2016年5月IB数学SL真题下载-Paper2
1.A random variable X is distributed normally with a mean of 20 and standard deviation of 4.
(a) On the following diagram, shade the region representing P (X ≤ 25) .
(b) Write down P (X ≤ 25) , correct to two decimal places.
(c) Let P (X ≤ c) = 0.7 . Write down the value of c .
2.Let f (x) = x2 and g (x) = 3 ln (x + 1) , for x > −1 .
(a) Solve f (x) = g (x) .
(b) Find the area of the region enclosed by the graphs of f and g .
3.The following diagram shows three towns A, B and C. Town B is 5 km from Town A, on a bearing of 070˚. Town C is 8 km from Town B, on a bearing of 115˚.
(a) Find ABˆ C.
(b) Find the distance from Town A to Town C.
(c) Use the sine rule to find ACˆ B.
4.(a) Find the term in x6 in the expansion of (x + 2)9 .
(b) Hence, find the term in x7 in the expansion of 5x (x + 2)9 .
5.The mass M of a decaying substance is measured at one minute intervals. The points(t , ln M ) are plotted for 0 ≤ t ≤ 10 , where t is in minutes. The line of best fit is drawn.This is shown in the following diagram.
The correlation coefficient for this linear model is r = −0.998 .
(a) State two words that describe the linear correlation between ln M and t .
(b) The equation of the line of best fit is ln M = −0.12t + 4.67 . Given that M = a × bt ,find the value of b .
2016年5月IB数学SL真题余下省略！
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