Preparatory (3)
Midterm revision Algebra
1) complete
a) The two straight lines which represent the two equations x = 4 , y = 2 are
intersecting at the point …………
b) The two straight lines representing the two equations x – y = 2 ¸2x – 2y = 4 are…
c) The S.S. of the two equations x + y = 0 , y – 5 = 0 is …………
d) If the two straight lines which represent the two equations x + 3y = 4 , x + ay = 7
are parallel , then a = ……………………
e) If n(𝑿2) = 9, then n(𝑿)=........
f) If the point (a , 3) is located on the straight line which represents the function f
:𝑹 → 𝑹 where f(x) = 4 x - 5 then a=…..
g) If 𝑹 is a relation from a set 𝑿 to 𝑿 (itself) then 𝑹 is called a relation ….. and 𝑹⊂ …
h) The S.S of the 2 equations 𝒙-𝒚=1and 𝒚-𝒙=-1 is ……
i) The solution set of the equations x-1=y and 1-y=x is ……..
2) Choose the correct answer:
a) The point of intersect of the two straight lines whose equations:
2x –y =3 , 2x + y = 5 at the ....quadrant.
[ 1st , 2nd , 3ed , 4th ]
b) If y = 1 – x , (x + y)2 + y = 5 , then y = ………
[ 3 , -3 , 4 , -4 ]
c) If the two straight lines which represent the two equations x + 4 y = 7 ,
3x + ky = 21 have an infinite number of solutions , then k = ……
[ 4 , 7 , 12 , 21 ]
d) The two straight lines: 3x+5y= 0 , 5x-3y= 0 are intersected in…….
[ The origin , First quadrant , Second quadrant , Fourth quadrant ]
e) The function f where f (X) = X6 +2 X4 - 3 is a polynomial function of the degree .......
[ 6 , 4 , 2 , 10 ]
f) If there are infinite numbers of solutions of the two equations x+4y =7, 3x+ky=21
then k=…..
[ 4 , 7 , 12 , 21 ]
g) The linear function given by the rule
𝐗
𝐘
= 2 is represented graphically by a straight
line …. [ ∕∕ 𝑿-axis , ∕∕ 𝒀-axis , intersecting both axes , passing through the origin ]
h) The S.S. of the two equations x - y = 0 , x y =9 in R R is …………
[ ( 𝟎 , 𝟎 ) , (−𝟑 , −𝟑) , ( 𝟑 , 𝟑) , {(−𝟑 , −𝟑) , ( 𝟑 , 𝟑)} ]
i) If L and M are 2 straight lines in which L // M and the equation of L is 𝒚 = 1, then
the equation of M is ……
[ 𝒙 = 1 , 𝒚 = 𝒙 -1 , 𝒚 = 0 , 𝒙 = 0 ]
b) If 𝑨=]-1,2] and 𝑩=[-2,1[ which of the following points belongs to the Cartesian
product of 𝑨×𝑩
[ (-2,2) , (-1,1) , (1,-1) , (2,1) ]
c)If the function f(𝒙)=2, then 2 f(5) =…..
[ 4 , 10 , f(10) , 7 ]
3) a) Find in R the S.S. of the equation x2 = 4x – 1 using the general formula
approximating the result to 2-decimal digits.
b) Find the S.S. of each of the following two equations algebraically and
graphically: 3x – y + 4= 0 , y = 2x + 3
4) Graph the function F where f (x) = x2 + 4x +5 tacking x  [-4 , 0] and from the
graph , find:
a) The min. value of the function F.
b) The equation of the axis of symmetry.
c) The S.S. of the equation x2 + 4x + 5 = 0
(3) If 𝑿= {2, 3}, 𝒀= {6, 8, 11, 15} and 𝑹 is a relation from 𝑿 to 𝒀, where 𝒂 𝑹 𝒃
means « 𝒂 is the divisor of 𝒃 » for each of 𝒂 ∈ 𝑿, 𝒃 ∈ 𝒀. Write the relation 𝑹 and
represent it by an arrow diagram. Is 𝑹 a function? and why?
(4) A rectangle with a length more than its width by 4 cm. If the perimeter of the
rectangle is 28cm, find the area of the rectangle.
(5)The opposite figure: Representing the curve of the
function f, where
f (x) = m-x2,
If oa= 4 units, find:
① The vertex of the curve.
② The minimum (or the maximum) value of the function.
③ The equation of the symmetrical axis of the curve.
④ The solution set of the equation m-x2=0
(B) If 𝑿= {1, 3, 4}, 𝒀= [-3,3] and 𝑹 is a relation from 𝑿 to 𝒀, where 𝒂 𝑹 𝒃
means « 𝒂+𝒃2=4 » for each of 𝒂 ∈ 𝑿, 𝒃 ∈ 𝒀.
Write the relation 𝑹. Is 𝑹 a function? and why?
(B) Find the coordinates of the point which lying on the straight line 𝟑𝒙+𝒚=4, and its
𝒙-coordinate is the multiplicative inverse of its y-coordinate.