Ujian Akhir Sesi AkademikEnd of Academic Session Test
MatematikMathematics
Tingkatan 1, 2 jam / 2 hours, 100 marks
Nama / Name
Kelas / Class
Tarikh / Date
Markah / Marks: / 100
Instructions
Kertas soalan ini mengandungi tiga bahagian: Bahagian A, Bahagian B dan Bahagian C.This question paper consists of three sections: Section A, Section B and Section C.
Jawab semua soalan.Answer all questions.
Tunjukkan langkah-langkah penting dalam kerja mengira anda.Show your working. It may help you to get marks.
Rajah yang mengiringi soalan tidak dilukis mengikut skala kecuali dinyatakan.The diagrams in this paper are not drawn to scale unless stated.
Anda dibenarkan menggunakan kalkulator saintifik.You may use a scientific calculator.
Answer schemes are in English (DLP).
Practice shows answers as you go. Exam times you and hides answers until you submit.
Bahagian ASection A
20 marks
Jawab semua soalan. Setiap soalan diikuti oleh empat pilihan jawapan, A, B, C dan D. Pilih satu jawapan sahaja.Answer all questions. Each question is followed by four options, A, B, C and D. Choose one answer only.
1
Question 1
Sebuah lif di sebuah kompleks kediaman berada di aras −2 (tempat letak kereta bawah tanah). Lif itu naik 9 aras, kemudian turun 4 aras. Di aras manakah lif itu sekarang?A lift in a residential complex is at level −2 (the basement car park). The lift goes up 9 levels, then goes down 4 levels. At which level is the lift now?
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C
(−2) + 9 − 4 = 7 − 4 = 3. The lift is at level 3.
For the teacher: Applying, low difficulty, Chapter 1, standard 1.2
Textbook p. 8
2
Question 2
Sebuah tin mengandungi 41/2 liter cat. Aiman menggunakan 13/4 liter cat untuk mengecat pintu rumahnya dan 2/5 daripada baki cat itu untuk mengecat pagar. Berapakah isi padu, dalam liter, cat yang tinggal?A tin contains 41/2 litres of paint. Aiman uses 13/4 litres of paint to paint the door of his house and 2/5 of the remaining paint to paint the fence. What is the volume, in litres, of paint left?
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A
Remainder after the door = 4½ − 1¾ = 2¾ = 2.75 l. Fence = ⅖ × 2.75 = 1.1 l. Paint left = 2.75 − 1.1 = 1.65 l.
For the teacher: Applying, medium difficulty, Chapter 1, standard 1.3
Textbook p. 18
3
Question 3
Antara berikut, yang manakah semua faktor perdana bagi 84?Which of the following are all the prime factors of 84?
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B
84 = 2 × 2 × 3 × 7, so the prime factors are 2, 3 and 7. 1 and 4 are not prime numbers.
For the teacher: Remembering, low difficulty, Chapter 2, standard 2.1
Textbook p. 34
4
Question 4
Lantai sebuah bilik berbentuk segi empat tepat berukuran 360 cm × 270 cm. Lantai itu akan dipasang dengan jubin segi empat sama yang serupa dan bersaiz terbesar tanpa memotong mana-mana jubin. Berapakah panjang sisi, dalam cm, setiap jubin itu?The floor of a room is a rectangle measuring 360 cm × 270 cm. The floor will be covered with identical square tiles of the largest possible size without cutting any tile. What is the length of the side, in cm, of each tile?
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D
The side must be the HCF of 360 and 270. 360 = 2³ × 3² × 5 and 270 = 2 × 3³ × 5, so HCF = 2 × 3² × 5 = 90 cm.
For the teacher: Applying, medium difficulty, Chapter 2, standard 2.1
Textbook p. 38
5
Question 5
Sekeping jubin berbentuk segi empat sama mempunyai luas 324 cm2. Berapakah panjang sisi, dalam cm, jubin itu?A square tile has an area of 324 cm2. What is the length of the side, in cm, of the tile?
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B
Side = √324 = 18 cm, because 18 × 18 = 324. 162 is 324 ÷ 2, not the square root.
