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

21

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 6 years ago)

Reply 1

3317752

13

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

Reply 2

Notnek

OP

21

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

Reply 3

3317752

13

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

Spoiler

Reply 4

Notnek

OP

21

Original post

by Pretish

Spoiler

Reply 5

3317752

13

Original post

by notnek

Spoiler

Reply 6

Notnek

OP

21

Original post

by Pretish

Spoiler

Reply 7

3317752

13

Original post

by notnek

Spoiler

Reply 8

Notnek

OP

21

Original post

by Pretish

Spoiler

Reply 9

3317752

13

Original post

by notnek

Spoiler

it was good one lol

Reply 10

_gcx

21

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

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

Reply 11

Notnek

OP

21

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.

Reply 12

Notnek

OP

21

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 :smile:

Reply 13

_gcx

21

Original post

by notnek

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

Cheers

I'll take a look.

Reply 14

Notnek

OP

21

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 $n\rightarrow \infty$ .

Reply 15

3317752

13

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

Spoiler

Reply 16

Notnek

OP

21

Original post

by Pretish

is the answer?

in spoiler btw

Spoiler

Yes that's correct.

Reply 17

3317752

13

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.

Reply 18

Notnek

OP

21

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.

Reply 19

3317752

13

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

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

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