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.

I’ll keep this short since we are all busy. One thing about paper 1 we saw, there were many unknowns.

So topics which I think will come out…

Differentiation – I think a min/max problem will come out, possibly with r and h both not given and asked to express r in terms of h. But students should revise a on the properties of curves with differentiation; given a curve equation with an unknown, for instance , find the range of k such that there is stationary points.

Complex Number – Loci will definitely come out. I’m saying they will combine with trigonometry.

Integration – Modulus integration hasn’t really been tested. Else a question on Area/ Volume could be tested, and I’ll say they need students to do some
Conics too.

For statistics, my students should have gotten the h1 stats this year. And if it’s an indicator, then it should not be a struggle.

I expect PnC and probability to be combined. Conditional Probability in a poisson question should be tested too, so do revise it well. For hypothesis testing, students should be careful of their formula and read really carefully about the alternative hypothesis. Also, :9 know that the formulas for poison PDF and binompdf are both given in mf15. Lastly, know when to use CLT.

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 .

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. 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 and I have a lot of prepare. I’ll try my best to attend to the questions as there is H2 Math Paper 2 coming up and I have a lot of prepare.

Side note: I think the paper is tedious, but definitely manageable. Hard ones, could have been q3, q7a, 10, 11ib. So if you did your tutorials and past year papers well, with proper time management and no careless, 70 is manageable. To get an A, you need to fight for that 30 marks which really test you on your comprehension skills and precisions. And these questions should distinct the students who deserve an A.

Comments/Explanations: Very easy question so long as you do not make any careless mistake. Make sure you write “or”. Students can also check their answers with the GC, with the graphical method.

Comments/Explanations: Firstly, it is fine to give all answers in 3SF since the question did not mention anything about exact. I just happen to recognise such functions. Besides that, it can be easily done with the Graphic Calculator.

First, observe that turning point for is at and . This means that undergoes 3 transformations in the following order. Scale of factor parallel to y-axis, then a translation in units in the positive y-direction, followed by a translation in units in the positive x-direction.

Since we know the is simply after undergoing the above transformation, we can conclude that

. Since .

Coordinates of intersection

Coordinates of turning point

Comments/ Explanations: A rather tough question to be honest. Students must be able to relate the given and figure out what the question is asking. Students comprehension skills are put to test here.

Comments/ Explanations: Proving the first part is not that easy as students just got to just try and figure something out, rather than staring for link. Use the GC to solve the next part, but be careful to copy the correct . The last part tests the students’ understanding on summation of GP and using of .

Comments/ Explanations: Students could have evaluated the vector before doing the cross or dot product. Knowing that its a unit vector is a cue to students that the modulus is 1. This is also a fairly easy question

Since is true, and is true is true, by mathematical induction, is true for all positive integers n.

(ii)

(iii)

…

From (ii),

From (i),

Comments/Explanations: This is a standard tutorial question. Students should know that they are not required to memorise summation of or , though they are handy here. Thus, being a bit more observant, they should realise they can easily use (i) to resolve the sum. There should be no need to simplify the answer in (iii) since it is only 3 marks.

Since coefficients of given equation are all real, is also a root, given that is a root.

By comparing coefficients,

(rejected since )

Comments/ Explanation: First part of (a) is manageable, while the long division can be tedious. Students can also use the quadratic formula (b) is quite easy so long as students know their basics of roots well.

Comments/Explanations: Tricky a bit, as students are expected to leave (i) in terms of and . (iii) has several different methods, one can only use series expansion of

This value is in both the domains of and so it should satisfy.

(b)

(i)

(ii)

Consider

We have that is not . Thus, the inverse does not exist.

Comments/ Explanation: The first part is your typical tutorial question. Picking the correct is a bit hard though, so students need to give it a good thought. The second part, as point out by Mr. Wee WS, is similar to an Olympiad Question on functional equations. To prove that inverse does not exists, there are other ways too. So feel free to try.

Comments/Explanation: First part of the question is rather straightforward and students just need to be really meticulous. The next part tests students on their understand of a unit vector, or distance between planes. Students MUST leave the final answers in cartesian form. The last part is simply testing their knowledge of lines and planes. I will say that system of linear equations is tested in part 1 already.

You can find the solutions of all ten sets of the June Revision Exercise we did in class.

Have fun!

June Revision Exercise 1
June Revision Exercise 2 June Revision Exercise 3
June Revision Exercise 4
June Revision Exercise 5
June Revision Exercise 6
June Revision Exercise 7 June Revision Exercise 8
June Revision Exercise 9
June Revision Exercise 10