This document contains a mathematics exam with 7 sections covering topics such as: 1) Choosing correct answers and justifications for systems of equations and inequalities. 2) Solving systems of equations, calculating proportions, and simplifying polynomials. 3) Graphing lines and finding intersections of lines and circles. 4) Calculating angles, similarities of triangles, and loci of points. 5) Conducting statistical analysis on survey data including calculating range, mean, and percentages.

1. Page 1 of 3
CCS Mathematics April 2014
Class of G9 Sheet 2 of revision Duration : 120 min
Name :………………………
I. (2 points)
Choose the correct answer and justify .
Nb Questions Answers
a b c
1
If A(m-2 ; n-3) is a
solution of this system then :
m=2 and n=4 m=4 and n=2 m=0 and n= -4
2 and Are 2 opposite
numbers
One is the inverse
of the other
Are two equal
numbers
3 The distance of the point A(2 ;-1) at the
line (D) : is
2
4 The GCD of 360 and 48 is 24 18 48
5
The scientific notation of
is
II. (4 points)
1) Consider the three numbers :
; ; .
Verify that A, B and C are positive integers.
2) Given : and
a) Write m and n in the form of where r and s are two integers.
b) Let be a positive integer , calculate if the following table is proportional :
c) Let p = . Calculate and deduce a simplified form for p.
x m
n x

2. Page 2 of 3
III. (3 points)
1) Solve the following system :
2) If the average salary is calculated for an employee and a technician it will be 600 $. Moreover, we know
that if the employee's salary is increased by 10% and that of a technician decreased by 10% the average
salary will be 590 $. What is the salary of the employee and that of the technician.
IV. (4 points)
Given the following polynomials:
1) Develop and reduce .
2) Factorize and Q(x).
3) Solve the following equations :
a. .
b.
c. .
4) Let
a. For what values of , is defined?
b. Simplify .
c. Solve the equation .
d. Calculate and rationalize the denominator.
V. (7 points)
In an orthogonal system of axes x’Ox et y’Oy consider the points A(0 ;5) and B(-4 ;-2). Draw the lines
.
1) Does B belong to (D’) ?
2) Calculate the coordinate of the point C the intersection of (D) and (D’).
3) Prove that the triangle ABC is inscribed in a ( C) which the coordinates of its center I and the length of its
radius will be determined; draw this circle.
4) Calculate .
5) Calculate the coordinates of the point E such that .
6) Determine the equation of the line (CE).
7) The parallel at (yy’) passing through B cuts (CE) in K. Calculate the coordinates of K.
8) Write the equation of the tangent (T) on the circle (C) at B. This tangent cuts (CE) in F. Calculate the
coordinates of F.
9) (T) cuts y’Oy in P. Calculate rouded to nearest degree.

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VI. (6 points)
Let C(O ; R) and C’(O’ ; R’) be two intersecting circle at A and B with R< R’. By the A draw the parallel
to (OO’) wich cuts (C ) in C and (C’) in D.
1) Construct the figure.
2) Prove that (BC) passes by O and (BD) passes by O’.
3) Prove that (AB) is perpendicular at (OO’).
4) Consider a secant line passing through A and cuts (C ) in another point E and (C’) in F. Prove that the
triangles CDB and EBF are similar. By using the ratio of similarity calculate BF in the particular case
where EB= cm.
5) Let I be the midpoint [EB]. What is the locus of I when E varies on (C ) ?
6) Place the point J image of I by translation of vector . What is the locus of J ? Plot that locus.
VII. (2 points)
The creators of a website made a survey of Internet customers. They asked them to assign a score on 20 to the
site. They then gave the following table:
Note 6 8 10 12 14 15 17
Frequency 1 5 7 8 12 9 8
1) What is the range of this statistical table?
2) Calculate the mean of the note (rounded to the nearest degree)
3) The survey is considered satisfactory if 55% of users gave a rating greater than or equal to 14. Is this the
case? Why?
GOOD WORK