Name :. Class :.. Homework Rubric : ( 10 marks ) 8 marks for accuracy.( To be complete and correct ) 1 mark for punctuality. ( To be delivered on time ) 1 mark for organization ( To be clean, neat and tidy ) 1
Lesson Approximation QR code Adding, subtracting, Multiplying and Dividing decimals Multiplying by 10, 100, 1000 Multiplying fractions Comparing fractions Dividing fractions The Triangles The circle 2
Measuring units : 1) Measuring length : 2) Measuring area: 3) Measuring weight: 4) Measuring currency: 5) Measuring Time: 6) Capacity: 3
Perimeter and area: 1) Perimeter of a square = side length 4 2) Area of a square = side length itself 3) Perimeter of a rectangle = (length + width) 2 4 ) Area of a rectangle = length width Remember (Adding & Subtracting Decimals) A) 4.15 + 7.36 =.. B) 9.4-2.8 =.. Steps : 1- put the decimal points under each other 2- put zero in the empty space 3- start the addition or the subtraction from the right 4
Place value ` Multiples If 6 x 4 = 24 we can say 24 is a multiple of 4 & a multiple of 6. ZERO is the common multiple of all numbers. Any number is a multiple of itself. All EVEN numbers with units digit 0, 2, 4, 6, 8 are multiples of 2. Numbers with units digit 0 or 5 are multiples of 5. Numbers with units digit 0 are multiples of 10. Divisibility Any number is divisible by itself. All the multiples of any number are divisible by this number. All EVEN numbers are divisible by 2. Numbers with units digit 0 or 5 are divisible by 5. Numbers with units digit 0 are divisible by 10. A number is divisible by 3 if the Sum of its digits is divisible by 3. 5
Factors To Find the factors of 6 : 1 X 6 2 X 3 then, 6 has 4 factors which are ( 1, 2, 3, 6 ) To Find the factors of 16 : 1 X 16 2 X 8 4 X 4 then, 16 has 5 factors which are ( 1, 2, 4, 8, 16 ) don t repeat 4 One is a factor of all numbers. Each number is a factor of itself. All numbers are factors of Zero except Zero. The largest factor of any number is the number itself. One is the only number that has one factor. The numbers that have only 3 factors are 4, 9, 49 25 Prime numbers Factors of : 2 = 1 x 2, 3 = 1 x 3, 5 = 1 x 5, 7 = 1 x 7 Ex : 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37... etc. are called ʺPrime Numbersʺ. Prime number has 2 factors only ( 1 and the number itself ). Zero is not a prime number because all numbers are factors of it. One is not a prime number because it has 1 factor only. 6
A- Approximate to the nearest hundredths and thousandths 1) 5.614 (to the nearest hundredths) 2) 45.678.. (to the nearest 1 100 ) 3) 34.1834. ( to the nearest thousandths ) 4) 8.459. ( two decimal places) 5) 7.358 (to the nearest 0.01) 6) 0.5484. ( to the nearest thousandths) 7) 8.2568 (to the nearest 0.001) B. Find the result of the following: 1) 14.253 + 27.34 = (to the nearest hundredth) 2) 62.125-55.4 =...... (to the nearest 1 100 ) 3) 7.3225 + 8.4657 = (to the nearest thousandth) 4) 6.4839-5.862 = (to the nearest 0.001) 7
A. Write the greatest & the smallest decimal fraction formed from 4, 2, 9, 7 The greatest is The smallest is... B. Choose : 1-536.592 536.59 to the nearest.. a) Tenths b) Hundredths c) Thousandths d) Units 2-82.457 82.5 to the nearest.. a) Tenths b) Hundredths c) Thousandths d) Units 3-151.23 150 to the nearest.. a) units b) Hundredths c) Thousandths d) Tens 4-4.559 4.6 to the nearest. a) Tenths b) Hundredths c) Thousandths d) Units 5-73.7694 73. 77 to the nearest.. a) Tenths b) Hundredths c) Thousandths d) Units C. Given that L = 37.4289 & M = 14.081 Find L - M approximated to the nearest thousandth... 8
A) Put the suitable sign ( < or > or =) 1) 2) 3) 6 7 1 11 8 5 [...] 3 7 [.] 1 9 [...] 4 6 6) 6 8 [.] 2 4 6 7) 1 [.] 3 1 2 8) 1 3 [.] 0.5 4) 1 [..] 2 3 5) 10 5 [..] 4 6 B) Find the value of a, b and c if : 9) 2.5 [.] 2 4 7 10) 3.5 [..] 3.05 a) 2 7 = a 21 b) b 4 = 16 32 c) 3 c = 15 20 a=. b=... c=.. C) Compare the following fractions: a) 3 4.. 2 5 b) 4 12.. 1 2 c) 7 9. 3 4 d) 6 8.. 3 7 e) 5 20.. 1 9 f) 3 4 2 8 9
D) Arrange in an ascending order: 1) 4 5, 4 7, 4 6, 4 10 2) 1, 4, 8 8 3, 7 8 8 3) 7 1 4, 1 5 8, 3 1 2, 4, 5 3 4 4) 24 4, 7 9 10, 3 3 5 9 1 4,, 5 1 2 5) 3 2, 18, 3 24 5, 3 8 10
E) Arrange in a descending order: 1) 2 5, 2, 2 7 6, 2 10. 2) 3 5, 1 5, 20 25, 2 5 3) 3 2, 3 5, 3 8, 6 8. 4) 3 2 10, 5, 3.5, 4.7, 4 3 10 5) 35 5, 9 9 10, 3 3 5, 5 1 2 11
Remark Multiplying We move the decimal point to the right side Dividing We move the decimal point to the left side A. Find the result of each of the following a) 32.56 x 10 = d) 27. 8 10 = b) 0.347 x 100 = c) 43.218 x 1000 = e) 123.54 100 = F ) 72.243 1000 = B. Complete 1) 3.6 km. =.. m. 2) 12.46 dm. = cm. 3) 3.002 kg. = gm. 4) 1.08 m. = cm. 6) 34.7 cm =. meters. 7) 458 meters =.. Km 8) 940 gm =. Kg. 9) 419 kg. =... Ton 5) L.E. 637.7 = P.T. 10) P.T. 25 = L.E.... 12
