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ประกอบด้วยใบงานท่ี 1 – 6
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ใบงานที่ 1 ร้อยละ
ใบงานท่ี 2 ดอกเบยี้
ใบงานท่ี 3 การตง้ั ราคาขาย
ใบงานท่ี 4 การซ้ือขายในระบบผอ่ นชาระ
ใบงานที่ 5 อสมการ
ใบงานท่ี 6 ความน่าจะเปน็
เกณฑ์การประเมินผลใบงาน 1-6 (สาหรับครู TA)
1
ใบงานท่ี 1 คณิตศาสตร์
ร้อยละ ธุรกิจและบรกิ าร
1. จงเขยี นร้อยละต่อไปนี้ ให้อยูใ่ นรปู เศษสว่ น (อยา่ งต่า)
1.1 42% = .............................................................................................................
1.2 5.5% = .............................................................................................................
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1.3 2 5% = .............................................................................................................
1.4 0.0005% =
1.5 150% = .............................................................................................................
2. จงเขยี นร้อยละต่อไปน้ีให้อยู่ในรปู ของทศนิยม
2.1 60% = .............................................................................................................
2.2 150% = .............................................................................................................
2.3 0.35% = .............................................................................................................
2.4 2 43% = .............................................................................................................
2.5 0.005% = .............................................................................................................
3. จงเขยี นจานวนต่อไปนใ้ี ห้อยูใ่ นรปู ของร้อยละ
3.1 4 : 25 = .............................................................................................................
3.2 1 : 20 = .............................................................................................................
3.3 0.75 = .............................................................................................................
3.4 7 = .............................................................................................................
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3.5 12
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4. 20% ของ 240 มคี า่ เท่าไร 5. 9 เปน็ ก่ีเปอร์เซ็นตข์ อง 63
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6. 15 เป็น 60% ของจานวนใด
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7. ในการสอบคัดเลือกเข้าวิทยาลัยแห่งหน่ึง ปรากฏว่ามีผู้สอบเข้าได้ 35% ของจานวนผู้ท่ีเข้าสอบท้ังหมด ถ้าผู้สอบได้มี
จานวน 250 คน จะมีผสู้ อบเขา้ ไม่ได้กค่ี น
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8. เมื่อห้าปีที่แล้ว รถยนต์คนหน่ึง ราคาคันละ 500,000 บาท ปีน้ีราคาเพ่ิมข้ึนเป็นคันละ 800,000 บาท รถยนต์คันนี้ข้ึน
ราคาก่ีเปอร์เซน็ ต์
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9. ในการปิดราคาขายตู้ Open Type ราคาที่ปิดไว้จะเป็นราคาท่ีได้จากราคาสินค้ารวมกับการตมี ูลค่าเพิ่ม 7% ขายสินคา้
ถ้าตั้งราคาขายไว้ 4,000 บาท จะตอ้ งปิดราคาขายตู้ Open Type เป็นเทา่ ใด
