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Practice paper, not an official KPM paper
50
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
  1. 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.
  2. Jawab semua soalan.Answer all questions.
  3. Tunjukkan langkah-langkah penting dalam kerja mengira anda.Show your working. It may help you to get marks.
  4. Rajah yang mengiringi soalan tidak dilukis mengikut skala kecuali dinyatakan.The diagrams in this paper are not drawn to scale unless stated.
  5. 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

Seorang ahli farmasi menyediakan larutan dengan menghasilkan satu pecahan bagi kepekatan asal sebanyak 2−4. Nyatakan nilai 2−4.A pharmacist prepares a solution using a fraction of the original concentration equal to 2−4. State the value of 2−4.
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B
A negative index means the reciprocal: 2−4 = 1 ÷ 24 = 1/16. The value −8 comes from multiplying 2 by −4, and 1/8 is 2−3.
For the teacher: Understanding, low difficulty, Chapter 1, standard 1.2.5
Textbook p. 14
2

Question 2

Ringkaskan (3m2n−3)2 ÷ (m3n−4).Simplify (3m2n−3)2 ÷ (m3n−4).
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D
(3m2n−3)2 = 9m4n−6. Then 9m4n−6 ÷ m3n−4 = 9m4−3n−6−(−4) = 9mn−2. Option A forgets to square the 3.
For the teacher: Applying, medium difficulty, Chapter 1, standard 1.2.3
Textbook p. 11
3

Question 3

Diberi 23x+1 ÷ 4x−1 = 32. Cari nilai x.Given 23x+1 ÷ 4x−1 = 32. Find the value of x.
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A
Write every term with base 2: 4x−1 = 22x−2 and 32 = 25. Then 23x+1−(2x−2) = 25, so x + 3 = 5 and x = 2. Check: 27 ÷ 4 = 32.
For the teacher: Analysing, high difficulty, Chapter 1, standard 1.2.9
Textbook p. 23
4

Question 4

Panjang sejenis bakteria ialah 0.0000023 m. Ungkapkan panjang itu dalam bentuk piawai.A type of bacterium is 0.0000023 m long. Express the length in standard form.
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C
Move the decimal point 6 places to the right to get 2.3, so the index is −6: 2.3 × 10−6. Option B is not in standard form because 23 is not between 1 and 10.
For the teacher: Remembering, low difficulty, Chapter 2, standard 2.2.1
Textbook p. 37
5

Question 5

Dua buah takungan air masing-masing mengandungi 3.2 × 105 liter dan 4.8 × 104 liter air. Hitung jumlah isi padu air, dalam liter, dan ungkapkan dalam bentuk piawai.Two water reservoirs hold 3.2 × 105 litres and 4.8 × 104 litres of water. Calculate the total volume of water, in litres, in standard form.
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B
Make the powers equal: 4.8 × 104 = 0.48 × 105. Then 3.2 × 105 + 0.48 × 105 = 3.68 × 105. Adding 3.2 and 4.8 straight away ignores the different powers.
For the teacher: Applying, medium difficulty, Chapter 2, standard 2.2.2
Textbook p. 40
6

Question 6

Sebiji tablet vitamin mengandungi 0.0040597 g bahan aktif. Bundarkan 0.0040597 kepada tiga angka bererti.A vitamin tablet contains 0.0040597 g of active ingredient. Round off 0.0040597 to three significant figures.
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D
The zeros before the 4 are not significant. The three significant figures are 4, 0, 5, and the next digit (9) rounds the 5 up to 6: 0.00406.
For the teacher: Understanding, low difficulty, Chapter 2, standard 2.1.1
Textbook p. 34
7

Question 7

Puan Aini mendepositkan RM6 000 dalam akaun yang membayar faedah mudah 3.5% setahun. Hitung faedah yang diterima selepas 18 bulan.Puan Aini deposits RM6 000 in an account that pays simple interest of 3.5% per annum. Calculate the interest earned after 18 months.
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A
I = Prt = 6 000 × 0.035 × (18 ÷ 12) = RM315. RM210 uses t = 1 year, and RM6 315 is the total savings, not the interest.
For the teacher: Applying, low difficulty, Chapter 3, standard 3.1.2
Textbook p. 55
8

