Questions and Worked Solutions for C2 Edexcel Core Mathematics June 2010.

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Edexcel Core Mathematics C2 June 2010 Past Paper

Core 2 Mathematics Edexcel June 2010 Question 6

Figure 1 shows the sector OAB of a circle with centre O, radius 9 cm and angle 0.7 radians.

(a) Find the length of the arc AB.

(b) Find the area of the sector OAB.

The line AC shown in Figure 1 is perpendicular to OA, and OBC is a straight line.

(c) Find the length of AC, giving your answer to 2 decimal places.

The region H is bounded by the arc AB and the lines AC and CB.

(d) Find the area of H, giving your answer to 2 decimal places.

7. (a) Given that

2log_{3}(x - 5) - l0g_{3}(2x - 13) = 1

show that x^{2} - 16x + 64 = 0

(b) Hence, or otherwise, solve 2log_{3}(x - 5) - l0g_{3}(2x - 13) = 1

Figure 2 shows a sketch of part of the curve C with equation

y = x

where k is a constant.

The point P on C is the maximum turning point.

Given that the x-coordinate of P is 2,

(a) show that k = 28 .

The line through P parallel to the x-axis cuts the y-axis at the point N.

The region R is bounded by C, the y-axis and PN, as shown shaded in Figure 2.

(b) Use calculus to find the exact area of R.

9. The adult population of a town is 25 000 at the end of Year 1.

A model predicts that the adult population of the town will increase by 3% each year, forming a geometric sequence.

(a) Show that the predicted adult population at the end of Year 2 is 25 750.

(b) Write down the common ratio of the geometric sequence.

The model predicts that Year N will be the first year in which the adult population of the town exceeds 40 000.

(c) Show that (N - 1)log1.03 > log1.6 N

(d) Find the value of N.

At the end of each year, each member of the adult population of the town will give £1 to a charity fund.

Assuming the population model,

(e) find the total amount that will be given to the charity fund for the 10 years from the end of Year 1 to the end of Year 10, giving your answer to the nearest £1000.

Core 2 Mathematics Edexcel June 2010 Question 10

10. The circle C has centre A(2,1) and passes through the point B(10, 7).

(a) Find an equation for C.

The line 1_{1} is the tangent to C at the point B.

(b) Find an equation for 1_{1}

The line l_{2} is parallel to 1_{1} and passes through the mid-point of AB.

Given that l_{2} intersects C at the points P and Q,

(c) find the length of PQ, giving your answer in its simplest surd form.

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