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10. บุญสมมีเงินเดือน เดือนละ15,000บาท ต้องจ่ายเป็นค่าเช่าบา้ น 3,000 บาท ค่าอาหาร 3,000 บาท เก็บสะสมได้10%
ของเงนิ เดือน จ่ายค่านา้ และคา่ ไฟฟา้ ใหเ้ จ้าของบ้าน 300 บาท ที่เหลอื เก็บไวจ้ า่ ยเบด็ เตลด็ อ่นื ๆ จงหาว่า
10.1 คา่ เช่าบ้านเปน็ ร้อยละเท่าใดของเงนิ เดอื น
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10.2 เกง็ เงินสะสมไวเ้ ดือนละเท่าไร
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10.3 เบ็ดเตลด็ อนื่ ๆ เปน็ ร้อยละเทา่ ใดของเงนิ เดือน
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ใบงานที่ 2 คณติ ศาสตร์
ดอกเบ้ีย ธรุ กิจและบรกิ าร
1. กเู้ งนิ 5,000 บาท คิดดอกเบีย้ 10% ระยะเวลา 2 ปี จงหาดอกเบ้ยี
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2. กู้เงนิ 10,000 บาท คดิ ดอกเบีย้ 5% จ่ายดอกเบ้ยี 500 บาท กู้นานเทา่ ไร
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3. กู้เงนิ ในเวลา 3 ปี อัตราดอกเบี้ย 12% จ่ายดอกเบี้ย 300 บาท เงนิ ต้นเท่าไร
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4. จากเงนิ 5,000 บาท ระยะเวลา 2 ปี จ่ายดอกเบยี้ ไป 500 บาท คดิ ดอกเบีย้ ในอตั ราเท่าใด
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5. บุญเลิศกู้เงิน 10,000 บาท ต้ังแต่วันที่ 10 ก.พ. 2559 ถึงวันท่ี 23 เม.ย. 2559 จ่ายดอกเบ้ีย 500 บาท คิดดอกเบี้ยใน
อตั ราเทา่ ใด
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6. กู้เงนิ 5,000 บาท ต้องใช้เงินคืนเป็นเงินรวม 6,000 บาท ในเวลา 1 ปี คิดอตั ราดอกเบ้ียเท่าใด
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7. เงนิ 10,000 บาท คดิ อัตราดอกเบีย้ 5% ต่อ 6 เดือน ทบต้นทกุ 6 เดือน ระยะเวลา 2 ปี จงหาเงินรวมและดอกเบย้ี
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8. เงิน 20,000 บาท คดิ อตั ราดอกเบีย้ 20% ทบตน้ ทุก ๆ 3 เดอื น ระยะเวลา 1 ปี จงหาเงนิ รวมและดอกเบย้ี
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9. กู้เงนิ 20,000 บาท ในอัตราดอกเบย้ี 10% คิดทบต้นทุก 6 เดอื น ได้เงินรวม 22,050 บาทกนู้ านเทา่ ใด
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10. ก้เู งนิ 10,000 บาท คดิ ดอกเบีย้ ทบตน้ ทุก 6 เดอื น ระยะเวลา 1 ปี จ่ายคนื เป็นเงนิ รวม 12,100 บาท ผู้ใหก้ ู้คิดดอกเบย้ี
ในอตั ราเท่าใด
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ใบงานท่ี 3 คณิตศาสตร์
การตัง้ ราคาขาย ธรุ กิจและบรกิ าร
> > > มารค์ อัพ (Mark Up) < < <
1. บญุ นาซ้อื เก้าอมี้ าตวั ละ 210 บาท ถา้ ต้องการมาร์คอพั 90 บาท จงหาราคาขาย
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2. บุญทุ่มซอื้ เตาไฟฟ้าเคร่ืองหนึง่ ราคา 4,000 บาท ถ้าต้องการขายในราคา 5,000 บาท จงหามารค์ อัพ
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3. บุญชว่ ยลงทนุ ซ้อื โทรศพั ท์ราคา 1,200 บาท ต้องการขายโดยกาหนดอตั รามาร์คอัพ 10% เมื่อเทยี บกับราคาซ้ือ จงหา
มาร์คอัพ
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4. บุญชมซ้อื เสอื้ ยดื มาตัวหน่ึงราคา 90 บาท ต้องการขายโดยกาหนดอัตรามารค์ อพั 20% เมอื่ เทยี บกับราคาขาย บญุ ชม
จะต้องตัง้ ราคาขายเท่าไร
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5. บุญธรรมตั้งราคาขาย เครื่องคานวณ เคร่ืองหนึ่งราคา 2,000 บาท โดยท่ีต้นทุนราคา 1,800 บาท จงหาอัตรามาร์คอัพ
เมอ่ื เทียบกับราคาขาย
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6. บญุ ล้นลงทนุ ซือ้ เครื่องดูดฝนุ่ เครือ่ งหนงึ่ ราคา 15,000 บาท ตอ้ งการขายตอ่ ในราคา 18,000 บาท จงหาอตั รามาร์คอัพ
