web view1.for each of the numbers below , state whether it is . natural numbers, integers...
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Real Numbers practice 3.1
1.For each of the numbers below , state whether it is Natural numbers , integers numbers,rational numbers, irrationl numbers 1)
Natural N
Integers N
Rational N
Irrationl N
-9−72
523√2
01
2)Natural N
Integers N
Rational N
Irrationl N
√5
−7
−73
3.12
54
2
3)Natural N Integers N Rational N Irrationl N
2.01
0.666…
−13
0.010110111…
2.0101…√16
−√5
5.4564)
Natural N Integers N Rational N Irrationl N2.3030030003…
0.7575
−4.63
√10
-22.3451.888…3.5674
5)Natural N Integers N Rational N Irrationl N
π
3
−1363√22
−7.5
√23
+4
5.73214-2.1189…
6)Natural N
Integers N
Rational N
Irrationl N
25−17
−125√9
3.12
−12π
√1024
2) State the following questions wheter they are “True” or “ False”
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1) 0.001001001… is an rational number ……………………………..2) 0.110110110110… is an rational number ………………………………3) 0.767667666766667… is an rational number ………………………………4) 0.59999… is an rational number ………………………………5) 0 is an real numbers ………………………………6) Repeating decimals is not a rational number ………………………………7) Not repeating decimals is a real numbers ………………………………
8.√ (a−b )2=a−b a ,b∈R ………………………………
3. The number mentioned there or not1 ) The most integer less than nine . ……………………………………………….2 ) is the most rational, less than nine . ……………………………………………….
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3 ) a minimum integer greater than one . ……………………………………………….4 ) There are at least more rational one . ……………………………………………….
Practice 3.21. Name the porperties of the following real
number in each of the following equation 1.q⋅37=37⋅q ………………………………………………………………..2. (2+3 ) p=2 p+3 p
………………………………………………………………..3. 6+(5+ y )=(6+5 )+ y
………………………………………………………………..4. (2+3 )(5+6)=(5+6 )(2+3 )
………………………………………………………………..5. 3+(4+6)=3+(6+4 )
………………………………………………………………..6. a (b+c )=(b+c )a
………………………………………………………………..7. 5( x+ y )=5x+5 y
………………………………………………………………..
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8. −5+π Is a real number ………………………………………………………………..9. There are real numbers plus 0 and -15 . ………………………………………………………………..10. 1×1=1 ………………………………………………………………..
2. Consider the following statement is true or not . If truth is the treasure of truth when p, q, x, y and z are any real number .
1.6+(2⋅3 )=(6+3)⋅2 ………………………………………………………………..
2.x−( y−z )=( x− y )−z ………………………………………………………………..
3.x− y= y−x ………………………………………………………………..
4.3⋅(2−x )=(3⋅2)+(3 )(−x ) ………………………………………………………………..
5.5 p+5q=5( p+q ) ………………………………………………………………..
3.Set the following properties of realNatural numbers Nagative Integers Integers numbers Rational numbers
1.สมบติัปิดการบวก2.สมบติัปิดการลบ
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3.สมบติัปิดการคณู4.สมบติัปิดการหาร
Practice 3.3.11.Expend and Simplify each of the following
1)( x + 2 ) ( x – 2 )………………………………………………………………..
2) ( x + 3 ) ( x – 3 ) ………………………………………………………………..
3) ( 2x + 3 ) (2x – 3 ) ………………………………………………………………..
4) ( 5x + 4 ) (5x – 4 ) ………………………………………………………………..
5) ( 3x + 1 ) (3x – 1 ) ………………………………………………………………..
6) ( x – 5 ) (x – 5 ) ………………………………………………………………..
7) (5x – 4 ) ( 5x – 4)………………………………………………………………..
8) (3x – 4 ) ( 3x – 4 ) ………………………………………………………………..
9) (2x + 1 ) ( 3x + 2 ) ………………………………………………………………..
10) (4x + 2 ) ( x + 4 ) ………………………………………………………………..
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2. Factorise each of the following
1) x2−25 x ………………………………………………………………..
2) x3−4 x2………………………………………………………………..
3 ) x4−4 x ………………………………………………………………..