C. Approximate 1) 0.637 m.... cm. 4) 9.38 dm.... cm. 2) 0.58 m. dm. 5) 8.92 cm... dm. 3) 4.7995 km m. 6) 749 cm.. m. D. Choose: 1) 0.45752 x 100 = ------- a) 45.752 b) 4.5752 c) 457.52 d) 45 2) 21.43 x10 = ------- a) 214.3 b) 2.143 c) 21.43 d) 2.1 3) 0.0175 x 1000 = ------ a) 175 b) 17.5 c) 0.175 d) 1.75 4) 42.06 x10 = ------- a) 420.6 b) 4.20 c) 4.2 d) 4206 5) 0.067 x 1000 = --------- a) 6.7 b) 67 c) 0.067 d) 670 6) 21.3 x 10 = --------- a) 2130 b) 2.13 c) 213 d) 0.213 7) 0.00008 x 1000 = -------- a) 0.8 b) 0.08 c) 8 d) 8000 8) 0.45752 x 100 = -------------- a) 45.752 b) 4.5752 c) 457.52 d) 45752 9) 21.43 10 =------------- a) 214.3 b) 2.143 c) 21.43 d) 2143 13
10) 0.0175 x 1000 =----------- a) 175 b) 17.5 c) 0.175 d) 1.75 11) 42.06 x10 =------------ a) 420.6 b) 4.20 c) 4.2 d) 4206 12) 37.53 100 =----------- a) 375.3 b) 3.753 c) 0.3753 d) 375300 13) 0.27 100 = ------------- a) 0.027 b) 0.0027 c) 0.270 d) 2700 14) 329 1000 =-------------- a) 0.0329 b) 0.329 c) 0.00329 d) 3290000 E- Find the area of the rectangle with length 3.5 cm and width 10 cm. F- Ahmed bought 100 books for 17.75 L.E a book. How much did he pay? G- A piece of land of area 36600 m 2 is distributed among 1000 citizen. Find the share of each? 14
A. Complete each of the following : 1. 3.456 + 2.362 =...... to the nearest hundredth. 2. 16.357 x 100 =... 3. 856.32 1000 =... 4. 26548 gm.... Kg. 5. 453 cm... m. 6. 975 P.T... L.E. 7. 42.256... to the nearest hundredth. 8. 863.23... to the nearest hundred. B. Write the smallest and the greatest decimal fraction. can be formed of 3, 8, 2, 9. Smallest = greatest =.. C. L = 3.256 & M = 7.35 Find ( M L ) approximated to the nearest hundredth. D. The distance between two cities is 83 564 m, find the distance in km approximated to the nearest 0.01. 15
The Circle The circle is a closed curve, all the points on it having the same distance from a fixed point The fixed point is called the Centre of the circle We denote (name) the circle by its Centre, we say the circle M when its Centre point is M The radius of the circle ( r ): The radius is the line segment which joins any point lying on the circle to its Centre. ( all radii are equal in length ) The chord of the circle :The chord is the line segment that joins two points on the circle The diameter of the circle (d): The diameter is a line segment that passes through the Centre of the circle and joining two points on a circle. Notice that:.the diameter of the circle is the longest chord.all diameter of a circle are equal in length.the length of any diameter in a circle is equal to twice the length of its radius. The length of the diameter = (2 the length of the radius ) = ( r 2)..We can draw an infinite number of diameters in a circle. 16
Draw a circle M of radius length 3cm Step 1:- Mark a point M on a piece of Paper Step 2:- Open the compasses such that the distance between the metal tip and the pencil is 3 cm Step 3:- Put the metal tip M and swing the pencil around to draw closed curve that is the circle M of radius length 3 cm. 17
A- Choose the correct answer : 1) The diameter is the longest.. a) Radius b) chord c) center d) diagonal 2) All the diameters are..in the circle. a) Different b) equal c) approximately d) smaller than 3) The lengths of 2 radii in the same circle are. a) Different b) equal c) approximately d) smaller than 4) The diameter is a.chord in the circle a) Longest b) shortest c) equal d) approximately 5) The length of the diameter of a circle with radius 2cm is. cm. a) 6 b) 4 c) 8 d) 10 6) We name the circle by it s a) Radius b) center c) diameter d) diagonal 7) Any chord passing through the center of the circle is called a) Radius b) diameter c) center d) diagonal 8) Any line segment connects between any two points on the circle is called a) Radius b) center c) diameter d) Chord 9) the length of the radius = the length of the diameter in the same circle a) Double b) half c) triple d) quarter 18
B-Put ( ) or ( x): 1) The length of radius is greater than the length of diameter ( ) 2) The radius of the circle is the longest line segment can be drawn in the Circle. ( ) 3) All the radii in the same circle are different. ( ) 4) The longest chord in the circle is called diameter. ( ) 5) The diameter is twice the radius. ( ) 6) The diameter = 3r. ( ) C- From the opposite figure complete M and N are two circles. Find the length of MN. D- Choose the correct answer : 1) Any chord passing through the center of the circle is called... (radius, diameter, center ) 2)The length of the radius =... the length of the diameter in the same circle. ( double, half, triple ) 3)A circle, the length of its radius is 8 cm. then the length of the greatest chord in it =...cm. ( 4, 16, 12) 4) We can draw...of diameters in a circle. (2, 20, infinite number) 19
E- a) Draw the circle M with radius 4 cm. b) Draw the circle A with diameter 6 cm. c) Draw a circle M of radius length 2.5 cm, draw the diameter AB and find its length. (a) (b) (c) 20
How to multiply two fractions? 1) Multiply the numerators of the two fractions to get the numerator of the product. 2) Multiply the denominators of the two fractions to get the denominator of the product. 3) If we have mixed number we have to change it to improper fraction before multiplying it. 4) Put the resulting fractions in its simplest form. 21
