Ujian Akhir Sesi AkademikEnd of Academic Session Test
MatematikMathematics
Tingkatan 3, 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 yang terbaik.Answer all questions. Each question is followed by four options, A, B, C and D. Choose the best answer.
1
Question 1
Permudahkan p6 × p−2 ÷ p3.Simplify p6 × p−2 ÷ p3.
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B
Add the indices when multiplying and subtract when dividing: 6 + (−2) − 3 = 1, so the answer is p¹ = p.
For the teacher: Applying, low difficulty, Chapter 1, standard 1.2
Textbook p. 12
2
Question 2
Hitung nilai bagi 493/2.Calculate the value of 493/2.
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D
493/2 = (√49)³ = 7³ = 343. The denominator 2 of the index means square root and the numerator 3 means cube. (21 = 7 × 3 and 73.5 = 49 × 1.5 come from treating the index as multiplication.)
For the teacher: Understanding, low difficulty, Chapter 1, standard 1.2
Textbook p. 17
3
Question 3
Diberi 4x+1 = 8x−1. Hitung nilai x.Given 4x+1 = 8x−1. Calculate the value of x.
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C
Write both sides with base 2: 22(x+1) = 23(x−1), so 2x + 2 = 3x − 3 and x = 5. Check: 4⁶ = 4 096 = 8⁴.
For the teacher: Applying, high difficulty, Chapter 1, standard 1.2
Textbook p. 22
4
Question 4
Bundarkan 0.0040375 kepada tiga angka bererti.Round off 0.0040375 to three significant figures.
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A
The significant figures start at the first non-zero digit: 4, 0, 3, 7, 5. The fourth significant figure is 7, so the third (3) rounds up to 4: 0.00404.
For the teacher: Applying, low difficulty, Chapter 2, standard 2.1
Textbook p. 34
5
Question 5
Nyatakan (3.6 × 105) ÷ (9 × 10−3) dalam bentuk piawai.Express (3.6 × 105) ÷ (9 × 10−3) in standard form.
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B
3.6 ÷ 9 = 0.4 and 105 ÷ 10−3 = 108, giving 0.4 × 108. This is not standard form because 0.4 is less than 1, so write 4 × 107.
For the teacher: Applying, medium difficulty, Chapter 2, standard 2.2
Textbook p. 41
6
Question 6
Jisim seekor semut ialah 4 × 10−3 g. Berapakah bilangan semut yang jisim keseluruhannya 1 kg?The mass of one ant is 4 × 10−3 g. How many ants have a total mass of 1 kg?
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D
1 kg = 103 g. Number of ants = 103 ÷ (4 × 10−3) = 0.25 × 106 = 2.5 × 105.
For the teacher: Applying, high difficulty, Chapter 2, standard 2.2
Textbook p. 45
7
Question 7
Encik Daud menyimpan RM8 000 dalam akaun yang membayar faedah mudah 3.5% setahun. Berapakah faedah yang diperolehnya selepas 4 tahun?Encik Daud saves RM8 000 in an account that pays 3.5% per annum simple interest. How much interest does he earn after 4 years?
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C
I = Prn = 8 000 × 0.035 × 4 = RM1 120. RM9 120 is the total amount, not the interest.
For the teacher: Applying, low difficulty, Chapter 3, standard 3.1
Textbook p. 57
8
Question 8
RM5 000 disimpan dengan kadar faedah 6% setahun, dikompaunkan setiap setengah tahun. Berapakah jumlah wang selepas 1 tahun?RM5 000 is saved at an interest rate of 6% per annum, compounded half-yearly. What is the total amount after 1 year?
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B
Half-yearly: rate 3% per period, 2 periods. MV = 5 000 × (1.03)² = RM5 304.50. RM5 300.00 is simple interest for the year.
For the teacher: Applying, medium difficulty, Chapter 3, standard 3.1
Textbook p. 62
9
Question 9
Jarak antara dua pekan pada peta berskala 1 : 50 000 ialah 6.4 cm. Hitung jarak sebenar, dalam km.The distance between two towns on a map drawn to a scale of 1 : 50 000 is 6.4 cm. Calculate the actual distance, in km.
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A
6.4 × 50 000 = 320 000 cm = 3 200 m = 3.2 km.
For the teacher: Applying, low difficulty, Chapter 4, standard 4.1
Textbook p. 97
10
Question 10
Sebuah ladang pada pelan berskala 1 : 200 000 mempunyai luas 12 cm². Berapakah luas sebenar ladang itu, dalam km²?A plantation on a plan drawn to a scale of 1 : 200 000 has an area of 12 cm². What is the actual area of the plantation, in km²?