Question 8

Encik Ravi mengambil pinjaman RM12 000 untuk membeli sebuah motosikal. Kadar faedah ialah 5% setahun (kadar rata) dan pinjaman itu dibayar dalam masa 3 tahun. Hitung ansuran bulanan.Encik Ravi takes a loan of RM12 000 to buy a motorcycle. The interest rate is 5% per annum (flat rate) and the loan is repaid in 3 years. Calculate the monthly instalment.
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C
Interest = 12 000 × 0.05 × 3 = RM1 800. Total repayment = RM13 800. Monthly instalment = 13 800 ÷ 36 = RM383.33. RM333.33 ignores the interest.
For the teacher: Applying, medium difficulty, Chapter 3, standard 3.2.5
Textbook p. 78
9

Question 9

Skala sebuah peta ialah 1 : 50 000. Jarak antara dua pekan pada peta itu ialah 4.6 cm. Cari jarak sebenar, dalam km, antara dua pekan itu.The scale of a map is 1 : 50 000. The distance between two towns on the map is 4.6 cm. Find the actual distance, in km, between the two towns.
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B
Actual distance = 4.6 × 50 000 = 230 000 cm = 2 300 m = 2.3 km (1 km = 100 000 cm).
For the teacher: Applying, low difficulty, Chapter 4, standard 4.1.3
Textbook p. 93
10

Question 10

Sebidang taman berbentuk segi empat tepat mempunyai luas 72 m2. Taman itu dilukis pada pelan berskala 1 : 200. Berapakah luas taman pada pelan itu?A rectangular garden has an area of 72 m2. The garden is drawn on a plan to the scale 1 : 200. What is the area of the garden on the plan?
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A
Areas change by the square of the scale: 72 m2 = 720 000 cm2, and 720 000 × (1/200)2 = 720 000 ÷ 40 000 = 18 cm2. Dividing by 200 only gives 3 600 cm2.
For the teacher: Analysing, high difficulty, Chapter 4, standard 4.1.5
Textbook p. 101
11

Question 11

Sebatang tangga panjangnya 13 m disandarkan pada dinding. Kaki tangga berada 5 m dari dinding. Jika sudut antara tangga dengan tanah ialah θ, apakah nilai kos θ?A 13 m ladder leans against a wall. The foot of the ladder is 5 m from the wall. If the angle between the ladder and the ground is θ, what is the value of cos θ?
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D
The foot of the ladder (5 m) is the side adjacent to θ, and the ladder (13 m) is the hypotenuse. cos θ = adjacent ÷ hypotenuse = 5/13.
For the teacher: Understanding, low difficulty, Chapter 5, standard 5.1.1
Textbook p. 108
12

Question 12

Seutas tali layang-layang yang panjangnya 40 m membentuk sudut dongakan 35° dengan tanah mengufuk. Tali itu lurus. Hitung tinggi layang-layang itu dari tanah, betul kepada 0.1 m.A kite string 40 m long makes an angle of elevation of 35° with the horizontal ground. The string is straight. Calculate the height of the kite above the ground, correct to 0.1 m.
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C
Height is opposite the angle and the string is the hypotenuse: height = 40 sin 35° = 22.9 m. 32.8 m is 40 cos 35°, 28.0 m is 40 tan 35° and 69.7 m is 40 ÷ sin 35°.
For the teacher: Applying, medium difficulty, Chapter 5, standard 5.1.7
Textbook p. 122
13

Question 13

Diberi 4 tan θ = 3 dengan keadaan θ ialah sudut tirus. Cari nilai sin θ + kos θ.Given 4 tan θ = 3 where θ is an acute angle. Find the value of sin θ + cos θ.
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B
tan θ = 3/4, so take a right-angled triangle with opposite 3 and adjacent 4; the hypotenuse is √(9 + 16) = 5. sin θ = 3/5 and cos θ = 4/5, so the sum is 7/5. (12/25 is the product; 1/5 is the difference.)
For the teacher: Analysing, high difficulty, Chapter 5, standard 5.1.4
Textbook p. 115
14