A) Find the result of each of the following: a) 3 4 X 5 7 =.. b) 3 5 X 3 8 =.. c) 5 9 X 2 3 =.. d) 3 5 X 2 = e) 5 7 X 4 = f) 4 X 1 8 =.. g) 1 1 5 X 2 3 = h) 3 5 X 2 1 5 = i) 1 1 2 X 2 3 =.. B) In a classroom there are 30 pupils, 2 3 of them are boys, How many boys are there in the class? C) Ahmed bought 3 4 Kg. of meat for L.E. 20 for each kg. How much money did he pay? 22
How to divide two fractions? To divide two fractions: Exchange the numerator and the denominator of the second fractions, then multiply it by the first fraction. A-Write the reciprocal of each of the following: a) 1 5. d) 9 7.. b) 3 8. e) 7 c) 5 1 10. f) 3 2 5 23
B- Choose the correct answer : 1) 2 3 3 7 =. a) 5 9 b) 4 9 c) 1 5 9 d) 2 2 9 2) 4 3 2 9 = a) 6 b) 4 c) 3 d) 5 3) 2 3 1 6 =.. a) 4 b) 6 c) 7 d) 8 4) 5 6 25 36 =... a) 1 6 b) 1 5 6 c) 2 3 d) 1 1 5 5) 6 1 3 =. a) 7 b) 9 c) 18 d) 25 6) 1 4 2 = a) 8 b) 1 8 c) 2 d) 1 2 7) 9 10 3 = a) 30 b) 10 3 c) 3 10 d) 18 24
How to multiply Decimals: 1) Ignore the decimal point in both numbers. 2) Multiply the two numbers. 3) Count the number of decimal places in both numbers and find their sum. 4) The number of decimal places in the product equals the sum you have got. A- Find the product: (with steps) a) 0.15 x 2 -------------... b) 0.819 x 5 -------------... c) 3.7 x 0.6 -----------... d) 98. 21 x 0. 1 -------------... e) 9.72 x 0. 6 ------------... f) 0.12 x 0.11 -----------... g) 37 x 0.002 --------------... h) 1.89 x 0.3 ------------... i) 2.3 x 0.4 -------------... 25
B- Choose the correct answer: (With steps) a- 3.24 x 4.3 =. a) 13.932 b) 13.100 c) 14.932 d) 14.933 b- 6.84 x 0.34 = a) 2.426 b) 2.3256 c) 3.426 d)4.3256 c- 8.915 x 1.2 =. a) 11.698 b) 10.987 c) 10.698 d) 12.698 d- 34.56 x 2.5 =. a) 86.4 b) 87.5 c) 83.4 d) 85.4 e- 8.33 x 1.1 =. a) 9.163 b) 10.163 c) 9.153 d) 9.263 26
C. Hala bought 3.5 kg of grapes each for L.E 2.25 How much money did she pay? (With steps).. D. Find the product of 2.2 and 16.44 approximating the result to the nearest hundredths. (With steps)... E. Mariam went to the market. she bought 4.5 Kg of fish each for L.E 15 and 6 Kg of apples each for L.E 5.5 How many pounds did she pay? (With steps). F. A rectangular piece of land with width of 3.2 m and length of 5.8 m. Find the perimeter of the land. (With steps). 27
G. Find the perimeter of each of the following figures: (With steps) H. Compare the products by putting [ <, > or = ] a) 0.3 x 1.5 3 x 0.5 b) 0.342 x 1.2 3.42 x 0.12 c) 7.3 x 0.28 0.73 x 2.8 d) 172 x 0.003 0.172 x 0.3 e) 4.2 x 1.53 4.2 x 15.3 28
Revision First:- Choose the correct answer : 1) The diameter is a.chord in the circle a) Longest b) shortest c) equal d) same 2) 1 4 2 = a) 8 b) 1 8 c) 2 d) 1 2 3) The lengths of 2 radii in the same circle are. a) Different b) equal c) approximately d) smaller than 4) 37.53 100 =----------- a) 375.3 b) 3.753 c) 0.3753 d) 375300 5) 4.559 4.6 to the nearest. a) Tenths b) Hundredths c) Thousandths d) Units 6) Any line segment connects between the center of the circle and any point on the circle is called a) Radius b) center c) diameter d) diagonal 7) The diameter length of a circle with radius 5 cm equal.. a) 10 b) 5 c) 11 d) 7 8) 4.578 x = 4578 a) 10 b) 100 c) 1000 d) 2000 29
9) 3 1 8. (To the nearest hundredths) a) 3.1 b) 3.12 c) 3.13 d) 3.125 10) To draw a circle with diameter length 12 cm, then open the compass with length cm. a) 5 b)10 c)12 d) 6 11) 4 3 x = 1 a) 5 4 b) 1 4 c) 0.8 d) 3 4 12) 0.059.. (to the nearest hundredth) a) 0.6 b) 0.06 c) 0.006 d) 6 13) 225 25 = 2.25.. a) 2.5 b) 0.25 c)25 d) 2500 14) The length of the diameter = a) 1 2 r b) r c) 2r d) 3r 15) 736.592 736.59 to the nearest.. a) 0.1 b) 0.01 c) 0.001 d) 0.0001 16) 55.241 x 100 552.41 x10 a) < b) > c) = d) 17) 1 4 1 2 =. a) 1 4 b) 1 2 c) 3 4 d) 1 8 30
18) If 3 5 = x 20 then x =. a) 7 b)12 c) 18 d)15 19) 54.593 54.6 to the nearest. a) 1 10000 b) 1 100 c) 1 1000 d) 1 10 Second: - Complete the following: 1) 3 1 2 x 4 7 =. 2) 4.679 (to the nearest hundredth ) 3) If the length of the chord equal twice the length of the radius then it will called.. 4) 8 x 3 = 1 1 2 5) 26.273 + 24.28 =. (to the nearest tenth) 6) 6.7155 x 100 =. 7) 2550 cm m 8) A point inside the circle is at equal distance from any point on the circle is called 9) If the radius length equals 2.5 then its diameter length =.. 31
Third: - Answer the following A- Arrange the following in an ascending order: 11 12, 5 12, 3 4, 2 3 and 5 6. B- Write the greatest decimal fraction which consists of 3, 5, 4 and 2, then approximate it to the nearest hundredth and to the nearest thousandth... C- Draw the circle of center M with radius length 4 cm., draw the diameter AB, then draw the chord BC with length 6 cm.,then draw AC and find its length. 32
8 4 = 2 Dividend Divisor Quotient` 33
A-Find the quotient, and then choose: (With steps) 1) 625 25 =..... 2) 2385 53 =..... 3) 1404 27 =..... 34
4) 1545 15 =..... 5) 1728 32 =..... 6) 1375 25 =..... 35
