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Edexcel Core Mathematics C1 June 2009




 

Questions and Video Solutions for C1 Edexcel Core Mathematics June 2009

Edexcel Core Mathematics C1 June 2009 Past Paper


C1 Mathematics Edexcel June 2009 Question 6

6. The equation x2 + 3px + p = 0, where p is a non-zero constant, has equal roots.
Find the value of p.




C1 Mathematics Edexcel June 2009 Question 7

7. A sequence a1, a2, a3, ... is defined by
a1 = k,
an+1 = 2 an - 7, n & ge; 1,
where k is a constant.
(a) Write down an expression for a2 in terms of k.
(b) Show that a3 = 4k – 21.
Given that Σar = 43,
(c) find the value of k.



 

C1 Mathematics Edexcel June 2009 Question 8

The points A and B have coordinates (6, 7) and (8, 2) respectively.
The line l passes through the point A and is perpendicular to the line AB, as shown in Figure 1.
(a) Find an equation for l in the form ax + by + c = 0, where a, b and c are integers.
Given that l intersects the y-axis at the point C, find
(b) the coordinates of C,
(c) the area of △OCB, where O is the origin.



C1 Mathematics Edexcel June 2009 Question 9

f(x) = (3 - 4√x)2/√x, x > 0
(a) Show that f(x) = 9x-1/2 + Ax1/2 + B, where A and B are constants to be found.
(b) Find f'(x).
(c) Evaluate f'(9).



 

C1 Mathematics Edexcel June 2009 Question 10

10. (a) Factorise completely x3 – 6x2 + 9x
(b) Sketch the curve with equation
y = x3 – 6x2 + 9x
showing the coordinates of the points at which the curve meets the x-axis.
Using your answer to part (b), or otherwise,
(c) sketch, on a separate diagram, the curve with equation
y = (x – 2)3 – 6(x – 2)2 + 9(x – 2)
showing the coordinates of the points at which the curve meets the x-axis.



C1 Mathematics Edexcel June 2009 Question 11

11. The curve C has equation y = x3 – 2x2 – x + 9, x > 0
The point P has coordinates (2, 7).
(a) Show that P lies on C.
(b) Find the equation of the tangent to C at P, giving your answer in the form y = mx + c,
where m and c are constants.
The point Q also lies on C.
Given that the tangent to C at Q is perpendicular to the tangent to C at P,
(c) show that the x-coordinate of Q is ⅓(2 + √6)



 

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