For the teacher: Remembering, low difficulty, Chapter 3, standard 3.1
Textbook p. 52
6
Question 6
Hitung nilai bagi ∛(−0.125) + (−2)3.Calculate the value of ∛(−0.125) + (−2)3.
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A
∛(−0.125) = −0.5 and (−2)³ = −8, so the value is −0.5 + (−8) = −8.5.
For the teacher: Applying, medium difficulty, Chapter 3, standard 3.2
Textbook p. 66
7
Question 7
Dalam pelan sebuah rumah, panjang ruang tamu ialah 4.2 m dan lebarnya ialah 280 cm. Nyatakan nisbah panjang kepada lebar ruang tamu itu dalam bentuk termudah.In the plan of a house, the length of the living room is 4.2 m and its width is 280 cm. State the ratio of the length to the width of the living room in its simplest form.
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C
Use the same unit: 4.2 m = 420 cm. 420 : 280 = 3 : 2 (divide both by the HCF 140).
For the teacher: Understanding, low difficulty, Chapter 4, standard 4.1
Textbook p. 79
8
Question 8
Seorang tukang cat dapat mengecat 54 m2 dinding dalam masa 4.5 jam. Dengan kadar yang sama, berapakah masa, dalam jam, yang diperlukan untuk mengecat 84 m2 dinding?A painter can paint 54 m2 of wall in 4.5 hours. At the same rate, how long, in hours, does he need to paint 84 m2 of wall?
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D
Rate = 54 ÷ 4.5 = 12 m² per hour. Time = 84 ÷ 12 = 7 hours.
For the teacher: Applying, medium difficulty, Chapter 4, standard 4.2
Textbook p. 83
9
Question 9
Antara pasangan berikut, yang manakah pasangan sebutan serupa?Which of the following pairs are like terms?
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A
Like terms have the same variables with the same powers. xy and yx are the same product; the other pairs differ in variables or powers.
For the teacher: Remembering, low difficulty, Chapter 5, standard 5.2
Textbook p. 112
10
Question 10
Sebuah bingkai tingkap berbentuk segi empat tepat mempunyai panjang (3x + 2) cm dan lebar (x − 1) cm. Ungkapkan perimeter, dalam cm, bingkai tingkap itu dalam sebutan x.A rectangular window frame has a length of (3x + 2) cm and a width of (x − 1) cm. Express the perimeter, in cm, of the window frame in terms of x.
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B
Perimeter = 2[(3x + 2) + (x − 1)] = 2(4x + 1) = 8x + 2. 4x + 1 is only half the perimeter.
For the teacher: Applying, medium difficulty, Chapter 5, standard 5.2
Textbook p. 114
11
Question 11
Diberi 3(2m − 4) = 18, cari nilai m.Given 3(2m − 4) = 18, find the value of m.
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C
6m − 12 = 18, so 6m = 30 and m = 5.
For the teacher: Applying, low difficulty, Chapter 6, standard 6.1
Textbook p. 128
12
Question 12
Sebuah kedai perkakasan menjual penyangkut dan engsel pintu. Harga 2 penyangkut dan 3 engsel ialah RM23, manakala harga 4 penyangkut dan 1 engsel ialah RM21. Berapakah harga sebuah engsel?A hardware shop sells hooks and door hinges. The price of 2 hooks and 3 hinges is RM23, while the price of 4 hooks and 1 hinge is RM21. What is the price of one hinge?
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D
Let a hook cost k and a hinge g: 2k + 3g = 23 and 4k + g = 21. From the second, g = 21 − 4k; substitute: 2k + 63 − 12k = 23, so k = 4 and g = 21 − 16 = 5. A hinge costs RM5 (RM4 is the hook).
For the teacher: Analysing, medium difficulty, Chapter 6, standard 6.3
Textbook p. 141
13
Question 13
Sebuah lif barang di tapak pembinaan boleh membawa beban tidak melebihi 630 kg. Seorang pekerja berjisim 70 kg menaiki lif itu bersama n kotak jubin. Jisim setiap kotak jubin ialah 35 kg. Antara ketaksamaan linear berikut, yang manakah mewakili situasi itu?A goods lift at a construction site can carry a load of not more than 630 kg. A worker with a mass of 70 kg rides the lift with n boxes of tiles. The mass of each box of tiles is 35 kg. Which of the following linear inequalities represents the situation?
