2018年5月IB数学SL真题下载-Paper2
1.Let f (x) = ln x - 5x , for x > 0 .
(a) Find f'(x) .
(b) Find f"(x) .
(c) Solve f'(x) = f"(x) .
2.A biased four-sided die is rolled. The following table gives the probability of each score.
(a) Find the value of k .
(b) Calculate the expected value of the score.
(c) The die is rolled 80 times. On how many rolls would you expect to obtain a three?
3.The diagram shows a circle, centre O, with radius 4 cm. Points A and B lie on the circumference of the circle and AÔB = θ , where 0 ≤ θ ≤ π .
(a) Find the area of the shaded region, in terms of θ .
(b) The area of the shaded region is 12 cm2. Find the value of θ .
4.Let g (x) = - (x - 1)2 + 5 .
(a) Write down the coordinates of the vertex of the graph of g .
Let f (x) = x2 . The following diagram shows part of the graph of f .
The graph of g intersects the graph of f at x = -1 and x = 2 .
(b) On the grid above, sketch the graph of g for -2 ≤ x ≤ 4 .
(c) Find the area of the region enclosed by the graphs of f and g .
5.Two events A and B are such that P (A) = 0.62 and P (A ∩ B) = 0.18 .
(a) Find P (A ∩ B′) .
(b) Given that ( ) P ()0.19 A∪B′= B, find P (A | B′) .
2018年5月IB数学SL真题余下省略！
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