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

Notnek
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105 Mark Unofficial Practice Paper 2

Hi :wavey:

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.

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
Last edited by Notnek; 5 days 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
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Notnek
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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 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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i got a point where it was sinx . cosx = 0

Am i at the right place.
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Notnek
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(Original post by Pretish)
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i got a point where it was sinx . cosx = 0

Am i at the right place.

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Looks good so far! Any ideas what to do next?
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(Original post by notnek)
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Looks good so far! Any ideas what to do next?

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well i'm thinking about having the values everywhere thats the sin graph and cos the graph meet the 0 x axis

This would mean my answers would be

0, 180, 360
and
90, 270
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Notnek
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(Original post by Pretish)
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well i'm thinking about having the values everywhere thats the sin graph and cos the graph meet the 0 x axis

This would mean my answers would be

0, 180, 360
and
90, 270


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You've done very well but there's that tricky part that I mentioned earlier that you missed. Hint : Try substituting all of these answers into the original equation and check if they work.
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(Original post by notnek)
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You've done very well but there's that tricky part that I mentioned earlier that you missed. Hint : Try substituting all of these answers into the original equation and check if they work.

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i put in all the values and 180, and 270 gave me an error. Could u explain why/
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Notnek
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(Original post by Pretish)
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i put in all the values and 180, and 270 gave me an error. Could u explain why/


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In maths you can't divide by 0 since division by 0 is undefined. So any answer that leads to denominators equal to 0 in the original equation cannot be a solution. Don't worry too much about this - I doubt this will come up in your exam but I thought it was a nice thing to include.

Your answers were correct if you exclude 180 and 270

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(Original post by notnek)
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In maths you can't divide by 0 since division by 0 is undefined. So any answer that leads to denominators equal to 0 in the original equation cannot be a solution. Don't worry too much about this - I doubt this will come up in your exam but I thought it was a nice thing to include.

Your answers were correct if you exclude 180 and 270


it was good one lol
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_gcx
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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}.
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Notnek
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(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.
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Notnek
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(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
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_gcx
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(Original post by notnek)
Here's the spec if you decide to make another question
Cheers I'll take a look.
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Notnek
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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 nth term of the sequence is u_n. Find the limiting value of u_n as n\rightarrow \infty.
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(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 nth 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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3/2?
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Notnek
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(Original post by Pretish)
is the answer?

in spoiler btw
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3/2?

Yes that's correct.
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(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.
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Notnek
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(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.
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(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
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