Penaakulan Matematik Mtes 3023 Tutorial M14: Ahli Kumpulan: Alex Lau Sie Hui Chong Meng Xuan Pun Yi Boon Alexandra

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PENAAKULAN MATEMATIK MTES 3023 TUTORIAL M14 AHLI KUMPULAN : ALEX LAU SIE HUI CHONG MENG XUAN PUN YI BOON ALEXANDRA

Bentang ringkasan bacaan rujukan termasuk buku dan bina satu jadual rumusan rumus perimeter, luas, luas permukaan, isipadu poligon, bulatan dan pepejal 3D (guna kertas mahjong)

1. Chai M., Lee L. M. (2005). Mathematics : form 1 PMR. Selangor Darul Ehsan : Pearson Malaysia Sdn. Bhd. • Perimeter is the total distance measured around the outside edges of a closed figure or region. While area is the measurement of the size of surface covered by a region. • Geometric solids are three-dimensional shapes that have length, width and height.

Bentang 3 soalan bukan rutin geometri / ukuran dan penyelesaiannya dengan langkah Polya.

Question 1 :

1. Memahami Soalan • • • •

sisi segi empat sama = 23 cm Luas segi empat sama yang kecil = 49 𝑐𝑚2 8 segi tiga tepat yang sama Figure 2 merupakan segi tiga tepat

2. Merancang Stategi - Menyelesaikan masalah kecil terlebih dahulu 3. Melaksanakan Strategi Luas segi empat sama = 23 × 23 = 529 𝑐𝑚2 Luas 8 segi tiga tepat = 529 − 49 = 480 𝑐𝑚2 Luas 1 segi tiga tepat = 480 ÷ 8 = 60 𝑐𝑚2

Luas 4 segi empat tepat = 60 × 4 = 240𝑐𝑚2 Luas untuk segi empat PQNO = 529 − 240 = 289𝑐𝑚2

PQNO merupakan segi empat sama, oleh itu 𝑃𝑄 = 289 = 17𝑐𝑚.

4. Menyemak semula PQ = 17 cm PQNO = 172 = 289𝑐𝑚2 Luas PQNO + luas 4 segi tiga tepat = segi empat sama 289 + 240 = 529𝑐𝑚2 Sisi segi empat sama = 529 = 23 𝑐𝑚 ∴ 𝐏𝐚𝐧𝐣𝐚𝐧𝐠 𝐏𝐐 𝐢𝐚𝐥𝐚𝐡 𝟏𝟕 𝐜𝐦.

Question 2: There are 45 questions in an exam. For every correct answer, 5 marks is awarded and for every wrong answer, 3 marks is deducted. Melissa scored 185 marks. How many correct answers did she give?

Step 1: Understanding the problem Total questions in exam: 45 Marks awarded for every correct answer: 5 Marks deducted for every wrong answer: 3 Marks that Melissa scored: 185 What to find: How many correct answers did Melissa give?

Step 2: Plan a strategi Use a table.

Step 3: Carry out the strategi No. of correct answers

Marks awarded +5

No. of mistakes

Makrs deducted -3

Total score

45

225

0

0

225

44

220

1

-3

117 225-117=8

Step 3: Carry out the strategi 225 - 117 = 8 For every mistake Melissa make, she loses 8 marks. 225 - 185 = 40 (total of marks Melissa lost) 40 ÷ 8 = 5 questions. How many answers did Melissa give? 45 – 5 = 40 questions.

Step 4: Check the answers (40 × 5)+ (5 × -3) = 200 – 15 = 185 (Checked)

3. Jonathan ingin meneka jisim bentuk-bentuk yang berikut dengan jelas dan tepat semasa pertandingan. Dia hanya diberitahu bahawa jisim kon ialah 3kg. Carikan jisim bentuk kiub dan silinder.

= =

Langkah 1: Memahami masalah • Jisim kon ialah 3kg • Carikan jisim bentuk lain Langkah 2: Merancang strategi • menggunakan strategi algebra • menggunakan sifat penambahan dan penolakan • anggap kiub sebagai x, silinder sebagai y dan kon sebagai z • 3+2x=y • y+x=3z

Langkah 3: Melaksanakan startegi y+x=3(3) y+x=9 x=9-y…….eq(1) 3+2x=y……..eq(2) 3+2(9-y)=y 3+18-2y=y 21=3y y=7 y=7 ke eq(1)

x=9-7 =2 ∴Jisim sebuah kiub ialah 2kg dan silinder ialah 7kg.

Langkah 4: Semak semula x=9-y…….eq(1) 2=9-7

3+2x=y……..eq(2) 3+2(2)=7 3+4=7

Rujukan 1. University of Cambridge. (2011, February). Volume of a Pyramid and a Cone. Retrieved from https://nrich.maths.org/1408 2. Joanna Gutt-Lehr. Formulas for Perimeter, Area, Surface, Volume. Diakses pada 7 September 2017. Boleh didapati: http://www.austincc.edu/pintutor/pin_mh/_source/Hand outs/Geometry_Formulas/Geometry_Formulas_2D_3D_P erimeter_Area_Volume.pdf 3. Peter. B, Michael. E. (2011). Area, Volume and Surface Area. Boleh didapati: http://amsi.org.au/teacher_modules/pdfs/area_volume_s urface_area.pdf

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