4 ) 15 x2−25x………………………………………………………………..
5 ) 81x2−x ………………………………………………………………..
6 ) 7x2+49 x ………………………………………………………………..
7 ) 88 x3−8 x2………………………………………………………………..
8 ) 13 x4−x2………………………………………………………………..
9 ) 5x3−15 x2………………………………………………………………..
10 ) 100 x4+10 x3
………………………………………………………………..
11) x2+3x−4………………………………………………………………..
12) x2+10 x+25………………………………………………………………..
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13 ) x2+6x+9………………………………………………………………..
14 ) x2+4 x+4………………………………………………………………..
15 ) x2+8x−20………………………………………………………………..
16 ) x2−10 x+25………………………………………………………………..
17 ) x2−14 x+49………………………………………………………………..
18 ) x2+6x−16………………………………………………………………..
19 ) x2+6 x+8………………………………………………………………..
20 ) x2+x−30………………………………………………………………..
21) x2+13 x+30………………………………………………………………..
22) x2+8 x+7………………………………………………………………..
23 ) x2+10 x+21………………………………………………………………..
24 ) x2−5 x−50………………………………………………………………..
25 ) x2+9x+20………………………………………………………………..
26 ) x2−10 x−11………………………………………………………………..
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27 ) x2+14 x+13………………………………………………………………..
28 ) 3 x2+10 x+3………………………………………………………………..
29 ) 2 x2+x−6………………………………………………………………..
30 ) 2 x2−x−1………………………………………………………………..
31) 8 x2+2 x−3………………………………………………………………..
32) 25 x2+15 x+2………………………………………………………………..
33 ) 4 x2+5 x−9………………………………………………………………..
34 ) 3 x2+4 x−15………………………………………………………………..
35 ) 4 x2−1………………………………………………………………..Practice 3.3.1
3 Completing the Square
1) x2+4 x−32………………………………………………………………..
2) x2−2x−3………………………………………………………………..
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3 ) x2−4 x+2………………………………………………………………..
4 ) x2+8x−5………………………………………………………………..
5 ) x2+6x+2………………………………………………………………..
6 ) x2+8 x+14………………………………………………………………..
7 ) x2−10 x+7………………………………………………………………..
8 ) x2+7 x+11………………………………………………………………..
9 ) x2−2 x
………………………………………………………………..
10 ) x2−4 x………………………………………………………………..
11)−2 x2−8x+8………………………………………………………………..
12) 8+4 x−x2
………………………………………………………………..
13 )−3 x2+6 x+4………………………………………………………………..
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14 ) 4 x2−4 x−9………………………………………………………………..
15 )−3 x2+6 x+2………………………………………………………………..
16 )−2 x2+2 x+1………………………………………………………………..
Practice 3.3.2
1.Solve the following equations by factorisation
1) x2+7 x+10=0………………………………………………………………..
………………………………………………………………..………………………………………………………………..………………………………………………………………..
2) x2+8 x+12=0………………………………………………………………..
………………………………………………………………..………………………………………………………………..………………………………………………………………..
3 ) x2−3 x−18=0………………………………………………………………..
………………………………………………………………..………………………………………………………………..
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………………………………………………………………..
4 ) x2−6 x−16=0………………………………………………………………..
………………………………………………………………..………………………………………………………………..………………………………………………………………..
5 ) x2+5 x−24=0………………………………………………………………..
………………………………………………………………..………………………………………………………………..………………………………………………………………..
6 ) x2+x−30=0………………………………………………………………..
………………………………………………………………..
………………………………………………………………..
………………………………………………………………..
7 ) x2−14 x+48=0………………………………………………………………..
………………………………………………………………..………………………………………………………………..
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8 ) 21−10 x+x2=0………………………………………………………………..
………………………………………………………………..………………………………………………………………..………………………………………………………………..
9 ) 2+ x−x2=0………………………………………………………………..
………………………………………………………………..………………………………………………………………..
10 ) 2 x2+7 x+3=0………………………………………………………………..
………………………………………………………………..
………………………………………………………………..
………………………………………………………………..
11) 3 x2+7 x+2=0………………………………………………………………..
………………………………………………………………..………………………………………………………………..………………………………………………………………..………………………………………………………………..
