Central College - Jounieh

Intermediate Cycle

Summer work.

Grade 8.

“Mathematics”

Prepared to the students of Grade 8 of Central College – Jounieh. This work

provides you a revision of all the main points of the program.

It allows the student to have an entrance with the best conditions after

having reviewed the program of the previous scholastic year and having spend

a good vacation.

1st week Exercise 1

Give the decimal writing of each of the following numbers:

7. 3 102 : _______________

0. 68 103 : _______________

0. 08 104 : _______________

Exercise 2

Out of the following expressions, indicate those that are already factorized.

The factorized expressions are:

_________________________________________________________________

_________________________________________________________________

Exercise 3 Calculate:

𝟗 = _________ 𝟏 = _________

𝟏𝟔 = _________ 𝟖𝟏 = _________

𝟏𝟎𝟎 = _________ 𝟒𝟎𝟎 = _________

𝟎. 𝟐𝟓 = _________ 𝟎. 𝟑𝟔 = _________

𝟎 = _________ 𝟒 𝟗𝟎𝟎 = _________

( 𝟒)𝟐 = _________ ( 𝟔𝟒)𝟐 = _________

( 𝟏𝟎𝟎)𝟐 = _________ 𝟓𝟐 = _________

(−𝟑)𝟐 = _________ 𝟏𝟏𝟐 = _________

𝟗

𝟒 = _________

𝟏𝟔

𝟐𝟓 = _________

𝟏𝟔 × 𝟐𝟓 = _________ 𝟗 × 𝟒 = _________

Exercise 4 Complete the following tables:

𝑥

4

0.36

49

(−5)2

𝑥

4

3

49

25

9

4

𝑥

𝑥2

1.69

0.04

25

104

4

9

Exercise 5 In the following figure:

MODE is a parallelogram such that:

MO = OE.

P is the midpoint of [ME].

L is the symmetric of O with respect to P.

a) What is the nature of MOEL? Justify

__________________________________

__________________________________

__________________________________

__________________________________

__________________________________

b) Show that E is the midpoint of [DL].

__________________________________

__________________________________

__________________________________

__________________________________

__________________________________

__________________________________

__________________________________

c) Let I be the symmetric of O with respect to E.

What is the nature of the quadrilateral IDOL? Justify

__________________________________

__________________________________

__________________________________

__________________________________

__________________________________

__________________________________

__________________________________

__________________________________

Exercise 6 What to say about Marc’s solution to whom we asked

to calculate the hypotenuse [AB] of a right triangle

ABC knowing that its legs measure 1 et 2?

______________________________________

______________________________________

______________________________________

______________________________________

______________________________________

______________________________________

______________________________________

Exercise 7 How to choose the digit « a » so that the number « 2 7 6 1 a » be:

1) Divisible par 5? ___________________

2) Divisible par 3? ___________________

3) Divisible par 9? ___________________

Pythagoras theorem gives: 2 2 2

22 2

2 2

1 2

1 2

1 2

3

AB AC BC

AB

AB

AB

AB

2nd week Exercise 1

1) From the numbered regions, what are those

that are images of the region 1 by a translation?

In each case precise the translation

___________________________________

___________________________________

___________________________________

___________________________________

2) From the numbered regions, what are those

that have as image by a translation the region

9 ? In each case precise the translation

___________________________________

___________________________________

___________________________________

___________________________________

Exercise 2 Answer by true or false:

a) The diagonals of a rectangle are two axes of symmetry. _____________

b) In a parallelogram the angles adjacent to a side are supplementary.

_____________

c) The diagonals of a square are congruent. _____________

Exercise 3 With the points of this figure, write:

1) All the vectors that are equal to BC

_________________________________

2) All the vectors that are equal to FB

_________________________________

Exercise 4

The age of Mike is the double of the age of Peter. From 10 years, the age of Peter

was equal to the third of the age of Mike. How old are they?

__________________________________

___________________________________

___________________________________

___________________________________

Exercise 5

By which translation the triangle

F1 is the image of the triangle ABC?

_______________________________

By which translation the triangle

F2 is the image of the triangle ABC?

_______________________________

Same question for F3 : _____________________________

F4: _____________________________

F5: _____________________________

F6: _____________________________

Exercise 6 The results of 180 students on a test are given in the following incomplete table

Complete the table:

Grade 0 1 2 3 4 5

Frequency

9 45 54 18

Relative

frequency in %

10 20

3rd week Exercise 1

Find the missing number in each of the following proportionality table.

9 4 12.5 3 13.6

11.7 5 7 17 1 2.4 2.1

Exercise 2

Alicia and Alexis did they do any mistake

while solving the following equation

4 3 2 7 1 x x ?

