MatematikMathematics

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1

Question 1

Rajah 1 menunjukkan sekeping kad nombor.Diagram 1 shows a number card.

[1 mark] Nyatakan nilai digit bagi digit 6 dalam nombor itu.State the digit value of the digit 6 in the number.

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The 6 is in the ten thousands place (7 468 215), so its digit value is 60 000.

• 60 000 [1]1

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For the teacher: Remembering, low difficulty, Unit 1, standard 1.1.1

Textbook p. 3

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Question 2

[1 mark] Saya ialah nombor perdana dua digit antara 40 dengan 60. Hasil tambah dua digit saya ialah 8. Apakah nombor saya?I am a two-digit prime number between 40 and 60. The sum of my two digits is 8. What is my number?

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Numbers between 40 and 60 with digit sum 8: 44 and 53. 44 is even (composite). 53 has no factor other than 1 and 53, so it is prime.

• 53 [1]1

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For the teacher: Analysing, high difficulty, Unit 1, standard 1.3.1

Textbook p. 43

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Question 3

[2 marks] 7 350 000 − 2⁴⁄₅ juta = ______ Beri jawapan sebagai nombor bulat.7 350 000 − 2⁴⁄₅ million = ______ Give the answer as a whole number.

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7.35 million − 2.8 million = 4.55 million = 4 550 000.

• 2⁴⁄₅ million = 2.8 million = 2 800 000 [1]1
• 7 350 000 − 2 800 000 = 4 550 000 [1]1

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For the teacher: Applying, low difficulty, Unit 1, standard 1.2.1

Textbook p. 15

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Question 4

[2 marks] 2¹⁄₄ ÷ ³⁄₁₀ = ______ Beri jawapan dalam bentuk yang paling ringkas.2¹⁄₄ ÷ ³⁄₁₀ = ______ Give the answer in its simplest form.

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9/4 × 10/3 = 3 × 5/2 = 15/2 = 7 1/2 after cancelling 9 with 3 and 10 with 4.

• 2¹⁄₄ = ⁹⁄₄; ⁹⁄₄ × ¹⁰⁄₃ [1]1
• ⁹⁰⁄₁₂ = 7¹⁄₂ [1]1

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For the teacher: Applying, low difficulty, Unit 2, standard 2.1.1

Textbook p. 63

5

Question 5

[2 marks] 8.28 ÷ 0.46 =

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8.28 ÷ 0.46 = 828 ÷ 46 = 18 (check: 18 × 0.46 = 8.28).

• Multiply both numbers by 100: 828 ÷ 46 [1]1
• 18 [1]1

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For the teacher: Applying, low difficulty, Unit 2, standard 2.2.2

Textbook p. 71

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Question 6

[2 marks] Sebuah gerai menjual 65 biji kek pada hari Isnin. Pada hari Selasa, gerai itu menjual 140% daripada bilangan kek hari Isnin. Berapakah bilangan kek yang dijual pada hari Selasa?A stall sells 65 cakes on Monday. On Tuesday the stall sells 140% of the number of cakes sold on Monday. How many cakes are sold on Tuesday?

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100% of 65 = 65 and 40% of 65 = 26, so 65 + 26 = 91.

• 140 ÷ 100 × 65 (or 100% = 65, 40% = 26) [1]1
• 91 cakes [1]1

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For the teacher: Applying, medium difficulty, Unit 2, standard 2.3.3

Textbook p. 78

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Question 7

Jadual dalam Rajah 2 menunjukkan harga kos, harga jualan serta untung atau rugi bagi dua barang.The table in Diagram 2 shows the cost price, selling price and profit or loss of two items.

[2 marks] Cari nilai P dan nilai Q.Find the value of P and the value of Q.

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Profit = selling price − cost price, so P = RM17. A loss means the selling price is lower than the cost price, so Q = RM240 − RM35 = RM205.

• P = 102 − 85 = RM17 [1]1
• Q = 240 − 35 = RM205 [1]1

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For the teacher: Applying, low difficulty, Unit 3, standard 3.1.1

Textbook p. 104

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Question 8

Rajah 3 menunjukkan waktu di dua buah bandar pada saat yang sama.Diagram 3 shows the time in two cities at the same moment.