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D
1 cm represents 200 000 cm = 2 km, so 1 cm² represents 4 km². Area = 12 × 4 = 48 km². (Areas use the square of the scale: do not multiply by 2 only.)
For the teacher: Applying, medium difficulty, Chapter 4, standard 4.1
Textbook p. 101
11
Question 11
Rajah 1 menunjukkan segi tiga bersudut tegak KLM. Cari nilai tan ∠KML.Diagram 1 shows a right-angled triangle KLM. Find the value of tan ∠KML.
Rajah 1Diagram 1
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A
For ∠KML, the opposite side is KL = 8 and the adjacent side is LM = 15, so tan ∠KML = 8/15. (8/17 is sin, 15/17 is cos.)
For the teacher: Understanding, low difficulty, Chapter 5, standard 5.1
Textbook p. 110
12
Question 12
Diberi sin θ = 5/13, dengan θ ialah sudut tirus. Cari nilai tan θ.Given sin θ = 5/13, where θ is an acute angle. Find the value of tan θ.
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C
Draw a right-angled triangle with opposite 5 and hypotenuse 13. The adjacent side is √(13² − 5²) = 12, so tan θ = opposite/adjacent = 5/12.
For the teacher: Applying, medium difficulty, Chapter 5, standard 5.1
Textbook p. 114
13
Question 13
Seorang murid berdiri di atas tanah yang rata sejauh 40 m dari kaki sebuah menara. Sudut dongakan puncak menara dari tempat dia berdiri ialah 35°. Hitung tinggi menara itu, dalam m, betul kepada dua tempat perpuluhan.A student stands on level ground 40 m from the foot of a tower. The angle of elevation of the top of the tower from where she stands is 35°. Calculate the height of the tower, in m, correct to two decimal places.
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B
Height is opposite the angle and 40 m is adjacent: h = 40 × tan 35° = 28.01 m. (22.94 uses sin, 32.77 uses cos and 57.13 divides by tan.)
For the teacher: Applying, high difficulty, Chapter 5, standard 5.1
Textbook p. 122
14
Question 14
Dalam Rajah 2, O ialah pusat bulatan. Cari nilai x.In Diagram 2, O is the centre of the circle. Find the value of x.
Rajah 2Diagram 2
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C
The angle at the circumference is half the angle at the centre on the same arc PQ: x = 148° ÷ 2 = 74°.
For the teacher: Applying, low difficulty, Chapter 6, standard 6.1
Textbook p. 135
15
Question 15
Dalam Rajah 3, PAQ ialah tangen kepada bulatan di A. ABCD ialah sisi empat kitaran. Cari ∠DBC.In Diagram 3, PAQ is a tangent to the circle at A. ABCD is a cyclic quadrilateral. Find ∠DBC.
Rajah 3Diagram 3
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D
Angle in the alternate segment: ∠ABD = ∠PAD = 58°. Opposite angles of a cyclic quadrilateral: ∠ABC = 180° − 95° = 85°. So ∠DBC = 85° − 58° = 27°.
For the teacher: Analysing, high difficulty, Chapter 6, standard 6.3
Textbook p. 156
16
Question 16
Sebuah kon berjejari tapak 3 cm dan tinggi 4 cm diletakkan dengan tapaknya pada satah mengufuk. Apakah luas unjuran ortogon kon itu pada satah mencancang?A cone of base radius 3 cm and height 4 cm is placed with its base on a horizontal plane. What is the area of the orthogonal projection of the cone on a vertical plane?
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A
On a vertical plane the projection is an isosceles triangle with base 2 × 3 = 6 cm and height 4 cm. Area = ½ × 6 × 4 = 12 cm². (The projection on a horizontal plane would be a circle.)
For the teacher: Applying, low difficulty, Chapter 7, standard 7.1
Textbook p. 174
17
Question 17
Dua batang paip air lurus yang selari terletak 14 m antara satu sama lain. Sebuah pili bomba mesti terletak sama jauh daripada kedua-dua paip itu. Antara berikut, yang manakah lokus kedudukan pili bomba itu?Two straight water pipes run parallel and are 14 m apart. A fire hydrant must be placed at the same distance from both pipes. Which of the following is the locus of the hydrant's position?
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C
The locus of points equidistant from two parallel lines is a line parallel to both, halfway between them: 14 ÷ 2 = 7 m from each pipe.
For the teacher: Understanding, low difficulty, Chapter 8, standard 8.2
Textbook p. 209
18
Question 18
Cari kecerunan bagi garis lurus 5x − 2y = 10.Find the gradient of the straight line 5x − 2y = 10.