Question 14

Dalam Rajah 1, O ialah pusat bulatan. Cari nilai x.In Diagram 1, O is the centre of the circle. Find the value of x.
Circle with centre O; A and B on the lower arc with angle AOB 112 degrees; C on the top; x is angle ACB
Rajah 1Diagram 1
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A
The angle at the centre is twice the angle at the circumference subtended by the same arc AB: x = 112° ÷ 2 = 56°. C is on the major arc, so no reflex angle is needed.
For the teacher: Understanding, low difficulty, Chapter 6, standard 6.1.1
Textbook p. 139
15

Question 15

Dalam Rajah 2, PT ialah tangen kepada bulatan berpusat O di T. Jejari bulatan itu ialah 5 m dan OP = 13 m. Hitung panjang PT.In Diagram 2, PT is a tangent to the circle with centre O at T. The radius of the circle is 5 m and OP = 13 m. Calculate the length of PT.
Circle with centre O, radius OT 5 m, tangent TP and OP 13 m
Rajah 2Diagram 2
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C
The tangent is perpendicular to the radius, so ∠OTP = 90°. By Pythagoras, PT = √(132 − 52) = √144 = 12 m. 13.9 m comes from adding 25 instead of subtracting.
For the teacher: Applying, medium difficulty, Chapter 6, standard 6.3.1
Textbook p. 150
16

Question 16

Sebuah pondok taman berbentuk prisma segi tiga yang terletak pada satu permukaan segi empat tepat berukuran 8 m × 5 m. Bumbungnya mempunyai rabung setinggi 2 m yang selari dengan sisi 8 m. Yang manakah menerangkan dongakan apabila dilihat dari satu hujung rabung (menghadap sisi 5 m)?A garden shelter is a triangular prism resting on a rectangular face measuring 8 m × 5 m. Its roof ridge is 2 m high and is parallel to the 8 m side. Which describes the elevation when viewed from one end of the ridge (looking along the 8 m side)?
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D
Looking along the ridge you see the end face, a triangle whose base is the 5 m side and whose height is the 2 m ridge height. The rectangle 8 m × 2 m is the view from the side, and 8 m × 5 m is the plan.
For the teacher: Applying, medium difficulty, Chapter 7, standard 7.1.2
Textbook p. 180
17

Question 17

Dua pagar lurus yang selari dipasang 8 m antara satu sama lain. Seekor kambing bergerak supaya sentiasa sama jarak dari kedua-dua pagar itu. Apakah lokus kambing itu?Two straight parallel fences are 8 m apart. A goat moves so that it is always the same distance from both fences. What is the locus of the goat?
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A
A point equidistant from two parallel lines lies on a straight line parallel to both, halfway between them: 8 ÷ 2 = 4 m from each fence.
For the teacher: Understanding, low difficulty, Chapter 8, standard 8.2.4
Textbook p. 210
18

Question 18

Sebatang jalan lurus pada peta berpetak melalui titik (2, −1) dan (6, 7). Cari kecerunan jalan itu.A straight road on a gridded map passes through the points (2, −1) and (6, 7). Find the gradient of the road.
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B
m = (7 − (−1)) ÷ (6 − 2) = 8 ÷ 4 = 2. Option A turns the fraction upside down, and 4 is only the change in x.
For the teacher: Applying, low difficulty, Chapter 9, standard 9.1.1
Textbook p. 229
19

Question 19

Satu garis lurus mempunyai kecerunan −2 dan melalui titik (3, 4). Cari persamaan garis lurus itu.A straight line has gradient −2 and passes through the point (3, 4). Find the equation of the straight line.
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D
Substitute into y = mx + c: 4 = −2(3) + c, so c = 10. The equation is y = −2x + 10.
For the teacher: Applying, medium difficulty, Chapter 9, standard 9.1.5
Textbook p. 240
20

