Edexcel GCE Core Mathematics C1 January 2011 exam answers review

A sequence a₁, a₂ , a₃ ,… is defined by

where c is a constant.

1. Find an expression for a_c in terms of c.(1)

Given that:

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2. find the value of c.(4)

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

The curve passes through the origin and has two asymptotes, with equations y =1 and x = 2 , as shown in Figure 1.

1. In the space below, sketch the curve with equation y = f (x −1) and state the equations of the asymptotes of this curve.(3)
2. Find the coordinates of the points where the curve with equation y = f (x −1) crosses the coordinate axes.(4)

An arithmetic sequence has first term a and common difference d. The sum of the first 10 terms of the sequence is 162.

1. Show that 10a + 45d =162(2)

Given also that the sixth term of the sequence is 17,

2. write down a second equation in a and d,(1)
3. find the value of a and the value of d.(4)

The curve with equation y = f (x) passes through the point (−1,0).

Given that

find f (x).

(5)

The equation x² + (k − 3)x + (3− 2k) = 0, where k is a constant, has two distinct real roots.

1. Show that k satisfies

   k² + 2k − 3 > 0

   (3)

2. Find the set of possible values of k.(4)

The line L₁ has equation 2y − 3x − k = 0, where k is a constant.

Given that the point A (1, 4) lies on L₁ , find

1. the value of k,(1)
2. the gradient of L₁.(2)

The line L₂ passes through A and is perpendicular to L₁ .

3. Find an equation of L₂ giving your answer in the form ax + by + c = 0, where a, b and c are integers.(4)

The line L₂ crosses the x-axis at the point B.

4. Find the coordinates of B.(2)
5. Find the exact length of AB.(2)

1. On the axes below, sketch the graphs of
   1. y = x(x + 2)(3− x)
   2. y = –2/x

   showing clearly the coordinates of all the points where the curves cross the coordinate
   axes.(6)

2. Using your sketch state, giving a reason, the number of real solutions to the equation

   x(x 2)(3 x) + 2/x = 0

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