__________________________________

__________________________________

_______________________________________________________

_______________________________________________________

Exercise 3 Complete each equation by a number so that it admits as solution the given number.

a) 5 4x x+___________ ; the solution: 7.

b) 3 x x+____________ ; the solution: 3.

c) 2 x x+____________ ; the solution: 1.

d) 7x+_____ = -1x ; the solution: 4.

Exercise 4

Find the missing numbers by observing the inequalities written by a student.

One of the sides of a rectangle measure cm.

What should be the measure of the other side so

its perimeter be strictly less than cm and

its area strictly greater than 60 2cm ?

Inequalities of the student

Let x be the measure of the other

side.

Inequalities: 12 60x and

2 12 44x+

Exercise 5

For each question, indicate the correct answer(s).

Answers A B C D

a b c d

is equal to:

ac bd

a(c d) b(c d)

ac ad bc bd

ac ad bc bd

The developed

form of :

( 3) 2 x x

is equal to:

2 6x

2 5 6x x+

2 5 6 x x

2 6x

ka 5k is equal to:

k a 5 25ak a 5 k 2k a 5

2 4x x is equal to:

6x

4x x+

34x

4 1x x+

πR 2R is equal to:

2π 1 R

22πR

π R 2

3,14 R 2

Exercise 6

Complete the following table that represents the sides of a triangle ABC right at A.

AB

2 6

3 2

5 − 1

3 + 2

AC

5

4 3

5 + 1

2 3 − 1

BC

7

5 2

Exercise 7 Answer by true or false each of the following statements:

40 20

0.25 0.5

0 does not exist

3 π does not exist

The opposite of 2 is 2

2

3 3

2

4 4

The equation 2 1x admits two solutions

The equation 2 100 75 x admits two solutions.

8 2 4

2 3 6 6

3 2 3 2 1

The square of 1 2 is: 3 2 2

The three numbers A, B and C are equal :

A 18 32 ; B 7 2 ; C 98

Exercise 8 A farmer sells 55% from the quantity of wheat that he owns, then sells 13 tons of

wheat. He still has 24.8 tons.

What is the initial quantity of wheat?

________________________________________________________________

________________________________________________________________

4th week Exercise 1

1) Anna chose a number x. She multiplies it by 4 then add 10. She obtains 58.

What was the number chosen by Anna?

2) Clara chose a number. She multiplies it by 4 then add 54. She finds the same result

of multiplying the same number by 13.

What is the number chosen by Clara?

Exercise 2 The following bar diagram represents a statistical study.

1- Calculate the total frequency.

_______________________________________________________________

2- Complete the following table :

Values 2 3 4 5 6 7 8

Frequencies

Cumulative

frequencies

Relative

frequencies

in %

Cumulative

relative

frequencies

in %

Angles in

degrees

Exercise 3 In the following figure:

(C) is a circle of center O and fixed diameter

[AB] such that AB = 6cm.

[MN] is variable diameter of (C).

E is the symmetric of A with respect to M.

a) Show that (OM) and (BE) are parallel.

_________________________________

_________________________________

_________________________________

_________________________________

_________________________________

_________________________________

b) Show that (BM) is the perpendicular bisector of [AE].

_________________________________

_________________________________

_________________________________

_________________________________

_________________________________

_________________________________

c) Show that the triangle ABE is isosceles of vertex B.

_______________________________________________________________

_______________________________________________________________

_______________________________________________________________

d) Show that, when M moves on (C), the point E moves on a fixed circle of center and

Radius to be determined.

________________________________________________________________

________________________________________________________________

________________________________________________________________

4 liters

3 liters

Exercise 4

In Physics, we study

the elasticity with respect

to the mass to the object.

Mass m (in g) 20 50 90 120 150

Elasticity L (in cm) 0.8 2 3.6 4.8 6

a) Is it a proportionality table? Explain.

______________________________________________________________

______________________________________________________________

b) Express L in function of m.

______________________________________________________________

c) Calculate L when m = 225g

______________________________________________________________

d) Calculate L when m = 100 Kg.

______________________________________________________________

Exercise 5 We have two cans that can contain respectively 4 liters and 3 liters.

What to do in order to obtain an exact quantity of 2 liters?

_______________________________________________

_______________________________________________

_______________________________________________

_______________________________________________

Exercise 6

For each question, choose one answer out of the 4 proposed ones. Place in the yellow

box to the right side the letter that corresponds to the answer.

