Level 2 Further Maths - Post some hard questions (Includes unofficial practice paper)

Hi!

This is a thread to share some of the hard AQA Level 2 Further maths questions that you've seen. Then others can attempt them to prepare for the exam. I will be creating a few of my own questions between now and Paper 2 and maybe some other users will create some too.

Here's my first one. There's a very tricky part in this question that you need to watch out for (most A Level students would miss it) but apart from that it's good practice for Level 2 FM.


Solve the equation


$\displaystyle \frac{\sin \theta}{\cos \theta + 1} + \frac{\cos \theta}{\sin \theta + 1} = 1$


for $0^o \leq \theta \leq 360^o$.

Would a quadratic in trigonometric functions be outside the realms of FM?

Solve $\displaystyle 17= 4\cos^2\theta + 17\sin\theta$ where $-360^{\circ}< \theta < 360^{\circ}$.

Would a quadratic in trigonometric functions be outside the realms of FM?

Solve $\displaystyle 17= 4\cos^2\theta + 17\sin\theta$ where $0^{\circ}< \theta < 360^{\circ}$.

Here's the spec if you decide to make another question

Sequences. It's definitely grade A^ and I've seen a question like this but easier in textbooks but not in an exam (yet).

Here are the first five terms of a sequence:

$\displaystyle \frac{3}{3},\frac{20}{15}, \frac{49}{35}, \frac{90}{63}, \frac{143}{99}$

The $n$^th term of the sequence is $u_n$. Find the limiting value of $u_n$ as $n\rightarrow \infty$.

is the answer?

in spoiler btw

Yes that's correct.

could you work out the answer to what GCX posted? I want to see if i got it right.

i got 90 but not sure.

If @_gcx hasn't replied later then I'll take a look.

Hopefully some other students can join in with the thread. I'll continue to post questions if it's just you answering since I think this thread could be useful for future years.