[2 marks] Berapakah beza masa, dalam minit, antara kedua-dua bandar itu?What is the time difference, in minutes, between the two cities?

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11:55 a.m. to 12:00 noon is 5 minutes, then 2 hours 10 minutes to 2:10 p.m.: 2 hours 15 minutes = 135 minutes.

• 2:10 p.m. − 11:55 a.m. = 2 hours 15 minutes [1]1
• 2 × 60 + 15 = 135 minutes [1]1

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For the teacher: Applying, medium difficulty, Unit 4, standard 4.1.2

Textbook p. 146

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Question 9

[2 marks] Sebuah kereta menggunakan 9 ℓ petrol untuk perjalanan sejauh 117 km. Berapakah jarak, dalam km, yang dapat dilalui oleh kereta itu dengan menggunakan 15 ℓ petrol? Kereta itu menggunakan petrol pada kadar yang sama.A car uses 9 ℓ of petrol to travel 117 km. What distance, in km, can the car travel using 15 ℓ of petrol? The car uses petrol at the same rate.

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• 117 ÷ 9 = 13 km for 1 ℓ [1]1
• 15 × 13 = 195 km [1]1

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For the teacher: Applying, low difficulty, Unit 5, standard 5.1.1 (ii)

Textbook p. 158

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Question 10

Rajah 4 menunjukkan lima bulatan yang sama saiz disusun dalam satu baris dan bersentuhan antara satu sama lain. Jumlah panjang baris itu ialah 90 cm.Diagram 4 shows five identical circles in a row, each touching the next. The total length of the row is 90 cm.

[2 marks] Berapakah jejari, dalam cm, satu bulatan itu?What is the radius, in cm, of one circle?

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The row is 5 diameters long. One diameter is 18 cm, and the radius is half the diameter.

• 90 ÷ 5 = 18 cm (diameter) [1]1
• 18 ÷ 2 = 9 cm [1]1

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For the teacher: Applying, medium difficulty, Unit 6, standard 6.2.1

Textbook p. 179

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Question 11

[2 marks] Nurul mempunyai enam keping kad bernombor 2, 4, 6, 8, 10 dan 12. Dia memilih sekeping kad tanpa melihatnya. Nyatakan kemungkinan kad yang dipilih itu ialah nombor genap. Beri satu sebab bagi jawapan anda.Nurul has six cards numbered 2, 4, 6, 8, 10 and 12. She picks one card without looking. State the likelihood that the card is an even number. Give one reason for your answer.

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• Certain [1]1
• All the cards are even numbers [1] (accept: every card has an even number, so it cannot be anything else)1

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For the teacher: Understanding, low difficulty, Unit 8, standard 8.2.1

Textbook p. 213

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Question 12

Nisbah bilangan pelekat Mei kepada bilangan pelekat Nora ialah 3 : 5. Rajah 5 menunjukkan model bar bagi pelekat mereka. Nora mempunyai 48 keping pelekat lebih banyak daripada Mei.The ratio of the number of Mei's stickers to the number of Nora's stickers is 3 : 5. Diagram 5 shows a bar model of their stickers. Nora has 48 more stickers than Mei.

[3 marks] Hitung jumlah bilangan pelekat Mei dan Nora.Calculate the total number of stickers that Mei and Nora have.

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Mei has 72 and Nora has 120; 72 + 120 = 192.

• 5 − 3 = 2 units stand for 48 stickers [1]1
• 1 unit = 48 ÷ 2 = 24 [1]1
• (3 + 5) × 24 = 192 stickers [1]1

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For the teacher: Analysing, high difficulty, Unit 7, standard 7.3.1

Textbook p. 199

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Question 13

[3 marks] Rayyan mempunyai RM150. Dia membelanjakan ²⁄₅ daripada wang itu untuk membeli sehelai kemeja. Kemudian, dia membelanjakan 0.35 daripada baki wangnya untuk membeli sebuah topi. Berapakah baki wang Rayyan sekarang?Rayyan has RM150. He spends ²⁄₅ of the money on a shirt. Then he spends 0.35 of the money that is left on a cap. How much money does Rayyan have now?

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RM58.50 (check: 0.65 × RM90 = RM58.50).