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A
Total mass = 35n + 70 and 'not more than 630' means ≤ 630. (This gives n ≤ 16 boxes.)
For the teacher: Applying, medium difficulty, Chapter 7, standard 7.2
Textbook p. 160
14
Question 14
Rajah 1 menunjukkan dua batang pemegang tangga, PQ dan RS, yang selari. TU ialah sebatang tiang tegak. Cari nilai x.Diagram 1 shows two parallel stair handrails, PQ and RS. TU is a vertical post. Find the value of x.
Rajah 1Diagram 1
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C
58° and x are interior angles between the parallel lines on the same side of the transversal TU, so they add up to 180°: x = 180° − 58° = 122°.
For the teacher: Applying, low difficulty, Chapter 8, standard 8.3
Textbook p. 191
15
Question 15
Dalam Rajah 2, PQRS ialah sebuah segi empat selari dan PQT ialah garis lurus. Cari nilai y.In Diagram 2, PQRS is a parallelogram and PQT is a straight line. Find the value of y.
Rajah 2Diagram 2
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B
∠PQR = 180° − 70° = 110°. PS ∥ QR, so ∠SQR = ∠PSQ = 45° (alternate angles). y = 110° − 45° = 65°. (Or: ∠SPQ = 70°, so y = 180° − 70° − 45° = 65°.)
For the teacher: Analysing, medium difficulty, Chapter 9, standard 9.3
Textbook p. 216
16
Question 16
Rajah 3 menunjukkan sekeping panel kaca berbentuk trapezium pada hadapan sebuah kedai. Hitung luas, dalam m2, panel kaca itu.Diagram 3 shows a trapezium-shaped glass panel at the front of a shop. Calculate the area, in m2, of the glass panel.
Rajah 3Diagram 3
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D
Area of trapezium = ½ × (sum of parallel sides) × height = ½ × (5 + 3) × 2.4 = 9.6 m².
For the teacher: Applying, low difficulty, Chapter 10, standard 10.2
Textbook p. 236
17
Question 17
Diberi set semesta ξ = {x : x ialah integer, 1 ≤ x ≤ 10} dan P = {x : x ialah gandaan 3}. Cari n(P').Given the universal set ξ = {x : x is an integer, 1 ≤ x ≤ 10} and P = {x : x is a multiple of 3}. Find n(P').
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C
P = {3, 6, 9}, so P' = {1, 2, 4, 5, 7, 8, 10} and n(P') = 10 − 3 = 7.
For the teacher: Understanding, low difficulty, Chapter 11, standard 11.2
Textbook p. 256
18
Question 18
Seorang pereka dalaman mengumpul data tentang rumah pelanggannya. Antara berikut, yang manakah data kategori?An interior designer collects data about her clients' houses. Which of the following is categorical data?
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B
Colour is a category (a description), not a number. Number of bedrooms, floor area and height are numerical data.
For the teacher: Remembering, low difficulty, Chapter 12, standard 12.1
Textbook p. 268
19
Question 19
Carta pai dalam Rajah 4 menunjukkan pembahagian kos mengubah suai sebuah rumah. Jumlah kos ialah RM18 000. Hitung kos perabot.The pie chart in Diagram 4 shows how the cost of renovating a house is divided. The total cost is RM18 000. Calculate the cost of the furniture.
Rajah 4Diagram 4
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A
x = 360° − 90° − 60° − 72° = 138°. Cost = 138/360 × RM18 000 = RM6 900. (RM4 500 is the cost of the tiles.)
For the teacher: Applying, medium difficulty, Chapter 12, standard 12.1
Textbook p. 278
20
Question 20
Rajah 5 menunjukkan sebatang tangga sepanjang 5 m yang disandarkan pada dinding tegak. Hujung atas tangga mencecah dinding pada ketinggian 4.8 m. Kaki tangga itu kemudian dialihkan 1.6 m lagi menjauhi dinding. Berapakah jarak, dalam m, hujung atas tangga itu menggelongsor ke bawah?Diagram 5 shows a 5 m ladder leaning against a vertical wall. The top of the ladder touches the wall at a height of 4.8 m. The foot of the ladder is then moved 1.6 m further away from the wall. How far, in m, does the top of the ladder slide down?
