Practice paper, not an official KPM paper
50
Ujian Akhir Sesi AkademikEnd of Academic Session Test
MatematikMathematics
Tingkatan 5, 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 marksJawab 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
Dalam satu projek menanam pokok, bilangan hari, d, untuk menyiapkan kerja berubah secara songsang dengan punca kuasa dua bilangan sukarelawan, v. Hubungan yang betul ialahIn a tree-planting project, the number of days, d, to finish the work varies inversely as the square root of the number of volunteers, v. The correct relation is
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D
'Varies inversely as the square root of v' means d ∝ 1/√v. d ∝ 1/v² would be inverse variation with the square of v.
2
Question 2
Kos, RMC, mencetak sebuah sepanduk segi empat sama berubah secara langsung dengan kuasa dua panjang sisinya, s cm. Sebuah sepanduk dengan sisi 20 cm berharga RM12. Hitung kos sebuah sepanduk dengan sisi 50 cm.The cost, RMC, of printing a square banner varies directly as the square of its side length, s cm. A banner with side 20 cm costs RM12. Calculate the cost of a banner with side 50 cm.
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C
C = ks². 12 = k(20²), so k = 0.03. C = 0.03 × 50² = RM75. RM30 comes from treating the cost as directly proportional to s (12 × 50/20).
3
Question 3
Diberi bahawa y berubah secara langsung dengan x dan secara songsang dengan kuasa dua z. Apabila x = 6 dan z = 2, y = 3. Cari nilai y apabila x = 18 dan z = 3.It is given that y varies directly as x and inversely as the square of z. When x = 6 and z = 2, y = 3. Find the value of y when x = 18 and z = 3.
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B
y = kx/z². 3 = k(6)/4, so k = 2. y = 2(18)/3² = 36/9 = 4. 12 comes from using z instead of z².
4
Question 4
Diberi Q = 4−215 dan R = 13−20. Cari Q − 2R.Given Q = 4−215 and R = 13−20. Find Q − 2R.
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B
2R = [2 6; −4 0]. Q − 2R = [4 − 2, −2 − 6; 1 + 4, 5 − 0] = [2 −8; 5 5]. The first option is Q − R.
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Question 5
Matriks 346 memberi harga (RM) bagi tiga jenis gantungan kunci yang dijual oleh sebuah kelab, dan matriks 402515 memberi bilangan setiap jenis yang dijual. Apakah jumlah jualan, dalam RM?The matrix 346 gives the prices (RM) of three kinds of keychains sold by a club, and the matrix 402515 gives the number of each kind sold. What are the total sales, in RM?
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D
A 1 × 3 matrix times a 3 × 1 matrix gives a 1 × 1 matrix: 3(40) + 4(25) + 6(15) = 120 + 100 + 90 = 310.
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Question 6
Persamaan serentak 3x + 2y = 12 dan x + y = 5 ditulis sebagai persamaan matriks. Cari matriks xy.The simultaneous equations 3x + 2y = 12 and x + y = 5 are written as a matrix equation. Find the matrix xy.
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A
A = [3 2; 1 1], det A = 3(1) − 2(1) = 1, A⁻¹ = [1 −2; −1 3]. [x; y] = A⁻¹[12; 5] = [12 − 10; −12 + 15] = [2; 3]. Check: 3(2) + 2(3) = 12 and 2 + 3 = 5.
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Question 7
Sebuah van sekolah mempunyai polisi insurans dengan deduktibel RM500. Van itu rosak dalam satu kemalangan dan kos pembaikan ialah RM3 200. Berapakah jumlah yang akan dibayar oleh syarikat insurans?A school van has an insurance policy with a deductible of RM500. The van is damaged in an accident and the repair cost is RM3 200. How much will the insurance company pay?
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C
Compensation = loss − deductible = 3 200 − 500 = RM2 700. The policyholder bears the first RM500.
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Question 8
Nilai boleh insurans sebuah dewan komuniti ialah RM250 000 dan peratusan insurans bersama ialah 80%. Dewan itu diinsuranskan dengan RM150 000. Satu kebakaran menyebabkan kerugian separa RM20 000. Tiada deduktibel. Hitung pampasan yang dibayar.The insurable value of a community hall is RM250 000 and the co-insurance percentage is 80%. The hall is insured for RM150 000. A fire causes a partial loss of RM20 000. There is no deductible. Calculate the compensation paid.
