2011年5月IB数学SL真题下载-Paper1

2011年5月IB数学SL真题下载-Paper1

1.Let f (x) = 7 − 2x and g (x) = x + 3.

(a) Find (g ° f ) (x).

(b) Write down g−1(x).

(c) Find ( f ° g-1)(5).

(a) Write down a vector equation for L in the form r = a + tb.

2.

The line L passes through point P when t = 2.

(b) Find

3.

4.The probability distribution of a discrete random variable X is given by

P(X=x)=x2/14, x∈{1, 2, k}, where k > 0 .

(a) Write down P(X = 2) .

(b) Show that k = 3.

(c) Find E(X ) .

 

5.Letg(x)=ln x/x2,for x > 0 .

(a) Use the quotient rule to show that g'(x)=1-2lnx/x3.

(b) The graph of g has a maximum point at A. Find the x-coordinate of A.

 

6.Solve the equation 2cos x = sin 2x , for 0 ≤ x ≤ 3π.

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