Rajah 5Diagram 5
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D
First foot distance = √(5² − 4.8²) = √1.96 = 1.4 m. New distance = 1.4 + 1.6 = 3.0 m. New height = √(5² − 3²) = 4 m. The top slides down 4.8 − 4 = 0.8 m.
For the teacher: Analysing, medium difficulty, Chapter 13, standard 13.1
Textbook p. 298
Bahagian BSection B
20 marks
Jawab semua soalan.Answer all questions.
21
Question 21
Tentukan sama ada setiap pernyataan berikut Benar atau Palsu.Determine whether each of the following statements is True or False.
[1 mark](a)−7 > −4Show answerHide answer
False
On a number line −7 lies to the left of −4, so −7 < −4.
[1 mark](b)−2/3 ialah nombor nisbah.−2/3 is a rational number.Show answerHide answer
True
A rational number can be written as p/q with p and q integers, q ≠ 0: −2/3 is already in this form.
0.75 − 1.2 = −0.45 (the answer is negative because 1.2 > 0.75).
For the teacher: Understanding, low difficulty, Chapter 1, standard 1.5
Textbook p. 24
22
Question 22
Seorang tukang kayu menulis ungkapan algebra 7p − 4pq + 9 untuk mewakili kos bahan, dalam RM, bagi sebuah almari.A carpenter writes the algebraic expression 7p − 4pq + 9 to represent the cost of materials, in RM, for a cupboard.
[1 mark](a)Berapakah bilangan sebutan dalam ungkapan itu?How many terms are there in the expression?Show answerHide answer
3
The terms are 7p, −4pq and 9: three terms.
[1 mark](b)Nyatakan pekali bagi pq.State the coefficient of pq.Show answerHide answer
−4
In the term −4pq the number multiplying pq is −4 (the sign belongs to the coefficient).
For the teacher: Applying, low difficulty, Chapter 5, standard 5.1
Textbook p. 111
23
Question 23
Rajah 6 menunjukkan reka bentuk jeriji tingkap. PQ dan RS ialah garis lurus yang bersilang di titik O.Diagram 6 shows the design of a window grille. PQ and RS are straight lines that intersect at point O.
Rajah 6Diagram 6
[2 marks](a)Cari nilai x.Find the value of x.
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[1 mark](b)∠ROQ dan ∠QOS ialah sudut …∠ROQ and ∠QOS are …Show answerHide answer
supplementary angles
They are adjacent angles on the straight line RS, so they add up to 180°: supplementary angles.
[1 mark](c)Cari nilai y.Find the value of y.
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For the teacher: Applying, medium difficulty, Chapter 8, standard 8.2
Textbook p. 187
24
Question 24
Carta palang dalam Rajah 7 menunjukkan bilangan rumah mengikut jenis yang dijual oleh sebuah syarikat pemaju perumahan pada bulan Jun.The bar chart in Diagram 7 shows the number of houses by type sold by a housing developer in June.
Rajah 7Diagram 7
[1 mark](a)Jenis rumah yang manakah paling banyak dijual?Which type of house was sold the most?Show answerHide answer
Terrace
The terrace bar is the tallest (18 houses).
[1 mark](b)Hitung jumlah rumah yang dijual pada bulan Jun.Calculate the total number of houses sold in June.
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[1 mark](c)Hitung peratusan rumah teres yang dijual.Calculate the percentage of terrace houses sold.
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[1 mark](d)Data itu akan diwakili dengan carta pai. Hitung sudut sektor bagi pangsapuri.The data will be represented by a pie chart. Calculate the angle of the sector for apartments.
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For the teacher: Applying, low difficulty, Chapter 12, standard 12.1
Textbook p. 276
25
Question 25
Rajah 8 menunjukkan sebuah kekuda bumbung PQR berbentuk segi tiga sama kaki dengan PQ = PR. PM ialah tiang tegak dan M ialah titik tengah QR.Diagram 8 shows a roof truss PQR in the shape of an isosceles triangle with PQ = PR. PM is a vertical post and M is the midpoint of QR.
