Sidenote: I think Vectors is a very important topic for 9758 as its applications are wide. Students should do their best to understand the topic. I will share a few more applied questions next week when I have time.

Since , then the parallelogram with sides determined by vectors and is a rhombus and corresponds to its diagonal. But a diagonal of a rhombus bisects its angle: the obtained two triangles are congruent by SSS. Clearly the same argument gives a more general statement: the sum of two vectors of equal length bisects the angle between them.

It has been awhile since the A’levels. We talked and met up with several of our students. Some students are working and some are preparing their Personal Statements for overseas University Applications.

A few of them also remarked that they wish they put more efforts into studying A’levels. An advice to this year JC2 – Do not wait till it is too late.

Students should also have a clear understanding of their syllabus, especially their scheme of exam. I still have JC2s this year who get stunned by the applications questions I threw at them (P.S. Aside from spending time with family, I wrote many sets of applied questions.). You may read more about your syllabus here. Or see the following images.

How much practice or emphasis your school put on this, is up to them. But it is clear that application takes up 25% of your marks. The entire syllabus can be found here.

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. KS will hold no liability for any errors. Comments are entirely personal opinions.

As these workings and answers are rushed out asap, please pardon me for my mistakes and let me know if there is any typo. Many thanks.
I’ll try my best to attend to the questions as there is H2 Math Paper 2 coming up.

Question 1
(i)

(ii)

Question 2

(rejected since ) or

Question 3
(i)

(ii)
Using GC, required answer (3SF)

(iii)
When

(3SF)

(iv)

Question 4
(i)

Let

When

When

Coordinates

(ii)

When . So is a minimum point.

When . So is a maximum point.

(iii)

x-intercept

(iv)
Using GC,

Question 5
(i)
Area of ABEDFCA

(ii)

Perimeter

When (rejected since )

When

Question 6
(i)
The store manager has to survey male students and female students in the college. He will do random sampling to obtain the required sample.

(ii)
Stratified sampling will give a more representative results of the students expenditure on music annually, compared to simple random sampling.

(iii)
Unbiased estimate of population mean,

Unbiased estimate of population variance,

Question 7
(i)
[Venn diagram to be inserted]

(ii)
(a)

(b)

(iii)

Question 8
(i)
Required Probability

(ii)
Find the probability that we get same color. then consider the complement.

Required Probability

(iii)

Question 9
(i)
Let X denote the number of batteries in a pack of 8 that has a life time of less than two years.

(a)
Required Probability

(b)
Required Probability

(ii)
Let Y denote the number of packs of batteries, out of 4 packs, that has at least half of the batteries having a lifetime of less than two years.

Required Probability

(iii)
Let W denote the number of batteries out of 80 that has a life time of less than two years.

Since n is large,

approximately

Required Probability

by continuity correction

Question 10
(i)
Let X be the top of speed of cheetahs.
Let be the population mean top speed of cheetahs.

Under

Test Statistic,

Using GC, is rejected.

…

(ii)

For to be not rejected,

(round down to satisfy the inequality)

Question 11
(i)
[Sketch to be inserted]

(ii)
Using GC, (3SF)

(iii)
Using GC,

(3SF)

(iv)
When (3SF)

Time taken minutes

Estimate is reliable since is within the given data range and is close to 1.

(v)
Using GC, (3SF)

(vi)
The answers in (ii) is more likely to represent since is close to 1. This shows a strong positive linear correlation between x and y.

Question 12
Let X, Y denotes the mass of the individual biscuits and its empty boxes respectively.

Comments/Explanations: The integration by parts can be really tedious. so just be careful. As for the part, it can be both -1 or 1, depending on what n is. So we have two values of a.

(ii)
The sample collected will be representative of the employee’s gender and department, instead of their age. Thus, it will not be suitable as it is not representative.

(iii)
Let be the age of employees.
Let be the population mean age of employees

(ii)
The scatter diagram shows a curvilinear relationship between x and y variables. Thus, a linear model is not appropriate.

(iii)
d is positive since it represent the maximum efficiency obtained as the power increases.
c is negative since the scatter show an increasing trend.

(iv)
Using GC,

(v)
When
The estimate would be reliable since it is within the data range. The value is close to 1 which shows a strong linear relationship.

(i)
The mean number of a particular type of weed that grow on the field is a constant.
A particular type of weed growing on the field is independent of another particular type of weed growing on the field.

(ii)
Let X be the number of dandelion growing per .