เม่อื เทียบกบั ราคาทุน
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7. บุญมนตซ์ ้อื เตารดี มาเคร่ืองหนง่ึ ราคา 2,400 บาท มคี า่ ใชจ้ า่ ย 400 บาท ถ้าขายไปในราคา 3,200 บาท จงหา
7.1 มาร์คอัพ 7.2 กาไรสุทธิ
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7.3 อัตรามาร์คอัพเม่ือเทยี บกับราคาทนุ 7.4 อัตรามารค์ อัพเม่ือเทยี บกับราคาทุน
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> > > มาร์คดาวน์ (Mark Down) < < <
8. สมชายตงั้ ราคาขายเตารีดไฟฟา้ ในราคา 1,250 บาท ต่อมาต้ังราคาขายต่อ โดยตงั้ ราคาขายใหม่เป็น 1,100 บาท มาร์ค
ดาวน์ เทา่ กับเทา่ ไร
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9. สมมาตรตง้ั ราคาขายเครื่องสบู นา้ เคร่อื งหน่ึง 3,700 บาท ตอ่ มาต้องการต้ังราคาขายใหม่ โดยกาหนดอัตรามาร์คดาวนไ์ ว้
20% เมอ่ื เทยี บกับราคาขายเดมิ มารด์ าวนเ์ ท่ากับเทา่ ไร
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10. ตู้ vault ชุดหน่ึงราคา 120,000 บาท ต่อมาพ่อค้าต้องการต้งั ราคาขายใหม่ โดยกาหนดอัตรามาร์คดาวน์ 30% เมอื่
เทยี บกบั ราคาเดมิ จงหาราคาขายใหม่
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11. เครื่องทาน้าแขง็ 7-Eleven เครอื่ งหนึ่งราคา 44,000 บาท ตอ่ มาบริษทั ตั้งราคาขายใหม่ โดยกาหนดอัตรามาร์คดาวน์
20% เมื่อเทยี บกับราคาขายใหม่ จงหาราคาขายใหม่
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ใบงานที่ 4 คณติ ศาสตร์
การซอื้ ขายในระบบผอ่ นชาระ ธุรกจิ และบริการ
1. วิชุดาขายโทรศัพท์มือถือราคาเงินสด 15,000 บาท ถ้าลดาต้องการซื้อในระบบผ่อนชาระจะต้องจ่ายเงินดาวน์ 5,000
บาท เงินตน้ ของหนี้เรมิ่ แรกเป้นเทา่ ไร
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2. ยาใจขายนาฬิกาข้อมือราคาเงินสด 6,000 บาท ถ้าไอรดาต้องการซื้อในระบบผ่อนชาระจะต้องจ่ายเงินดาวน์ในอัตรา
25% ไอรดาต้องจา่ ยเงนิ ดาวนเ์ ทา่ ไร
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3. สมหมายขายรถยนตร์ าคาเงินสด 500,000 บาท สายลมตอ้ งการซือ้ ขายในระบบผ่อนชาระจะต้องจา่ ยเงนิ ดาวนใ์ นอัตรา
25% ของราคาเงินสด สว่ นท่ีเหลือผ่อนชาระเป็นรายเดือน เดอื นละ 6,500 บาท เปน็ เวลา 5 ปี จงหาเงินผอ่ นชาระ
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4. พอ่ ค้าขายเคร่ืองทาน้าอ่นุ ราคา 5,000 บาท ผู้ซอื้ ต้องการซอื้ ในระบบผ่อนชาระ จะต้องจ่ายเงินดาวนใ์ นอัตรา 20% ของ
ราคางเงินสด ส่วนท่เี หลอื ผอ่ นชาระเปน็ รายเดือน เดือนละ 600 บาท เป็นเวลา 8 เดอื น จงหาเงนิ ดาวน์ ราคาเงินผ่อน
ดอกเบ้ยี ผ่อนชาระ
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5. วิทยเุ ครอื่ งหน่ึงราคาเงินสด 2,400 บาท ถา้ ซื้อขายในระบบผ่อนชาระจะต้องจ่ายเงนิ ดาวน์ 400 บาท หลงั จากน้นั จะต้อง
ชาระเป็นรายงวด เดือนละเท่ากัน เป็นเวลา 5 เดือน โดยคิดดอกเบ้ียผ่อนชาระ 200 บาท จงหาเงินผ่อนชาระรายงวด
เท่ากนั
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6. ตู้เย็นเคร่ืองหน่ึงราคาเงินสด 15,000 บาท ถ้าผู้ซ้ือต้องการซ้ือขายในระบบผ่อนชาระไม่ต้องจ่ายเงินดาวน์ แต่ต้องผ่อน
เป็นรายเดอื น เดอื นละเทา่ กัน เปน็ เวลา 10 เดือน โดยคิดดอกเบ้ยี ผ่อนชาระ 1,000 บาท จงหาเงินผอ่ นชาระรายงวดเทา่ กนั
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7. เคร่อื งดดู ฝนุ่ ราคาเงินสด 5,500 บาท ถ้าผูซ้ ือ้ ต้องการซ้ือขายในระบบผ่อนชาระจะต้องจ่ายเงินดาวน์ 700 บาท หลงั จาก
นั้นผ่อนชาระเป็นรายเดือน เดือนละเท่ากัน เป็นเวลา 5 เดือน ถ้าผู้ขายคิดอัตราดอกเบ้ีย 10% จงหาเงินผ่อนชาระรายงวด
