 # Edexcel Core Mathematics C1 June 2012

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

Core 1 Mathematics Edexcel June 2012 Question 8
Completing the Square
4x - 5 - x2 = q - (x + p)2 where p and q are integers.

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

(b) Calculate the discriminant of 4x – 5 – x2

(c) On the axes on page 17, sketch the curve with equation y = 4x – 5 – x2 showing clearly the coordinates of any points where the curve crosses the coordinate axes.

Core 1 Mathematics Edexcel June 2012 Question 9
Coordinate Geometry
The line L1 has equation 4y + 3 = 2x
The point A (p, 4) lies on L1

(a) Find the value of the constant p.

The line L2 passes through the point C (2, 4) and is perpendicular to L1

(b) Find an equation for L2 giving your answer in the form ax + by + c = 0, where a, b and c are integers.

Intersection of Graphs
The line L1and the line L2 intersect at the point D.

(c) Find the coordinates of 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 L1 and the length of AB = √(80)
The point E lies on L2 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) = x2(9 – 2x)

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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