Question 20

Garis lurus L selari dengan garis 3x + 2y = 7 dan melalui titik (4, 3). Cari pintasan-x bagi L.The straight line L is parallel to the line 3x + 2y = 7 and passes through the point (4, 3). Find the x-intercept of L.
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C
3x + 2y = 7 gives y = −(3/2)x + 7/2, so the gradient is −3/2 and L has the same gradient. Using (4, 3): 3 = −(3/2)(4) + c, so c = 9 and y = −(3/2)x + 9. When y = 0, x = 6. The number 9 is the y-intercept.
For the teacher: Analysing, high difficulty, Chapter 9, standard 9.1.4
Textbook p. 238

Bahagian BSection B

20 marks
Jawab semua soalan.Answer all questions.
21

Question 21

Sebuah makmal hospital mengkaji sel darah merah di bawah mikroskop.A hospital laboratory studies red blood cells under a microscope.
[1 mark] (a)Diameter sebutir sel darah merah ialah 0.0000075 m. Ungkapkan 0.0000075 dalam bentuk piawai.The diameter of a red blood cell is 0.0000075 m. Express 0.0000075 in standard form.
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[3 marks] (b)Sebanyak 8 × 104 sel darah merah disusun bersebelahan dalam satu baris. Hitung jumlah panjang baris itu, dalam m, dan ungkapkan jawapan dalam bentuk piawai.A total of 8 × 104 red blood cells are placed side by side in one row. Calculate the total length of the row, in m, and express the answer in standard form.
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For the teacher: Applying, low difficulty, Chapter 2, standard 2.2.2
Textbook p. 41
22

Question 22

Baki penyata kad kredit Hasnah ialah RM2 650. Bayaran minimum ialah 4% daripada baki penyata atau RM60, mengikut yang lebih besar. Bank mengenakan caj kewangan 15% setahun ke atas baki yang belum dibayar, dikira mengikut bilangan hari ÷ 365.Hasnah's credit card statement balance is RM2 650. The minimum payment is 4% of the statement balance or RM60, whichever is more. The bank charges a finance charge of 15% per annum on the unpaid balance, worked out as the number of days ÷ 365.
[1 mark] (a)Hitung bayaran minimum yang perlu dibuat oleh Hasnah.Calculate the minimum payment that Hasnah must make.
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[3 marks] (b)Hasnah membayar bayaran minimum sahaja. Hitung caj kewangan yang dikenakan ke atas baki yang belum dibayar selama 45 hari.Hasnah pays the minimum payment only. Calculate the finance charge on the unpaid balance for 45 days.
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For the teacher: Applying, medium difficulty, Chapter 3, standard 3.2.3
Textbook p. 76
23

Question 23

Rajah 3 menunjukkan sebuah bulatan berpusat O di tengah-tengah sebuah bulatan jalan. Dua jalan lurus PA dan PB menyentuh bulatan itu di A dan B.Diagram 3 shows a circle with centre O at the middle of a roundabout. Two straight roads PA and PB touch the circle at A and B.
Circle with centre O; tangents PA and PB meeting at P with angle APB 54 degrees; C on the circle
Rajah 3Diagram 3
[1 mark] (a)Nyatakan nilai ∠OAP.State the value of ∠OAP.
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[1 mark] (b)Hitung ∠AOB.Calculate ∠AOB.
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[2 marks] (c)C ialah satu titik pada lilitan bulatan itu pada lengkok major AB. Hitung ∠ACB.C is a point on the circumference on the major arc AB. Calculate ∠ACB.
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For the teacher: Applying, low difficulty, Chapter 6, standard 6.3.2
Textbook p. 152
24

