- 1 -

ชอ – นามสกล...................................................................................................................

1. จดตดกราฟ 2x + y – 10 = 0 และ x – y – 8 = 0 อยบนกราฟของเสนตรงใด 1. 2x + 3y – 8 = 0 2. 3x + 2y – 14 = 0 3. 2x – 3y – 8 = 0 4. 3x – 2y – 14 = 0 ............................................................................... ............................................................................. ............................................................................... ............................................................................. ............................................................................... ............................................................................. ............................................................................................................................................................ ............................................................................... ............................................................................. ............................................................................... ............................................................................. ............................................................................... ............................................................................. ............................................................................... ............................................................................. ............................................................................................................................................................ ............................................................................... ............................................................................. ............................................................................... ............................................................................. ............................................................................................................................................................ ............................................................................................................................................................ 2. ก าหนดให a, b และ c เปนจ านวนเตมบวก ซง b < a และ c < a และ a2 = 2(b + c) จะได a + b + c มคาเทาใด 1. 8 2. 6 3. 4 4. 2 ............................................................................... ............................................................................. ............................................................................... ............................................................................. ............................................................................................................................................................ ............................................................................... ............................................................................. ............................................................................... ............................................................................. ....................................................................... ..................................................................................... ............................................................................... ............................................................................. ............................................................................................................................................................

152 ตวฟร ! วชาคณตศาสตร

วนท 2 ม.ค. 61

- 2 -

3. ปงปอนดมกระดาษรปสเหลยมผนผา ขนาด 52 × 42 ตารางเซนตเมตร ถาเพมความยาวอก 5% ตองเพมความกวางอกกเปอรเซนต จงจะไดกระดาษแผนใหมเปนสเหลยมจตรส 1. 20% 2. 25% 3. 30% 4. 40% ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ 4. ณเดชนมเงนอยไมถง 260 บาท ถาแจกเดก 7 คน คนละเทาๆ กน จะเหลอเงนอย 2 บาท และถา แจกใหเดก 9 คน คนละเทาๆ กน กจะเหลอเงนอย 2 บาท เชนกน ถาเดกทกคนไดรบเงนเปน จ านวนเตมบาท ณเดชนจะมเงนมากทสดกบาท 1. 252 2. 254 3. 256 4. 258 ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................

- 3 -

5. ในการประกวดผลงานโฆษณาประจ าป 2016 ม 4 บรษท ไดเหรยญทองรวม 24 เหรยญ บรษท G ได จ านวนเหรยญทองเทากบบรษท S บรษท M ไดจ านวนเหรยญทองเทากบบรษท C บรษท G ได จ านวนเหรยญทองเปน 3 เทาของบรษท M บรษท G ไดเหรยญทองเปนจ านวนกเหรยญ 1. 6 2. 7 3. 8 4. 9 ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ 6. ถงใบหนงมทอน าสองทอ เมอเปดทงสองทอพรอมกน น าไหลเขาเตมถงในเวลา 15 นาท ถาเปด ทอใหญทอเดยวใหน าไหลเขาเตมถง ใชเวลานอยกวาเปดทอเลกทอเดยวใหน าไหลเขาเตมถง 16 นาท ถาเปดแตละทอ น าจะไหลเขาเตมถงในเวลาเทาไร 1. 10 และ 26 นาท 2. 14 และ 30 นาท 3. 16 และ 32 นาท 4. 24 และ 40 นาท ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................

- 4 -

7. วาดภาพลงบนกระดาษรปสเหลยมผนผา โดยเวนขอบดานบนและดานลางดานละ 1 นว และเวนขอบ

ดานขางดานละ 1 12 นว เพอท ากรอบ ปรากฏวาเหลอพนทส าหรบวาดภาพเทากบ 18 ตารางนว

กระดาษรปสเหลยมผนผานมเสนรอบรปยาวเทาใด ถากระดาษชนนดานยาวยาวกวาดานกวาง 2 นว 1. 26 2. 28 3. 30 4. 32 ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................

8. จงหาคาของ (11 +

12 +

13 +

14 +

15) + 3x (

12 +

13 +

14 +

15) + 5x (

13 +

14 +

15)

1. 8 120 2. 9

120 3. 10

120 4. 11

120

............................................................................................................................................................

............................................................................................................................................................

............................................................................................................................................................

............................................................................................................................................................

............................................................................................................................................................

............................................................................................................................................................

............................................................................................................................................................

............................................................................................................................................................

............................................................................................................................................................

............................................................................................................................................................

- 5 -

9. วงกลมวงหนงมพนท 15.2π ตารางหนวย ความยาวของเสนทแยงมมของรปสเหลยมจตรสทแนบ ในวงกลมมคาตรงกบขอใด 1. 3.8 หนวย 2. 4.2 หนวย 3. 6.2 หนวย 4. 7.8 หนวย ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ 10. มนมอย 2 ใน 3 ขวด เมอเทน าลงไป 1 ใน 4 ของนมทมอยในขวด จะท าใหของเหลวในขวดม ปรมาตรเทากบ 150 ลกบาศกเซนตเมตร ความจทงหมดของขวดใบนมกลกบาศกเซนตเมตร 1. 180 2. 240 3. 580 4. 640 ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................