7) 8908 17 =..... 8) 15042 23 =..... C- Find the quotient : (With steps) 1) 25625 125 =.... 36
2) 19912 152 =... 3) 12552 523 =... 4) 72795 345=.... 37
5) 9262 842 =... 6) 2925 117 =..... 7) 209934 654 =..... 38
C- A truck can carry 265 watermelons. Find the number of trips needed to transport 54060 watermelons.... D- An owner of packing food factory wanted to pack 5904 kilograms of sugar equally in 492 packs. What is the weight of each pack?.... 39
E. Find the number: 1. Find the number which multiplied by 324, the result will be 11988.... 2. Find the number which divided by 17, the result will be 85. 3. Find the number if divided by 24 the quotient is 125.... 4. Find the number which if divided by 25 the result will be 256.... 5. I am a number, if you multiply me by 13, the result will be 169, who am I?... 40
Remark: Change the divisor into a whole number by multiplying the divisor and the dividend by 10, 100, 1000, according to the number of places of the decimal part of the divisor to make the divisor a whole number. A. Find the result of each of the following: (With steps) 1) 4.2 0.7 =..... 2) 0.28 0.04 =..... 41
3) 27.2 0.8 =..... 4) 55.33 0.11 =..... 5) 2.016 0.84 =... 42
6) 48.24 1. 2 =... 7) 3.375 13.5 =... B. Choose the correct answer: a) 87.5 8.75 =. ( 1, 10, 0.1, 100 ) b) 87.29 0.29 =872.9.. ( 2.9, 29, 290, 0.29) c) 2 1 0.125 =. ( 17, 1.7, 71, 1.07) 8 d) 327 24 = 3.27 ( 2.4, 0.24, 24, 2004) 43
C. Story problems: (With steps) 1) A fruit seller had 289.6 kg of oranges; he put them equally in 8 baskets. How many kilograms were there in each basket approximated to the nearest kilogram?... 2) Habiba bought 9.25 m of cloth for L.E. 92.5, Find the price of one meter of cloth?... 3) The price of one kg of oil is L.E. 3.75, Find the price of 2.5 kg. of oil.... 44
4) The area of rectangle is 10.25 square meters, and its length is 4.1 meter. Find its width and perimeter.... 5) A train covered a distance 221.65 km. in 2.75 hours. Calculate the distance it covers in one hour..... 45
How to find the missing number D. Complete: 1. If the divisor = 8.5 and the quotient = 0.02, then the dividend =... 2. If the dividend = 419.7 and the quotient = 41.97, then the divisor =.... 46
3. If the divisor = 17, the quotient = 15, then the dividend =...... 4. If the dividend = 7.049 and the quotient = 0.07, then the divisor =..... 47
F- Find the result: a) 7 3.. (to the nearest 1 10 ).... b) 5 9 ( to the nearest hundredth)... c) 3 11. ( to the nearest thousandth).... 48
Complete: Answer: 49
A. Complete: 1) 7... to the nearest hundredth. 8.. 2) The divisor =... 3) 6.14 x 8.5 =...... to the nearest ten.. 4) The area of the square whose side length 4.2 cm is.... 5) 326.5 x 1000 =...... to the nearest thousandth. 6) The reciprocal of 2 1 5 is 7) Any fraction x.. = 1 8) 8.528 8 1 5 =...... to the nearest tenth. 50
36 9) 72 = in the simplest form.. A. Arrange in a descending order : 1, 6 6 18, 5 6, 9 18..... B. Ali bought a car for 46 400 L.E and he paid 20 000 L.E in advance, and the rest on 24 monthly instalments. Find the value of each instalment.. 51
A B The triangle it is a polygon having 3 sides, 3 vertices & 3 angles. m ( < A ) + m ( < B ) + m ( < C ) = 180. C The sum of the measures of the interior angles of any triangle = 180. Types of Triangles a) According to the measure of ANGLES : Right-angled Acute-angled Obtuse-angled X A D Y Z B C E F It has one right angle and 2 acute angles. The three angles are acute angles. It has one obtuse angle and 2 acute angles. 52
b) According to the length of SIDES : Equilateral Isosceles Scalene A X D B C Y Z E F - 3 sides are equal in length. AB = BC = CA - 3 angles are equal in measure. - each angle = 60. - 2 sides are equal in length. XY = XZ - 2 angles are equal in measure. m <Y ) = m (< Z ) - 3 sides are different in length. AB BC CA - 3 angles are different in measure. 53
Important remarks: We can draw a triangle if: given the lengths of its three sides Example: Draw the triangle ABC in which AB = 3 cm, BC = 6 cm and CA = 5 Step 1 :- Use the ruler to draw the line segment BC of length 6 cm Step 2 :- Open the compasses on the ruler such that the distance between the sharp point and the pencil equals 3 cm to draw AB Step 3 :- Put the sharp point fixed at B and turn the compasses to draw an arc on one side of BC as in figure 54
Step 4 : Put the sharp point fixed at C and reopen the compasses of distance 5 cm. to draw an arc on the same side of thefirst arc to intersect it at the point A Step 5 : Draw each of BA and CA then, the triangle ABC is the required triangle (Don t remove the arcs) 55
Remarks: -Any triangle has at least two acute angles. -In the right-angled triangle the sum of two acute angles is 90º -In the right -angled triangle one right angle & 2 acute angles. -In the acute-angled triangle three acute angles. -In the obtuse-angled triangle one obtuse angle & 2 acute angles. 1] Draw the Δ ABC in which AB = 6 cm, BC = 5 cm & CA = 4 cm. 2] Draw the Δ DEF in which DE = DF = 6 cm & EF = 4 cm. 56
