แบบฝึกหัดท่ี 1 เรื่อง จำ�นวนตรรกยะ และจำ�นวนอตรรกยะ

ชื่อ.......................................................สกลุ.........................................ชัน้ ม...........เลขท่ี..............1. จงเขยีนเศษสว่นต่อไปน้ีใหอ้ยูใ่นรูปทศนิยม1) ............................................ 2) .......................................................3) ............................................ 4) .......................................................5) ........................................... 6) .......................................................2. จงเขยีนทศนิยมต่อไปน้ีใหอ้ยูใ่นรูปเศษสว่น1) 0.75......................................................... 2) 0.0002....................................................3) วธิีทำ$....................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................4) วธิีทำ$....................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................

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6) วธิีทำ$......................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................7) วธิีทำ$...........................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................3. จงพจิ$รณ$ว$่จำ$นวนที่กำ$หนดใหต่้อไปน้ีเป็นตรรกยะ หรอืจำ$นวนอตรรกยะ โดยเขยีน เครื่องหม$ย ลงในชอ่งว$่งพรอ้มใหเ้หตผุล

จำ$นวน จำ$นวนตรรกยะ

จำ$นวนอตรรกยะ

เหตผุล

1) 32) 0

3) -54) 5) 4.1226) 0.0097) 8) 9) -0.0410)

แบบฝึกหัดท่ี 2( แนวทดสอบ ) เรื่อง จำ�นวนตรรกยะ และจำ�นวนอตรรกยะ ( ต่อ )

ชื่อ.......................................................สกลุ.........................................ชัน้ ม...........เลขท่ี..............1. จงเขยีนจำ$นวนต่อไปน้ีใหอ้ยูใ่นรูปทศนิยม

1) 2) 3) 4) 5) วธิีทำ$......................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................

..............................................................2.จงเขยีนทศนิยมต่อไปน้ีใหอ้ยูใ่นรูปเศษสว่น1)

วธิีทำ$....................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................2) วธิีทำ$.........................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................3) วธิีทำ$..................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................

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..........................................................................3. จงทำ$เครื่องหม$ย หน้$ขอ้คว$มที่เป็นจรงิ และเครื่องหม$ย หน้$ขอ้คว$มที่เป็นเท็จ...............1) 22.2232232232.... เป็นจำ$นวนอตรรกยะ...............2) 1.123123412345.. . เป็นจำ$นวนตรรกยะ...............3) -3.6766766676... เป็นจำ$นวนอตรรกยะ...............4) 0 เป็นจำ$นวนอตรรกยะ...............5) เป็นจำ$นวนตรรกยะ..............6) มจีำ$นวนจรงิ X ท่ี ...............7) 0 เป็นจำ$นวนนับ................8) -1.123234 เป็นจำ$นวนตรรกยะ................9) มจีำ$นวนตรรกยะท่ีม$กท่ีสดุที่น้อยกว$่ 1.................10) –6 เป็นจำ$นวนนับ.................11) เป็นจำ$นวนตรรกยะ

4. จำ$นวนต่อไปนี้เป็นจำ$นวนชนิดใด โดยเติมลงในชอ่งว$่งจำ$นวน จำ$นวนนับ จำ$นวนเต็ม

ลบจำ$นวนตรรกยะ

จำ$นวนอตรรกยะ

บทท่ี 1 ระบบจำ�นวนจรงิ แบบฝึกทักษะท่ี 2( สมบติัจำ�นวนจรงิ ) พื้นฐ�น

ชื่อ...........................................สกลุ.................................................ชัน้ม...............เลขท่ี..............1. จงบอกสมบติัที่ใชแ้สดงประโยคคณิตศ$สตร์1) ตอบ....................................................................................................................................................2) ตอบ.....................................................................................................................................................3) ตอบ....................................................................................................................................................4) ตอบ..................................................................................................................................................5) เป็นจำ$นวนจรงิ (-9) เป็นจำ$นวนจรงิ ดังนัน้ +(-9) เป็นจำ$นวนจรงิตอบ..................................................................................................................................................... 6) 4 เป็นจำ$นวนจรงิ เป็นจำ$นวนจรงิ ดังนัน้ 4 เป็นจำ$นวนจรงิตอบ....................................................................................................................................................7) ตอบ....................................................................................................................................................8) ตอบ.....................................................................................................................................................9) ตอบ....................................................................................................................................................10) ตอบ....................................................................................................................................................

11) ตอบ....................................................................................................................................................12) ตอบ.....................................................................................................................................................13) ตอบ.....................................................................................................................................................

