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AQA Pure Mathematics A Level Unofficial Mark Scheme
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Here by popular request 😉. Submit the answers you guys got below and we can work out what the answers are together in one place.
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#4
Last question i got the derivative to be -2(e^-x)(sinx), the rest of that question was show that questions, for the last part they wanted you to identify that it was a geometric series where r<1 so it converges for the sum to infinity, then you use the formula and rearrange, must have been 14? marks in total
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#6
Correct
(Original post by ridwan157)
For the intersection between f(x) and f^-1(x), i got (1,1), unsure about this tho
For the intersection between f(x) and f^-1(x), i got (1,1), unsure about this tho
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#7
Proof - 5 marks: (not sure if this is right :/ )
Consider n to be a rational number such that n= a/b, and m is an irrational number such that it cannot be represented as a fraction, a and b are integers with no common factors
Assume the sum of n and m is always rational : n +m = x/y where x/y is in its simplest form and x and y share no common factors
Rearrange:
m= x/y - n
m= x/y - a/b
m= (xb-ay) / (by)
However this is a contradiction as it has been assumed that m cannot be represented as a fraction, therefore the sum must always be irrational
Consider n to be a rational number such that n= a/b, and m is an irrational number such that it cannot be represented as a fraction, a and b are integers with no common factors
Assume the sum of n and m is always rational : n +m = x/y where x/y is in its simplest form and x and y share no common factors
Rearrange:
m= x/y - n
m= x/y - a/b
m= (xb-ay) / (by)
However this is a contradiction as it has been assumed that m cannot be represented as a fraction, therefore the sum must always be irrational
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#8
-2/sqrt5 for the tanx one
proof of rational + irrational number let rational = a/b and irrational = c a/b + c = d/e expand and rearrange for c=(bd-ae)/be which is writing c as a rational number which contradicts the original statement
proof of rational + irrational number let rational = a/b and irrational = c a/b + c = d/e expand and rearrange for c=(bd-ae)/be which is writing c as a rational number which contradicts the original statement
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#9
Parametric question:
tide at 2am is when t=0, i think h was like 5. something cant remember
next high tide is at 8am
Maximum velocity is when h=3 ? I used dv/dt = 0 for that question
tide at 2am is when t=0, i think h was like 5. something cant remember
next high tide is at 8am
Maximum velocity is when h=3 ? I used dv/dt = 0 for that question
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#10
Follow up question about dY/dX asked about the integral of e^-X(sinx) and how to represent it as ae^-X(cosx+sinx) i got a=-1/2
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#12
For the combined rate of change question you needed to show that dr/dt = (k/(4pi))*r^-2 => dr/dt is inversely proportional to r^2
dr/dt = dr/dv * dv/dt
where dv/dr = 4pir^2, dv/dt = k (as it increases at a constant rate)
dr/dt = dr/dv * dv/dt
where dv/dr = 4pir^2, dv/dt = k (as it increases at a constant rate)
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#14
i got a as 2...
(Original post by ridwan157)
For the combined rate of change question you needed to show that dr/dt = (k/(4pi))*r^-2 => dr/dt is inversely proportional to r^2
dr/dt = dr/dv * dv/dt
where dv/dr = 4pir^2, dv/dt = k (as it increases at a constant rate)
For the combined rate of change question you needed to show that dr/dt = (k/(4pi))*r^-2 => dr/dt is inversely proportional to r^2
dr/dt = dr/dv * dv/dt
where dv/dr = 4pir^2, dv/dt = k (as it increases at a constant rate)
(Original post by Ttxxkingxxtt)
Follow up question about dY/dX asked about the integral of e^-X(sinx) and how to represent it as ae^-X(cosx+sinx) i got a=-1/2
Follow up question about dY/dX asked about the integral of e^-X(sinx) and how to represent it as ae^-X(cosx+sinx) i got a=-1/2
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#15
Does anyone have any ideas of grade boundaries? I think I have done really bad and I need an A in maths. Any predictions
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#17
For the functions question:
f(x)= (x^2+1)/2
range is y>=0.5 ??? I used the minimum point to figure this out
f^-1(x) = sqrt(2x-1)
Range of f^-1(x) is the domain of f(x) which was restricted to x>=0, so range of f^-1(x) is f^-1(x)>=0
Transformation from f(x) to f^-1(x) was reflection in line y=x
Intersection is (1,1)
f(x)= (x^2+1)/2
range is y>=0.5 ??? I used the minimum point to figure this out
f^-1(x) = sqrt(2x-1)
Range of f^-1(x) is the domain of f(x) which was restricted to x>=0, so range of f^-1(x) is f^-1(x)>=0
Transformation from f(x) to f^-1(x) was reflection in line y=x
Intersection is (1,1)
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#18
My GUESS is 55/100 for an A on this paper, don't be worried we got 2 papers left
(Original post by tostiw)
Does anyone have any ideas of grade boundaries? I think I have done really bad and I need an A in maths. Any predictions
Does anyone have any ideas of grade boundaries? I think I have done really bad and I need an A in maths. Any predictions
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#19
(Original post by unagdi)
for point of intersection why did i get 2 sets of coordinates :*((
for point of intersection why did i get 2 sets of coordinates :*((
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#20
(Original post by ridwan157)
My GUESS is 55/100 for an A on this paper, don't be worried we got 2 papers left
My GUESS is 55/100 for an A on this paper, don't be worried we got 2 papers left
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