3] Draw the equilateral Δ XYZ in which XY = 6 cm 4] Draw the equilateral Δ LMN whose perimeter is 9 cm. 5] Draw the Δ LMN in which LM =5 cm, MN = 8 cm & NL = 6 cm, Find the type of the triangle according to the measures of its angles and the lengths of its sides. 57
6] Draw a circle M with radius 3.5 cm, then draw the diameter DE, then draw the equilateral Δ DEF, then choose: a) The point F lies.. the circle. ( inside, on, outside) b) DF is..( chord, radius, otherwise ) 7] Draw the triangle ABC in which AB= 4 cm, BC = 3 cm, and CA= 5cm.Find the type of the triangle according to its side length and according to its angles. 58
8] Draw a circle whose diameter is 8 cm. and its center is O, AB is a diameter of this circle. Draw the triangle DAB where the chord DA=6 cm, draw DB and find its length. Then find the type of the triangle DAB according to its angles and sides. 9) From the opposite figure : a) The longest chord in the circle is b) BC is called. in the circle M 1 2 c) AM =.. 10) Three circles of centers A, B, C of radius length 4 cm for each Find the perimeter of ABC.... 59
Acute angled Obtuse angled Right angled AD is the altitude of the triangle ABC from the vertex A to the corresponding base BC (AD BC) Notice that:- XO is the altitude of the triangle XYZ from vertex X to the corresponding base YZ (XO YZ) LM is the altitude of the triangle LMN from vertex L to the corresponding base MN (LM MN) The acute angle have 3 altitudes intersect at one point inside the triangle The right angle have 3 altitudes intersect at the vertex of right angle The obtuse angle have 3 altitudes intersect at one point outside the triangle 60
1] A. Draw the equilateral Δ XYZ with side length 5 cm, then draw the Perpendicular segments XM, YN, ZL from its vertices to the opposite sides ZY, XZ, XY respectively. Measure the heights of the triangle. 2]Draw the Δ ABC in which AB = 3 cm, BC = 4 cm, AC = 5 cm,,then draw from B perpendicular line cuts AC at E. Find the lengths of BE. 61
3] Draw the Δ DEF in which DE = 6 cm, EF = FD = 5 cm, then draw perpendicular from the point F to DE and find its length. 4] Draw the isosceles Δ ABC right angled at B in which AB = 4 cm, then draw a line segment perpendicular from B on AC to be BX and find its length. 5] Draw the triangle LMN in which LM = 6 cm. and LN = MN = 5cm., using Your geometric instruments, draw the three altitudes LX, MY and NZ. And find the length of each one of them. 62
The set is a collection of well-defined things having a common property. 1) Which of the following is a set and which is not a set? 1) Digits of no. 12358... 2) Letters of the word (Shereen).... 3) Delicious meals.... 4) Days of the week.... 5) Months of the year.... 6) High buildings 7) Nice fruits.. 8) The Arabic alphabet 2] Write all the elements for each of the following sets: 1) The set of digits of number 56057.... 2) The set of letters of the word (maths).... 3) The set of even numbers between 0 & five.. 4) The set of days of the week.... 5) The set of the number 2221.... 63
3] State all the elements in each set of the following: 1. The set of months of the year.. 2. The set of even numbers between 5 and 15.. 3. The set of prime numbers less than 10. 4. The set of the main three colors of Egyptian flag... 5. The set of odd numbers smaller than 12.. 6. The set of letters of the word "Football "... 4] Express each of the following sets by the listing method: 1) X= the set of the digits of number 718213.. 2) Y= the set of months of the year beginning with the letter (J). 3) The set of even prime number.. 4) The set of letters of the word "Peter" 5] List all the elements in each of the following sets : 1) Set of letters of the word (apple).. 2) Set of digits of the number (7). 3) Set of days of the week that beginning with the letter (S).. 4) Set of prime numbers less than (14). 64
7] Express the following sets by description method: 1. A = { 0, 2, 4, 6 }. 2. C = { S, A, Y, M } 3. H = { 1, 0, 5, 8, 2 }.. 4. Y = { January, February, March,, December }.. 5. B = { 2, 4, 6, 8, 10, 12, 14,.. } 6. V = { m, n, o } 7. M= { Winter, Spring, Summer, Autumn} 8. N= { 0, 1, 2, 3, 4 }. 65
1] By using the opposite Venn diagram write each of the following sets: Y Z X 7. 6. 2. 0. 3. 8. 1. 5. X = {,.., } Y = {..,.,..} Z= {,..} A = {.,.,. } B = {.,.,.} The common element between A and B is 2] By using the opposite Venn diagram write the element inside each set : B = { 5, 1, 9 } C = { 0, 4, 7 } D = { 7, 3, 1 } B C D 66
1] Put or : 1) 5. { 2, 5, 9 } It is the relation between an element and a set. 2) 35. { 3, 5 } 3) 32. { 10, 12, 14, 23 } 4) 6.. { 2, 5, 9 } 5) 7.. { 77, 17 } 6) 0.. { 10, 20 } 7) e.. { letters of the modern } 8) 19.. { 1, 3, 5,..}s 9) 2. { 4, 5 } 10) 0. { } 2] If X = { 1, 2, 3, 4 } then complete using or : a) 1... X b) 6. X c) 4.. X d) 23. X e) 2.. X f) 0.5. X 67
3] Complete: 1) If 9 { 5, x }, then x = 2) If 6 { 7, 2, a }, then a =. 3) If 3 { 9, 8, b }, then b =. 4) If 4 { 1, n, 3 }, then n =. 5) If 5 { 7, b + 1, 9 }, then b =. 6) If 8 { n 2, 6, 4 }, then n = 4] Choose : 1) If 4 { 3, y }, then y = ( 3, 5, 4, ) 2) If 0 { x 3, 4 }, then x = (, 3, 4, 5 ) 3) If 3 { 6, x + 1, 5 }, then x =.. ( 2, 3, 7, 6 ) 4) If y { 3, 10, 7 } and also belongs to the multiples of 5, then y =. (7, 3, 5, 10) 68
