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Revision 1st secondary Nov 2015
Answer the following questions
Choose the correct answer from those given:
1) If the two roots of the equation: 4 χ – 12 χ + c = 0 are equal ,
then c = ………………..
a( 3
b( 4
c) 9
d) 16
2
2) If = - 1 is one of the roots of equation : χ – a χ – 2 = 0, then
a = ………..
a) 1
b) -1
c) 3
d) -3
2
3) If a = 1 + 2 i, b = 1 - 2 i, then ab = …………..
a) -1
b) 1
c) 2
d) 3
2
4) If the two roots of the equation : χ – 6 χ + k = 0 are
different and real , then k Є …………………..
a) ] - ∞,9[
b) ]9, ∞[
c) ] - ∞,9]
d) [9, ∞[
5) The angle of measure 50º in the standard position is
equivalent to the angle of measure ………………
a) 130 º
b) 310 º
c) 140 º
d) 410 º
6) All the following are measures of angle that lie in the
second quadrant except……………
a) 210 º
b) 120 º
c) 120 º
d) 850 º
7) The angle whose measure is (750º) lies in the …… quadrant
a) first
b) second
c) third
d) fourth
8) All the following directed angles are not in standard position
except ……………….
a)
b)
c)
d)
1
9π
9) The angle whose measure is 4 lies in the ……… quadrant
a) first
b) second
c) third
d) fourth
9) The degree measure of central angle in the circle o radius
6cm. and opposite to an arc of length 3 π cm. equals …………
a) 30 º
b) 60 º
c) 90 º
d) 120 º
rad
10) The angles whose measure is 7.3 is equivalent to the angle
whose degree measure is ……………..
a) 58º 15 33
b) 301º 44 27 c) 233º 15 33 d) 211º 44 27
11) The radian measure of the central angle subtending an arc
of length 3cm. in a circle whose diameter length is 4cm. equals
rad
rad
rad
rad
a) ( 2 )
b) ( 3 )
c) 5
d) 6
3
2
12) The radian measure of the central angle which subtends an
arc of length 5cm. in a circle of diameter length 10cm. equals
rad
rad
rad
a) ( 1 )
b) (1)
c) 2
d) π
2
13) The measure of the small positive angle equivalent to the
angle whose measure is ( - 870º) is ………………
a) 210 º
b) 150 º
c) -210 º d) 120 º
14) If θ is the measure of a directed angle drawn in the standard
position where sin θ < 0, in which quadrant does the terminal
side of the angle θ lie?
a) first
b) first and second
c) second and third
d third and fourth
15) If sec θ = 2 where θ is an acute positive angle, then θ =…….
a) 30º
b) 60º
c) 45 º
d) 90 º
Complete the following :
1) Two polygons of the same number of sides are similar
if …….
2
2) If the scale factor of similarity of two polygons = 1, then the two
polygons are ………………..
3) Two similar polygons, the ratio between the length of two
corresponding sides in them is 2:3, if the perimeter of the smaller is
14cm., then perimeter of the bigger is ……… cm.
4) In the opposite figure:
If rectangle ABCD ~ rectangle AXYZ,
DC = 16cm.
BC = ZY = 12 cm., then AY = ……….. cm.
5) Two similar rectangle, the two dimensions of the first are 12cm.,
8cm. and the perimeter of the second is 60cm., then the length of the
second rectangle = …………………
a) 12cm.
b) 18cm.
c) 24cm.
d) 16cm
6) In the opposite figure:
Which of the following expression is wrong?
2
2
a) (AB) = BD x DC
2
c) (AD) = DB x DC
b) (AC) = CD x CB
d) AB x AC = BC x AD
7) In the opposite figure:
If DE // BC , then χ = ………
(a) 6 cm.
(b) 3cm.
c) 5cm.
d) 1.2cm.
8) In the opposite figure:
AB // CD , AE = 3cm.
, BE = 4cm. , EC = 6cm
, then ED = …………..
a) 4cm.
b) 6 cm.
d) 4 12 cm.
c) 3cm
3
In each of the following figure, find the value of the symbol
used in measure. Explain your answer.
2
16) If χ = 4 is one of the two roots of the equations: χ + m χ = 4,
then m = ……………..