1 One of these numbers is decimal; which one?

A : 17

9

B : 37

14

C : 68

23

D : 39

15

2 One of these numbers is not decimal; which one?

A : 19

25

B : 1,35 10-4

C : 45

13

D : 24 %

3 One of these expressions is not a product; which one?

A : 3x(x - 1) B : 3 + x(x - 1) C : 3x(x - 1)² D : (3 + x)(x - 1)

4 One of these expressions is not a sum; which one?

A : x + 3 + y B : (x + 3) + y C : (x + 3)y D : x + 3y

5 What is the value of:

6

18

10

5 ?

A : 16

23

B : 7

3

C : 186

90

D : 2.33

6 The number 632.45 was rounded to the hundredth of :

A : 63.,4436 B : 632.4636 C : 632.4536 D : 632.4586

7 The highest number is :

A : 17

13

B : 19

13

C : 19

14

D : 9

7

8 One of these numbers is not equal to the other three ; which one?

A : 3.4 B : 3

4

C : 0.75 D : 7.5 10-1

9 The simplified form of the expression :

8 16

4

x is :

A : 2 - 16x B : 8 - 4x C : - 2x D : 2 - 4x

1

0

One of these numbers is not equal to the other three; which one?

A : 532 103 B : 5.32 10

5 C : 0.0532 10

6 D : 532 000

5th week

Exercise 1

For each question, choose one answer from the 4 proposed answers.

Place in the yellow box to the right side the letter that corresponds to the answer.

1 Which is the non-factorized form out of these 4 expressions?

A : 2 +x(x + 3) B : 2x(x + 3)² C : 2x(x + 3) D : (2 + x)(x + 3)

2 What is the reduced form of : 4 - (3 - 2x) + 3(2x - 7) - 1

A : 4x - 7 B : 8x - 21 C : 4x - 21 D : 8x - 7

3 Which expression translates : ''the double of the square of the sum of x and 3''

A : 2x + 3² B : 2x² + 3 C : 2(x + 3)² D : (2x + 3)²

4 What is the unique expression equivalent to 2x(- 3x)²

A : - 6x3 B : - 18x

3 C : 18x

3 D : 6x

3

5 What is the double product of : (- 2x)and ( - 3

4 )

A : - 3

2 x B : - 3x C : 3x D : 3

4 x

6 What is the developed and reduced form of : (1 - 2x)(5 - 3x) -2(3 -x)²

A : 4x² - 13x - 13 B : 4x² - x - 13 C : - 8x² - x - 13 D : 8x² - x -13

7 What is the developed and reduced form of : (4x - 5)² - (3 - 5x)²

A : - 9x² - 36 B : 41x² - 7x + 6 C : - 9x² + 16 D : - 9x² - 10x + 16

8 What is the factorized form of : 12x - 9 - 4x²

A : x(12 - 9 - 4x) B : - (2x - 3)² C : - (2x + 3)² D : (- 2x - 3)²

9 What is the factorized form of : (3x + 7)² - 2(x - 1)(3x + 7)

A : (3x+7)(1- 2x) B : (3x+7)(3- 2x) C : (3x+7)(x - 1) D : (x + 9)(3x + 7)

Exercise 2 The students of a college are divided in the following way:

47 % in the primary cycle

27 % in the intermediate cycle

130 students in the secondary cycle.

1) What is the percentage of students in the secondary cycle?

________________________________________________________________

2) Calculate the number of students in the college.

________________________________________________________________

________________________________________________________________

________________________________________________________________

Exercise 3 What misses for:

A parallelogram to be a rectangle?

_________________________________________________________________

A parallelogram to be a rhombus?

_________________________________________________________________

A rectangle to be a square?

_________________________________________________________________

A square to be a rectangle?

_________________________________________________________________

A rhombus to be a square?

_________________________________________________________________

A rectangle to be a parallelogram?

_________________________________________________________________

6th week

Answer by « True » or « False » or « I don’t know ».

If a quadrilateral has two opposite sides that are parallel,

then it is a parallelogram

If a quadrilateral has two consecutive sides that are poarallel,

then it is a rectangle

If a quadrilateral has two opposite sides that are congruent,

then it is a parallelogram

If a parallelogram has perpendicualr diagonals,

then it is a square

If a rhombus has two consecutive sides that are perpendicular,

then it is a square

If a quadrilateral has its diagonals that bisect each other,

then it is a parallelogram

If a rhombus is at the same time a rectangle,

then it is a square

If aquadrilateral has perpendicular diagonals,

then it is arhombus

If aparallellogram has congruent diagonals,

then it is a rectangle

If aquadriateral has two right angles,

then it is a rectangle

If aquadrilateral has four congruent sides,

then it is a rhombus

If a parallelogram has one right angle,

then it is a square

If a rhombus has congruent diagonals,

then it is square

The area of a rectangle is equal to the product of its length by its width

The area of a square is equal to the square of its side