Download The ratio between the side length of a square and its perimeter is 1

Final Revision
* Ratio: is a comparison between 2 or more quantities have the same type and unit.
* Ratio has no unit.
* Ratio between 2 numbers =
𝟏𝒔𝒕 𝒏𝒖𝒎𝒃𝒆𝒓
𝟐𝒏𝒅 𝒏𝒖𝒎𝒃𝒆𝒓
* a : b a is called antecedent (1st term) and b is called consequent (2nd term).
* The two terms of the ratio should be the same type and unit.
* The ratio between the side length of a square and its perimeter is 1 : 4.
* The ratio between the side length of an equilateral triangle and its perimeter is 1 : 3.
* The ratio between the circumference of a circle and its radius is 2𝜋 ∶ 1.
* The ratio between the diameter of a circle and its circumference is 1 ∶ 𝜋 .
* The ratio between the perimeter of a square of side length 3cm and the perimeter
of a square of side length 5cm is 3 : 5.
* The rate is the ratio between two quantities of different type and unit.
* The proportion is equality between 2 or more ratios.
* The product of means = the product of extremes
* The drawing scale =
* The real length =
𝐷.𝐿
𝐷.𝑆
𝐷.𝐿
𝑅.𝐿
* The drawing length = R.L X D.S
* If the drawing scale > 1 this expresses magnification (maximization).
* If the drawing scale < 1 this expresses reduction (minimization).
*The percentage is ratio whose 2nd term is 100.
* The parallelogram is a quadrilateral in which each 2 opposite sides are parallel.
* In the parallelogram each two opposites sides are equal in length.
* Each two opposite angles in the parallelogram are equal in measure.
* The sum of the measures of any two consecutive angles equals 180°.
* The two diagonals of the parallelogram bisect each other.
* The square is a parallelogram with equal sides and right angles
perpendicular diagonals.
or equal and
* The rectangle is a parallelogram with right angles or equal diagonals.
* The rhombus is a parallelogram with 2 adjacent sides are equal
diagonals.
or perpendicular
* The diagonals of the rhombus are perpendicular and bisect each other.
* The diagonals of the rectangle are equal andbisect each other.
* The four angles are right angles in each of rectangle and square.
* The two diagonals are perpendicular in each of rhombus and square.
* The two diagonals are equal in length in each of rectangle and square.
* The four sides are equal in length in each of rhombus and square.
* The parallelogram with two adjacent sides are equal is called rhombus.
* The parallelogram with one right angle is called rectangle.
* The trapezium is a quadrilateral with only 2 opposite sides are parallel.
* The rectangle with two adjacent sides are equal is called square.
* The rhombus with one right angle is called square.
* The solid is the body that occupies room in the space.
* The volume is the magnitude of the room that the body occupies in the space.
* The cubic meter is the volume of a cube with edge length 1m.
* The cube has 6 faces in the form of square.
* The cuboid has 8 vertices.
* The cube has 12 edges.
* All faces of the cube are equal in area.
* All edges of the cube are equal in length.
* In the cuboid each two opposite faces are parallel and equal in area.
* The face of the cuboid is in the shape of rectangle.
* Each two adjacent faces intersect at a line segment which is called edge.
* The cuboid has a 3 dimensions.* The volume of the cuboid =L x W x H
* The volume of the cuboid = base area x H
* The area of base of the cuboid =
* The length of the cuboid =
𝑉
*The height of the cuboid =
ℎ
𝑉
*The width of the cuboid =
ℎ×𝑤
𝑉
𝑙×𝑤
𝑉
𝑙×ℎ
* The cube is a cuboid with equal dimensions.
*The capacity is the inner volume of a hollow solid
* The unit used for measuring capacity is liters
* The type of the statistical data are quantitive ,descriptive
* The favorite color , the place of birth , social case are from the descriptive data.
* The weight , the shoes size , your mark in math are from the quantitivedata.