เทา่ กนั
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8. โทรทัศน์เคร่ืองหนึ่งราคาเงินสด 10,000 บาท ถ้าผู้ซ้ือต้องการซท้อขายในระบบผ่อนชาระจะต้องจ่ายเงินดาวน์ 20%
ของราคาเงนิ สด หลงั จากนั้นผอ่ นชาระเป็นรายเดอื น แบบรายงวดลดลง เปน็ เวลา 10 เดอื น ถา้ ผขู้ ายคดิ ดอกเบยี้ แบบคงต้น
ในอัตรา 12% จงหาเงินผอ่ นชาระรายงวดลดลง
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13
งวดท่ี เงินตน้ เงนิ ต้นที่ ดอกเบ้ยี ผ่อนชาระ เงนิ ผอ่ นชาระงวด
ค้างชาระ ผอ่ นชาระ
1
2
3
4
5
6
7
8
9
10
14
ใบงานที่ 5 คณติ ศาสตร์
อสมการ ธรุ กิจและบริการ
1. จงพิจารณาว่า ข้อใดถูกข้อใดผดิ
1.1 x2 > 0 เปน็ จริงเมื่อ x เป็นจานวนจรงิ ..............................................
1.2 5x > 0 เป็นจรงิ เม่ือ x > 2 ..............................................
1.3 -4x < -2x เป็นจรงิ เมอ่ื x < 0 ..............................................
1.4 -2x > -3x เป็นจริงเมอ่ื x > 0 ..............................................
1.5 3x > x เป็นจรงิ เม่ือ x > 0 ..............................................
2. จงแกอ้ สมการต่อไปน้ี
2.1 x + 2 > 0 2.2 3x – 1 ≥ x + 5
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2.3 2 – 5 x < - 27 2.4 5x – 6 > 24 – x
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2.5 3 – 1.5y ≤ 15 – 4.5y 2.6 2x + 6 > 12
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15
2.7 15 – 3x ≥ 0 2.8 3 - x ≤ 5
4
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x x x
2.9 3 – 5 > 2 2.10 2 - 3 < 1
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3. สามเทา่ ของเลขจานวนหน่ึงมากกว่า 3 อยูไ่ ม่เกนิ 15 จงเขยี นเปน็ อสมการ แล้วหาค่าของจานวนนั้น
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4. ซื้อสม้ มาจานวนหน่งึ เน่าเสียไป 15 ผล เหลือสม้ ไม่ถึง 50 ผล จงเขยี นอสมการ แลว้ หาจานวนส้มท่ซี ื้อมา
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16
5. ผลบวกของจานวนเต็มคู่สามจานวนทอ่ี ยู่ตดิ กันมีคา่ น้อยกว่า 96 จงหาจานวนเต็มคู่ท่มี ีคา่ มาท่สุด
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17
ใบงานท่ี 6 คณิตศาสตร์
ความนา่ จะเป็น ธรุ กิจและบรกิ าร
1. ในการโยนเหรียญ 1 อนั 2 ครั้ง จงหา
1.1 แซมเปลิ สเปซ
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1.2 E1 แทนเหตุการณ์ท่ีข้นึ หัว 2 ครัง้
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1.3 E2 แทนเหตุการณท์ ี่ข้ึนก้อยอย่างน้อย 1 ครั้ง
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2. ในการโยนลูกเต๋า 2 ลกู 1 คร้ัง จงหา
2.1 แซมเปลิ สเปซ
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2.2 E1 แทนผลรวมของแต้มเปน็ 10
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2.3 E2 แทนเหตุการณ์ที่ออกหนา้ เหมอื นกัน
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2.4 E3 แทนผลรวมของแตม้ มากกว่า 9
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2.5 E1 U E2
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2.6 E1 U E3
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2.7 E2 ∩ E3
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2.8 E1 ∩ E2 ∩ E3
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2.9 E1 - E2
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2.10 E2 – E3
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3. ครอบครวั หน่งึ มีบุตร 3 คน จงหา
3.1 แซมเปิลสเปซ