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12) 5 x2+13 x+6=0………………………………………………………………..
………………………………………………………………..………………………………………………………………..………………………………………………………………..………………………………………………………………..
13 ) 7 x2+3 x−4=0………………………………………………………………..
………………………………………………………………..………………………………………………………………..………………………………………………………………..………………………………………………………………..
14 ) 9 x2+12x+4=0………………………………………………………………..
………………………………………………………………..
………………………………………………………………..
………………………………………………………………..
………………………………………………………………..
15 ) 4 x2+8 x+3=0………………………………………………………………..
………………………………………………………………..
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16 ) 4 x2+16 x+15=0………………………………………………………………..………………………………………………………………..………………………………………………………………..………………………………………………………………..
17 ) x2−9=0 ………………………………………………………………..………………………………………………………………..………………………………………………………………..………………………………………………………………..
18 ) 25−x2=0………………………………………………………………..
………………………………………………………………..
………………………………………………………………..
………………………………………………………………..
19 ) 9x2−16=0………………………………………………………………..
………………………………………………………………..………………………………………………………………..
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20 ) 36 x2−25=0………………………………………………………………..………………………………………………………………..………………………………………………………………..………………………………………………………………..………………………………………………………………..
2.Solve the following equations by completing the square
1) x2+8 x+6=0………………………………………………………………..……………………………………………………………………………………………………………………………....................................
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2) x2+10 x+3=0………………………………………………………………..
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3 ) x2+4 x+2=0………………………………………………………………..
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4 ) x2+6 x+3=0………………………………………………………………..
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5 ) x2+8x−1=0………………………………………………………………..
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6 ) x2−4 x−2=0………………………………………………………………..
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7 ) x2−6 x+4=0………………………………………………………………..
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8 ) x2−10 x−2=0………………………………………………………………..
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9 ) x2+5x+1=0………………………………………………………………..
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10 ) x2+3 x+2=0………………………………………………………………..
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3.Solve the following equations by Quadratic Formula
1) x2−4 x−21=0
……………………………………………………………………………………………………………………………....................................
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2) x2=4 x
……………………………………………………………………………………………………………………………....................................
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3 )x2−2x=6
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4 )3 x2+2 x−3=0……………………………………………………………………………………………………………………………....................................
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5 )2 x2+4 x=1
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6 )2 x2=x+2……………………………………………………………………………………………………………………………....................................
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Work sheet G1Name…………………..……………………………………………..…………………….NO………………Class………………………
3.Solve the following equations by Quadratic Formula
1) x2−4 x−21=0
a = 1 , b = -4 c= -21 Quadratic Formula x=−b±√b2−4 ac
2a
x=−(−4 )±√(−4 )2−4 (1)(−21)
2(1)
,
x=4±√16−(−84 )2
x= 4±√1002 ,
x=4±102 ,x=7 x=−3
2) x2=4 x
……………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………3 )x2−2x=6
…………………………………………………………………………………………………………………………………………………………
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……………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………
4 )3 x2+2 x−3=0
…………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………5 )2 x2+4 x=1
…………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………6 )2 x2=x+2……………………………
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……………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………
4.Calculate the length of each side of the triangle below
x
A
B C
A
x
x
x x
29
5)
If this box has a capacity of 320 cubic centimeters The base of a square box. Find the width of this boxถ้ากล่องกระดาษในรูปมคีวามจุ 320 ลกูบาศก์เซนติเมตร โดยท่ีฐานของกล่องเป็นรูปสีเ่หล่ียมจตัรุสั
จงหาความกวา้งของกล่องใบน้ี
………………………………………………………………………………………………………………………………………………………………………………………………………………………………………
B Cx
A
B C
x3x
2x
30
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6)
กล่องใน รูปท่ี 1 ทำาจากกระดาษในรูปท่ี 2 ซึ่งมพีื้นท่ีเท่ากับ x2+4 ax ตารางหน่วย
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จงหาค่าของ x เมื่อกำาหนดค่าของ a และx2+4 ax ดังตาราง
