Questions and Worked Solutions for C1 Edexcel Core Mathematics June 2012.

**Completing the Square**

4x - 5 - x^{2} = q - (x + p)^{2} where p and q are integers.

**Coordinate Geometry**

The line L_{1} has equation 4y + 3 = 2x

The point A (p, 4) lies on L_{1}

**Intersection of Graphs**

The line L_{1}and the line L_{2} intersect at the point D.
**Distance between two points**

(d) Show that the length of CD is 3/2 √5

**Area - Coordinate Geometry**

A point B lies on L_{1} and the length of AB = √(80)

The point E lies on L_{2} such that the length of the line CDE = 3 times the length of CD.
(e) Find the area of the quadrilateral ACBE.
Core 1 Mathematics Edexcel June 2012 Question 10

**Graph Transformations**

Figure 1 shows a sketch of the curve C with equation y = f(x) where f (x) = x^{2}(9 – 2x)

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Edexcel Core Mathematics C1 June 2012 Past Paper

4x - 5 - x

(a) Find the value of p and the value of q.

(b) Calculate the discriminant of 4x – 5 – x^{2}

(c) On the axes on page 17, sketch the curve with equation y = 4x – 5 – x^{2} showing clearly the coordinates of any points where the curve crosses the coordinate axes.

The line L

The point A (p, 4) lies on L

(a) Find the value of the constant p.

The line L_{2} passes through the point C (2, 4) and is perpendicular to L_{1}

(b) Find an equation for L_{2} giving your answer in the form ax + by + c = 0, where a, b and c are integers.

The line L

(c) Find the coordinates of the point D.

(d) Show that the length of CD is 3/2 √5

A point B lies on L

The point E lies on L

Figure 1 shows a sketch of the curve C with equation y = f(x) where f (x) = x

There is a minimum at the origin, a maximum at the point (3, 27) and C cuts the x-axis at the point A.

(a) Write down the coordinates of the point A.

(b) On separate diagrams sketch the curve with equation

(i) y = f(x + 3)

(ii) y = f(3x)

On each sketch you should indicate clearly the coordinates of the maximum point and any points where the curves cross or meet the coordinate axes.

The curve with equation y = f (x) + k, where k is a constant, has a maximum point at (3, 10).

(c) Write down the value of k.

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