exams

Extra Problems

Sample -1-
I–

Given the three points A , B & C defined by:
1 1
OA = 2u + v ; OB = -v + 2u ; OC = -u + v
2 2

1) Plot the points A , B & C on the adjacent grid.
2) Are the point O, B & C collinear? Justify.


II- In the table below, only one of the proposed answers to each question is correct .
Write the number of each question & the corresponding answer& justify.

N Given Answers
o A B C

1- If U = AB + BC - CD + AD then: U = AC U = 2 AC U = - AC
2- A,B & C are three points 1 AC = 3AB AC = -3AB
AC = AB
Such that: 5 AC  3 AB  2BC then: 3
3- ABC is a triangle ,M is defined by: A ,M & B are A ,M & C are B,M & C are
AM  3 AB - 2AC then the points : collinear collinear collinear
ABCD is a rectangle with
AB=4cm & AD=2m then : 2 AB  BC = 2 17 10 4+2 5


III- Given :
 ABC is a triangle.
 M, N and P are the points defined by:
2 1
AM  AB ; NA  2NC  0 ; CP  BC
5 2
2
1)a- Prove that: AN  AC
3
b- Construct the points M , N and P.
2) Write MN then NP as linear combination of AB and AC .
3) Deduce that the points M, N and P are collinear.