2019年11月IB数学SL真题下载-Paper2
1.The number of messages, M , that six randomly selected teenagers sent during the month of October is shown in the following table. The table also shows the time, T , that they spent talking on their phone during the same month.
The relationship between the variables can be modelled by the regression equation M = aT + b .
(a)Write down the value of a and of b .
(b)Use your regression equation to predict the number of messages sent by a teenager that spent 154 minutes talking on their phone in October.
2.Consider the lines L1 and L2 with respective equations
L1:y=-2/3x+9 and L2:y=2/5x-19/5
(a)Find the point of intersection of L1 and L2 .
A third line, L3 , has gradient -3/4
(b)Write down a direction vector for L3 .
L3 passes through the intersection of L1 and L2 .
(c)Write down a vector equation for L3 .
3.Let f(x) = x - 8 , g(x) = x4 - 3 and h (x) = f(g(x)) .
(a)Find h(x) .
Let C be a point on the graph of h . The tangent to the graph of h at C is parallel to the graph of f .
(b)Find the x-coordinate of C.
4.The following diagram shows a right-angled triangle, ABC, with AC = 10 cm , AB = 6 cm and BC = 8 cm .
The points D and F lie on [AC].
[BD] is perpendicular to [AC].
BEF is the arc of a circle, centred at A.
The region R is bounded by [BD], [DF] and arc BEF.
(a)Find BÂC.
(b)Find the area of R .
5.The first two terms of a geometric sequence are u1 = 2.1 and u2 = 2.226 .
(a)Find the value of r .
(b)Find the value of u10 .
(c)Find the least value of n such that Sn > 5543 .
2019年11月IB数学SL真题余下省略！
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