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EUROPEAN BACCALAUREATE 2012
MATHEMATICS 5 PERIODS
PART A
DATE : 11 June 2012, afternoon
DURATION OF THE EXAMINATION:
1 hour (60 minutes)
AUTHORIZED MATERIAL:
Examination without technological tool
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EN
EUROPEAN BACCALAUREATE 2012: MATH 5 PERIODS
PART A
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1)
Marks
Only one of the three diagrams a, b and c below shows the graphs of both a
function f and its derivative.
Identify that diagram, and explain your answer.
Diagram a
Diagram b
Diagram c
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4 marks
EUROPEAN BACCALAUREATE 2012: MATH 5 PERIODS
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EUROPEAN BACCALAUREATE 2012: MATH 5 PERIODS
PART A
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2)
Marks
In 3-dimensional space consider the planes  and  given by
 : 3x  y  z  12
 : x  y  2z  8 .
Let d be the line of intersection of the planes  and .
Determine parametric equations for the line d.
3)
4 marks
George and Laura work at an orchard. They pack boxes with peaches.
George packs twice as many boxes as Laura.
The probability that a box packed by George contains at least one damaged
1
peach is .
6
The probability that a box packed by Laura contains at least one damaged
1
peach is
.
10
A box is selected at random from the boxes packed by George and Laura.
Calculate the probability that this box does not contain any damaged peaches.
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4 marks
EUROPEAN BACCALAUREATE 2012: MATH 5 PERIODS
PART A
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4)
Marks
A wavy line consists of an infinite number of connected semicircles.
The diagram below shows the first semicircles. The radius of the first
semicircle is called r. After this, the radius of each semicircle is half the radius
of the previous one.
5)
Calculate r in terms of , given that the total length of the wavy line is 30 cm.
4 marks
Solve the equation z 2  2  2 3 i , and plot the solutions in the complex
plane.
5 marks
6)
e
ln(e  x)
dx .
Calculate 

x
1
7)
In 3-dimensional space
4 marks
 x  1 
a
   
the line l :  y    2     2  ,  
 z   1
 2a 
   
 
lies in the plane  : 2 x  y  3z  b  0 .
Determine the numbers a and b.
5 marks
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