Given that , find the approximate percentage change in when increases from 2 by 2%.

Cultivating Champions, Moulding Success

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…

Another interesting vectors question.

The fixed point has position vector **a** relative to a fixed point . A variable point has position vector **r** relative to . Find the locus of if **r** (**r** – **a**) = 0.

This is a question a student sent me a few days back, and I shared with my class.

Find the Cartesian equation of the locus of all points (plane) that is equidistant of the plane and plane.

The following should aid students to visualise.

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.

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 .

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.

All the best!

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

Thoughts before 2016 A-level H2 Mathematics

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. 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.

(i)

(ii)

(iii)

Let and