Questions and Worked Solutions for C1 Edexcel Core Mathematics January 2013.

Edexcel Core Mathematics C1 January 2013 Past Paper

Core 1 Mathematics Edexcel January 2013 Question 1

Factorising

1. Factorise completely x − 4x^{3}

Indices

2. Express 8

Surds

3. (i) Express (5 - √8)(1 + √2) in the form a + b√2, where a and b are integers.

(ii) Express √80 + 30/√5 in the form c√5, where c is an integer.

Sequences

4. A sequence u

Given that u

(a) find the value of u

(b) evaluate

Coordinate Geometry

5. The line l

The line l

(a) Find an equation for l

The line l_{2} crosses the x-axis at the point A and the y-axis at the point B.

(b) Find the x-coordinate of A and the y-coordinate of B.

Given that O is the origin,

(c) find the area of the triangle OAB.

Sketching Graphs

Figure 1 shows a sketch of the curve with equation y = 2/x, x ≠ 0 and the line l has equation y = 4x + 2

The curve C has equation y = 2/x - 5

(a) Sketch and clearly label the graphs of C and l on a single diagram.

On your diagram, show clearly the coordinates of the points where C and l cross the coordinate axes.

(b) Write down the equations of the asymptotes of the curve C.

(c) Find the coordinates of the points of intersection of y = 2/x - 5 and y = 4x + 2

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