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B
Required insurance = 0.80 × 250 000 = RM200 000. Insured amount is less than required, so compensation = (150 000 ÷ 200 000) × 20 000 = RM15 000. RM12 000 wrongly uses the full insurable value.
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Question 9
Jumlah pendapatan tahunan Puan Salmah ialah RM64 000. Dia menderma RM1 500 kepada sebuah pertubuhan amal yang diluluskan (pengecualian cukai) dan jumlah pelepasan cukainya ialah RM21 000. Berapakah pendapatan bercukainya?Puan Salmah's total annual income is RM64 000. She donates RM1 500 to an approved charity (tax exemption) and her total tax relief is RM21 000. What is her chargeable income?
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A
Chargeable income = total income − exemption − relief = 64 000 − 1 500 − 21 000 = RM41 500.
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Question 10
Pendapatan bercukai seorang pekerja ialah RM45 000 dan dia membayar zakat RM300. Cukai pendapatan bagi RM35 000 pertama ialah RM600 dan kadar bagi baki sehingga RM50 000 ialah 8%. Hitung cukai pendapatan yang perlu dibayar.A worker's chargeable income is RM45 000 and she pays zakat of RM300. The income tax on the first RM35 000 is RM600 and the rate on the balance up to RM50 000 is 8%. Calculate the income tax payable.
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C
Tax = 600 + 8% × (45 000 − 35 000) − 300 = 600 + 800 − 300 = RM1 100. RM1 400 forgets the zakat rebate.
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Question 11
Dua bendera segi tiga DEF dan XYZ adalah kongruen, dengan D sepadan dengan X, E dengan Y dan F dengan Z. Diberi DE = 12 cm, EF = 9 cm dan ∠E = 64°. Antara pernyataan berikut, yang manakah betul?Two triangular flags DEF and XYZ are congruent, with D corresponding to X, E to Y and F to Z. Given DE = 12 cm, EF = 9 cm and ∠E = 64°. Which of the following statements is correct?
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A
D↔X and E↔Y, so DE = XY = 12 cm. EF = YZ = 9 cm and ∠E = ∠Y = 64°.
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Question 12
Sebuah poster berukuran 150 cm² dibesarkan kepada 600 cm². Imej itu terletak pada sisi yang sama dengan objek relatif kepada pusat pembesaran. Apakah faktor skala pembesaran itu?A poster of area 150 cm² is enlarged to 600 cm². The image lies on the same side of the centre of enlargement as the object. What is the scale factor of the enlargement?
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A
k² = 600 ÷ 150 = 4, so k = 2 (positive, since the image is on the same side as the object). 4 is the ratio of the areas, not of the lengths.
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Question 13
Titik K(4, −1) dipetakan di bawah penjelmaan gabungan PQ, dengan Q ialah putaran 90° lawan arah jam pada asalan dan P ialah translasi 3−2. Cari imej bagi K.Point K(4, −1) is mapped under the combined transformation PQ, where Q is a rotation of 90° anticlockwise about the origin and P is the translation 3−2. Find the image of K.
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D
PQ means Q first. Rotation 90° anticlockwise: (x, y) → (−y, x), so K → (1, 4). Then translate by (3, −2): (1 + 3, 4 − 2) = (4, 2). (2, −6) uses a clockwise rotation and (4, 6) adds the 2 instead of subtracting it.
14
Question 14
Antara yang berikut, yang manakah sama dengan tan 310°?Which of the following is equal to tan 310°?
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D
310° is in quadrant IV, α = 360° − 310° = 50°. Tangent is negative in quadrant IV: tan 310° = −tan 50°.
15
Question 15
Bagi 0° ≤ θ ≤ 360°, jika sin θ = −√32, cari nilai-nilai θ.For 0° ≤ θ ≤ 360°, if sin θ = −√32, find the values of θ.
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C
sin is negative in quadrants III and IV. sin α = √3/2 gives α = 60°. θ = 180° + 60° = 240° or 360° − 60° = 300°. Using α = 30° would give 210° and 330°.
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Question 16
Graf bagi y = a kos bx + c, dengan a > 0 dan b > 0, mempunyai nilai maksimum 5, nilai minimum −3 dan kala 120°. Persamaan graf itu ialahThe graph of y = a cos bx + c, where a > 0 and b > 0, has a maximum value of 5, a minimum value of −3 and a period of 120°. The equation of the graph is
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A
a = ½(5 − (−3)) = 4 and c = ½(5 + (−3)) = 1. b = 360° ÷ 120° = 3. So y = 4 cos 3x + 1.