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B
Rearrange to y = mx + c: −2y = −5x + 10, so y = (5/2)x − 5. The gradient is 5/2 and the y-intercept is −5.
For the teacher: Understanding, low difficulty, Chapter 9, standard 9.1
Textbook p. 232
19
Question 19
Garis lurus L selari dengan garis y = 3x − 2 dan melalui titik (2, 7). Apakah persamaan L?The straight line L is parallel to the line y = 3x − 2 and passes through the point (2, 7). What is the equation of L?
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D
Parallel lines have the same gradient, m = 3. Substitute (2, 7) into y = 3x + c: 7 = 6 + c, so c = 1 and y = 3x + 1.
For the teacher: Applying, medium difficulty, Chapter 9, standard 9.1
Textbook p. 239
20
Question 20
Cari koordinat titik persilangan bagi garis y = 2x − 3 dan 3x + 2y = 22.Find the coordinates of the point of intersection of the lines y = 2x − 3 and 3x + 2y = 22.
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A
Substitute y = 2x − 3 into 3x + 2y = 22: 3x + 4x − 6 = 22, so 7x = 28 and x = 4, y = 5. Check: 3(4) + 2(5) = 22.
For the teacher: Applying, high difficulty, Chapter 9, standard 9.1
Textbook p. 245
Bahagian BSection B
20 marks
Jawab semua soalan. Tunjukkan langkah-langkah penting dalam kerja mengira anda.Answer all questions. Show the important steps in your working.
21
Question 21
[2 marks](a)Permudahkan (2m3n−2)3 ÷ 4m5n−3. Nyatakan jawapan dalam indeks positif.Simplify (2m3n−2)3 ÷ 4m5n−3. Give the answer with positive indices.
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[1 mark](b)Hitung nilai bagi (18)−2/3.Calculate the value of (18)−2/3.
For the teacher: Applying, low difficulty, Chapter 1, standard 1.2
Textbook p. 20
22
Question 22
[1 mark](a)Berapakah bilangan angka bererti bagi 0.03070?How many significant figures does 0.03070 have?Show answerHide answer
4
The leading zeros are not significant. The significant figures are 3, 0, 7, 0: the zero between 3 and 7 and the final zero both count, so there are 4.
[1 mark](b)Bundarkan 0.0070496 kepada tiga angka bererti.Round off 0.0070496 to three significant figures.
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[2 marks](c)Hitung 5.2 × 10−3 + 3.8 × 10−4. Nyatakan jawapan dalam bentuk piawai.Calculate 5.2 × 10−3 + 3.8 × 10−4. Give the answer in standard form.
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For the teacher: Understanding, low difficulty, Chapter 2, standard 2.1
Textbook p. 36
23
Question 23
Dalam Rajah 4, O ialah pusat bulatan. TA dan TB ialah tangen kepada bulatan di A dan B.In Diagram 4, O is the centre of the circle. TA and TB are tangents to the circle at A and B.
Rajah 4Diagram 4
[1 mark](a)Cari ∠AOB.Find ∠AOB.
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[1 mark](b)Cari ∠ACB.Find ∠ACB.
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[2 marks](c)Hitung panjang OA, dalam cm, betul kepada dua tempat perpuluhan.Calculate the length of OA, in cm, correct to two decimal places.
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For the teacher: Applying, medium difficulty, Chapter 6, standard 6.3
Textbook p. 158
24
Question 24
[2 marks](a)Tanpa menggunakan kalkulator, cari nilai bagi sin 30° × cos 60° + tan 45°.Without using a calculator, find the value of sin 30° × cos 60° + tan 45°.
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[2 marks](b)Rajah 5 menunjukkan sebuah tanjakan sepanjang 9 m yang naik setinggi 2.1 m. Hitung sudut kecondongan, θ, betul kepada satu tempat perpuluhan.Diagram 5 shows a ramp 9 m long that rises 2.1 m. Calculate the angle of inclination, θ, correct to one decimal place.Rajah 5Diagram 5
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For the teacher: Applying, medium difficulty, Chapter 5, standard 5.1
Textbook p. 118
25
Question 25
Garis lurus L melalui titik (−2, 5) dan (4, −1).The straight line L passes through the points (−2, 5) and (4, −1).
[1 mark](a)Cari kecerunan L.Find the gradient of L.
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[1 mark](b)Cari persamaan L.Find the equation of L.
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[1 mark](c)Tandakan BENAR atau PALSU: Titik (7, −3) terletak pada L.Mark TRUE or FALSE: The point (7, −3) lies on L.Show answerHide answer
False
Substitute x = 7: y = −7 + 3 = −4, not −3. The point does not satisfy the equation, so it is not on L.
