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

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Okay i've got x^3-3x^2y-3xy^2-y^3 but I don't know how to simplify it further and I know you probably can

When simplifying you want to try to avoid expanding as much as possible or you may get something like this and then get stuck.

There's a few ways to approach this question. One way is to use "difference of two squares" on the numerator.

Reply 141

_gcx

Study Forum Helper

Original post by notnek

Spoiler

Reply 142

alyttelton

Original post by notnek

Simplify:

\displaystyle \frac{(x^2-xy)^2-(xy-y^2)^2}{(x+y)}

Would it be (x-y)^3(x+y) ?

Reply 143

boi_

Original post by notnek

Simplify:

\displaystyle \frac{(x^2-xy)^2-(xy-y^2)^2}{(x+y)}

(x-y)^3.

This is really useful BTW! :smile:

p.s. is your previous matrices question on the spec? never seen anything like it! i somehow managed to get both theta and alpha as -1 xD

Reply 144

Notnek

Original post by _gcx

Spoiler

Nice solution. It sounds like you're not doing Further Maths - is that right? I'm sure you would have done well in it.

Reply 145

Notnek

Here's a type of question that I've seen a few times in papers but it's often not done well by students:

A function

f

is defined by

f(x)=x^2-3x-4

and

-2\leq x \leq 6

.

Find the range of

f(x)

.

EDIT : Now I'm getting confused and wondering if I have seen this type of question in Level 2 FM. But it's worth trying anyway.

(edited 6 years ago)

Reply 146

Notnek

Original post by chinkinator

(x-y)^3.

This is really useful BTW! :smile:

p.s. is your previous matrices question on the spec? never seen anything like it! i somehow managed to get both theta and alpha as -1 xD

It's too hard to be a question in the exam (probably) but it can be done with Level 2 FM knowledge/methods, as I showed in the solution.

Reply 147

B0redBrioche

Original post by notnek

Here's a type of question that I've seen a few times in papers but it's often not done well by students:

A function

f

is defined by

f(x)=x^2-3x-4

and

-2\leq x \leq 6

.

Find the range of

f(x)

Spoiler

(edited 6 years ago)

Reply 148

boi_

Original post by notnek

Here's a type of question that I've seen a few times in papers but it's often not done well by students:

A function

f

is defined by

f(x)=x^2-3x-4

and

-2\leq x \leq 6

.

Find the range of

f(x)

-16<f(x)<14? (< or equal to)

Reply 149

TheMightyBadger

Original post by notnek

Here's a type of question that I've seen a few times in papers but it's often not done well by students:

A function

f

is defined by

f(x)=x^2-3x-4

and

-2\leq x \leq 6

.

Find the range of

f(x)

.

EDIT : Now I'm getting confused and wondering if I have seen this type of question in Level 2 FM. But it's worth trying anyway.

Spoiler

Reply 150

etothepiiplusone

Original post by TheMightyBadger

Spoiler

I got the same.

Reply 151

Notnek

@TheMightyBadger is correct. Unfortunately not correct @chinkinator @B0redBrioche- think about the shape of a quadratic graph and how you would work out its range.

Reply 152

B0redBrioche

Original post by notnek

@TheMightyBadger is correct. Unfortunately not correct @chinkinator @B0redBrioche- think about the shape of a quadratic graph and how you would work out its range.

Ahh yes i get it now, find the minimum turning point for the lowest bound of the range (1.5) instead of substituting -2. An easy mistake to make!

Reply 153

etothepiiplusone

Latex-ed my questions:

1.Prove

\tan ^2 \theta + \cos ^2 \theta = \tan ^2 \theta \sin ^2 \theta + 1

2. Let

f(x)=\sqrt{\frac{-1}{x}}

a. Find a suitable domain for

f

b. Find the range of

f

Reply 154

TheMightyBadger

Original post by etothepiiplusone

Latex-ed my questions:

1.Prove

\tan ^2 \theta + \cos ^2 \theta = \tan ^2 \theta \sin ^2 \theta + 1

2. Let

f(x)=\sqrt{\frac{-1}{x}}

a. Find a suitable domain for

f

b. Find the range of

f

I will try number 1 later because it requires more thought, but for number 2:

Spoiler

Reply 155

boi_

Original post by etothepiiplusone

Latex-ed my questions:

1.Prove

\tan ^2 \theta + \cos ^2 \theta = \tan ^2 \theta \sin ^2 \theta + 1

2. Let

f(x)=\sqrt{\frac{-1}{x}}

a. Find a suitable domain for

f

b. Find the range of

f

domain: x<0
range: 0<fx<infinity

Reply 156

Notnek

Probably the last one from me today. If I have free days then I'll try to post more questions before Paper 2. I wish everyone luck in their exam tomorrow :smile:

The diagram shows a circle which touches the

y

-axis and has a centre at the point

(a, 0)

where

a

is a positive constant.

Given that the point

(4, -3)

lies on the circle, find the value of

a

Reply 157

etothepiiplusone

Original post by chinkinator

domain: x<0
range: 0<fx<infinity

< infinity is a bit unnecessary, but yes

Reply 158

TheMightyBadger

Original post by notnek

Probably the last one from me today. If I have free days then I'll try to post more questions before Paper 2. I wish everyone luck in their exam tomorrow :smile:

The diagram shows a circle which touches the

y

-axis and has a centre at the point

(a, 0)

where

a

is a positive constant.

Given that the point

(4, -3)

lies on the circle, find the value of

a

Spoiler

Reply 159

etothepiiplusone

Original post by notnek

Probably the last one from me today. If I have free days then I'll try to post more questions before Paper 2. I wish everyone luck in their exam tomorrow :smile:

The diagram shows a circle which touches the

y

-axis and has a centre at the point

(a, 0)

where

a

is a positive constant.

Given that the point

(4, -3)

lies on the circle, find the value of

a

Spoiler

(edited 6 years ago)

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

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