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Questions and Worked Solutions for C1 Edexcel Core Mathematics June 2011.

Edexcel Core Mathematics C1 June 2011 Past Paper

Core 1 Mathematics Edexcel June 2011 Question 6
6. Given that

(6x + 3x^{5/2}) / √ x can be written in the form 6x^{p} + 3x^{q}

(a) write down the value of p and the value of q.

Given that

dy/dx = (6x + 3x^{5/2}) / √ x and that y = 90 when x = 4,

(b) find y in terms of x, simplifying the coefficient of each term.

6.(b)

Core 1 Mathematics Edexcel June 2011 Question 7
7. f(x) = x2 + (k + 3)x + k,

where k is a real constant.

(a) Find the discriminant of f (x) in terms of k.

(b) Show that the discriminant of f (x) can be expressed in the form (k + a)^{2} + b where

a and b are integers to be found.

(c) Show that, for all values of k, the equation f(x) = 0 has real roots.

- (b)

- (c)

Core 1 Mathematics Edexcel June 2011 Question 8
8. Figure 1 shows a sketch of the curve C with equation y = f (x).

The curve C passes through the origin and through (6, 0).

The curve C has a minimum at the point (3, –1).

On separate diagrams, sketch the curve with equation

(a) y = f(2x),

(b) y = −f(x),

(c) y = f (x + p), where p is a constant and 0 < p < 3.

On each diagram show the coordinates of any points where the curve intersects the x-axis

and of any minimum or maximum points.

Core 1 Mathematics Edexcel June 2011 Question 9
9. (a) Calculate the sum of all the even numbers from 2 to 100 inclusive,

2 + 4 + 6 + …… + 100

(b) In the arithmetic series

k + 2k + 3k + …… + 100

k is a positive integer and k is a factor of 100.

(i) Find, in terms of k, an expression for the number of terms in this series.

(ii) Show that the sum of this series is

50 + 5000/k

(c) Find, in terms of k, the 50th term of the arithmetic sequence

(2k + 1), (4k + 4), (6k + 7), …… ,

giving your answer in its simplest form.

- (b)

- (c)

Core 1 Mathematics Edexcel June 2011 Question 10
10. The curve C has equation

y = (x + 1)(x + 3)^{2}

(a) Sketch C, showing the coordinates of the points at which C meets the axes.

(4)

(b) Show that dy/dx = 3x^{2} + 14x + 15

The point A, with x-coordinate -5, lies on C.

(c) Find the equation of the tangent to C at A, giving your answer in the form y = mx + c,

where m and c are constants.

Another point B also lies on C. The tangents to C at A and B are parallel.

(d) Find the x-coordinate of B.

- (b)

- (c)

- (d)

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