Rajah 8Diagram 8
[1 mark](a)Namakan hipotenus bagi segi tiga PQM.Name the hypotenuse of triangle PQM.Show answerHide answer
PQ
The hypotenuse is the side opposite the right angle at M, which is PQ.
[2 marks](b)Hitung panjang, dalam m, kasau PQ.Calculate the length, in m, of the rafter PQ.
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[1 mark](c)Rumah itu memerlukan 9 kekuda yang sama. Hitung jumlah panjang, dalam m, kayu bagi semua kasau PQ dan PR.The house needs 9 identical trusses. Calculate the total length, in m, of timber for all the rafters PQ and PR.
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For the teacher: Applying, medium difficulty, Chapter 13, standard 13.1
Textbook p. 297
Bahagian CSection C
60 marks
Jawab semua soalan.Answer all questions.
26
Question 26
Encik Rahman sedang membina sebuah bilik tambahan di rumahnya.Encik Rahman is building an extra room in his house.
[2 marks](a)Konkrit untuk lantai bilik itu dibancuh dengan simen, pasir dan batu kerikil mengikut nisbah isi padu 1 : 2 : 4. Hitung isi padu, dalam m3, pasir yang diperlukan untuk menghasilkan 2.8 m3 konkrit.The concrete for the floor of the room is mixed from cement, sand and gravel in the volume ratio 1 : 2 : 4. Calculate the volume, in m3, of sand needed to make 2.8 m3 of concrete.
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[3 marks](b)Kedai A menjual sekotak 12 keping jubin dengan harga RM54. Kedai B menjual sekotak 15 keping jubin yang sama dengan harga RM63. Kedai manakah yang menawarkan harga yang lebih murah bagi sekeping jubin? Tunjukkan pengiraan anda.Shop A sells a box of 12 tiles for RM54. Shop B sells a box of 15 of the same tiles for RM63. Which shop offers the cheaper price for one tile? Show your calculation.
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[3 marks](c)Encik Rahman menggunakan 3 liter cat untuk mengecat 36 m2 dinding. Dengan kadaran yang sama, berapakah isi padu, dalam liter, cat yang diperlukan untuk mengecat 102 m2 dinding?Encik Rahman uses 3 litres of paint to paint 36 m2 of wall. In the same proportion, what volume, in litres, of paint is needed to paint 102 m2 of wall?
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For the teacher: Applying, low difficulty, Chapter 4, standard 4.4
Textbook p. 89
27
Question 27
Seorang arkitek menggunakan beberapa bentuk poligon dalam reka bentuk sebuah rumah.An architect uses several polygons in the design of a house.
Rajah 9Diagram 9
Rajah 10Diagram 10
Rajah 11Diagram 11
[1 mark](a)Rajah 9 menunjukkan sekeping jubin lantai. Namakan poligon itu.Diagram 9 shows a floor tile. Name the polygon.Show answerHide answer
Hexagon
The tile has 6 sides, so it is a hexagon.
[1 mark](b)Berapakah bilangan pepenjuru bagi poligon dalam Rajah 9?How many diagonals does the polygon in Diagram 9 have?
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Each vertex joins to 3 non-adjacent vertices: 6 × 3 ÷ 2 = 9 diagonals.
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[2 marks](c)Rajah 10 menunjukkan bahagian hadapan bumbung, PQR, yang berbentuk segi tiga sama kaki dengan PQ = PR. Cari nilai x.Diagram 10 shows the front part of a roof, PQR, which is an isosceles triangle with PQ = PR. Find the value of x.
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[4 marks](d)Rajah 11 menunjukkan sebuah tingkap berbentuk lelayang PQRS. RST ialah garis lurus. Cari nilai (i) y, (ii) ∠PST.Diagram 11 shows a kite-shaped window PQRS. RST is a straight line. Find the value of (i) y, (ii) ∠PST.
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For the teacher: Applying, low difficulty, Chapter 9, standard 9.2
Textbook p. 209
28
Question 28
Puan Siti sedang menghias rumah barunya.Puan Siti is decorating her new house.