14) ตอบ.................................................................................................................................................... 2. จงบอกสมบติัที่ใชแ้สดงคว$มเกี่ยวขอ้งในแต่ละขอ้1) ดังนัน้ ตอบ..................................................................................................................................................2) และ ดังนัน้ ตอบ..................................................................................................................................................3) และ ดังนัน้ ตอบ..................................................................................................................................................4) ถ้$ แล้ว ตอบ..................................................................................................................................................5) ถ้$ แล้ว

ตอบ..................................................................................................................................................6) ถ้$ และ แล้ว ตอบ..................................................................................................................................................7) ถ้$ แล้ว ตอบ..................................................................................................................................................8) ถ้$ และ แล้ว ตอบ..................................................................................................................................................9) ถ้$ และ แล้ว ตอบ..................................................................................................................................................10) ถ้$ และ แล้ว ตอบ..................................................................................................................................................

แบบฝึกทักษะท่ี 3 สมบติัจำ�นวนจรงิ พื้นฐ�น ( ต่อ )

ชื่อ...........................................สกลุ.................................................ชัน้ม...............เลขท่ี..............

1. จงบอกสมบติัของจำ$นวนจรงิต่อไปน้ี1) 4+5 R

..........................................................................................................................2) (1+2)+3 1+(2+3)

..........................................................................................................................3) (2+3)+4 4+(2+3)

..........................................................................................................................4) (3+4)+(-5) 3+(4+(-5))

.........................................................................................................................5) -(2.5)+2.5 0

........................................................................................................................6) ( y)a (yx)a

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.......................................................................................................................8) (8+4) 6 (8 6)+(4 6)

........................................................................................................................9) 4 เป็นจำ$นวนจรงิ เป็นจำ$นวนจรงิ ดังนัน้ 4 เป็นจำ$นวนจรงิ ..................................................................10) 0+0 0

.........................................................................................................................11) (8+4) 6 (8 6)+(4 6)

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2. จงห$อินเวอรส์ก$รบวกของจำ$นวนจรงิต่อไปน้ี1)

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5.จงห$อินเวอรส์ก$รคณูของจำ$นวนจรงิต่อไปน้ี1)

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6.จงบอกสมบติัที่ใชแ้สดงคว$มเกี่ยวขอ้งในแต่ละขอ้1) 5 เป็นจำ$นวนจรงิใดๆ ดังนัน้ 5

ตอบ..................................................................................................................................................2) และ ดังนัน้ ตอบ..................................................................................................................................................3) และ ดังนัน้ ตอบ..................................................................................................................................................4) ถ้$ แล้ว ตอบ..................................................................................................................................................5) ถ้$ แล้ว ตอบ..................................................................................................................................................6) ถ้$ แล้ว ตอบ..................................................................................................................................................7) ถ้$ และ แล้ว

ตอบ..................................................................................................................................................8) ถ้$ และ แล้ว

ตอบ..................................................................................................................................................9) ถ้$ และ แล้ว ตอบ..................................................................................................................................................

บทท่ี 1 ระบบจำ�นวนจรงิ แบบฝึกทักษะท่ี 4( ก�รแยกตัวประกอบพหนุ�ม )

ชื่อ...........................................สกลุ.................................................ชัน้ม...............เลขท่ี..............1. จงแยกตัวประกอบของพหนุ$มต่อไปนี้1) ................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................2) ................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................3) ...............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................4)

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2. แยกตัวประกอบของพหนุ$มต่อไปนี้1) ................................................................................6) ...................................................................................7) .....................................................................................8) .........................................................................................9) ..........................................................................................10) ...............................................................................11) ..................................................................................12) ..............................................................................13) ..............................................................................14) .................................................................................15) .................................................................................16) ..............................................................................17) .................................................................................19) .......................................................................................

บทท่ี 1 ระบบจำ�นวนจรงิ แบบฝึกทักษะท่ี 4 ( ก�รแยกตัวประกอบพหนุ�ม )

ชื่อ...........................................สกลุ.................................................ชัน้ม...............เลขท่ี..............1. จงแยกตัวประกอบของพหนุ$มต่อไปนี้1) .......................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................2) .......................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................3) .......................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................4) ......................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................

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6) .......................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................7) .......................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................8) .......................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................9) .......................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................10) ....................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................

