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) = 3x^{2} -3x + 5

find the value of f(1).

Differentiation, Curve Sketching, Transformation of Graphs

The curve C1 has equation y = x

(a) Find dy/dx

(b) Sketch C1 , showing the coordinates of the points where C_{1} meets the x-axis.

(c) Find the gradient of C_{1} at each point where C_{1} meets the x-axis.

where k is a constant and k > 2

(d) Sketch C_{2} , showing the coordinates of the points where C_{2} meets the x and y axes.

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.

(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.

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