Some C1 questions...could somebody pls help me?!

Hi, could someone pls help me out with the following Qs?:

1) Solve the equation x^2-4x-8=), giving your answers in the form a+b sqrt3 where a and b are integers. (how do I give it in that form?) (3 marks)
2) Find the set of values for which (x-1)(x-2)<20. (4 marks)
3) The curve with equation y=f(x) passes through the point (8,7). Given that f ‘ (x)=4x^1/3 –5, find f(x). (6 marks)
4) a) Evaluate (5 4/9) ^-1/2. (2 marks)
b) Find the value of x such that 1+x/x=sqrt3, giving your answer in the form a+b sqrt3 where a and b are integers. (4 marks)
5) a) Given that y=x+5+3/sqrt x, find dy/dx. (3 marks)
b) Find integral of y. (4 marks)
6) f(x)=x^3/2 –8x^-1/2.
a) Evaluate f(3), giving your answer in its simplest form with a rational denominator. (3 marks)
b) Solve the equation f(x)=0, giving your answers in the form k sqrt 2. (4 marks)

Reply 1

footballhead

thats alot of questions, ill tell u how to do some of them

1. complete the square so
(x-2)2 -4 -8 = 0
go on from there

2. solve it like an equation then put the sign back in

3. integrate it dont forgot + c (u find this by putting in the points 8,7 for x and y, and see what u get for c)

4. something to the power of -.5 is the same as 1/square root that

Reply 2

footballhead

5.a differnitate it
b. integrate dont forget + c

6. a just put 3 in instead of X see what u get
b. set the equation = 0 then its just an easy quadratic

Reply 3

*girlie*

thank you!!! Could you also help me with these 2 Qs? Esp. the first...

9) a) Prove that the sum of the first n terms of an arithmetic series with the first term a and common difference d is given by: 1/2n(2a+(n-1)d).
A novelist begins writing a new book. She plans to write 16 pages during the first week, 18 during the second and so on, with the number of pages increasing by 2 each week. Find, according to her plan,
b) how many pages she will write in the fifth week.
c) The total number of pages she will write in the first five weeks.
d) Using algebra, find how long it will take her to write the book if it has 250 pages.

10) The curve C has the equation y=f(x) where f(x)=(x+2)^3.
a) Sketch the curve C, showing the coordinates of any points of intersection with the coordinate axes.
b) Find f’(x).
The straight line l is the tangent to C at the point P(-1,1).
c) Find an equation for L. (not a problem, but the next one..?)
The straight line m is parallel to l and is also a tangent to C.
d) Show that m has the equation y=3x+8.

Reply 4

footballhead

9. its a general proof google for it, ive forgotten how to do it, you have to write it out like n,n+1 i think

novelist: just put the figures into the equation for nth term above so d=2, a=16, n=5

c. put above values for a,d,n into 1/5n(2a etc

d. set the equation above i.e .5n(2a+n-1)d = 250 (with the specifics for a,d leaving N the one u need to find, like X in quadratics.

10. a. sketch it? put x = 0 to find the interesction with axis etc
b. differntiate it - first multiply out the brackets though

d. ok if itsa parrallel the the gradient is going to be the same as the above so take the gradient - the number in front of the X (if it is in this form y=mx+c) If it has a tangent to C then it goes through the Point P so put those numbers in to find the +C

remember general equation y=mx+c