Son stuck on one maths question which apparently flummoxed the entire year.
Question:

x squared + y squared =9
x+y=2

give values for x and y (two possible answers)

Can anyone do this via formula rather than graphing it?
Please show working.

go go go…..stw brainiacs are unleashed!

And before the English pedants get unleashed, should I have added an apostrophe in today’s?

2.5 or -0.5

From second equation – x=2-y

So: x^2 + y^2=9 -> (2-y)^2 + y^2 = 9

So multiply out to something like – > 2y^2 – 4y – 5 = 0

The y comes from the standard (-b +/- sqrt (b^2 – 4ac))/2a

Then x=2-y for each value of y.. if that makes sense.

(some of the algebra may be wrong – doing in my head..) but the idea should work.

Edit – fixed the -5 at end. Doh

X**2+y**2 = 9
x+y = 2. i.e. x = 2-y

therefore , by substitution
(2-y)**2 + y**2 = 9
4-4y+y**2 +y**2 = 9
2y**2-4y+4=9
2y**2-4y-5 = 0

by quadratic formula

y=2.5 or -0.5 then derive x by substitution

Think you are wrong, but not by much.
I bought an app for the ipad called quickgraph.

That shows the answer to be approx -.84 and +2.88

Buggered if I can rearrange the formula to do it from first principles.

Shocked by how much I have forgotten in nearly a quarter of a century.

x^2 + y^2 = 9
x + y = 2

x = 2-y

(2-y)^2 + y^2 = 9

4 – 4y +y^2 + y^2 = 9

2y^2 – 4y – 5 = 0

using

y = (-b +/- sqrt(b^2 – 4ac))/2a

y = 4 +/- (sqrt(16 – – 40))/4

y = (4+7.483)/4 = 2.87075
y = (4-7.483)/4 = -0.87075

I sat a Maths GCSE today too. I didn’t have that exact question but I did have a more complex simultaneous equation that used the same method. I sat OCR Unit C High Tier. I might well have done a different exam, I don’t know. I’ll give a go anyway, though.

Cancel that. After doing a 2 hour Maths exam (which took about an hour) myself, I can’t summon the will power do write it all out in an annoying format using a keyboard.

The basic idea is that you substitute the second equation into the first and then simplify it. Once that’s done, it needs to be factorised in the form (x+?)(x+?)=0 or something similar, so long as the x or a 2x is at the beginning of each bracket.

Those 2 brackets can then be rearranged (with the =0) to give 2 x= answers.

Finally, substiute those 2 answers into the second equation in the place of x and work out the y value.

It’s not that hard once you know how to do it.

Wife had already solved it. International Baccalaureate beats late 1980’s comprehensive education.
And still we think that education in the UK doesn’t need a kick up the backside!

Still impressed with how close HB junior got!

I got the same answer as Stoner.
not done that in a while.
friday fun…

UK Secondary education might need an overhaul, but I doubt it needs a final exam and no coursework.

@gofasterstripes. I think maths by exam is the right way.
For history and english certainly not the right way.
Science mainly exam, with a small amount of lab assesment.

@CHB- With lab assessment for the sciences, there will be lots of cheating going on though. In fact, in some places, that’s already happening with the ISAs. 🙁

Overall, I’ve found all my GCSEs easy really. I spent most of my time riding my bike, instead of revising and should still come away with about 5-6 A*s out of 10 sat. I’m not sure if that’s a reflection on me or the system, though.

My son is in YR10, but is part of a group taking maths early.
Good luck with your own GCSE’s, with grades like you are hoping for the world is your oyster.
Hope you do fab in A levels too.

And without the solution for a quadratic?

x^2+y^2 = 9 – circle radius 3 centred at origin
(x+y) = 2 – line y = 2-x must cross circle at (-ve,+ve) and (+ve,-ve)
(x+y)(x+y)-2xy = 9 – Complete the square
4-2xy = 9 – substitute second equation
xy = -5/2
x-5/2x = 2
2x^2-4x-5 = 0

almost… Go back to b^2-4ac. Was hopeful!

That might be why he took a different exam to me then. Good luck to him for the rest of them. Tell him to try not to get too stressed from me. From about the 1st quarter of Year 11 onwards is the most stressful time I found, with lots of coursework, or controlled assessments as they’re actually called, to do.