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3.2 E1 แทนเป็นชายท้งั 3 คน
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3.3 E2 แทนเป็นหญงิ 2 คน
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3.4 E3 แทนเป็นหญิงคนแรก ชายคนสดุ ท้อง
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3.5 E4 แทนเป็นชาย 2 คนแรก
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3.6 E1 U E2
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3.7 E1 ∩ E3
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3.8 E1/
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3.9 (E3 – E4)/
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3.10 E1 – E2
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4. กล่องใบหนง่ึ มลี ูกปิงปองสีแดง สเี ขียว และสเี หลือง อยา่ งละ 1 ลกู จงหา
4.1 แซมเปิลสเปซของการหยิบลูกปงิ ปองข้ึนมาจากกล่องคร้ังละ 1 ลกู
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4.2 แซมเปลิ สเปซของการหยิบลูกปิงปองข้ึนมาจากกล่องครั้งละ 2 ลูก พร้อมกนั
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4.3 แซมเปลิ สเปซของการหยิบลูกปิงปองขึน้ มาจากกล่องครง้ั ละ 2 ลูก ทีละลูก หยิบแล้วไมใ่ ส่คนื
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19
5. ให้ s = {1, 2, 3, …, 10} E1 = {3, 4, 5} ,
E2 = {1, 3, 5, 7}
E3 = {2, 3, 4} จงหา
5.1 E1 ∩ E2 = ……………………………………………………………………….
5.2 E2 ∩ E3 = ……………………………………………………………………….
5.3 E1 ∩ E3 = ……………………………………………………………………….
5.4 E1 – E3 = ……………………………………………………………………….
5.5 E3 – E2 = ……………………………………………………………………….
5.6 E1/ = ……………………………………………………………………….
5.7 E2/ = ……………………………………………………………………….
5.8 E1/ - E2/ = ……………………………………………………………………….
5.9 E1 – (E1 ∩ E2)/ = ……………………………………………………………………….
5.10 (E1 ∩ E2) U E3 = ……………………………………………………………………….
6. ให้ E1 และ E2 เป็นเหตกุ ารณ์ 2 เหตุการณ์ โดยท่ี P (E1) = 0.6 , P(E1) = 0.2 และ P(E1∩ E2) = 0.1 จงหา
6.1 P(E1 U E2)
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6.2 P(E1 - E2)
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6.3 P(E2 - E1)
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6.4 P(E1/ )
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6.5 P(E/2)
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7. ให้ E1 และ E2 เป็นเหตุการณ์ 2 เหตุการณ์ โดยท่ี P(E1) = 0.5 , P(E2) =0.4 และ P (E1 ∩ E2) = 0 จงหา
7.1 P(E1UE2)
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7.2 P(E1- E2)
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7.3 P(E2-E1)
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7.4 P(E/1)
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7.5 P(E1∩ E2)/
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8. ให้ A และ B เป็นเหตกุ ารณ์ 2 เหตกุ ารณ์ โดยท่ี P(A) = 4 , P (B) = 5 และ P(A∩B) = 1
9 9 3
8.1 P(A∩B)
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8.2 P(A-B)
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8.3 P(B-A)
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8.4 P (A/)
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21
8.5 P (A∩B) /
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9. โยนเหรยี ญ 3 อนั 1 ครั้ง
9.1 S = ……………………………………………………………………….
9.2 n(S) = ……………………………………………………………………….