Question 24

Pada peta berpetak, jalan lurus R1 melalui titik A(−1, 3) dan B(3, 11). Satu jalan baharu R2 akan dibina selari dengan R1 dan melalui titik C(2, −5).On a gridded map, the straight road R1 passes through the points A(−1, 3) and B(3, 11). A new road R2 will be built parallel to R1 and passes through the point C(2, −5).
[2 marks] (a)Cari persamaan bagi R1.Find the equation of R1.
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[1 mark] (b)R2 selari dengan R1. Cari persamaan bagi R2.R2 is parallel to R1. Find the equation of R2.
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[1 mark] (c)Titik D(k, 7) terletak pada R2. Cari nilai k.The point D(k, 7) lies on R2. Find the value of k.
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For the teacher: Analysing, high difficulty, Chapter 9, standard 9.1.5
Textbook p. 240
25

Question 25

Rajah 4 menunjukkan sebuah taman segi empat tepat PQRS. Sebatang pokok T akan ditanam dengan keadaan sama jarak dari sisi PQ dan sisi SR, dan berjarak 5 m dari sudut P.Diagram 4 shows a rectangular garden PQRS. A tree T is to be planted so that it is the same distance from sides PQ and SR, and 5 m from corner P.
Rectangle PQRS with PQ 10 m along the bottom and QR 6 m
Rajah 4Diagram 4
[1 mark] (a)Huraikan lokus bagi T yang sama jarak dari PQ dan SR.Describe the locus of T that is equidistant from PQ and SR.
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[1 mark] (b)Huraikan lokus bagi T yang berjarak 5 m dari P.Describe the locus of T that is 5 m from P.
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[2 marks] (c)Hitung jarak, dalam m, pokok itu dari sisi PS.Calculate the distance, in m, of the tree from the side PS.
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For the teacher: Applying, low difficulty, Chapter 8, standard 8.2.6
Textbook p. 214

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

Soalan ini tentang indeks dan pertumbuhan bakteria.This question is about indices and the growth of bacteria.
[2 marks] (a)Ringkaskan (4x3y−2)2 ÷ 2x5y−4.Simplify (4x3y−2)2 ÷ 2x5y−4.
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[2 marks] (b)Nilaikan (278)2/3 × 2−2.Evaluate (278)2/3 × 2−2.
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[3 marks] (c)Bilangan bakteria N dalam satu kultur dengan t sela 20 minit diberi oleh N = 500 × 2t. (i) Hitung bilangan bakteria selepas 2 jam. (ii) Cari bilangan jam yang diambil untuk bilangan bakteria mencapai 256 000.The number of bacteria N in a culture after t intervals of 20 minutes is given by N = 500 × 2t. (i) Calculate the number of bacteria after 2 hours. (ii) Find the number of hours taken for the number of bacteria to reach 256 000.
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[3 marks] (d)Dani mendakwa bahawa 4n+1 − 4n = 4 bagi semua nilai n. Adakah dakwaan Dani betul? Berikan satu bukti.Dani claims that 4n+1 − 4n = 4 for every value of n. Is Dani's claim correct? Give evidence.
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For the teacher: Evaluating, low difficulty, Chapter 1, standard 1.2.9
Textbook p. 22
27

Question 27

Rajah 5 ialah pelan dua buah bilik, A dan B, sebuah rumah pangsa yang dilukis dengan skala 1 : 150.Diagram 5 is a plan of two rooms, A and B, in a flat, drawn to the scale 1 : 150.
Plan of room A, 6.4 cm by 4.0 cm, and room B, 3.2 cm wide, side by side
Rajah 5Diagram 5
[2 marks] (a)Cari ukuran sebenar, dalam m, bilik A.Find the actual measurements, in m, of room A.
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[2 marks] (b)Sebuah meja makan lebarnya 1.2 m. Berapakah lebarnya, dalam cm, pada pelan itu?A dining table is 1.2 m wide. What is its width, in cm, on the plan?
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[3 marks] (c)Luas bilik A pada pelan ialah 25.6 cm2. Hitung luas sebenar, dalam m2, bilik A. Kemudian hitung kos memasang permaidani pada harga RM38 setiap m2.The area of room A on the plan is 25.6 cm2. Calculate the actual area, in m2, of room A. Then calculate the cost of laying carpet at RM38 per m2.
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[3 marks] (d)Wei Ming ingin melukis bilik A semula pada sehelai kertas supaya lukisan itu muat dalam segi empat tepat berukuran 25 cm × 16 cm. Dia memilih satu daripada skala 1 : 20, 1 : 25, 1 : 30, 1 : 40, 1 : 50 dan 1 : 100. Skala yang manakah menghasilkan lukisan terbesar yang muat? Tunjukkan pengiraan anda.Wei Ming wants to redraw room A on a sheet of paper so that the drawing fits inside a rectangle measuring 25 cm × 16 cm. He chooses one of the scales 1 : 20, 1 : 25, 1 : 30, 1 : 40, 1 : 50 and 1 : 100. Which scale gives the largest drawing that fits? Show your calculations.
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For the teacher: Creating, low difficulty, Chapter 4, standard 4.1.3
Textbook p. 93
28