• Shirt: ²⁄₅ × 150 = RM60, left RM150 − RM60 = RM90 [1]1
• Cap: 0.35 × RM90 = RM31.50 [1]1
• RM90 − RM31.50 = RM58.50 [1]1

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For the teacher: Applying, high difficulty, Unit 2, standard 2.4.1

Textbook p. 85

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Question 14

Rajah 6 menunjukkan bahan-bahan untuk membuat sejenis apam di dapur keluarga Kak Hasnah. Dia menggunakan 1.8 ℓ susu.Diagram 6 shows the ingredients for making a kind of pancake in Kak Hasnah's family kitchen. She uses 1.8 ℓ of milk.

[1 mark] (a)Berapakah jisim tepung, dalam g, yang diperlukan?What mass of flour, in g, is needed?

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• 1.8 ℓ = 1 800 mℓ = 3 × 600 mℓ, so 3 × 150 = 450 g [1]1

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[2 marks] (b)Hitung jumlah jisim tepung dan gula, dalam kg.Calculate the total mass of the flour and the sugar, in kg.

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• Sugar: 3 × 90 = 270 g [1]1
• 450 + 270 = 720 g = 0.72 kg [1] (follow through from (a))1

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For the teacher: Applying, low difficulty, Unit 5, standard 5.1.1 (iii)

Textbook p. 161

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Question 15

Rajah 7 menunjukkan kedudukan Taman, Pekan, Pantai dan Hospital pada satah Cartes. Keluarga Faris pergi membeli-belah dengan memandu dari Taman ke Pekan, kemudian dari Pekan ke Pantai. Satu unit pada satah itu mewakili 2 km.Diagram 7 shows the positions of Taman, Pekan, Pantai and Hospital on a Cartesian plane. Faris's family goes on a shopping trip, driving from Taman to Pekan and then from Pekan to Pantai. One unit on the plane represents 2 km.

[1 mark] (a)Nyatakan koordinat Pantai.State the coordinates of Pantai.

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• (9, 2) [1]1

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[2 marks] (b)Hitung jumlah jarak, dalam km, perjalanan keluarga itu dari Taman ke Pantai melalui Pekan.Calculate the total distance, in km, of the family's journey from Taman to Pantai through Pekan.

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• Taman to Pekan 7 − 2 = 5 units; Pekan to Pantai 9 − 3 = 6 units, 11 units altogether [1]1
• 11 × 2 = 22 km [1]1

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For the teacher: Applying, medium difficulty, Unit 7, standard 7.1.1

Textbook p. 188

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Question 16

Rajah 8 menunjukkan label harga sebuah basikal di sebuah kedai. Faris membeli basikal itu untuk adiknya.Diagram 8 shows the price tag of a bicycle in a shop. Faris buys the bicycle for his younger brother.

[2 marks] (a)Hitung nilai diskaun, dalam RM.Calculate the value of the discount, in RM.

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• 15 ÷ 100 × 480 (or 10% = 48, 5% = 24) [1]1
• RM72 [1]1

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[1 mark] (b)Berapakah harga yang perlu dibayar oleh Faris?What price must Faris pay?

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• RM480 − RM72 = RM408 [1] (follow through from (a))1

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For the teacher: Applying, low difficulty, Unit 3, standard 3.1.2

Textbook p. 109

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Question 17

Rajah 9 menunjukkan sebuah dulang berbentuk pentagon sekata. Puan Hasnah menampal reben pada tepi dulang itu. Panjang reben yang diperlukan ialah 75 cm. Dia kemudian membuat sebuah dulang berbentuk oktagon sekata yang panjang sisinya sama dengan panjang sisi dulang pentagon itu.Diagram 9 shows a tray in the shape of a regular pentagon. Puan Hasnah sticks ribbon along the edge of the tray. The length of ribbon needed is 75 cm. She then makes a tray in the shape of a regular octagon whose side is the same length as the side of the pentagon tray.

[3 marks] Berapakah panjang reben tambahan, dalam cm, yang diperlukan untuk dulang oktagon itu berbanding dulang pentagon?How much more ribbon, in cm, is needed for the octagon tray than for the pentagon tray?

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A regular polygon has equal sides, so the perimeter is the number of sides times one side. 3 sides more means 3 × 15 = 45 cm more.

