 # Edexcel Core Mathematics C1 January 2012

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Questions and Worked Solutions for C1 Edexcel Core Mathematics January 2012.

Edexcel Core Mathematics C1 January 2012 Past Paper

Core 1 Mathematics Edexcel January 2012 Question 7
Integration
A curve with equation y = f(x) passes through the point (2, 10). Given that
f'(x) = 3x2 -3x + 5

find the value of f(1).

Core 1 Mathematics Edexcel January 2012 Question 8
Differentiation, Curve Sketching, Transformation of Graphs
The curve C1 has equation y = x2(x + 2)

(a) Find dy/dx

(b) Sketch C1 , showing the coordinates of the points where C1 meets the x-axis.

(c) Find the gradient of C1 at each point where C1 meets the x-axis.

The curve C2 has equation y = (x - k)2(x - k + 2)

where k is a constant and k > 2

(d) Sketch C2 , showing the coordinates of the points where C2 meets the x and y axes.

Core 1 Mathematics Edexcel January 2012 Question 9
Arithmetic Series
9. A company offers two salary schemes for a 10-year period, Year 1 to Year 10 inclusive. Scheme 1: Salary in Year 1 is £P.
Salary increases by £(2T) each year, forming an arithmetic sequence.

Scheme 2: Salary in Year 1 is £(P + 1800).
Salary increases by £T each year, forming an arithmetic sequence.

(a) Show that the total earned under Salary Scheme 1 for the 10-year period is £(10P + 90T).

For the 10-year period, the total earned is the same for both salary schemes.
(b) Find the value of T. For this value of T, the salary in Year 10 under Salary Scheme 2 is £29 850
(c) Find the value of P. Core 1 Mathematics Edexcel January 2012 Question 10
Equation of a Normal, Intersection of Graphs

Figure 2 shows a sketch of the curve C with equation

y = 2 - 1/x , x ≠ 0

The curve crosses the x-axis at the point A.

(a) Find the coordinates of A.

(b) Show that the equation of the normal to C at A can be written as 2x + 8y - 1 = 0

The normal to C at A meets C again at the point B, as shown in Figure 2.
(c) Find the coordinates of B.

10 (c)

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