Questions and Worked Solutions for C1 Edexcel Core Mathematics January 2010.
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.
Core 1 Mathematics Edexcel January 2010 Question 7
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.
Core 1 Mathematics Edexcel January 2010 Question 8
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.
Core 1 Mathematics Edexcel January 2010 Question 9
(a) Factorise completely x3 − 4x
(b) Sketch the curve C with equation
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.
Core 1 Mathematics Edexcel January 2010 Question 10
f(x) = x2 + 4kx + (3 + 11k)
(a) Express f(x) in the form (x+p)2 + q , where p and q are constants to be found in terms 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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