Question 28

Encik Zul mempunyai RM20 000 yang tidak akan digunakan selama 3 tahun. Dia membandingkan dua pelan.
Pelan 1: deposit tetap dengan kadar faedah 4% setahun, dikompaun setiap suku tahun.
Pelan 2: unit amanah. Dia membeli unit pada harga RM1.25 seunit. Dividen sebanyak RM2 400 diterima dalam tempoh 3 tahun dan dia menjual semua unit itu pada harga RM1.40 seunit.Encik Zul has RM20 000 that he will not need for 3 years. He compares two plans.
Plan 1: a fixed deposit at 4% per annum, compounded quarterly.
Plan 2: a unit trust. He buys units at RM1.25 each. Dividends totalling RM2 400 are received over the 3 years and he then sells all the units at RM1.40 each.
[2 marks] (a)Hitung nilai matang bagi pelan 1 dan faedah kompaun yang diperoleh.Calculate the matured value of Plan 1 and the compound interest earned.
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[3 marks] (b)Hitung jumlah pulangan dan ROI bagi pelan 2 selepas 3 tahun.Calculate the total return and the ROI of Plan 2 after 3 years.
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[2 marks] (c)Hitung ROI bagi pelan 1 dan nyatakan pelan yang memberi ROI lebih tinggi.Calculate the ROI of Plan 1 and state which plan gives the higher ROI.
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[3 marks] (d)Hani berkata bahawa Pelan 2 lebih bijak kerana pulangannya lebih tinggi. Adakah anda bersetuju? Berikan dua sebab.Hani says that Plan 2 is wiser because its return is higher. Do you agree? Give two reasons.
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For the teacher: Evaluating, high difficulty, Chapter 3, standard 3.1.6
Textbook p. 71
29

Question 29

Rajah 6 menunjukkan sebuah ramp kerusi roda AB yang panjangnya 6 m dan condong 4.5° dengan tanah mengufuk BC.Diagram 6 shows a wheelchair ramp AB of length 6 m inclined at 4.5° to the horizontal ground BC.
Right-angled triangle ABC: ramp AB 6 m, angle at B 4.5 degrees, right angle at C
Rajah 6Diagram 6
[2 marks] (a)Hitung tinggi, dalam m, hujung A ramp itu di atas tanah, betul kepada dua tempat perpuluhan.Calculate the height, in m, of the end A of the ramp above the ground, correct to two decimal places.
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[2 marks] (b)Hitung jarak mengufuk, dalam m, BC, betul kepada dua tempat perpuluhan.Calculate the horizontal distance, in m, BC, correct to two decimal places.
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[3 marks] (c)Sebuah ramp lain naik 0.45 m dalam jarak mengufuk 4 m. Peraturan sekolah menetapkan sudut kecondongan ramp tidak melebihi 5°. Adakah ramp itu mematuhi peraturan? Tunjukkan pengiraan anda.Another ramp rises 0.45 m over a horizontal distance of 4 m. A school rule says that the angle of inclination of a ramp must not be more than 5°. Does the ramp follow the rule? Show your calculation.
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[3 marks] (d)Ramp yang sama (naik 0.45 m) mahu dibina semula supaya sudut kecondongannya tepat 5°. Hitung jarak mengufuk yang diperlukan, betul kepada 0.01 m.The same ramp (rising 0.45 m) is to be rebuilt so that its angle of inclination is exactly 5°. Calculate the horizontal distance needed, correct to 0.01 m.
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For the teacher: Evaluating, low difficulty, Chapter 5, standard 5.1.7
Textbook p. 122
30