[2 marks](a)Senaraikan semua faktor sepunya bagi 24 dan 36.List all the common factors of 24 and 36.
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[2 marks](b)Cari gandaan sepunya terkecil (GSTK) bagi 12, 18 dan 30.Find the lowest common multiple (LCM) of 12, 18 and 30.
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[2 marks](c)Puan Siti mempunyai 84 keping jubin merah, 126 keping jubin biru dan 210 keping jubin putih. Dia mahu menyusun semua jubin itu kepada beberapa panel hiasan yang serupa supaya setiap panel mempunyai bilangan jubin setiap warna yang sama dan tiada jubin berbaki. Berapakah bilangan maksimum panel yang boleh dibuat?Puan Siti has 84 red tiles, 126 blue tiles and 210 white tiles. She wants to arrange all the tiles into identical decorative panels so that each panel has the same number of tiles of each colour and no tiles are left over. What is the maximum number of panels she can make?
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[1 mark](d)Berapakah bilangan jubin dalam setiap panel?How many tiles are there in each panel?
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[2 marks](e)Tiga lampu hiasan di ruang tamu berkelip setiap 12 saat, 15 saat dan 20 saat. Ketiga-tiga lampu berkelip serentak pada jam 8:00:00 malam. Pada pukul berapakah ketiga-tiga lampu itu berkelip serentak sekali lagi?Three decorative lights in the living room blink every 12 seconds, 15 seconds and 20 seconds. All three lights blink together at 8:00:00 p.m. At what time do the three lights next blink together?
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[1 mark](f)Berapa kalikah ketiga-tiga lampu itu berkelip serentak selepas 8:00:00 malam hingga 8:10:00 malam?How many times do the three lights blink together after 8:00:00 p.m. up to 8:10:00 p.m.?
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For the teacher: Applying, medium difficulty, Chapter 2, standard 2.2
Textbook p. 42
29
Question 29
[1 mark](a)Ketinggian, h m, siling sebuah rumah mestilah sekurang-kurangnya 2.6 m. Tulis satu ketaksamaan bagi h.The height, h m, of the ceiling of a house must be at least 2.6 m. Write an inequality for h.
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[1 mark](b)Nyatakan ketaksamaan linear yang diwakili oleh garis nombor dalam Rajah 12.State the linear inequality represented by the number line in Diagram 12.Rajah 12Diagram 12
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[2 marks](c)Selesaikan ketaksamaan linear 3 − 2x < 11.Solve the linear inequality 3 − 2x < 11.
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[3 marks](d)Selesaikan ketaksamaan linear serentak 2x − 1 ≥ 5 dan x + 4 < 12. Seterusnya, senaraikan semua integer x yang memuaskan kedua-dua ketaksamaan itu.Solve the simultaneous linear inequalities 2x − 1 ≥ 5 and x + 4 < 12. Hence, list all the integers x that satisfy both inequalities.
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[3 marks](e)Sebuah keluarga mempunyai bajet tidak lebih daripada RM850 untuk membeli sebuah sofa berharga RM460 dan beberapa biji kusyen berharga RM35 sebiji. Hitung bilangan maksimum kusyen yang boleh dibeli.A family has a budget of not more than RM850 to buy a sofa costing RM460 and some cushions costing RM35 each. Calculate the maximum number of cushions they can buy.
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For the teacher: Applying, low difficulty, Chapter 7, standard 7.2
Textbook p. 163
30
Question 30
[2 marks](a)Dengan menggunakan pemfaktoran perdana, tentukan sama ada 2 025 ialah kuasa dua sempurna.Using prime factorisation, determine whether 2 025 is a perfect square.
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[2 marks](b)Hitung nilai bagi (∛(−64) + √1.44)2.Calculate the value of (∛(−64) + √1.44)2.
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[3 marks](c)Sebuah laman rumah berbentuk segi empat sama mempunyai luas 441 m2. Laman itu akan dipagar di sekelilingnya kecuali bahagian pintu pagar selebar 3 m. Hitung panjang, dalam m, pagar yang diperlukan.A square courtyard of a house has an area of 441 m2. A fence will be built around it except for a gate 3 m wide. Calculate the length, in m, of fence needed.