(a) 3
(b) -3
(c) -4
(d) 1
2
(2) The solution set of the equation : χ + 5 = 0 R is ……….
(a) {5}
(b) { 5 }
(c) { 5,- 5}
(d) Ø
2
(3) The solution set of the equation : χ – χ- 72=0 R is ……….
(a) {8 , 9}
(b) {-8,9 }
(c) {-8 -9}
2
(d) {8 ,-9}
(4) The solution set of the equation : (χ-3) – (χ-3) in R is……….
(a) {3}
(b) {4 }
(c) {-3, -4}
(d) {3 ,4}
(5) -2 x -8 = ……………
(a) 4
(b) -4
(d) – 16
(c) 4 i
42
(6) The simplest from of the imaginary number i is ………..
(a) -1
(d) – I
(b) 1 (c) i
(7) If the curve of the quadratic function f intersected the χ axis
in the two points (3,0), (-1,0), then the solution set of the
equation : f (χ) = 0 R is …………….
(a) {3 , 0}
(b) {-1,0 }
(c) {-3 -1}
(d) {3 ,-1}
4
Second questions:
2
a- Prove that the two roots the equation: 3 χ – 4 χ + 5 = 0 are not
real, then find the solution set of the equation in C.
b- Fin the value of k which make the equation : k χ – 4 χ+4 = 0
have two complex and not real roots.
c- Determine the quadrant in which each of the following
angles lie:
(1) 52º
(2) 220º
(3) 1120º 15
d- Find two angles, one of them with positive measure are
the other with negative measure having common terminal
side for each of the following angles:
(1) 132º
(2) 70º
(3) 730º
e- Find the length of the arc which is opposite to an inscribed
angle of measure 60º, in a circle whose radius length is 10cm.
f- ABC is a triangle in which: m (<A) = 70º , m(<B) = 60º find
in radian measure m (< C).
g- Convert the degree measure to the radian measure and the
radian measure to the degree measure:
8π
(1) 225º
(2)
5
f- A central angel of measure 60º subtends an arc of
7π
length
cm., calculate the radius length of its circle
3
I- in the opposite figure:
Polygons ABCD ~ polygon XECF
(1) Prove that : AB // XE
(2) If XE = 12 AB, CF = 6cm.
(3) Find the length of FD
J- in the opposite figure:
If Polygons ABCD ~ polygon XBZY
1- Prove that : XY // AD
2- If the perimeter of the polygon ABCD = 18cm
, the perimeter of the polygon XBZY = 12cm
, XB = 3cm. then find the length of : AB
5
I- in the opposite figure:
AE bisect < DAB
2
, area of Δ ADE = 12cm
Find the area of Δ ABC
(a) Find in C the solution set of the equation :
2
χ–2χ+4=0
(b) Find the values of χ , y which satisfy that :
χ+iy=
(2 + i) (2 – i)
3+2i
Third questions:
a- Put in the simplest from :
(3 + i) (3 – i)
3 -4i
2-3i
b) Find the value of χ an y which satisfy the equation: χ + iy = i
c) Find the measure of the directed angle θ in each of the
two figures:
d) In the opposite figure :
2
If the area of Δ AMB equals 8 cm.,
Find the length of : AB
M
v
B
A
e) Without using calculate, find the value of:
2
3 sin 30º sin2 60º - cos sec 60º + sin 270º cos 45º
π
f) [If sin θ = 35 θ Є ] 2 , π [ , find all trigonometric functions
of the angle whose measure is θ
6
g- in the opposite figure:
Polygons ABCD ~ polygon XYZL
(1) Find the scale factor of similarity between the
polygon ABCD and polygon XYZL
(2) Find the value of each of : m , k
h- Using the givens in the opposite figure, prove that:
1) Δ ABC ~ Δ DBA
2) BA bisects < DBC
I- ABCD , XYZL are two similar polygon. If M is the
midpoint of BC, N is the midpoint of YZ, AM = 4c, XN =
9cm., prove that:
Area of polygon ABCD: area of polygon XYZL = 16:81
2
(a) If 2, - 1 are two roots of the equation : χ + a χ + b = 0, then
find the values of a , b
(b) Put in the simplest from each of :
(1)
(2)
5
1–2i
2+3i
2–3i
7
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