GRADE:9(A,B) Midyear Math
GRADE:9(A,B) Midyear Math.Test
I)1)Consider the NOs: A’2−2+ & B’+−7
a)Simplify A & B.
b)Show that is an integer.
2)In ΔABC we have AB’ 5+ ,AC’5−, &BC’8.
a)Calculate the exact values of AB2 & AC2 .
b)Deduce that ABC is right at A .
II)Given the inequality: 3(x+1) ≤ x+11.
a)Which of these NOs. 6,4,& −2 is a solution for the given inequation?
b)Solve the above inequation,graph its solution,then write the interval.
c)In this part x represents a digit & satisfies the given inequality,find all values of x.
III)”The sum of ages of the father & his son is now−−−−−−−−− .After−−−−−−−−−−−years the
Age of the father will be−−−−−−−−−more than −−−−−−−−the age of his−−−−−−−−−−−“.
This system is translation of the above text: [pic]
a)What do x & y represent?
b)Recopy & complete the above text.
c)Calculate the actual ages of the father & his son.
IV)Given the expression : E(x)’(2x+3)2+(x−1)(2x+3).
a)Evaluate E(−3/2).What do you conclude?
b)Factorize E(x).
c)Solve the equation (2x+3)(3x+2)’0 .
V)After a certain raise the price of a T−Shirt changed from x to y according
to this relation : y’1.2x .
a)What do x & y represent.
b)Calculate the raise as percentage.
c)Find the sale price of the T−Shirt knowing that its real price was 30000 LL.
VI)In an orthonormal system x’ox,y’oy, given the pts
A(1;), B(2;2), C( − 4, − 3), D( − 5,), & the line (D) : y ’x + 3
a)Verify that A & C are on (D).
b)Plot A,B,C,D,&draw (D).
c) 1)Calculate the coordinates of I the midpt. Of [AC].
2)Verify that I is midpt. Of [BD].
3)What is the type of ABCD? Justify your answer.
VII)ABCD is a rectangle of dimensions 6cm & 3cm where AB>BC.
E is midpt. Of [CD]
a)Calculate AB &BC. Justify.
b)Show that BE’AE’3cm.
c)Prove that ΔAEB is right at E .
d)(AE) is tangent to a circle (C).
1)Precise the center O of (C) &calculate its radius.
2)Draw (C). (T)
VIII)Consider the circle C(O,4cm) of diameter [AB]. D
(T) is tangent to (C) at A.
D is any pt. On (T). (DC) is tangent to (C) at C that C
cuts (AB) in I.
a)Reproduce the figure with correct measures. A B I
b)What is the type of ΔADC?Why?
c)(DO) meets [AC] in E.Show that (DE) is the
┴ bisector of [AC].
d)(OC) CUTS (T) at F.What does O represent in ΔFDI?
e)Deduce that (DO) is perpendicular to (FI).
f)Prove that ADCO is inscribed in a circle.Determine one of its diameters.
g)Determine the locus of E as D moves on (T).
IX)Consider the two pieces of lands,one having a square shape & the other
triangular shape as shown.Unit of length is the meter.
Jad payed 320,000,000 LL for the squared piece
ABCD where each square meter costs 200,000 LL. A D
1)a )Calculate the area of ABCD.
b)Deduce that AB’40m.
2)Given that DE’50m.
a)Find the area of ΔCDE. B C E
b)Deduce the price of the land CDE.
T.IBRAHIM KHALIL
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