ways ways

(ii)

Number of ways ways

(iii)

Number of ways ways

(iv)

Case 1: 2 A’s together and B’s separated

Case 2: 2 B’s together and A’s separated

Case 3: 2 A’s together and 2 B’s together

720

Number of ways =10080 – 1800 – 1800 – 720 = 5760 ways

All solutions here are SUGGESTED. Mr. Teng will hold no liability for any errors. Comments are entirely personal opinions.

(i)

Graph to be inserted

(ii)

(a) (4 DP)

(b) (4 DP)

(c) (4 DP)

(iii)

Using GC,

(3 SF)

(iv)

(3 SF)