2013年05月IB数学SL真题下载-Paper1
1.
(a) Find
(i) 2a + b ;
(ii) |2a + b|.
Let 2a + b + c = 0 , where 0 is the zero vector.
(b) Find c .
2.The diagram below shows part of the graph of f (x) = (x −1)(x + 3) .
(a) Write down the x-intercepts of the graph of f .
(b) Find the coordinates of the vertex of the graph of f .
3.Consider f (x) = x2 sin x .
(a) Find f'(x) .
(b) Find the gradient of the curve of f at x=π/2.
4.Let A , B , C and X be square matrices, such that XA+ B = C .
(a) Find an expression for X in terms of A , B and C .
b.
5.Let f (x) = √x − 5 , for x ≥ 5 .
(a) Find f −1 (2) .
(b) Let g be a function such that g−1 exists for all real numbers. Given that g (30) = 3, find ( f ° g−1)(3) .
6.Let f(x)=∫12/2x-5dx, for x>5/2. The graph of f passes through (4, 0).Find f (x) .
7.Find the value of
(a)log240 − log25;
(b) 8log25 .
2013年05月IB数学SL真题余下省略！
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