ความน่าจะเป็นที่เหรียญทัง้ 3 ข้ึนหวั 2 เหรยี ญ
9.3 E = ……………………………………………………………………….
9.4 n(E) = ……………………………………………………………………….
9.5 P(E) = ……………………………………………………………………….
10. โยนลกู เต๋า 2 ลูก 1 ครั้ง
10.1 S = ……………………………………………………………………….
10.2 n(S) = ……………………………………………………………………….
ความนา่ จะเปน็ ทล่ี กู เต๋าทงั้ สองมผี ลรวมเท่ากับ 10
10.3 E = ……………………………………………………………………….
10.4 n(E) = ……………………………………………………………………….
10.5 P(E) = ……………………………………………………………………….
11. ผลการลงทุน คอื กาไร (ก) และขาดทุน (ข) ลงทนุ 3 ปี
11.1 S = ……………………………………………………………………….
11.2 n(S) = ……………………………………………………………………….
ความนา่ จะเป็นทจี่ ะได้กาไร 2 ปี
11.3 E = ……………………………………………………………………….
11.4 n(E) = ……………………………………………………………………….
11.5 P(E) = ……………………………………………………………………….
ความนา่ จะเปน็ ท่จี ะขาดทุนปีที่ 3
11.6 E = ……………………………………………………………………….
11.7 n(E) = ……………………………………………………………………….
22
11.8 P(E) = ……………………………………………………………………….
ความน่าจะเปน็ ทีจ่ ะขาดทนุ ปีแรก
11.9 E = ……………………………………………………………………….
11.10 n(E) = ……………………………………………………………………….
11.11 P(E) = ……………………………………………………………………….
12. ครอบครัวหนง่ึ ต้องการมีบุตร 3 คน
12.1 S = ……………………………………………………………………….
12.2 n(S) = ……………………………………………………………………….
ความน่าจะเป็นทจ่ี ะได้บุตรคนแรกเปน็ ชาย
12.3 E = ……………………………………………………………………….
12.4 n(E) = ……………………………………………………………………….
12.5 P(E) = ……………………………………………………………………….
ความน่าจะเปน็ ทจ่ี ะได้บตุ รชายมากกว่า 2 คนข้นึ ไป
12.6 E = ……………………………………………………………………….
12.7 n(E) = ……………………………………………………………………….
12.8 P(E) = ……………………………………………………………………….
23
สาหรับครู TA
คาชีแ้ จง เกณฑ์การประเมินผล
ใบงาน 10 คะแนน
1. ให้ทาเคร่ือง ลงในช่องว่างตามความเปน็ จรงิ
2. รวบรวมคะแนนตามเกณฑ์กาหนด
การสง่ งาน 5 คะแนน คณุ ภาพ 5 คะแนน รวม
ใบงาน (ครบถว้ นและถกู ต้อง)
ตามกาหนด
(5 คะแนน)
ล่า ้ชา 1 วัน
(4 คะแนน)
ล่าช้า 2 วัน
(3 คะแนน)
ล่า ้ชา 3 วัน
(2 คะแนน)
ล่า ้ชา 4 วัน
(1 คะแนน)
91% - 100%
(5 คะแนน)
81% - 90%
(4 คะแนน)
71% - 80%
(3 คะแนน)
61% - 70%
(2 คะแนน)
51% - 60%
(1 คะแนน)
ใบงานที่ 1 รอ้ ยละ
ใบงานที่ 2 ดอกเบย้ี
ใบงานท่ี 3 การต้ังราคาขาย
ใบงานที่ 4 การซอ้ื ขายในระบบผอ่ นชาระ
ใบงานที่ 5 อสมการ
ใบงานที่ 6 ความนา่ จะเป็น
คะแนนรวมทงั้ หมด
คะแนนรวมทั้งหมด / 6 (เต็ม 10 คะแนน)
ลงช่อื ................................................................ผู้ตรวจ
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ใบงานคณิต ปวช22
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