a x2+4 ax
14
20
1 16512
80
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7. ถ้าความสงูของ (h) ของลกูเทนนิส เมื่อวดัจากพื้นขณะท่ีนักกีฬาตีลกูเทนนิสขึ้นไปนาน t วนิาทีหาได้จากสูตร h=1+15 t−5 t 2 อยากทราบวา่ นานเท่าใด หลังจากนักกีฬาตีลกูเทนนิส ลกูเทนนิสจงึจะสงูจากพื้นดิน 10 เมตร
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……………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………8 . ต้นทนุในการผลิต
สนิค้าของบรษัิทแหง่หน่ึง 600 x−5 x2 เมอืราคาต้นทนุสนิค้าต่อหน่วยคือ x บาท ถ้าต้นทนุสนิค้าต่อหน่วยมากกวา่ 50 บาท และบรษัิทต้องการกำาไรจากสนิค้าชิน้ละ 25 % จะต้องขายสนิค้าในราคาชิน้ละเท่าใด ถ้ามต้ีนทนุในการผลิตเท่ากับ 6,000 บาท……………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………
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9. ถ้าผลคณูของจำานวนค่ีบวกท่ีเรยีงกันสองจำานวนคือ 35 จงหาจำานวนท่ีสอง……………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………10. ถ้าระยะเบรกของรถคันหน่ึงแทนด้วยสตูร d=s+ s2
20 เมื่อ d คือ ระยะเบรกมหีน่วยเป็นเมตรและ s คือ อัตราเรว็ของรถมีหน่วยเป็นกิโลเมตร/ชัว่โมง จงหาระยะเบรกของรถคันน้ีเมื่อรถคันนี้วิง่ด้วยอัตราเรว็1) 40 กิโลเมตร/ชัว่โมง 2) 100 กิโลเมตร / ชัว่โมง………………………………………………………………………………………………………………………………………………………………………………………………………………………
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Practice 3.4.1
1. Solve the inequality and show the solution with a number line
1) x+2>2
……………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………….
2) x−4≤2
…………………………………………………………………………………………………………………………………………………………
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3 ) 3+ y<7
……………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………….
4 ) y−2≥−1
……………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………….
5 ) x+3<2
………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………
.
6 ) x−9≤0
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7 ) 2x≥4
……………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………
………………………………………………….8 ) 1
3x≥3
……………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………….
9 ) x2≤−1
……………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………….10 ) 10≤5 x
37
……………………………………………………………………………
……………………………………………………………………………
……………………………………………………………………………
……………………………………………………………………………
………………………………………………….
11 ) x7>0
………………………………………………………………………………………………………………………………………………………………………………………………………………………………………
…12) x4<0
……………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………….
13 ) x−1≤12
…………………………………………………………………………………………………………………………………………………………
38
…………………………………………………………………………………………………………………………………………………………………………………………………………….
14 ) 5 x+1≤4
……………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………….
15 )−3+3 x≤2
……………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………….
……………………………………………………………………………………………………………………
2. Solve the inequality and show the solution with a number line
1 ) −3 x≥9
…………………………………………………………………………………………………………………………………………………………
39
…………………………………………………………………………………………………………………………………………………………………………………………………………….
2) −x3
≤2
……………………………………………………………………………
……………………………………………………………………………
……………………………………………………………………………
……………………………………………………………………………
………………………………………………….
3 ) −x6
<1
……………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………….
4 ) −4 x≤20
……………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………….
5 ) 18+6 x>0
40
……………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………….
6 ) −x5
≤0
……………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………….
7 ) −3 x≥12
……………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………….
8 ) −x7
≤1
……………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………….
41
9 ) −3x−21≥0
……………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………….
10 ) −x2
−1>0
……………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………….
Exersies 3.4.3
1) 4 x+2>x+7
……………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………….
2) 2 x−1<x+9
……………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………….
3 ) 8 x−5≥3 x+15
42
……………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………….
4 ) 3 x−2≤x
……………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………….
5 ) 8−3 x>x
……………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………….
…………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………
6 ) 5−3m≤6−4m
………………………………………………………………………………………………………………………………………………………………………………………………………………………………………
43
……………………………………………………………………………………………………………………………….
7 ) 6−3m≥3m
……………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………….
8 ) 3m<m−2
……………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………….
9 ) 4(m−3 )≤3 (m−2)
……………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………….
