Questions and Worked Solutions for C1 Edexcel Core Mathematics January 2010.

Question Paper (pdf)

Core 1 Mathematics Edexcel January 2010 Question 6

The curve C has equation

y = [(x + 3)(x - 8)]/x, x > 0

(a) Find dy/dx in its simplest form.

(b) Find an equation of the tangent to C at the point where x = 2.

Jill gave money to a charity over a 20-year period, from Year 1 to Year 20 inclusive.

She gave £150 in Year 1, £160 in Year 2, £170 in Year 3, and so on, so that the amounts

of money she gave each year formed an arithmetic sequence.

(a) Find the amount of money she gave in Year 10.

(b) Calculate the total amount of money she gave over the 20-year period.

Kevin also gave money to the charity over the same 20-year period.

He gave £A in Year 1 and the amounts of money he gave each year increased, forming an

arithmetic sequence with common difference £30.

The total amount of money that Kevin gave over the 20-year period was twice the total

amount of money that Jill gave.

(c) Calculate the value of A.

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

The curve has a maximum point (−2, 5) and an asymptote y = 1, as shown in Figure 1.

On separate diagrams, sketch the curve with equation

(a) y = f(x) + 2

(b) y = 4f(x)

(c) y = f(x + 1)

On each diagram, show clearly the coordinates of the maximum point and the equation of

the asymptote.

(a) Factorise completely x

(b) Sketch the curve C with equation

y = ,

showing the coordinates of the points at which the curve meets the x-axis.

The point A with x-coordinate −1 and the point B with x-coordinate 3 lie on the curve C.

(c) Find an equation of the line which passes through A and B, giving your answer in the

form y = mx + c, where m and c are constants.

(d) Show that the length of AB is k √10, where k is a constant to be found.

f(x) = x

(a) Express f(x) in the form (x+p)

of k.

Given that the equation f(x) = 0 has no real roots,

(b) find the set of possible values of k.

Given that k = 1,

(c) sketch the graph of y = f(x), showing the coordinates of any point at which the graph

crosses a coordinate axis.

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