[1 mark](d)Cari koordinat titik persilangan L dengan garis y = 2x − 6.Find the coordinates of the point of intersection of L and the line y = 2x − 6.
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For the teacher: Applying, high difficulty, Chapter 9, standard 9.1
Textbook p. 242
Bahagian CSection C
60 marks
Jawab semua soalan. Tunjukkan langkah-langkah penting dalam kerja mengira anda.Answer all questions. Show the important steps in your working.
26
Question 26
Encik Hakim mempunyai RM20 000 untuk disimpan selama 3 tahun. Bank A menawarkan faedah mudah 4.5% setahun. Bank B menawarkan kadar faedah 4% setahun yang dikompaunkan setiap setengah tahun.Encik Hakim has RM20 000 to save for 3 years. Bank A offers 4.5% per annum simple interest. Bank B offers an interest rate of 4% per annum compounded half-yearly.
[2 marks](a)Hitung jumlah faedah yang diperoleh jika dia menyimpan di Bank A.Calculate the total interest he earns if he saves in Bank A.
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[3 marks](b)Hitung jumlah wang di Bank B pada akhir 3 tahun.Calculate the total amount in Bank B at the end of 3 years.
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[2 marks](c)Bank manakah yang memberi pulangan yang lebih tinggi? Berikan alasan dengan menyatakan perbezaan faedah.Which bank gives the higher return? Justify your answer by stating the difference in interest.
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[3 marks](d)Encik Hakim kemudian meminjam RM30 000 untuk membeli kereta pada kadar faedah rata 5% setahun selama 4 tahun. Hitung jumlah faedah, jumlah bayaran balik dan ansuran bulanan.Encik Hakim later borrows RM30 000 to buy a car at a flat interest rate of 5% per annum for 4 years. Calculate the total interest, the total repayment and the monthly instalment.
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For the teacher: Evaluating, low difficulty, Chapter 3, standard 3.1
Textbook p. 66
27
Question 27
Rajah 6 menunjukkan segi empat selari ABCD pada suatu satah Cartes.Diagram 6 shows a parallelogram ABCD on a Cartesian plane.
Rajah 6Diagram 6
[2 marks](a)Cari kecerunan AB dan kecerunan DC. Seterusnya, nyatakan hubungan antara AB dengan DC.Find the gradient of AB and the gradient of DC. Hence state the relationship between AB and DC.
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[2 marks](b)Cari persamaan garis lurus AD.Find the equation of the straight line AD.
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[2 marks](c)Cari persamaan garis lurus BD.Find the equation of the straight line BD.
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[4 marks](d)Garis lurus AC ialah y = x. Dengan menyelesaikan persamaan serentak, cari koordinat titik persilangan AC dan BD. Seterusnya, tunjukkan bahawa pepenjuru-pepenjuru ABCD saling membahagi dua sama.The straight line AC is y = x. By solving simultaneous equations, find the coordinates of the point of intersection of AC and BD. Hence show that the diagonals of ABCD bisect each other.
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For the teacher: Analysing, low difficulty, Chapter 9, standard 9.1
Textbook p. 246
28
Question 28
Rajah 7 menunjukkan sebuah bangunan ST setinggi 18 m yang berdiri tegak di atas tanah mengufuk. R dan U ialah dua titik di atas tanah itu. SR = 24 m dan sudut dongakan T dari U ialah 50°.Diagram 7 shows a building ST, 18 m high, standing vertically on horizontal ground. R and U are two points on the ground. SR = 24 m and the angle of elevation of T from U is 50°.
Rajah 7Diagram 7
[2 marks](a)Hitung sudut dongakan T dari R, betul kepada satu tempat perpuluhan.Calculate the angle of elevation of T from R, correct to one decimal place.
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[2 marks](b)Hitung panjang SU, dalam m, betul kepada dua tempat perpuluhan.Calculate the length of SU, in m, correct to two decimal places.
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[1 mark](c)Hitung jarak UR, dalam m.Calculate the distance UR, in m.
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[3 marks](d)Sebatang tiang pemancar akan didirikan tegak di atas bangunan itu supaya sudut dongakan puncak tiang dari R ialah 50°. Hitung tinggi tiang itu, dalam m.A transmission mast is to be fixed vertically on top of the building so that the angle of elevation of the top of the mast from R is 50°. Calculate the height of the mast, in m.
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[2 marks](e)Hitung sudut dongakan puncak tiang itu dari U, betul kepada satu tempat perpuluhan.Calculate the angle of elevation of the top of the mast from U, correct to one decimal place.