10 ) m+2<6(2+m )
………………………………………………………………………………………………………………………………………………………………………………………………………………………………………
44
……………………………………………………………………………………………………………………………….
11) x2<9
……………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………….
12) x2>4
……………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………….
13 ) x2+2 x>3
……………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………….14 ) x2−4 x<5
45
……………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………….
15 ) ( x−1 ) ( x+1 )>0
……………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………….
16 )x2−6 x+9<0
……………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………….
17 ) x2+6 x+9<0
………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………….
46
18 ) x2+4 x+4≥0
……………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………….
19 ) ( x−3 )2>0
……………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………
20 ) x−9 x−10<0
……………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………….
2. Lift of the holding capacity of n people, the average weight of each is equal .If this lift 80 kg body weight of 1650 kg lift most of this should be.Capacity of no more than a few people.
47
ลิฟท์ ของท่ีทำางานแหง่หน่ึง สามารถจุคนได้ n คน โดยท่ีนำ้าหนักเฉล่ียของแต่ละคนเท่ากับ 80 กิโลกรมั ถ้าลิฟท์ตัวน้ีบรรทกุนำ้าหนักได้มากท่ีสดุ 1,650 กิโลกรมั ลิฟท์ตัวน้ีควรจะจุได้ไมเ่กินกี่คน
……………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………….
……………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………….
3. the parking lot of a shopping center with an area not exceeding 8,000 square meters and will be broken into The car ran 950 square meters if the parking space for one car is 20 square meters .Parking is to serve the customer with a car park a few cars as possible .ท่ีจอดรถของศูนยก์ารค้าแหง่หน่ึงมพีื้นท่ีไมเ่กิน 8,000 ตารางเมตร และจะต้องแบง่เป็นทางวิง่รถ 950 ตารางเมตร ถ้ากำาหนดใหพ้ื้นท่ีสำาหรบัจอดรถหนึ่งคันเท่ากับ 20 ตารางเมตร ท่ีจอดรถแหง่น้ีจะใหบ้รกิารกับรถท่ีลกูค้านำามาจอดได้มากท่ีสดุกี่คัน
48
……………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………….
……………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………….
4. The car is 1,800 baht per day without charge other companies charge the car .
1,000 baht and rents increased by the number of kilometers the car to the other 2 baht per kilometer .
บรษัิท ก คิดค่าเชา่รถวนัละ 1,800 บาท โดยไมค่ิดค่าใชจ้า่ยอ่ืนอีก บรษัิท ข คิดค่าเชา่รถวนัละ 1,000
บาท และคิดค่าเชา่เพิม่จากจำานวนกิโลเมตร ท่ีนำารถไปใชอี้กกิโลเมตรละ 2 บาท
1.If the car from the car rental company to be run a few kilometers. The rents are less than a day .
1,800
1. ถ้าเชา่รถจากบรษัิท ข รถท่ีเชา่ไปจะใชว้ิง่ได้กี่กิโลเมตร จงึจะไมเ่กินวนัละ 1,800 บาท
……………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………….
…………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………….
49
……………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………….
………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………….
2.To use the car at 600 kilometers should rent a car from any firm . To save the car
ถ้าต้องการใชร้ถวนัละ 600 กิโลเมตร ควรเชา่รถจากบรษัิทใด ถึงประประหยดัค่าเชา่รถ
……………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………….
……………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………….
………………………………………………………………………………………………………………………………………………………………………………………………………………………………………
50
……………………………………………………………………………………………………………………………….
5. grilled chicken trade Roast the chicken for 80 baht, the cost is 100 baht per day for the rental shop .
And other expenses , including the cost of a chicken and a profit of 60 million baht per day .
Not less than 500 baht a day to sell chicken bits
แมค่่าขายไก่ยา่งขายไก่ยา่งตัวละ 60 บาท โยมคี่าใชจ้า่ยท่ีเป็นค่าเชา่รา้นวนัละ 100 บาท และค่าใชจ้า่ยอ่ืนรวมทัง้ค่าไก่สดคิดเป็นต้นทนุแล้วตัวละ 60 บาท ถ้าต้องการกำาไรวนัละไมต่ำ่ากวา่ 500 บาท จะต้องขายไก่ใหไ้ด้วนัละกี่ตัว
……………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………….
