2020年11月IB数学SL真题下载-Paper1
1.In a class of 30 students, 19 play tennis, 3 play both tennis and volleyball, and 6 do not play either sport.
The following Venn diagram shows the events “plays tennis” and “plays volleyball”.The values t and v represent numbers of students.
(a) (i) Find the value of t .
(ii) Find the value of v .
(b) Find the probability that a randomly selected student from the class plays tennis or volleyball, but not both.
2.The following diagram shows a triangle ABC.
AC = 15 cm , BC = 10 cm , and AB̂ C = θ .
Let sin CÂB =√3/3
(a) Given that AB̂ C is acute, find sin θ .
(b) Find cos (2 × CÂB) .
3.Let f (x) =√12 - 2x , x ≤ a . The following diagram shows part of the graph of f .The shaded region is enclosed by the graph of f , the x-axis and the y-axis.
The graph of f intersects the x-axis at the point (a , 0) .
(a) Find the value of a .
(b) Find the volume of the solid formed when the shaded region is revolved 360° about the x-axis.
4.Let f (x) = a log3 (x - 4) , for x > 4 , where a > 0 .
Point A(13 , 7) lies on the graph of f .
(a) Find the value of a .
The x-intercept of the graph of f is (5 , 0) .
(b) On the following grid, sketch the graph of f .
5.Let f (x) = - x2 + 4x + 5 and g (x) = - f (x) + k .
Find the values of k so that g (x) = 0 has no real roots.
2020年11月IB数学SL真题余下省略！
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