* The center of the number 10- , 20- is
10+20
2
= 15
* The range is the difference between the maximum value and the minimum value
* The number of sets = the range ÷ length of the set
How to solve:
1- ratio
diff: more than – less than –exceed – increase – decrease – difference
2- rate(÷ )
3- proportion
unit :
…… / ……
=
4- drawing scale D.S=
𝐷.𝐿
𝑅.𝐿
5- percentage + " profit , loss , discount ,interest , shrink , sale " before : pro : after
Percentage Total :boys : girls
6- volume: a) find the number = big V ÷ small V
c) thickness big V – small V
d) pool
water
b) the price = V x money
needed
l
60
60
60
w 25
25
25
h
3
4-3=1
4
1) If the sum of the 3 dimensions of a cuboid is 60cm and the ratio between them is
2:1:3 , find its volume?
2) Mai , Mona and Heba start a business , Mai paid third what Mona paid and
𝟐
Mona paid what Heba paid , if the business loss L.E. 23 000 , calculate the share of
𝟓
each of them of the loss.
3)If the ratio between the measure of the three angles of a triangle is 5:2:3 , find the
measure of each angle
4) A factory produces 5000 juice cans in 8 hours find the production rate then find
the time needed to produces 1000 juice cans.
5) If the distance between two cities on a map is 10 cm and the real distance
between them is 120 km , find the drawing scale of this map then find the real
distance between two other cities on the same map if the distance between then on
it is 6cm.
6) A class contains 40 pupils , 32 of them were present find the percentage of the
absentees.
7) Khaled bought a car for L.E. 50 000 then he spent L.E. 5 000 for repairing it,after
selling it he found that the percentage of his loss was 5 % , calculate the selling price
of the flat?
8) A cubic tank of edge length 64 dm , the solar rushes inside it at a rate of 8192
dm3/min, calculate the capacity of the tank ,when will the tank be filled?
9)A cuboid shaped swimming pool has a base of dimensions 60 m, 40 m and its
height is 3 m .Water was poured in it of volume 4800 m3
a) find the height of the water in the pool.
b) find the volume of water needed to fill the pool completely.
10)A wooden box for transporting goods ,it is cube shape with lid its inner
dimension is 150cm find the volume of wood of the box if the thickness of the wood
is 2cm.
11)A man distribute 6300 pounds between his three sons , if the share of the first
was third of the money and the ratio between the second and the third is 3:2
calculate the share of each of them.
