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

(i)

(ii)

Let be point on L that makes from P.

for some

So when , L is minimum.

(iii)

Cultivating Champions, Moulding Success

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

(i)

(ii)

Let be point on L that makes from P.

for some

So when , L is minimum.

(iii)

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

(i)

(ii)

When

When years.

Straightforward question.

(i)

(a)

P(faulty)

= P(made by A and faulty) + P(made by B and faulty)

= 0.6(0.05) + 0.4(0.07)

= 0.058

(b)

P(made by A | faulty)

=

=

=

(ii)

(a)

P(exactly one of them is faulty)

=

= 0.109272 (exact)

(b)

P(both were made by A | exactly one is faulty)

=

=

=

=

Question can be easily solved by drawing a tree diagram. Do take note that we only wrong off NON exact answers to 3sf, so for (iia), we keep the full exact answer.

Continue reading “2015 A-level H2 Mathematics (9740) Paper 2 Suggested Solutions”

(i)

(ii)

Let

(reject since

When , using trigonometry identity, we find

From

For since and for principal values of

We have that when , its is a maximum point.

(iii)

Using GC, Area

(iv)

At P,

At maximum point,

Back to 2015 A-level H2 Mathematics (9740) Paper 1 Suggested Solutions

To find the exact coordinates, students need to be able to either identify the correct trigonometry identify, or draw the right angled triangle to find and carefully. As for the show part for the parametric integration, students need to start from the definition of area then proceed carefully, not forgetting to change the limits.

(i)

(ii)

Vol

(iii)

When

When

Vol

Back to 2015 A-level H2 Mathematics (9740) Paper 1 Suggested Solutions

(a)

For to be purely imaginary,

(bi)

for

(bii)

and

By Cosine Rule,

Back to 2015 A-level H2 Mathematics (9740) Paper 1 Suggested Solutions

The first part of the question is rather interesting, since we don’t use the traditional argument method to solve it here. But that approach works fine too.

The next part, students just need to be really carful with the root finding, its a standard tutorial question. What follows is a bit tedious, but with an aid of a simple diagram and understanding the properties of roots on an argand diagram, students should not struggle that much.

(i)

Let and denote the total time A & B take respectively, in seconds.

(ii)

(3 SF)

(iii)

For A: Time taken

For B: Time taken

Difference (nearest seconds)

Back to 2015 A-level H2 Mathematics (9740) Paper 1 Suggested Solutions

- Be careful of the units, its in seconds.
- Be careful to write in sets.
- Be careful when you’re rounding off (ii) as you need to round off according to the range of values. If you rounded down to 63.8, this means you accept 63.81, which is out of range and will cause him to arrive before 1.5H. I reckon this part will get many students who are less careful. :/

(i)

(ii)

(iii)

At E,

Solving with GC, and

Back to 2015 A-level H2 Mathematics (9740) Paper 1 Suggested Solutions

Students that faced difficulties with ratio (like me) might struggle a bit here. But if you guys do listen in class, you should know the above method I use, should help a lot.

(ii) should be manageable. For (iii), students need to be careful if they use a GC to solve the question. Its like statistics, solving and .

(i)

From MF15,

(ii)

Comparing coefficients,

Coefficient of

Back to 2015 A-level H2 Mathematics (9740) Paper 1 Suggested Solutions

Hopefully you didn’t copy the formula wrongly.

The next parts, just need to be really careful. It is quite a lot of variables to juggle around here. For the last part, dont forget the and