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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