Finite set: It is a set has a limited number of elements {1, 2, 4 } Infinite set: It is a set has an unlimited number of elements {1, 2, 3, } Empty set : (null) it s a set that has no elements. { } or 1] State whether finite, infinite or empty set : 7) The set of dinosaurs in the zoo. (.. ) 8) The set of books in your school library. (.. ) 9) The set of pupils in your school. (...) 10) The set of prime odd numbers. (..) 11) The set of whole numbers between 18 and 19. (.. ) 2] Which of the following sets is finite and which is infinite, then list the elements of each set: 1. The set of letters of the word apple. 2. The set of days of the week.. 3. The set of multiples of the number 3... 4. The set of prime numbers. 69
Two sets are said to be equal if they have the same elements 1] Put ( = ) or ( ) : 1) {15,3}.. { 3, 1, 5 } 2) {213}.. { 3, 2, 1 } 3) {Months of the year beginning with K }... { } 4) { x: x >2 } { 3, 4, 5 } 5) {X: x >6} { 7, 8, 9, } 2] Complete: 12) {X: x <2} {0, 1 } 1) {0, X } = { Y,5 } then X=., Y =. 2) { 3, A, 9 } = {6, B, 3} then A =. B =. 3) { X, 2, 3 } = {Y, 2, 1} then X =. Y =. 4) { 4, A, 6 } = { 6, B, 5 } then A =.B =. 5) { 3, 2 } = { 2,m } then m = 6) { x+ 1, 5 } = { 5, 4 } then x = 70
1) Complete the following using or 1) {2, 3} { 1, 2, 3 } 2) {56} { 50, 6 } 3) {4, 7, 9} { 479 } 4) Ø. { 2, 3 } 5) {2, 1, 5} { 1, 2, 3, } 6) {9, 8} { even numbers } 2] Complete the following using (,,, or ) : 1) 47. { 4, 7 } 2 ) { 200 }. { 0, 2, 4 } 3) Ø { 60, 70 } 4) 3. { 1, 5, 3 } 5) { 6 }. { the digit of the number 666 } 3] Find the value of x, y in each of the following : 1) 3 { x, 9 } then x =. 2) { 4 } { x,6 } then x =.. 3) { 5 } { 1, y, 6 } then y =.. 4) { 7, x } {8, 9, 7 } then x =.. 71
A. Put the suitable sign (,,, or ) 1) 39.. { 3.9 } 2) 15 the set of digits of the number 125 3) { 9 }.. { 5, 6, 7 } 4) { 3, 8 }. { 8, 3 } 5) 2. { 22 } 6) { 3, 6 } { x : x is a prime number } 7) { 0 }. { 10, 20 } 8) { 2, 3, 5 }.. { 2, 3 } 9) M The set of letters in the word man B. If H = { 4, 6 }. List all subsets of H.. C. Use the listing method to express the months of the year... 72
1] In the opposite figure find : X =. Y =. X Y =.3 X.4.2.0 y.9 2] Use the Venn diagram to list the elements of: 1) X Y = X 2) Y Z =.1 3) X Z =.7 4) X Y Z = Y.4.3.2.9 Z.0 3] If X = { 1, 3, 5, 7 }, Y = { 1, 2, 3 }, Z = { 2, 3, 5 }, List : 1) X Y=.. 2) Y Z =. 3) X Z =. 4) X Y Z =. 4] Complete: 1) { 2, 7 } { 3, 7 } =.. 2) {, 9, 4 } { 9, 6, 1 } =.. 3) { 5, 6 } { 1, 3 } =.. 4) {9} { 9, 8 } =.. 5) { 6, 7 } Ø =.. 73
5] If X = { 2, 4, 6 }, Y = { 2, 6, 8 } Draw a Venn diagram to represent these 2 sets, then find (X Y) 6] Represent the two sets A and B by Venn diagram where A= {2, 3, 7} & B= {1, 4, 8} then find A B. 74
Q.1] In the opposite figure: 1) X=. 2) Y=. X.4.3.2.5 Y.9 3) X U Y = Q.2] Use the Venn diagram to list the elements of : 1) X U Y = X 2) Y U Z =.1 3) X U Z =..7 4) X U Y U Z =. Y.4.9.5.2 Z.6.0 Q.3] If X = { 1, 3, 5, 7 }, Y = { 1, 2, 3 }, Z = { 2, 3, 5 }, List : 1) X U Y=.. 2) Y U Z =. 3) X U Z =. 4) X U Y U Z =. 75
1] In the opposite Venn diagrams, Complete: 1) X =.., X \ =. 2) Y =., Y \ =.. 3) X Y =..,(X Y) \ =. 4) X Y =..., ( X Y ) \ =. 5) U =. 2] If U is the set of the even numbers less than 12 and A= { 2, 4, 6, 10 }, B = { 4, 8, 0, 6 } Find each of the following: 1) A \ =., B \ =.. 2) A U B =., A B =. 3) (A B) \ =.., (A U B) \ =... 4) A \ B \ =., A \ U B \ = 76
1] Find the following: 1) { 5, 4, 2 } - { 1, 2 } = 2) { 5, 6 } - Ø =. 3) { 55 } - { 25 } =. 4) { 2, 5, 7 } - { 8, 10, 2, 7, 5 } =. 5) { 7, 8 } - { 8, 7 } = 2] In the opposite Venn diagrams, Complete : 1) A = U 2) A \ =. A.1.6 3) A A \ = 4) A A \ =..2.5.8 5) U A =.. 6) A U =.. 3] If X = { 4, 8 } & Y = { 2, 4, 6 }, then find: 1) X Y =.. 2) Y X =.. 3) Y U X =..... 4) X Y =... 77
A. If X = {4, 8 } & Y = { 2, 4, 6 }, then find: 1. X Y =.. 2. Y X =. 3. Y U X =... 4. X Y =. B. If X = {6, 1, 9 } & Y = { 3, 8, 1, 2 }, then find: 1. X Y =... 2. Y X =. 3. Y U X =... 4. X Y =.. D. Use the operation of intersection and union, the difference and complement, express the shaded part in each of the following diagrams:... 78
E.Choose the correct answer: 1- { 25 } { 2, 5 } a) b) c) d) 2-. { } a) b) c) d) 3- The number of subsets of the set { 5, 7 } equals. a) 2 b) 3 c) 4 d) 5 4- { 2, 3, 6, 12 } the set of the factors of the number 6 a) {2, 3, 6, 12 } b) {3, 6} c) {4, 6} d) {2, 6, 3} 5- If x Y, then X Y = a) X b) Y c) d) U 6- If U is the set of odd numbers less than 25, then { 5, 15, 25 }. U a) b) c) d) 7- If { 3, 6} = { 1+ x, 3} then x=.. a) 2 b) 3 c) 4 d) 5 8- if { 2, a + 2 } { 2, 4, 6, 8}, then a =. a) 2 b) 4 c) 6 d) 8 79
9-5.{3, 5} { 4, 7 } a) b) c) d) 10- If x Y, then X Y = a) X b) Y c) d) U 11- If X Y = Y, Then X.Y a) b) c) d) 12- If { 7, 10 } { 10, x+4 } then x =.. a) 2 b) 3 c) 4 d) 5 13- If U = { 2, 3, 4, 5, 6, 7}, then : i).. U a) b) c) d) ii) U..U a) b) c) d) iii) { 6, 7 }. U a) b) c) d) 80
