2011年11月IB数学SL真题下载-Paper2

2011年11月IB数学SL真题下载-Paper2

1.Let f (x) = 2x + 4 and g (x) = 7x2 .

(a) Find f−1(x) . 

(b) Find ( f ° g) (x) . 

(c) Find ( f ° g) (3.5) .

 

2.The cumulative frequency curve below represents the heights of 200 sixteen-year-old boys.

Use the graph to answer the following.

(a) Write down the median value.

(b) A boy is chosen at random. Find the probability that he is shorter than 161 cm.

(c) Given that 82 % of the boys are taller than h cm, find h .

 

3.Consider the following circle with centre O and radius 6.8 cm.

The length of the arc PQR is 8.5 cm.

(a) Find the value of θ .

(b) Find the area of the shaded region.

 

4. Consider the triangle ABC, where AB =10 , BC = 7 and CAB = 30° .

(a) Find the two possible values of ACB.

(b) Hence, find ABC, given that it is acute.

 

5.Consider the expansion of (3x2 + 2)9 .

(a) Write down the number of terms in the expansion. 

(b) Find the term in x4 .

 

Jose takes medication. After t minutes, the concentration of medication left in his loodstream is given by A(t) =10(0.5)0.014t , where A is in milligrams per litre.

(a) Write down A(0) .

(b) Find the concentration of medication left in his bloodstream after 50 minutes.

(c) At 13:00, when there is no medication in Jose’s bloodstream, he takes his first dose of medication. He can take his medication again when the concentration of medication reaches 0.395 milligrams per litre. What time will Jose be able to take his medication again?

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