………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………….
…………………………………………………………………………………………………………………….
Exercise 3.51. Solve the following absolute value
1¿|8|+|3|=………….…… . .
2¿|−8|+|−2|=………….……. .
51
3¿|9|−|2|=………….…… . .
4 ¿|−12|+|−6|=………….……. .
5¿|−6|−|6|=………….…… . .
6¿|−13|−|−5|=………….…… . .
7¿|4+9|=………….…… . .
8¿|10−10|=………….……. .
9¿|−10|=………….…… . .
10¿|0|=………….…… . .
11¿|3−π|=………….…… . .
12¿|4−π|=………….…… ..
13¿|−5|−5||=………….……. .
14¿−3−|−3|=………….…… ..
15¿−3|−3|=………….……. .
16¿|−1|−|−2|=………….…… ..
17¿−|16.25|+20=………….…… ..
18¿2|33|=………….……. .
2.given x=|−2|∧ y=|5|find the following value
52
1¿ x−2 ………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………….
……………………………………………………………………………………………………………………2¿ y−5
……………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………
……………………………………………….
………………………………………………………………………………………………………………………………………………………………………………………………………………………………………
…3¿2x
……………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………
………………………………………………….
4 ¿ y2
53
……………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………
……………………………………………….
……………………………………………………………………………………………………………………
5¿ x+ y
…………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………
……………………………………………………………………………………….
6¿ x− y
…………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………
……………………………………………………………………………………….
7¿ xy
……………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………
……………………………………………….
8¿ xy
54
……………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………
……………………………………………….
2. Fill in the boxes with ¿ ,<¿=¿ to make each statement true
1) |−3|−|−3|
2) |−4||4|
3) −5−|−5|
4) |−4|−|4|
5) −|−6||6|
6) −|−2|−2
55
Work sheet G2Name…………………..……………………………………………..…………………….NO………………Class………………………2. Solve the inequality and show the solution with a number line
1) x+2>2
x>2−2
x>0 Answer inequality= {x / x>0}
2) x−4≤2…………………………………………………………………………………………………………………………………………………………………………………………………………………………………3 ) 3+ y<7…………………………………………………………………………………………………………………………………………………………………………………………………………………………………4 ) y−2≥−1…………………………………………………………………………………………………………………………………………………………………………………………………………………………………5 ) x+3<2……………………………………………………………………………
56
……………………………………………………………………………………………………………………………………………………
6 ) x−9≤0…………………………………………………………………………………………………………………………………………………………………………………………………………………………………7 ) 2x≥4………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………
8 ) 13x≥3
…………………………………………………………………………………………………………………………………………………………………………………………………………………………………
9 ) x2≤−1
…………………………………………………………………………………………………………………………………………………………………………………………………………………………10 ) 10≤5 x…………………………………………………………………………………………………………………………………………………………………………………………………………………………………
57
11) x7>0
…………………………………………………………………………………………………………………………………………………………………………………………………………………………………
12) x4<0
…………………………………………………………………………………………………………………………………………………………………………………………………………………………………
13 ) x−1≤12
…………………………………………………………………………………………………………………………………………………………………………………………………………………………………
Work sheet G3
58
Name…………………..……………………………………………..…………………….NO………………Class………………………
3. Solve the inequality and show the solution with a number line 1 ) −3 x≥9
−3 x×− 13≤9×− 1
3
x≤−3
2) −x3
≤2
……………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………
3 ) −x6
<1
…………………………………………………………………………………………………………………………………………
………………………………………………………………………………4 ) −4 x≤20
……………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………5 ) 18+6 x>0
……………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………
59
………………………………………………………………
6 ) −x5
≤0
……………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………7 ) −3 x≥12
……………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………8 ) −x
7≤1
……………………………………………………………………
………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………9 ) −3x−21≥0
……………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………10 ) −x
2−1>0
………………………………………………………………………………………………………………………………………………………………………………………………………………
60
…………………………………………………………………………………………………………………………………………………………………………………………………………………………………………… Work sheet G4Name…………………..……………………………………………..…………………….NO………………Class………………………
I
61
II
62
63
64