12) A cuboid-shaped box of dimensions 9 cm ,12 cm , 10 cm was filled with pieces of
sweets each piece in the shape of a cuboid with dimensions 1 cm ,2cm ,2cm find the
number of the pieces in the box.
13) The following data represents the marks in the math. test for students in one
classroom:
marks
10-
20-
30-
40-
Total
No . of students
10
15
20
5
50
a) Draw the frequency curve for this distributions.
b) Complete:
(1) The number of students whose marks are less than 30 = ……
(2) The greatest mark in the exam is ……… while the smallest mark is …………
(3) The percentage of the number of students whose marks are 40 and more = ……
Model Answer
1)
l : w : h : sum
5) 𝐷. 𝑆 =
Ratio 2 : 1 : 3 : 6
10 𝑐𝑚
120 𝑘𝑚 × 100 000
= 20 cm
𝐷. 𝑆 =
1
1200 000
= 10 cm
𝐷. 𝑆 =
𝐷. 𝐿
𝑅. 𝐿
6
60 ×1
w=
h=
: 60
60 ×2
6
60 ×3
= 30 cm
6
𝑅.𝐿
𝐷. 𝑆 =
Real
L=
𝐷.𝐿
1
6 𝑐𝑚
=
1200 000
𝑅. 𝐿
V=lxwxh
6 × 1200 000
1
= 20 x 10 x 30
𝑅. 𝐿 =
= 6000 cm3
𝑅. 𝐿 = 7200 000 𝑐𝑚 ( ÷ 100 000)
𝑅. 𝐿 = 72 𝑘𝑚
2)
Mai : Mona : Heba
1 :
2
3
x2
: 5x3
2 : 6
percentage of absentees =
2 : 6
: 15
: 23
real
: 23 000
Mai =
2 ×23000
23
Mona =
Heba =
= 2000 pounds
6 ×23000
23
15×23000
23
8
40
× 100 = 20 %
: 15
Mai : Mona : Heba : sum
ratio
6) number of absentees = 40 – 32 = 8 pupils
= 6000 pounds
7) cost price = 50 000 + 5 000 = 55 000 L.E
Before : loss : after
100 % : 5 % : 95 %
55 000 :
The selling price =
95 ×55 000
100
= 52 250 L.E
= 15000 pounds
8) Capacity = L x L x L
3)
1
Ratio
5
st
nd
: 2
:
rd
:3
2 : 3
Real
1st =
5 ×180
10
10
3×180
10
4) rate =
=262144 dm3
The time needed to fill tank =
= 90°
2 ×1800
= 64 X 64 X 64
: 10
: 180
2nd =
3rd =
: sum
262144
8192
= 32 𝑚𝑖𝑛𝑢𝑡𝑒𝑠
= 36 °
= 54 °
5000 𝑐𝑎𝑛𝑠
8 ℎ𝑜𝑢𝑟𝑠
9) ℎ𝑒𝑖𝑔ℎ𝑡 𝑜𝑓 𝑤𝑎𝑡𝑒𝑟 =
=
= 625 𝑐𝑎𝑛𝑠/ ℎ𝑜𝑢𝑟𝑠
1000 ×8
5000
4800
60 × 40
= 2𝑚
5000 𝑐𝑎𝑛𝑠 1000 𝑐𝑎𝑛𝑠
=
8 ℎ𝑜𝑢𝑟𝑠
?
The time needed =
𝑉
𝑙 ×𝑤
ℎ𝑒𝑖𝑔ℎ𝑡 𝑜𝑓 𝑤𝑎𝑡𝑒𝑟 𝑛𝑒𝑒𝑑𝑒𝑑 = 3 − 2 = 1 𝑚
= 1.6 ℎ𝑜𝑢𝑟𝑠
𝑉 = 𝑙 ×𝑤×ℎ
= 60 × 40 × 1
= 2400 𝑚3
10) 𝐼𝑛𝑛𝑒𝑟 𝑣𝑜𝑙𝑢𝑚𝑒 = 𝑙 × 𝑙 × 𝑙
13)
= 150 × 150 × 150
25.00
= 3375000 𝑐𝑚3
𝑂𝑢𝑡𝑡𝑒𝑟 𝑙𝑒𝑛𝑔𝑡ℎ = 150 + 2 + 2 = 154 𝑐𝑚
𝐼𝑛𝑛𝑒𝑟 𝑣𝑜𝑙𝑢𝑚𝑒 = 𝑙 × 𝑙 × 𝑙
20.00
15.00
= 154 × 154 × 154
= 3652264 𝑐𝑚3
10.00
𝑉𝑜𝑢𝑙𝑚𝑒 𝑜𝑓 𝑡ℎ𝑒 𝑤𝑜𝑜𝑑 = 3652264 − 3375000
5.00
= 277264 𝑐𝑚3
0.00
11) 𝑇ℎ𝑒 𝑠ℎ𝑎𝑟𝑒 𝑜𝑓 𝑡ℎ𝑒 1𝑠𝑡 =
1
3
× 6300 = 2100 𝐿. 𝐸
𝑇ℎ𝑒 𝑟𝑒𝑚𝑎𝑖𝑛𝑑𝑒𝑟 = 6300 − 2100 = 4200 𝐿. 𝐸
2nd : 3rd : sum
Ratio
3 : 2
Real
: 5
: 4200
2nd =
3 ×4200
3rd =
2 ×4200
5
5
= 2520 𝐿. 𝐸
= 1680 𝐿. 𝐸
12) 𝑉𝑜𝑙𝑢𝑚𝑒 𝑜𝑓 𝑏𝑜𝑥 = 𝑙 × 𝑤 × ℎ
= 9 × 12 × 10
= 1080 𝑐𝑚3
𝑉𝑜𝑙𝑢𝑚𝑒 𝑜𝑓 𝑏𝑎𝑟 = 𝑙 × 𝑤 × ℎ
=1×2×2
= 4 𝑐𝑚3
𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑏𝑎𝑟𝑠 =
1080
= 270 𝑏𝑎𝑟𝑠
4
b) (1) 15 + 10 = 25 students
(2) 50 , 10
(3)
5
50
× 100 = 10 %