Hopefully, you guys have started on the Set A. You will find the following solutions useful. Click on the question. Please do attempt them during this December Holidays. ðŸ™‚

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Firstly, either consider or square both sides. Its easier to do the latter (so I will).

Since for all

(i)

LHS

RHS.

(ii)

(Showing workings for Method of Difference)

(iii)

As .

Hence, the series converges to .

(i)

Let

— (1)

— (2)

— (3)

Using GC,

(ii)

Since arithmetic series is increasing, ,

Common ratio

Since , the geometric series converges.

(ii)

First term

By Pythagoras’ Theorem,

since

Area,

Let

Check with first derivative test.

Hence, maximises A.

Thus, dimensions are m and m (to 3.s.f.).

(i)

, where is an arbitrary constant.

When .

(ii)

As .

Thus, the population of salmon in the fish farm will decrease towards 6,000 in the long run.

(a)

(b)

(c)

For curve to cut the x axis at 2 distinct points,

or

(i)

(ii)

— (1)

— (2)

Coordinate of

When

Observe that passes through for all real values of .

Thus, for line to not intersect C, .

(iii)

or

(a)

(b)

(i)

(ii)

When

(a)

Firstly, scale by factor parallel to the y – axis.

Secondly, translate by 3 units in the positive x – direction.

Curve D is a circle.

(b)

(i)

(ii)

(i)

Since

Using Sine Rule,

So y coordinate is given by

(ii)

Gradient of

Since QS is always tangential to hump, gradient of

Since

(iii)

Area

(4dp)

Relevant Materials:Â MF26