• Side = 75 ÷ 5 = 15 cm [1]1
• Octagon perimeter = 8 × 15 = 120 cm [1]1
• 120 − 75 = 45 cm [1]1

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For the teacher: Analysing, high difficulty, Unit 6, standard 6.3.1

Textbook p. 185

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Question 18

Sekolah Rimbun mengadakan lawatan ke sebuah pameran sains. Jadual dalam Rajah 10 menunjukkan bilangan pengunjung pameran itu selama tiga hari.Sekolah Rimbun takes a school trip to a science exhibition. The table in Diagram 10 shows the number of visitors to the exhibition over three days.

[1 mark] (a)Berapakah bilangan pengunjung pada hari Ahad?How many visitors came on Sunday?

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• 2 × 386 400 = 772 800 [1]1

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[2 marks] (b)Penganjur menyasarkan 2 000 000 orang pengunjung. Berapakah bilangan pengunjung lagi yang diperlukan untuk mencapai sasaran itu?The organisers aim for 2 000 000 visitors. How many more visitors are needed to reach the target?

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• 386 400 + 524 750 + 772 800 = 1 683 950 [1]1
• 2 000 000 − 1 683 950 = 316 050 [1] (follow through from (a))1

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For the teacher: Applying, medium difficulty, Unit 1, standard 1.4.1

Textbook p. 48

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Question 19

Murid-murid yang pergi ke lawatan itu membuat panggilan video dengan sebuah sekolah di Auckland. Rajah 11 menunjukkan tarikh dan waktu panggilan itu bermula di Kuala Lumpur. Waktu di Auckland mendahului waktu di Kuala Lumpur selama 4 jam.The pupils on the trip make a video call to a school in Auckland. Diagram 11 shows the date and time the call starts in Kuala Lumpur. The time in Auckland is 4 hours ahead of the time in Kuala Lumpur.

[3 marks] Nyatakan tarikh dan waktu panggilan itu bermula di Auckland.State the date and the time the call starts in Auckland.

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9:20 p.m. + 3 hours 40 minutes reaches midnight, then 20 minutes more: 1:20 a.m. The date changes to 15 June.

• 9:20 p.m. + 4 hours [1]1
• 1:20 a.m. [1]1
• 15 June [1]1

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For the teacher: Applying, low difficulty, Unit 4, standard 4.2.1

Textbook p. 152

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Question 20

Tabung Hari Sukan sebuah sekolah mempunyai RM3 500. Sebanyak 24% daripada wang itu digunakan untuk membeli hadiah dan 15% digunakan untuk membeli minuman.A school's Sports Day fund has RM3 500. 24% of the money is used to buy prizes and 15% is used to buy drinks.

[1 mark] (a)Berapakah peratusan wang yang tinggal?What percentage of the money is left?

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• 100% − 24% − 15% = 61% [1]1

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[2 marks] (b)Berapakah baki wang tabung itu?How much money is left in the fund?

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1% of RM3 500 = RM35, so 61% = 61 × RM35 = RM2 135.

• 61 ÷ 100 × 3 500 [1]1
• RM2 135 [1] (follow through from (a))1

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For the teacher: Applying, medium difficulty, Unit 2, standard 2.5.1

Textbook p. 95

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Question 21

Carta pai dalam Rajah 12 menunjukkan sukan kegemaran murid Tahun 6 sebuah sekolah pada Hari Sukan. Seramai 24 orang murid memilih badminton.The pie chart in Diagram 12 shows the favourite sport of the Year 6 pupils of a school on Sports Day. 24 pupils chose badminton.

[1 mark] (a)Cari nilai P.Find the value of P.

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• 360 − 180 − 90 − 45 = 45 [1]1

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[1 mark] (b)Berapakah jumlah murid Tahun 6 itu?How many Year 6 pupils are there altogether?

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• 90° is ¹⁄₄ of 360°, so 4 × 24 = 96 pupils [1]1

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[1 mark] (c)Berapakah bilangan murid yang memilih bola sepak?How many pupils chose football?

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• ¹⁄₂ × 96 = 48 pupils [1] (follow through from (b))1

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For the teacher: Applying, low difficulty, Unit 8, standard 8.1.1

Textbook p. 210

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