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

105 Mark Unofficial Practice Paper 2

This is a thread to share some of the hard AQA Level 2 Further maths questions that you've seen or create some of your own. Then others can attempt them to prepare for the exam.

A lot of these questions are harder than real exam questions but none of them go beyond the spec.

Questions posted so far (you can also find solutions if you search through the thread)

Q1
Q2
Q3
Q4
Q5
Q6
Q7
Q8
Q9
Q10
Q11
Q12
Q13
Q14
Q15
Q16
(edited 4 years ago)

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Original post by notnek
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 are some of the general things to show up each year:

Quadratic Nth Term
Simultaneous Equations Using Matrices
Representing Ratios (2 markers)
Algebraic Fractions
At least 1 or 2 3D Trig
Representing a Certain Siny or cos or tan value in terms of another sin or cos or tan value. (i:e if siny = 5/3 whats cosy)
Trigonometry Identities
Solving Trig Identities Questions
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 $0^o \leq \theta \leq 360^o$.
Original post by notnek
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 $0^o \leq \theta \leq 360^o$.

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Original post by Pretish

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Original post by notnek

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Original post by Pretish

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Original post by notnek

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Original post by Pretish

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Original post by notnek

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it was good one lol
Would a quadratic in trigonometric functions be outside the realms of FM?

Solve $\displaystyle 17= 4\cos^2\theta + 17\sin\theta$ where $0^{\circ}< \theta < 360^{\circ}$.
(edited 6 years ago)
Original post by _gcx
Would a quadratic in trigonometric functions be outside the realms of FM?

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

That looks about the right level for FM but the angle range would be 0-360.
Original post by _gcx
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
Original post by notnek
Here's the spec if you decide to make another question

Cheers I'll take a look.
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 $n\rightarrow \infty$.
Original post by notnek
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

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Original post by Pretish
is the answer?

in spoiler btw

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Yes that's correct.
Original post by notnek
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.
UPDATE: Don't 90 isn't the answer. I did a minor error.
(edited 6 years ago)
Original post by Pretish
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.
Original post by notnek
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.

yes thank you! Non-calcultor questions would be preferable Btw considering the first paper is non-calc tommorow morning