Questions and Worked Solutions for C2 Edexcel Core Mathematics June 2010.
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(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.
2log3(x - 5) - l0g3(2x - 13) = 1
show that x2 - 16x + 64 = 0
(b) Hence, or otherwise, solve 2log3(x - 5) - l0g3(2x - 13) = 1
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.
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.
(a) Find an equation for C.
The line 11 is the tangent to C at the point B.
(b) Find an equation for 11
The line l2 is parallel to 11 and passes through the mid-point of AB.
Given that l2 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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