For the last question I got k=0 and k=4. I got that because y= - x + k, it had a gradient of -1 so the points on the curve must have done too. Then all I could think to do was differentiate (which as a retaker I can do but I know most of you may not have seen that yet), to find the x coordinates of where the gradient was -1 on the graph. Both seemed to match up graphically, so I hoped it worked ok!
Oh my God. I'm so relieved to see that someone else did that.
What did people get on the circle question? I couldn't find out where the circle intersected the y axis so I used the formula and got 2+root11 and 2-root11. Did I get this completely wrong? Gah I'm scared.
I did both ways, the formula and by setting y and x to 0 according to which intercept I was trying to find. I got the same as you with both methods, I only did both as I doubted myself with the formula thinking I may have gone wrong!!! So reassuringly, we got the same
Oh my God. I'm so relieved to see that someone else did that.
y=1/(x-2)
y=(x-2)-1
(chain rule)
dy/dx = -(x-2)-2 -(x-2)-2 = -1
(x-2)-2 = 1
1/(x-2)2=1
(x-2)2=1
x2-4x+3=0
(x-3)(x-1)=0
Gradient = -1 when x= 1 or 3
To find the y coordinates,
y=1/x-2 y=1/1-2=-1
y=-x+k is a tangent at point (1,-1)
-1=-1+k k=0
y=1/3-2 y=1
y=-x+k is also a tangent at the point (3,1)
1=-3+k k=4
So k=0 or 4
Hope this helps.
Everyone came out with different answers and I was so sure of 4 and 0 because both points had a gradient of -1 and I couldn't see it could be any different! Differentiation for once saved me on this
They won't know grade boundaries until they have all of the final results, then they adjust the boundaries to have a certain number of candidates walking away each grade. Hence for a hard paper they are lowered and vice versa, this seemed a reasonably fair paper so the boundaries may be slightly higher. But the general guide is 80% = A, 70% = B, 60% = C, 50% = D, 40% = E and 40% > U ........ Hope that gave you a vague idea!
I get that - but what do you all think it will be?
Ogod I failed. Well thanks for replying! I think I did okay on the other questions, fingers crossed!
Don't worry, there was no answer of (x-3)^2+(y-2)^2=20, that was the equation of the circle we were given! We didn't have to use complete the square on this either, it was substituting x and y in for 0 according to which intercept you were finding Hope you're not quite so worried!
but I think that question 13 (iii) was awkward for a lot of people, except for the few that spotted the correct way to do it. i've heard from a few of the higher graders in my year that thye found this a big hard at points so i'm going to say 55-53.