2019年11月IB数学SL真题下载-Paper1
1.In an arithmetic sequence, u2 = 5 and u3 = 11 .
(a)Find the common difference.
(b)Find the first term.
(c)Find the sum of the first 20 terms.
2.In a class of 30 students, 18 are fluent in Spanish, 10 are fluent in French, and 5 are not fluent in either of these languages. The following Venn diagram shows the events “fluent in Spanish” and “fluent in French”.
The values m , n , p and q represent numbers of students.
(a)Write down the value of q .
(b)Find the value of n .
(c)Write down the value of m and of p .
3.Let g (x) = x2 + bx + 11 . The point (-1 , 8) lies on the graph of g .
(a)Find the value of b .
(b)The graph of f (x) = x2 is transformed to obtain the graph of g .
Describe this transformation.
4.
(a)Find the value of a .
(b)Hence or otherwise find the coefficient of the term in x9 in the expansion of (x + 3)11 .
5.Consider the function f , with derivative f'(x) = 2x2 + 5kx + 3k2 + 2 where x , k∈R .
(a)Show that the discriminant of f ′(x) is k2 - 16 .
(b)Given that f is an increasing function, find all possible values of k .
2019年11月IB数学SL真题余下省略！
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