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Edexcel C1 2015 Q10. A curve with equation y = f (x) passes through the point (4, 9). Given that f′(x)=3x^(1/2)-9/(4x^(1/2))+2. Find f(x), giving each term in its simplest form.

I would go through a similar example of integration with the student using the whiteboard and would explain the use of integration, and would then get them to do the above question, giving them hints when ne...
IA
Answered by Issy A. • Maths tutor
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Solve the differential equation dy/dx = y/x(x + 1) , given that when x = 1, y = 1. Your answer should express y explicitly in terms of x.

Rearrange differential equation to get 1/x(x+1) dx = 1/y dy. Separate x side into partial fractions where 1/x(x+1) = 1/x - 1/(x+1). Integrate each side. Resulting equation involves natural logs. Substitute i...
AT
Answered by Alexander T. • Maths tutor
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The expansion of (1+x)^4 is 1 + 4x +nx^2 + 4x^3 + x^4. Find the value of n. Hence Find the integral of (1+√y)^4 between the values 1 and 0 (one top, zero bottom).

Using Binomial expansion or Pascal's triangle, expand (1+x)^4 to get 1+4x+6x^2+4x^3+x^4. Then, by substituting √y for x, get 1 + 4y^1/2 + 6y +4y^3/2 +y^2. Then, using the rules of integration, the expansion ...
TD
Answered by Tutor41123 D. • Maths tutor
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Express 4 sin(x) – 8 cos(x) in the form R sin(x-a), where R and a are constants, R >0 and 0< a< π/2

4 sin(x) – 8 cos(x)= Rsin(x-a) here use double angle formula 4 sin(x) – 8 cos(x)= Rsin(x)cos(a)-Rcos(x)sin(a) Rearrange so in same format as LHS 4 sin(x) – 8 cos(x)= Rcos(a)sin(x)-Rsin(a)cos(x) Equate terms ...
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Answered by Simon E. • Maths tutor
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The line L has equation y = 5 - 2x. (a) Show that the point P (3, -1) lies on L. (b) Find an equation of the line perpendicular to L that passes through P.

(a) To confirm that point P lies on L, we must substitute x = 3 into the equation and see if we get y = -1. y = 5 - 2(3) = -1, therefore P lies on the line L (b) The gradient of the perpendicular line is -1/...
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Answered by Kitty S. • Maths tutor
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