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แบบฝึกทักษะเรื่อง สมบติัจำ�นวนจรงิ และ ก�รแยกตัวประกอบ

ชื่อ..........................................................สกลุ...............................................ชัน้ม..............เลขท่ี.........1. จงบอกสมบติัของจำ$นวนจรงิต่อไปน้ี1) 9(11) R

...........................................................................................2) ..........................................................................................3) (x+y)+z = z+(x+y) ..........................................................................................4) 17.25+(-17.25) = 0

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.......................................................................................2. จงห$อินเวอรส์ก$รบวกและก$รคณูของจำ$นวนจรงิต่อไปน้ี1)

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...............................................................................................................3.จงบอกสมบติัก$รเท่$กันที่ใชแ้สดงประโยคคณิตศ$สตร์1) ถ้$ และ แล้ว

ตอบ....................................................................................................................................................2) ถ้$ และ แล้ว ตอบ.....................................................................................................................................................3) ถ้$ และ ดังนัน้ ตอบ....................................................................................................................................................4) ถ้$ แล้ว

ตอบ..................................................................................................................................................5) ถ้$ แล้ว ตอบ.....................................................................................................................................................

4.จงแยกตัวประกอบของพหนุ$มต่อไปนี้1) ...............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................2) ...............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................3)

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แบบฝึกทักษะท่ี 5 ( พื้นฐ�น )

ก�รแยกตัวประกอบพหนุ�ม ( ต่อ ) ชื่อ...........................................สกลุ.................................................ชัน้ม...............เลขท่ี..............1.จงแยกตัวประกอบของพหนุ$มต่อไปนี้1.1 ........................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................1.2 ........................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................1.3 ........................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................1.4 ........................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................1.5 ........................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................1.6 ........................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................

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2. จงแยกตัวประกอบของพหนุ$มต่อไปนี้ โดยก$รทำ$ใหเ้ป็นกำ$ลังสองสมบูรณ์1) ..............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................2) ...............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................3) ...............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................4) .............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................

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แบบฝึกหัดท่ี 6 เรื่อง ก�รแก้สมก�รกำ�ลังสองตัวแปรเดียว

ชื่อ.................................................สกลุ..........................................ชัน้ม...............เลขท่ี................คำ�สัง่ จงห$คำ$ตอบของสมก$รต่อไปน้ีโดยใชว้ธิใีดก็ได้1) วธิีทำ$..............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................2) วธิีทำ$.....................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................3) วธิีทำ$.............................................................................................................................................................................

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แบบฝึกทักษะท่ี 7 ( พื้นฐ�น ) ( ก�รแก้สมก�รกำ�ลังสองตัวแปรเดียว ) โดยก�รใชส้ตูร

ชื่อ...........................................สกลุ.................................................ชัน้ม...............เลขท่ี..............1. จงแก้สมก$รกำ$ลังสองตัวแปรเดียว โดยก$รใชส้ตูร1) ................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................2) ...........................................................................................................................................................................................................................................................................................................................................................................

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5) ...............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................6) ...............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................7) ...............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................8) ...............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................

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แบบตรวจสอบคว�มก้�วหน้�

เรื่อง อสมก�ร ชื่อ.....................................................สกลุ.............................................ชัน้ม.................เลขท่ี.............คำ�สัง่ 1.จงเปล่ียนประโยคคณิตศ$สตรต่์อไปน้ีเป็นขอ้คว$มท่ีสมมูลกัน และขอ้คว$มบอกตำ$แหน่งบนเสน้จำ$นวน โดยเติมต$ร$งต่อไปน้ี

ประโยคคณิตศ$สตร์

ขอ้คว$มที่สมมูลกัน ขอ้คว$มบอกตำ$แหน่ง

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2. แก้อสมก$ร วธิีทำ$......................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................3. แก้อสมก$ร

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แบบฝึกทักษะท่ี 7 ก�รไมเ่ท่�กัน ( อสมก�ร )

ชื่อ...........................................สกลุ.................................................ชัน้ม...............เลขท่ี..............1. จงห$เซตคำ$ตอบของอสมก$รต่อไปน้ี1) ..............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................2) ............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................... 3) ...............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................4) ................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................5) ...........................................................................................................................................................................................................................................................................................................................................................................

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แบบฝึกทักษะท่ี 8 ก�รไมเ่ท่�กัน ( อสมก�ร )

ชื่อ...........................................สกลุ.................................................ชัน้ม...............เลขท่ี..............1. จงห$เซตคำ$ตอบของอสมก$รต่อไปน้ี พรอ้มแสดงคำ$ตอบโดยใชเ้สน้จำ$นวน1) ...............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................2) ...............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................3)

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6) .......................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................7) ........................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................8) ........................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................9)

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...............10)

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แบบฝึกทักษะท่ี 9 ( อสมก�รสองชัน้ )

ชื่อ...........................................สกลุ.................................................ชัน้ม...............เลขท่ี..............1. เขยีนอสมก$รด้วยสญักรณ์ชว่ง1) ............................... 2) ...................................3) ............................................ 4) .............................................5) ......................................... 6) ................................2. ใหเ้ขยีนอสมก$รแสดงชว่งท่ีกำ$หนด1) .............................................. 2) ...............................................3) ............................................... 4) ..............................................5) ................................................ 6) ..............................................3.จงแก้อสมก$รต่อไปนี้ พรอ้มเขยีนกร$ฟแสดงคำ$ตอบ1) ......................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................2) ....................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................... 3) ..................................................................................................................................................................................................................................................

