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Edexcel Core Mathematics C1 June 2009




 

Questions and Video Solutions for C1 Edexcel Core Mathematics June 2009

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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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