2010年5月IB数学SL真题下载-Paper1

2010年5月IB数学SL真题下载-Paper1

1. Let f (x) = 8x − 2x2. Part of the graph of f is shown below.

(a) Find the x-intercepts of the graph.

(b)

  • (i) Write down the equation of the axis of symmetry.
  • (ii) Find the y-coordinate of the vertex.

3.(a) Expand (2 + x)4 and simplify your result.

(b) Hence, find the term in x2 in (2+x)4(1+1/x2)

 

4. The straight line with equation y = 3/4x makes an acute angle θ with the x-axis.

(a) Write down the value of tanθ .

(b) Find the value of

(i) sin 2θ ;

(ii) cos2θ .

 

5.Consider the events A and B, where P(A) = 0.5 , P(B) = 0.7 and P(A∩B) = 0.3 .

The Venn diagram below shows the events A and B, and the probabilities p, q and r.

(a) Write down the value of

(i) p ;

(ii) q ;

(iii) r.

(b) Find the value of P(A| B′).

(c) Hence, or otherwise, show that the events A and B are not independent.

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