Thanks. GCSEs are over and done with for me now, thank god! I’m hoping to do well in my A Levels and head off to Sheffield Uni to ride bikes while studying Aerospace Engineering. If I can actually make myself knuckle down and work, it should happen. 😆

Are you sure it wasn’t (or should have been) x^2-y^2=9?
That would have been a hell of a lot easier and more gcse like. Only one possible solution to x and y for that mind.

Certain its the way round I said. Apparently the paper had space for both possible x and y values. Is this extra hard by GCSE standards?

No standard gcse higher calc question

Ask Mr Gove – GCSEs too easy.

Interesting read for me this (I’m Head of maths in a secondary school).

It’s a typical hard GCSE higher question, there’s usually one rock hard question at the end of one of the papers (they do a calc and a non calc paper).

BTW Stoners solution is right, (getoyourbike), you can’t solve the resulting quadratic by factorising as it won’t factorise (Factors of -5 are either 1 and -5 or 5 and -1, neither of which pair with x and 2x to make -4x…. although I agree that’s always the first point of call and what I would have tried to do first.

(Tired), well spotted that it is a circle with straight line of negative gradient passing through it, unfortunately you can’t solve it geometrically, you could have done if the line had passed though 0 though as you could use the radius of the circle and two lots of pythag… but as you have realised, it doesn’t work as the line passes through 2 on the y axis.

P.S. (Gofaster stripes), the current maths GCSE is already no coursework and usually just final exams (modular system is now nearly phased out with the last exam series in March 2014)

P.P.S The current Maths GCSE works brilliantly, there is no need for Gove to interfere with it, it aint broke!

P.P.P.S (CHB) your program is giving a close approximate solution and the right answer is stoners. It probably plots the graphs and looks at where they cross, but doesn’t work on an infinitesimaly small substitution of point goes to the nearest ppoint/pixel or however the program works.. it’s out very slightly 😉

BTW Stoners solution is right

thank god for that!
Stoner (GCSE, AO Level, A Level & Further A Level Maths)

😉

(PS – I was wondering if it was solvable using trig applied to the circle and intercept?)

Whoops. If I’d actually worked it out, I would have realised that it didn’t work and done it a different way.

In fact, I think I did a question very similar to that in mine where substitution didn’t work, so I had to do it by doing one equation minus the other equation. It all worked out in the end, though.

You can only use a subtraction method if both are linear and you’ve made a coefficient of x or y the same for both equations… substitution will always work if they cross… and if they don’t cross you can use the resulting quadratic equation to prove they don’t cross so have no solutions as a pair due to the resulting quadratics discriminent being <0

If you want a more challenging one try one where you have a cubic equation an a quadratic equation that intersect at various locations.

Okay, I’m wrong again. 😳 It’s a good job I didn’t get that question then because although I was taught the quadratic equation method, it wasn’t one of the 3 things I revised during my one and only revision session an hour before the exam. 😆

Phew, correct!

My son (16) confirmed that this was not an unusual question. Harder than O level maths in my (and Gove’s) day though. Good final question to sort out higher abilities though IMO, but hopefully the first substitution step was not the challenge. Solving the resulting equation may have been.

(GCSE, AO Level, A Level & Further A Level Maths)

Interesting combination – GCSE and AO level. Did AO get scrapped and replaced with AS a bit later?
Did O, AO (in last ever year of O levels), A Pure (in lower 6th), A Applied (in upper 6th) plus A Pure+Special paper (that was a bastard), which is also a non typical combination (I think most do maths then further maths?)

AO was an elective paper that was still around in ’93 (ish?)
We took GCSE a year early (4th form), then AO in the normal GCSE year, then A Level in Lower sixth and further maths in upper sixth.

I didnt take the Step or S papers as my university didnt require them for my offer. Just as well as they were brutal, and TBH my maths mojo had maxed out with “damping and forcing in differential equations” 😯 so I went over to applied maths where I could hide my ignorance better 😀

Thought it was a pretty good question. Would have been nicer if it HAD factorised though. Spent the past week or two going over past higher papers with my 15yo in preparation. Maths is a bit like sport; once you’ve got the basics, it’s training. I also managed to get him to prove the Cosine and Sine rules and solve the quadratic – hint complete the square twice.

I have two B’s at O level maths 😳 (and a few other maths qualifications).

Didn’t need the S paper either, but did it anyway. Applied maths was easy.