81
Note that: The probability of impossible event = 0 The probability of certain event = 1 The probability of possible event is between 1 & 0 (fraction) The sum of all possible events = 1 A) In rolling a fair die, complete the following: 1. The probability of getting an even number = 2. The probability of appearance of an odd number =.. 3. The probability of appearance of a number greater than 2=.. 4. The probability of appearance of the number 4 =.. 5. The probability of appearance of a prime number =.. 6. The probability of appearance of a number divisible by 5 =. 7. The probability of appearance of a number less than 3 =.. 8. The probability of appearance of an even prime number = 82
B) A card is chosen randomly from twelve cards numbered from 1 to 12. What s the probability that the selected card shows: 1. An odd number.. 2. A prime number.. 3. An odd number greater than 3. 4. An even number less than 5. C. A bag contains 5 blue marbles, 3 red marbles and 4 green marbles, if a marble is chosen randomly, find the probability of the following: 1- Getting a blue marble =. 2- Getting a red marble =.. 3- Getting a green marble =. 4- Getting a black marble =. 5- Getting a blue or red marble =.. 6 Getting a red or green marble =. 7 Getting a non-red marble = D. complete: 1) The probability of impossible event is.. 2) The probability of certain event is. 3) The probability of possible event is between. and. 4) The probability of getting a head when tossing a coin once =.. 5) The sum of all possible probabilities = 83
E.A spinner has 5 equal colored sectors : 1. What are the possible outcomes?. 2. What are the chances to stop on red after spinning? 3. What are the chances of landing on black or red? 4. What are the chances of getting purple or yellow?.. 5. What are the chances of getting a white colour?.. 84
A. Choose the correct answer: 1- On tossing a coin the probability of getting a head=. a) 0.5 b) 0.4 c) 0.2 d) none of the previous 2- The probability of certain event is a) 0 b) 1 c) 2 d) 1 2 3- A fair die is thrown once; the probability of getting an even number is. a) 0 b) 1 c) 2 d) 1 2 4- A fair die is thrown once; the probability of getting a number less than 3 is a) 0 b) 1 c) 1 3 d) 1 2 5- A fair die is thrown once; the probability of getting a number greater than one is a) 0 b) 5 6 c) 1 3 d) 1 2 6- A fair die is thrown once; the probability of getting a number greater than nine is a) 0 b) 5 6 c) 1 3 d) 1 2 7- A fair die is thrown once; the probability of getting number 5 is.. a) 0 b) 1 6 c) 1 3 d) 1 2 85
8 As tossing a metallic coin once, the probability of appearing a head is.. a) 0 b) 1 c) 1 3 d) 1 2 9- A fair die is thrown once; the probability of getting a number divisible by 2 is a) 0 b) 5 6 c) 1 3 d) 1 2 10- As tossing a metallic coin once, the probability of appearing a tail is.. a) 0 b) 1 c) 1 3 d) 1 2 11- A fair die is thrown once; the probability of getting a prime number is a) 0 b) 5 6 c) 1 3 d) 1 2 12- The probability that the elephant flies =. a) 0 b) 1 c) 1 3 d) 1 2 13- It is that the sun rises from west. a) Expected b) possible c)sure d) impossible 14- The probability that a bird flies =.. a) 0 b) 1 c) 1 3 d) 1 2 15- A fair die is thrown once; the probability of getting a number smaller than or equal to 6 is. a) 0 b) 1 c) 1 3 d) 1 2 86
First: - Choose the correct answer: 1) { 4, 5} {2, 3, 7 } a) b) c) d) 2) The number of altitudes of the acute angled- triangle is a) zero b) 1 c) 2 d) 3 3) The probability of impossible event =.. a) zero b)1 c) 2 d)3 4) 7 {17, 77} a) b) c) d) 5) if { 3, 4 } = { 1 + y, 4 }, then y =. a) zero b)1 c) 2 d)3 6) 13542 100 =. a) 13542 b) 13.542 c) 1.3542 d) 1354.2 7) The probability of success of a pupil in an exam is then the probability of his failing is. 1 5 1 2 a) b) c) d) 8) If { 5, 3 } { 3, x } = Ø then x =. a) zero b)1 c) 5 d) 3 9) If X Y, then X Y =... 2 9 4 5 1 4 a) X b) Y c) U d) X \ 87
10) The shaded part in the opposite figure represents. a) X Y b) X Y c) U d) X Y 2 3 1 11) 2 x 1 = 4 3 7 a) 4 b) 3 c) 3 d) 2 4 12 1 4 12) The probability of the certain event = 2 12 a) zero b) 1 c) 2 d) 3 13) Ø the set of odd numbers. a) b) c) d) 14) If X Y, then X U Y =. a) X b) Y c) U d) X \ 15) The altitudes of the obtuse angled triangle intersect at one point located the triangle. a) on b) inside c) outside d) at the vertex 16) If a X, then a X \ a) b) c) d) 17) A fair die is thrown once; the probability of getting a number divisible by 2 is a) 0 b) 5 6 c) 1 3 d) 1 2 18) As tossing a metallic coin once, the probability of appearing a tail is.. a) 0 b) 1 c) 1 3 d) 1 2 88
19) A fair die is thrown once; the probability of getting a prime number is a) 0 b) 5 6 c) 1 3 d) 1 2 20)The longest chord the diameter in a circle a) Longest b) shortest c) equal d) different 21) 1 2 2 = a) 1 4 b) 1 8 c) 2 d) 1 2 22) The lengths of 2 diameters in the same circle are... a) Different b) equal c) approximately d)smaller than 23) 37.53 x 10 = a) 375.3 b) 3.753 c) 0.3753 d) 375300 24) 4.559 4.56 to the nearest. a) Tenths b) hundredths c) thousandths d) units 25) Any line segment joins any two points on the circle passing through the center of the circle is called. a) Radius b) center c) diameter d) chord 26) The radius length of a circle with diameter 10 cm equal.. a) 10 b) 5 c) 11 d) 7 27) 72.52 x = 7252 a) 10 b)100 c)1000 d)2000 89
