### C1 Mathematics Edexcel June 2009 Question 6

6. The equation x^{2} + 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 a_{1}, a_{2}, a_{3}, ... is defined by

a_{1} = k,

a_{n+1} = 2 a_{n} - 7, n & ge; 1,

where k is a constant.

(a) Write down an expression for a_{2} in terms of k.

(b) Show that a_{3} = 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} + Ax^{1/2} + 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 x^{3} – 6x^{2} + 9x

(b) Sketch the curve with equation

y = x^{3} – 6x^{2} + 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 = x^{3} – 2x^{2} – 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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