Question 30

Rajah 7 menunjukkan sebuah kolam ikan bulat berpusat O. Empat batang tiang A, B, C dan D terletak di tepi kolam. Garis lurus TAS ialah tangen kepada kolam itu di A. Diberi ∠TAB = 54° dan ∠BCD = 100°.Diagram 7 shows a circular fish pond with centre O. Four posts A, B, C and D are at the edge of the pond. The straight line TAS is a tangent to the pond at A. Given ∠TAB = 54° and ∠BCD = 100°.
Circle with centre O, cyclic quadrilateral ABCD, tangent TAS at A, angle TAB 54 degrees and angle BCD 100 degrees
Rajah 7Diagram 7
[2 marks] (a)Nyatakan nilai ∠ADB, dengan memberikan alasan anda.State the value of ∠ADB, giving your reason.
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[2 marks] (b)Hitung ∠BAD.Calculate ∠BAD.
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[3 marks] (c)Hitung ∠ABD.Calculate ∠ABD.
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[3 marks] (d)Aiman berkata bahawa BD ialah diameter bulatan itu kerana ∠BAD dan ∠BCD berjumlah 180°. Adakah Aiman betul? Terangkan.Aiman says that BD is a diameter of the circle because ∠BAD and ∠BCD add up to 180°. Is Aiman correct? Explain.
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For the teacher: Evaluating, medium difficulty, Chapter 6, standard 6.3.4
Textbook p. 155
31

Question 31

Rajah 8 ialah graf yang menunjukkan tinggi, y cm, dua batang lilin, A dan B, selepas dinyalakan selama x jam. Kedua-dua graf ialah garis lurus.Diagram 8 is a graph that shows the height, y cm, of two candles, A and B, after burning for x hours. Both graphs are straight lines.
Graph of two straight lines for candle A through (0, 30) and (8, 10) and candle B through (0, 24) and (4, 18)
Rajah 8Diagram 8
[2 marks] (a)Cari persamaan bagi lilin A.Find the equation for candle A.
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[2 marks] (b)Cari persamaan bagi lilin B.Find the equation for candle B.
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[3 marks] (c)Hitung masa, dalam jam, apabila kedua-dua lilin itu sama tinggi dan tinggi lilin pada masa itu.Calculate the time, in hours, when the two candles have the same height, and the height of the candles then.
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[3 marks] (d)Aina berkata bahawa lilin A sentiasa lebih tinggi daripada lilin B sehingga lilin A habis terbakar. Adakah Aina betul? Terangkan dengan menggunakan jawapan anda.Aina says that candle A is always taller than candle B until candle A has burnt out. Is Aina correct? Explain using your answers.
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For the teacher: Evaluating, medium difficulty, Chapter 9, standard 9.1.7
Textbook p. 245
Test specification (JSU)
ChapterRememberingUnderstandingApplyingAnalysingEvaluatingCreatingItemsmarks
1. Indices–1 (1)1 (1)1 (1)1 (10)–413
2. Standard Form1 (1)1 (1)2 (5)–––47
3. Consumer Mathematics: Savings and Investments, Credit and Debt––3 (6)–1 (10)–416
4. Scale Drawings––1 (1)1 (1)–1 (10)312
5. Trigonometric Ratios–1 (1)1 (1)1 (1)1 (10)–413
6. Angles and Tangents of Circles–1 (1)2 (5)–1 (10)–416
7. Plans and Elevations––1 (1)–––11
8. Loci in Two Dimensions–1 (1)1 (4)–––25
9. Straight Lines––2 (2)2 (5)1 (10)–517
Total1 (1)5 (5)14 (26)5 (8)5 (50)1 (10)31100
Each cell shows items (marks).