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For the teacher: Analysing, medium difficulty, Chapter 5, standard 5.1
Textbook p. 124
29
Question 29
Rajah 8 menunjukkan sebuah pepejal yang terdiri daripada dua kuboid. Tapak pepejal itu terletak pada satah mengufuk.Diagram 8 shows a solid made up of two cuboids. The base of the solid rests on a horizontal plane.
Rajah 8Diagram 8
[2 marks](a)Lakarkan pelan pepejal itu dan tandakan ukurannya.Sketch the plan of the solid and mark its dimensions.
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[2 marks](b)Lakarkan dongakan depan pepejal itu seperti yang dilihat dari F dan tandakan ukurannya.Sketch the front elevation of the solid as viewed from F and mark its dimensions.
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[3 marks](c)Hitung isi padu pepejal itu, dalam cm³.Calculate the volume of the solid, in cm³.
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[3 marks](d)Kuboid kecil itu dialihkan ke separuh kanan kuboid besar dan pepejal yang baharu terbentuk. Hamid berkata pelannya tidak sama dengan pelan asal. Adakah Hamid betul? Nyatakan juga sama ada dongakan depan berubah.The small cuboid is moved onto the right half of the large cuboid to form a new solid. Hamid says its plan is different from the original plan. Is Hamid correct? State also whether the front elevation changes.
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For the teacher: Evaluating, medium difficulty, Chapter 7, standard 7.2
Textbook p. 188
30
Question 30
Rajah 9 menunjukkan pelan sebuah dewan sekolah yang dilukis dengan skala 1 : 250.Diagram 9 shows the plan of a school hall drawn to a scale of 1 : 250.
Rajah 9Diagram 9
[2 marks](a)Hitung panjang dan lebar sebenar dewan itu, dalam m.Calculate the actual length and width of the hall, in m.
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[2 marks](b)Hitung luas sebenar lantai dewan itu, dalam m².Calculate the actual floor area of the hall, in m².
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[3 marks](c)Pihak sekolah ingin melukis semula pelan dewan itu pada sehelai kertas yang ruang lukisannya 25 cm × 18 cm. Skala yang tersedia ialah 1 : 50, 1 : 75, 1 : 100 dan 1 : 200. Skala manakah yang paling besar yang masih muat pada kertas itu? Tunjukkan pengiraan anda.The school wants to redraw the plan of the hall on a sheet of paper with a drawing space of 25 cm × 18 cm. The available scales are 1 : 50, 1 : 75, 1 : 100 and 1 : 200. Which is the largest scale that still fits on the paper? Show your calculations.
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[3 marks](d)Pada peta berskala 1 : 300 000, jarak antara sekolah itu dengan bandar ialah 7.5 cm. Sebuah bas mengambil masa 30 minit untuk perjalanan itu. Hitung purata laju bas itu, dalam km/j.On a map drawn to a scale of 1 : 300 000, the distance from the school to the town is 7.5 cm. A bus takes 30 minutes for the journey. Calculate the average speed of the bus, in km/h.
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For the teacher: Evaluating, low difficulty, Chapter 4, standard 4.1
Textbook p. 99
31
Question 31
Rajah 10 menunjukkan sebuah taman berbentuk segi empat tepat ABCD dengan AB = 12 m dan BC = 8 m. Sebuah lampu taman akan dipasang pada titik P di dalam taman itu.Diagram 10 shows a rectangular garden ABCD with AB = 12 m and BC = 8 m. A garden lamp is to be fixed at a point P inside the garden.
Rajah 10Diagram 10
[2 marks](a)P sama jauh dari AD dan BC. Huraikan lokus P.P is equidistant from AD and BC. Describe the locus of P.
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[2 marks](b)P juga berjarak 7.5 m dari A. Huraikan lokus P bagi syarat ini.P is also 7.5 m from A. Describe the locus of P for this condition.
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[3 marks](c)Hitung jarak P dari AB, dalam m.Calculate the distance of P from AB, in m.
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[3 marks](d)Pihak pengurusan mahu lampu itu lebih dekat dengan AB daripada DC. Adakah kedudukan P memenuhi syarat itu? Berikan alasan anda.The management wants the lamp to be nearer to AB than to DC. Does the position of P meet this requirement? Give your reason.
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For the teacher: Creating, high difficulty, Chapter 8, standard 8.2
Textbook p. 214
Test specification (JSU)
Chapter
Remembering
Understanding
Applying
Analysing
Evaluating
Creating
Items
marks
1. Indices
–
1 (1)
3 (6)
–
–
–
4
7
2. Standard Form
–
1 (4)
3 (3)
–
–
–
4
7
3. Consumer Mathematics: Savings and Investments, Credit and Debt