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

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)

Scroll to see replies

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.

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

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

Solve the equation

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

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

Spoiler

Original post by Pretish

Spoiler

Spoiler

Original post by notnek

Spoiler

Spoiler

Original post by Pretish

Spoiler

Spoiler

Original post by notnek

Spoiler

Spoiler

Original post by Pretish

Spoiler

Spoiler

Original post by notnek

Spoiler

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 $0^{\circ}< \theta < 360^{\circ}$.

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 $-360^{\circ}< \theta < 360^{\circ}$.

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 $0^{\circ}< \theta < 360^{\circ}$.

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 $n\rightarrow \infty$.

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 $n$

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 $n\rightarrow \infty$.

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 $n$

is the answer?

in spoiler btw

Spoiler

Original post by Pretish

is the answer?

in spoiler btw

in spoiler btw

Spoiler

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.

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.

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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