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How to I prepare for a Cambridge interview?

If you got an interview you are already halfway there - congratulations! The interviewers liked your application and think you have potential, so your job during the interview is just to try to convey that p...
LG
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Show that the lines y=3x+7 and 2y–6x=8 are parallel. Do not use a graphical method.

y=3x+7 2y-6x=8 2y-6x=82y=8+6xy= 4+3xy=3x+4When both equations equal y they both have a 3 in front of their x meaning that they both have a gradient of 3.
JM
Answered by Jordan M. • Maths tutor
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Curves C1 and C2 have equations y= ln(4x-7)+18 and y= a(x^2 +b)^1/2 respectively, where a and b are positive constants. The point P lies on both curves and has x-coordinate 2. It is given that the gradient of C1 at P is equal to the gradient of C2 at P.

y= ln(4x-7)+18 y= a(x^2 +b)^1/2 At x=2 dy/dx = dy/dx and y =y At x =2 y = ln(8-7) +18 y = ln 1 +18 y =18 At x = 2 18=a(4 +b)^1/2 18/(4+b)^1/2= a y=ln(4x-7)+18dy/dx= 4/(4x-7) At x= 2 dy/dx= 4/8-7= 4 y=a(x^2 +...
JM
Answered by Jordan M. • Maths tutor
10412 Views

Calculate the value of the definite integral (x^3 + 3x + 2) with limits x=2 and x=1

a) Integrate the given expression using integration laws we have learnt to give [(x^4)/4 + (3(x^2))/2 + 2x ] and you do not need a +c constant as we have limits.b) Substitute the limits into the equation we ...
Answered by • Maths tutor
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What is osmosis?

Osmosis is the passive diffusion of water, which therefore, doesn't require any energy to occur. Typically water will move from an area of high concentration to an area of low concentration across a semi-per...
MW
Answered by Matthew W. • Biology tutor
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