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แบบฝึกทักษะท่ี 10 ค่�สมับูรณ์ของอสมก�ร

ชื่อ...........................................สกลุ.................................................ชัน้ม...............เลขท่ี..............1. บอกสมบติัของอสมก$รที่ตัดสนิขอ้คว$มในแต่ละขอ้1) เน่ืองจ$ก ดังนัน้ ......................................................................................................................................................2) เน่ืองจ$ก และ ดังนัน้ ......................................................................................................................................................3) เน่ืองจ$ก ดังนัน้ ......................................................................................................................................................4) เน่ืองจ$ก ดังนัน้ 26 และ

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.............................5) เน่ืองจ$ก ดังนัน้ ......................................................................................................................................................6) เน่ืองจ$ก ดังนัน้ 12 เป็นจำ$นวนบวก......................................................................................................................................................2. แก้อสมก$รและเขยีนกร$ฟแสดงเซตคำ$ตอบ1) ................................................................................................................................................................................................................................................................................................................................................................................ ........................................................................................................................................................................................2) ................................................................................................................................................................................................................................................................................................................................................................................ ........................................................................................................................................................................................3) ................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................ ........................................................................................................................................................................................

4) ................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................ ........................................................................................................................................................................................5) ................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................ ........................................................................................................................................................................................3. แก้อสมก$รและเขยีนเซตคำ$ตอบด้วยสญักรณ์ชว่ง1) ................................................................................................................................................................................................................................................................................................................................................................................ ........................................................................................................................................................................................2) ................................................................................................................................................................................................................................................................................................................................................................................ ........................................................................................................................................................................................3) ........................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................4) ...........................................................................................................................................................................................................................................................................................................................................................................

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แบบฝึกทักษะ อสมก�รสองชัน้และค่�สมับูรณ์ของอสมก�ร

ชื่อ...........................................สกลุ.................................................ชัน้ม...............เลขท่ี..............1. เขยีนอสมก$รด้วยสญักรณ์ชว่ง1) ............................................ 2)...............................................3) ............................................ 4) .............................................

2. ใหเ้ขยีนอสมก$รแสดงชว่งท่ีกำ$หนด1) .............................................. 2) ...............................................3) ............................................... 4) ..............................................

3. จงแก้อสมก$รต่อไปนี้ พรอ้มเขยีนกร$ฟแสดงคำ$ตอบ1)

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4. แก้อสมก$ร เขยีนกร$ฟและสญักรณ์ชว่งของเซตคำ$ตอบ1) ................................................................................................................................................................................................................................................................................................................................................................................ ........................................................................................................................................................................................ ................................................................................................................................................................................................................................................................................................................................................................................ ........................................................................................................................................................................................

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แบบทดสอบ อสมก�รสองชัน้และค่�สมับูรณ์ของอสมก�ร

ชื่อ...........................................สกลุ.................................................ชัน้ม...............เลขท่ี..............1. เขยีนอสมก$รด้วยสญักรณ์ชว่ง1) ............................................ 2)...............................................3) ............................................ 4) .............................................

2. ใหเ้ขยีนอสมก$รแสดงชว่งท่ีกำ$หนด1) .............................................. 2) ...............................................3) ............................................... 4) ..............................................

3. จงแก้อสมก$รต่อไปนี้ พรอ้มเขยีนกร$ฟแสดงคำ$ตอบ1)

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4. แก้อสมก$ร เขยีนกร$ฟและสญักรณ์ชว่งของเซตคำ$ตอบ1) ................................................................................................................................................................................................................................................................................................................................................................................ ........................................................................................................................................................................................ ................................................................................................................................................................................................................................................................................................................................................................................ ........................................................................................................................................................................................

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แบบฝึกทักษะท่ี 11 ค่�สมับูรณ์ ( ต่อ )

ชื่อ...........................................สกลุ.................................................ชัน้ม...............เลขท่ี..............1. เติมคำ$ตอบในชอ่งว$่ง1) 2) 3) 4)

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2. จงห$ค่$ของ 1) 2) 3) 4) 5) 3. แก้อสมก$ร เขยีนกร$ฟและสญักรณ์ชว่งของเซตคำ$ตอบ1) ................................................................................................................................................................................................................................................................................................................................................................................ ........................................................................................................................................................................................2) ................................................................................................................................................................................................................................................................................................................................................................................ ........................................................................................................................................................................................3) ........................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................ 4) ..................................................................................................................................................................................................................................................

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