Ansar State High School

Mathematics Department

Name: / Academic year: / 2009-2010
Class: / Grade 10 / Duration: / 120 minutes
Subject: / Mathematics Mid Year Exam / Date: / Feb ,2010

The test consists of five questions. The use of non programmable calculators is allowed.

Exercise1: (2.5 points)
choose the correct answer , and justify

Questions / Answers
A / B / C
1 / = / / /
2 / / 1 / /
3 / / / / Doesn’t exist
4 / If ,then / / /
5 / If – 2< a < -1 and 4< b< 5 , then: / -5< ab< -8 / -8 < ab < -5 / -10 < ab < -4

Exercise2: (4.5 points)

We registered the number of books read by a group of 100 students.

Number of books read(xi) / 0 / 1 / 2 / 3 / 4 / 5 / 6
Frequency(ni) / 23 / 36 / 17 / 14 / 4 / 4 / 2

We obtained the following results:

  1. What is the population of this series? the variable and its nature?
  2. What is the mode? the range?
  3. What is the median? Give an interpretation of this result.
  4. Determine the frequency of the students who read:

a. at least 4 books.b. less than 3 books.

Exercise3: (4 points)

Let A=

  1. Show that A=1-
  2. Show that if -, then
  3. Frame |A|
  4. Solve |A|=1.

Exercise 4: (4.5points)

  1. Un arc, est compris entre - et 0, vérifie la relation: 3cot x = -4.

a- Calculer la valeur de sinx, cosx et tanx.

b- Déduire la valeur numérique de cette expression

F = 4 tan(3+x) – 6sin (-x) – 2cos(x-

  1. Prouver cette identité:

Tan2 + cot2+2 =

  1. Let g be a function defined, over IR, by g(x) = cos3x + sin3x.

1-Calculate and .

2-Find .

Exercise 5: (5.5points)

ABCD is a rectangle. O is the meeting point of the diagonals [AC] and [BD].

I and J are two points such that = and =

Let M and N be the mid points of [DC] and [BC] respectively.

PART A:

  1. Plot I and J.
  2. a) Write each of the two vectors and as a linear combination of and .

b) Deduce that DIBJ is a parallelogram.

Prove that: a) + =.

b) + =.

Prove that: + =.

Deduce that the points M, J, and N are collinear.

PART B:

Assume that the plane is reported to the system: (A,,).

  1. Find the coordinates of A, B, C, D, I and J.
  2. Deduce again That DIBJ is a parallelogram.
  3. Verify again the result of part 5.

Bareme(over 25)

№ / Parts / Answers / Mark 111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
1 / 1) / C / (0.5 Points)
2) / A / ( 0.5Points)
3) / B / ( 0.5Points)
4) / C / ( 0.5Points)
5) / A / ( 0,5points)
2 / 1) / 35 students,grades,quantitative / (0.5;0.25;0.25 Points)
2) / X==7,y=35-30=5 / (0.5;0.5Points)
3) / Table
Grades / 35 / 42 / 50 / 63 / 83 / 90 / 97
Frequency / 3 / 5 / 10 / 7 / 5 / 3 / 2
Increasing
Frequency / 3 / 8 / 18 / 25 / 30 / 33 / 35
/ (1Point)
4) / Graph+Histogram / (0.5:0.5points)
5) / Range26:,Mode50,Median50 / (0.25;0.25;
0.25points)
6) / (0.25;0.25points)
7) / =68.57% / (0.75 Points)
1) / Sinx=,Cosx=,tanx=-1,E= / (0.5;0.5;0.25;0.25 Points)
2) / a) / 1/2 / (0.5;0.5;0.5;1points)
b) / 2
c) / 0
d) / Sinx==cosx
3) / a) / x0 / (0.5;0.5;0.5;1points)
b) / No solution
c) /
d) / |x+2|=3x, x=1, or x=-
4) / Framing / (0.5;0.5 Points)
4 / 1) / Construction / ( 1.5Points)
2) / a) / = / (0.75 Points)
b) / = / (0.75 points)
c) / ,so collinear / (1 point)
5 / 1) / D(-2;-5) / ( 1point)
2) / F(9;0) / ( 1point)
3) / G(-2/3;1/3) / ( 0.5points)
4) / 1 / (0.5 points)
5) / a) / A(-3;2) and C(5;6) / (0.5;0.5 points)
b) / =(8;4).the same in any system / ( 1point)