2015年11月IB数学SL真题下载-Paper2
1.The following diagram shows a circle with centre O and radius 3 cm.
Points A, B, and C lie on the circle, and AOˆ C =1.3 radians .
(a) Find the length of arc ABC.
(b) Find the area of the shaded region.
2.The following table shows the probability distribution of a discrete random variable X .
(a) Find the value of k .
(b) Find E (X ) .
3.Let f (x) = 2 ln (x − 3) , for x > 3 . The following diagram shows part of the graph of f .
(a) Find the equation of the vertical asymptote to the graph of f .
(b) Find the x-intercept of the graph of f .
(c) The region enclosed by the graph of f , the x-axis and the line x = 10 is rotated 360˚
about the x-axis. Find the volume of the solid formed.
4.The first three terms of a geometric sequence are u1 = 0.64 , u2 = 1.6 , and u3 = 4 .
(a) Find the value of r .
(b) Find the value of S6 .
(c) Find the least value of n such that Sn > 75 000 .
5.Let C and D be independent events, with P (C ) = 2k and P (D) = 3k2 , where 0 < k < 0.5 .
(a) Write down an expression for P (C ∩ D) in terms of k .
(b) Given that P (C ∩ D) = 0.162 , find k .
(c) Find P(C′ | D) .
2015年11月IB数学SL真题余下省略！
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