28) 3 1 8. (to the nearest tenths) a) 3.1 b) 3.12 c) 3.13 d) 3.125 29) To draw a circle with diameter length 20 cm., then open the compass with length cm. a) 5 b) 10 c)12 d) 6 Second: - Complete the following: 1) Write the greatest decimal fraction which consists of 3, 5, 4 and 2, then approximate it to the nearest hundredth and to the nearest thousandth. 2) 16.4 0.4=.. 3) The number which multiplied by 112, the result will be 3584 is.. 90
4) 5.4 x 3.2 =.. 5) {8} { 2, 5, 8} =. 6) The altitudes of the right angled triangle intersects at the of the right angle. 7) The probability of an event = zero, then this is (a / an). event. 8) The complement of an empty set is the...set. 9) The number of sides of a triangle the number of its heights ( >, <,= ) 10) 6 1 4 12 1 2 =. 11) 4.2254 (to the nearest hundredth ) 12) In the opposite figure: i) AB is called.in the circle M ii) AC is called in the circle M 91
13) 478.347 134.834 =.. (to the nearest hundredth). 14) 26.273 + 24.28 =... (to the nearest tenth). Third: - Answer the following : A) From the opposite figure, Complete: X=.. Y= X Y X Y = X U Y = X Y = X =.. 92
B) Draw the Δ ABC in which AB = 4 cm, BC = 6 cm, and CA = 8 cm then draw a circle whose center is B and its radius length is equal to 4 cm then complete the following : a) The point A is located.. the circle b) The point C is located.. the circle c) The. is called the radius of the circle. 6) A bag contains 4 red, 6 orange and 8 yellow marbles. Randomly a marble is Selected. Calculate the probability of selecting : 1. Red marbles =.. 2. Black marbles =. 3. Yellow marbles = 93
First: - Choose the correct answer: 1) { 2, 8} { 2, 3, 7 } a) b) c) d) 2) 34596 gm Kg a) 35 b) 346 c) 3460 d) 34 3) The number of subsets of { 1, 7 } =.. a) 5 b) 4 c) 2 d) 3 4) 9 {19, 99} a) b) c) d) 5) If { 3, 4 } = { 2 + y, 4 }, then y =. a) zero b)1 c) 2 d)3 6) A A = a) U b) A c) A d) Ø 7) x 1 =. 2 1 2 a) 2 b)1 c) d) 4 8) 12.5 + 7.632.. ( to the nearest 0.01 ) a) 20.132 b) 20.133 c) 20.13 d) 2.013 9) If X Y, then X Y =... a) X b) Y c) U d) X \ 1 4 94
10) The shaded part in the opposite figure represents. a) X Y b) X Y c) U d)x Y 11) If U = { 2, 3, 4, 5, 6, 7,.. }, Then 9 U a) b) c) d) 3 20 12) The decimal form of the fraction = a) 0.15 b) 0.3 c) 0.9 d) 13) 1.25 x 3.2.. 32 x 12.5 a) > b) < c) = d) 14) If X Y, then X U Y =. a) X b) Y c) U d) X \ 15) The altitudes of the acute angled triangle intersect at one point located the triangle. a) on b) inside c) outside d) at the vertex 16) If a X, then a X \ a) b) c) d) 17) A fair die is thrown once; the probability of getting a number divisible by 5 is 1 2 a) 1 6 b) 5 6 c) 1 3 d) 1 2 18- As tossing a metallic coin once, the probability of appearing a head is a) 0 b) 1 c) 1 3 d) 1 2 95
19 - A fair die is thrown once; the probability of getting an even number is a) 0 b) 5 6 c) 1 3 d) 1 2 20) 4 x = 1 a) 5 4 b) 1 4 c) 0.8 d) 3 4 21) 0.059.. (to the nearest tenth) a) 0.6 b) 0.06 c) 0.006 d) 0.1 22) 225 25 = 22.5.. a) 2.5 b) 0.25 c)25 d) 2500 23) The length of the longest chord = a) 1 2 r b) r c) 2r d) 3r 24) 736.592 736.6 to the nearest.. a) 0.1 b) 0.01 c) 0.001 d) 0.0001 25) 55.241 100 552.41 x10 a) < b) > c) = d) 26) 1 4 x 1 2 =. a) 1 4 b) 1 2 c) 3 4 d) 1 8 27) If 3 5 = x 10 then x =. a) 6 b)12 c) 18 d)15 96
28) 25.257 25.26 to the nearest. a) 1 10000 b) 1 100 c) 1 1000 d) 1 10 Second: - Complete the following: 1) 9984 312 =.. 2) 12.5 2.5 =... 3) The number which multiplied by 9144, the result will be 91440 is.. 4) 2.7 x 0.44 =.... 97
5) {3,2,5} { 2, 5, 8} =. 6) Any triangle has... altitudes. 7) The probability of an event = 1, then this is (a / an). event. 8) The complement of the universal set is an...set. 9) The number of heights of an isosceles triangle equal... 10) 62.2236 x 100 =. 11) 25563 m.. cm 12) The line joining the center of the circle and any point on the circle is called 13) If the radius length equals 3.5 then its diameter length =.. 14) If L = 24.665 and M= 36.254, then find M L approximate the result to the nearest hundredth. 98
Third: - Answer the following: A) From the opposite figure, complete: In the opposite Venn diagrams, Complete: 1) X = X \ =.. 2) Y =, Y \ =. 3) X Y =, (X Y) \ =. 4) X Y =..., ( X Y ) \ = 5) U =. U X.2.8.9.4.3 Y 1. 7. B ) Find the perimeter of the rectangle whose length is 4.1 cm and its width is 3.5 cm, then calculate its perimeter. 99
C) Draw the Δ ABC in which AB = BC = 6 cm and AC = 5 cm, then draw AD perpendicular BC which intersect it at D then find the length of AD D) A box contain cards numbered from 1 to 10, find the probability of : i) Getting an even number.. ii) Getting a prim number. iv) Getting number 7. 100