2016年10月IB化学SL真题下载-Paper2
1.Let f (x) = x2 + 2x + 1 and g (x) = x − 5 , for x ∈ R .
(a) Find f (8) .
(b) Find (g ° f) (x) .
(c) Solve (g ° f ) (x) = 0 .
2.Let f (x) = 0.225x3 − 2.7x , for −3 ≤ x ≤ 3 . There is a local minimum point at A.
(a) Find the coordinates of A.
(b) On the following grid,
(i) sketch the graph of f , clearly indicating the point A;
(ii) sketch the tangent to the graph of f at A.
3.The following diagram shows a circle, centre O and radius r mm . The circle is divided into five equal sectors.
One sector is OAB, and AOˆB =θ .
(a) Write down the exact value of θ in radians. [1]
The area of sector AOB is 20π mm2 .
(b) Find the value of r .
(c) Find AB.
4.Let f (x) = xe−x and g (x) = −3 f (x) + 1 .
The graphs of f and g intersect at x = p and x = q , where p < q .
(a) Find the value of p and of q .
(b) Hence, find the area of the region enclosed by the graphs of f and g .
5.The weights, W , of newborn babies in Australia are normally distributed with a mean 3.41 kg and standard deviation 0.57 kg. A newborn baby has a low birth weight if it weighs less than w kg.
(a) Given that 5.3 % of newborn babies have a low birth weight, find w .
(b) A newborn baby has a low birth weight.Find the probability that the baby weighs at least 2.15 kg.
6.All lengths in this question are in metres.
Let f (x) = -0.8x2 + 0.5 , for -0.5 ≤ x ≤ 0.5 . Mark uses f (x) as a model to create a barrel.The region enclosed by the graph of f , the x-axis, the line x = -0.5 and the line x = 0.5 is rotated 360˚ about the x-axis. This is shown in the following diagram.
(a) Use the model to find the volume of the barrel.
(b) The empty barrel is being filled with water. The volume V m3 of water in the barrel after t minutes is given by V = 0.8(1− e−0.1t ). How long will it take for the barrel to be half-full?
2016年10月IB化学SL真题余下省略！
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