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[2 marks](d)Encik Lim mahu memasang sebuah tangki air berbentuk kubus di atas siling rumahnya. Tangki itu mesti dapat menyimpan sekurang-kurangnya 1 500 liter air. Hitung panjang sisi minimum, dalam m, tangki itu. Beri jawapan betul kepada dua tempat perpuluhan. (1 m3 = 1 000 liter)Encik Lim wants to install a cube-shaped water tank above the ceiling of his house. The tank must hold at least 1 500 litres of water. Calculate the minimum side length, in m, of the tank. Give your answer correct to two decimal places. (1 m3 = 1 000 litres)
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[3 marks](e)Sebuah kedai menjual tangki kubus dengan panjang sisi dalam 1.0 m, 1.1 m dan 1.2 m. Encik Lim mahu membeli tangki yang paling kecil yang memenuhi keperluannya. Tangki yang manakah patut dibeli? Berikan justifikasi anda.A shop sells cube-shaped tanks with inner side lengths 1.0 m, 1.1 m and 1.2 m. Encik Lim wants to buy the smallest tank that meets his needs. Which tank should he buy? Justify your answer.
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For the teacher: Evaluating, high difficulty, Chapter 3, standard 3.2
Textbook p. 68
31
Question 31
Rumah-rumah di Jalan Mawar bernombor 1 hingga 12. Gambar rajah Venn dalam Rajah 13 menunjukkan set semesta ξ = {nombor rumah di Jalan Mawar}, set E = {rumah bernombor genap} dan set S = {rumah yang memasang panel solar}.The houses on Jalan Mawar are numbered 1 to 12. The Venn diagram in Diagram 13 shows the universal set ξ = {house numbers on Jalan Mawar}, set E = {even-numbered houses} and set S = {houses with solar panels}.
Rajah 13Diagram 13
[1 mark](a)Senaraikan semua unsur bagi set E'.List all the elements of set E'.
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[1 mark](b)Cari n(S).Find n(S).
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[1 mark](c)Antara berikut, yang manakah menghubungkan set S dan set E dengan betul?Which of the following correctly relates set S and set E?Show answerHide answer
S ⊂ E
Every element of S (4, 8, 12) is also in E, but E has elements not in S, so S is a subset of E.
[1 mark](d)Perihalkan set S dengan menggunakan tatatanda pembina set.Describe set S using set builder notation.
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[2 marks](e)Pemaju mahu memilih tepat lima buah rumah untuk dipasang lampu pagar automatik. Diberi L = {rumah yang dipilih} dengan keadaan S ⊂ L dan L ⊂ E. Bina satu set L yang mungkin.The developer wants to choose exactly five houses to install automatic gate lights. Given L = {houses chosen} such that S ⊂ L and L ⊂ E. Construct one possible set L.
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S ⊂ L means 4, 8 and 12 must be in L; L ⊂ E means every other element must be even. Any two of 2, 6 and 10 complete the five houses, so there are 3 possible answers.
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[3 marks](f)Pemilik rumah nombor 4 boleh memilih aksesori daripada set A = {penapis air, kamera CCTV, kanopi}. Setiap pilihan yang mungkin ialah subset bagi A. Senaraikan semua subset bagi A dan nyatakan bilangannya.The owner of house number 4 can choose accessories from set A = {water filter, CCTV camera, awning}. Each possible choice is a subset of A. List all the subsets of A and state how many there are.
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[3 marks](g)Diberi P = {huruf dalam perkataan 'RAMAI'} dan Q = {huruf dalam perkataan 'MARI'}. Aina berkata, "P ≠ Q kerana perkataan RAMAI mempunyai 5 huruf tetapi perkataan MARI hanya mempunyai 4 huruf." Adakah anda bersetuju dengan Aina? Beri justifikasi anda.Given P = {letters in the word 'RAMAI'} and Q = {letters in the word 'MARI'}. Aina says, "P ≠ Q because the word RAMAI has 5 letters but the word MARI has only 4 letters." Do you agree with Aina? Justify your answer.
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For the teacher: Creating, high difficulty, Chapter 11, standard 11.2
