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Core 1 Mathematics Edexcel January 2011 Question 1 - Indices

1. (a) Find the value of 16

(b) Simplify x(2

2. Find

∫ (12x

giving each term in its simplest form.

3. Simplify

(5 - 2 √ 3)/( √ 3 - 1)

giving your answer in the form p + q √ 3, where p and q are rational numbers.

4. A sequence a

a1 = 2

a

where c is a constant.

(a) Find an expression for a

Given that

(b) find the value of c.

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

f(x) = x/(x - 2), x ≠ 2

The curve passes through the origin and has two asymptotes, with equations y =1 and

x = 2 , as shown in Figure 1.

(a) In the space below, sketch the curve with equation y = f(x - 1) and state the equations

of the asymptotes of this curve.

(b) Find the coordinates of the points where the curve with equation y = f(x - 1) crosses

the coordinate axes.

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