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Edexcel Core Mathematics C1 January 2013




 

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 − 4x3

Core 1 Mathematics Edexcel January 2013 Question 2
Indices
2. Express 82x+3 in the form 2y, stating y in terms of x.



Core 1 Mathematics Edexcel January 2013 Question 3
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.

Core 1 Mathematics Edexcel January 2013 Question 4
Sequences
4. A sequence u1, u2, u3 , ... satisfies un+1 = 2un - 1, n ≥ 1
Given that u2 = 9,
(a) find the value of u3 and the value of u4,
(b) evaluate


 
Core 1 Mathematics Edexcel January 2013 Question 5
Coordinate Geometry
5. The line l1 has equation y = -2x + 3
The line l2 is perpendicular to l1 and passes through the point (5, 6).
(a) Find an equation for l2 in the form ax + by + c = 0, where a b, and c are integers.

The line l2 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.

Core 1 Mathematics Edexcel January 2013 Question 6
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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