- 6 -

11. เมอ 3 ปทแลว พอมอายเปน 3 เทาของลก และแมมอายนอยกวาพออย 5 ป ถาทราบวาผลรวม ของอายของทงสามคนเมอ 3 ปทแลว เทากบ 100 ปพอด อยากทราบวาปจจบนพอมอายกป 1. 42 2. 48 3. 54 4. 58 ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ 12.

สามเหลยม ABC ; AB = BM = AN และมม ABC = 35° จงหาคามม APB 1. 110° 2. 115° 3. 120° 4. 125° ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................

- 7 -

13.

ABCD เปนรปสเหลยมผนผา มรปวงกลม 2 วงท สมผสกน แตละวงมรศมยาว 2 เซนตเมตร และ สมผสดานในของรปสเหลยมผนผา

ถาก าหนดให π = 3.14 ใหหาพนทสวนทแรเงา (ใหตอบเปนทศนยม 2 ต าแหนง)

1. 3.44 2. 3.64 3. 4.34 4. 5.44

............................................................................................................................................................

............................................................................................................................................................

............................................................................................................................................................

............................................................................................................................................................

............................................................................................................................................................

............................................................................................................................................................

............................................................................................................................................................

............................................................................................................................................................

............................................................................................................................................................

............................................................................................................................................................

............................................................................................................................................................

............................................................................................................................................................

............................................................................................................................................................

............................................................................................................................................................

............................................................................................................................................................

............................................................................................................................................................

............................................................................................................................................................

............................................................................................................................................................

............................................................................................................................................................

............................................................................................................................................................

............................................................................................................................................................

............................................................................................................................................................

............................................................................................................................................................

- 8 -

14. จงใชขอมลนตอบค าถาม ABCD เปนรปสเหลยมคางหม ม AC และ DB เปนเสนทแยงมม ดงรป

พจารณาขอความตอไปน (1) รปนมมมสองมมทรวมกนได 180° ทงหมด 6 ค (2) รปนมมมสองมมเทากน จ านวน 4 ค ขอสรปใดถกตอง 1. ถกขอ (1) เพยงขอเดยว 2. ถกขอ (2) เพยงขอเดยว 3. ถกทงสองขอ 4. ผดทงสองขอ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................

- 9 -

15. รปสเหลยมจตรสรปใหญมเสนรอบรปยาวเปน 3 เทาของรปสเหลยมจตรสรปเลก รปสเหลยมจตรส รปใหญจะมพนทเปนกเทาของพนทของรปสเหลยมจตรสรปเลก 1. 3 2. 6 3. 9 4. 12 ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ 16. ถงน าทรงสเหลยมมมฉากกวาง 6 เซนตเมตร ยาว 9 เซนตเมตร มน าบรรจอยภายในสง 5 เซนตเมตร เมอน าแทงไมทรงกระบอกใสลงไป ปรากกฎวาแทงไมจมใตน าเพยงครงเดยว และระดบน าสงขนอก 2 เซนตเมตร แทงไมมปรมาตรกลกบาศกเซนตเมตร 1. 108 2. 162 3. 216 4. 378 ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................

- 10 -

17. จากรป กขคง เปนรปสเหลยมจตรสทมดานยาวดานละ 14 เซนตเมตร กขจ, ขคจ และ กจง เปนรปครงวงกลม พนทสวนทแรเงาประมาณกตารางเซนตเมตร 1. 28 ตารางเซนตเมตร 2. 36 ตารางเซนตเมตร 3. 42 ตารางเซนตเมตร 4. 56 ตารางเซนตเมตร ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................

14

14

- 11 -

18. เอและบ ซอสมดปกออนชนดเดยวกนจากรานเครองเขยน ถาสมดปกออน 1 เลม มราคาเปน จ านวนเตม และมากกวา 10 บาท แตเอใชเงนไป 182 บาท ขณะทบใชเงนไป 221 บาท แลวทง สองคนซอสมดปกออนไดรวมกนกเลม 1. 14 2. 21 3. 30 4. 31 ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ 19. โคนนซออมยมมาจ านวนหนง ในราคา 6 อน 5 บาท แลวขายไปในราคา 4 อน 5 บาท ถาโคนน ตองการก าไรจากการขายอมยมเปนเงน 300 บาท โคนนจะตองซออมยมมาขายทงหมดกอน 1. 650 2. 680 3. 700 4. 720 ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................

- 12 -

20. อาฟงมชดออกก าลงกายคอ เสอสตางกน 4 ตว กางเกงสตางกน 3 ตว และรองเทาสตางกน 2 ค อาฟงสวมเสอ กางเกง และรองเทา เปนชดทตางกนไดทงหมดกชด (1 ชด หมายถง เสอ กางเกง และรองเทา) 1. 24 2. 26 3. 28 4. 30 ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................

- 13 -

21. จากรป ใหมม a มคาเทากบ 5y + 15o ใหหาวา y มคาเทาไร

1. 9 2. 10 3. 12 4. 15 ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ 22. ในหองเรยนคอรสโคงสดทาย จ านวนนกเรยนชายมเปนจ านวนครงหนงของจ านวนนกเรยนหญง และความสงเฉลยของนกเรยนหญงเปน 152 เซนตเมตร ซงนอยกวาความสงเฉลยของนกเรยนชาย อย 3 เซนตเมตร ความสงเฉลยของนกเรยนทงหองเปนเทาใด 1. 152 2. 153 3. 154 4. 155 ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................