2011年5月IB数学SL真题下载-Paper2

2011年5月IB数学SL真题下载-Paper2

1.The following diagram shows triangle ABC .

AB = 7 cm, BC = 9cm and ABC =120°。

(a) Find AC . 

(b) Find BAC.

 

2.Let f (x) = 3x2 . The graph of f is translated 1 unit to the right and 2 units down.

The graph of g is the image of the graph of f after this translation.

(a) Write down the coordinates of the vertex of the graph of g .

(b) Express g in the form g (x) = 3(x − p)2 + q . 

The graph of h is the reflection of the graph of g in the x-axis.

(c) Write down the coordinates of the vertex of the graph of h .

 

3.In an arithmetic sequence u1 = 7 , u20 = 64 and 3709 un =3709.

(a) Find the value of the common difference. 

(b) Find the value of n .

 

4.A random variable X is distributed normally with a mean of 20 and variance 9.

(a) Find P(X ≤ 24.5) . 

(b) Let P(X ≤ k) = 0.85 .

(i) Represent this information on the following diagram.

(ii) Find the value of k .

 

5.A box holds 240 eggs. The probability that an egg is brown is 0.05.

(a) Find the expected number of brown eggs in the box. [2 marks]

(b) Find the probability that there are 15 brown eggs in the box. [2 marks]

(c) Find the probability that there are at least 10 brown eggs in the box.

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