Jump to content

Past paper question


thepositiveclub

Recommended Posts

Okay I have something to clarify while we're at this: when they say "exactly two solutions" what do they mean?

 

I've got the same question, its really confusing :( Your answer is correct though..

 

This is the mark scheme: a) 

(ii) recognizing that it occurs at P and Q (M1)
e.g. x = −1.15, x =1.15
k = −1.13, k =1.13
 
Could you please explain how you got it?
Link to post
Share on other sites

 

Okay I have something to clarify while we're at this: when they say "exactly two solutions" what do they mean?

 

I've got the same question, its really confusing :( Your answer is correct though..

 

This is the mark scheme: a) 

(ii) recognizing that it occurs at P and Q (M1)
e.g. x = −1.15, x =1.15
k = −1.13, k =1.13
 
Could you please explain how you got it?

 

Well I assumed (which is the problem here, it was an assumption) that "exactly two solutions" were the x-coordinates that were found in (i) for two reasons

1) they would never have a (ii) if it weren't related to (i) 

2) And this is where I was confused...When they said tangent parallel to the x-axis, I visualized a line going through x=1.15 and x=-1.15 and it would pass through two points on the graph. So would those be "exactly two solutions" that the question refers to? <- This assumption led me to believe that the k values would simply be the y-coordinates of the x-values found previously.

 

I know that probably made no sense...I was just giving you what went through my head. I'll work on it unless someone else provides an answer

Link to post
Share on other sites

After some thought I think I found the answer. 

 

First thing I struggled with was to understand the question. Essentially it is asking you to find all values of y that that can be found with exactly two x-values. And the only y-values on the graph that have two x-values are at the max and min points.

 

The min is at (-1.15, -1.13). By plugging in a straight line, x= -1.13, and finding where it intersects with the graph, you will find it intersects at (1.86, -1.13). Hence one k value = -1.13.

 

The max is at (1.15, 1.13). Doing the same thing the intersection is at (-1.86, 1.13), owing to the symmetry of the function. Hence the other k value is = 1.13, as it has two x-values (1.15 and -1.86)

Edited by dorianb
  • Like 1
Link to post
Share on other sites

 

 

Okay I have something to clarify while we're at this: when they say "exactly two solutions" what do they mean?

 

I've got the same question, its really confusing :( Your answer is correct though..

 

This is the mark scheme: a) 

(ii) recognizing that it occurs at P and Q (M1)
e.g. x = −1.15, x =1.15
k = −1.13, k =1.13
 
Could you please explain how you got it?

 

Well I assumed (which is the problem here, it was an assumption) that "exactly two solutions" were the x-coordinates that were found in (i) for two reasons

1) they would never have a (ii) if it weren't related to (i) 

2) And this is where I was confused...When they said tangent parallel to the x-axis, I visualized a line going through x=1.15 and x=-1.15 and it would pass through two points on the graph. So would those be "exactly two solutions" that the question refers to? <- This assumption led me to believe that the k values would simply be the y-coordinates of the x-values found previously.

 

I know that probably made no sense...I was just giving you what went through my head. I'll work on it unless someone else provides an answer

 

 

 

After some thought I think I found the answer. 

 

First thing I struggled with was to understand the question. Essentially it is asking you to find all values of y that that can be found with exactly two x-values. And the only y-values on the graph that have two x-values are at the max and min points.

 

The min is at (-1.15, -1.13). By plugging in a straight line, x= -1.13, and finding where it intersects with the graph, you will find it intersects at (1.86, -1.13). Hence one k value = -1.13.

 

The max is at (1.15, 1.13). Doing the same thing the intersection is at (-1.86, 1.13), owing to the symmetry of the function. Hence the other k value is = 1.13, as it has two x-values (1.15 and -1.86)

This makes more sense now, thank you both so much! :D

Link to post
Share on other sites

Join the conversation

You can post now and register later. If you have an account, sign in now to post with your account.

Guest
Reply to this topic...

×   Pasted as rich text.   Paste as plain text instead

  Only 75 emoji are allowed.

×   Your link has been automatically embedded.   Display as a link instead

×   Your previous content has been restored.   Clear editor

×   You cannot paste images directly. Upload or insert images from URL.

×
×
  • Create New...