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Question 17
Satu selang kelas dalam jadual kekerapan ialah 125 – 134 dan selang kelas seterusnya ialah 135 – 144. Apakah sempadan atas bagi selang kelas 125 – 134?A class interval in a frequency table is 125 – 134 and the next class interval is 135 – 144. What is the upper boundary of the class interval 125 – 134?
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C
Upper boundary = (134 + 135) ÷ 2 = 134.5.
18
Question 18
Jadual menunjukkan bilangan buku yang disumbangkan oleh 30 murid dalam kempen perpustakaan komuniti.
Selang kelas yang manakah mengandungi median?The table shows the number of books donated by 30 pupils in a community library campaign.
Which class interval contains the median?
| Bilangan buku | 1 – 5 | 6 – 10 | 11 – 15 | 16 – 20 |
|---|---|---|---|---|
| Bilangan murid | 4 | 9 | 12 | 5 |
| Number of books | 1 – 5 | 6 – 10 | 11 – 15 | 16 – 20 |
|---|---|---|---|---|
| Number of pupils | 4 | 9 | 12 | 5 |
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C
N = 30, so the median is at position 15. Cumulative frequencies: 4, 13, 25, 30. The 15th value is in the third class, 11 – 15.
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Question 19
Sebuah kelas yang merancang jualan kuih untuk tabung sekolah memutuskan bahawa harga bahan tidak akan berubah sepanjang projek. Langkah dalam proses pemodelan matematik yang manakah ditunjukkan oleh keputusan ini?A class planning a cake sale for the school fund decides that the price of ingredients will not change during the project. Which step of the mathematical modeling process does this decision show?
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B
Deciding that the price stays fixed simplifies the situation. It is an assumption, step 2 of the process.
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Question 20
Jadual menunjukkan ketinggian, y m, sebuah jambatan lengkung pada jarak mengufuk x m dari tebing sungai.
Model yang manakah paling sesuai untuk data itu?The table shows the height, y m, of an arched bridge at horizontal distance x m from the river bank.
Which model is most suitable for the data?
| x | 0 | 1 | 2 | 3 | 4 |
|---|---|---|---|---|---|
| y | 0 | 3 | 4 | 3 | 0 |
| x | 0 | 1 | 2 | 3 | 4 |
|---|---|---|---|---|---|
| y | 0 | 3 | 4 | 3 | 0 |
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B
The values rise to a maximum at x = 2 and fall again symmetrically, like a parabola, so a quadratic model y = ax² + bx + c suits the data. A straight line, an exponential curve and y = kx do not rise and then fall.
Bahagian BSection B
20 marksJawab semua soalan.Answer all questions.
21
Question 21
Sekumpulan murid membungkus bakul makanan untuk keluarga yang memerlukan di taman perumahan mereka. Bilangan bakul, N, yang dibungkus berubah secara langsung dengan masa, t jam. Mereka membungkus 36 bakul dalam 4 jam.A group of pupils packs food baskets for needy families in their housing estate. The number of baskets, N, packed varies directly as the time, t hours. They pack 36 baskets in 4 hours.
[1 mark]
(a)Pilih hubungan yang betul.Choose the correct relation.
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N ∝ t
N varies directly as t, so N ∝ t.
[1 mark]
(b)Cari nilai pemalar k dalam N = kt.Find the value of the constant k in N = kt.
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9
36 = k(4), so k = 9.
[2 marks]
(c)Hitung bilangan bakul yang dibungkus dalam 7 jam.Calculate the number of baskets packed in 7 hours.
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22
Question 22
Encik Faizal, 35 tahun, bukan perokok, membeli polisi insurans hayat dengan nilai muka RM150 000 untuk melindungi keluarganya. Kadar premium ialah RM2.10 bagi setiap RM1 000 nilai muka.Encik Faizal, 35 years old and a non-smoker, buys a life insurance policy with a face value of RM150 000 to protect his family. The premium rate is RM2.10 for every RM1 000 of face value.
[1 mark]
(a)Siapakah yang membayar premium kepada syarikat insurans?Who pays the premium to the insurance company?
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The policyholder
The policyholder is the owner of the policy and pays the premium.
[2 marks]
(b)Hitung premium tahunan yang perlu dibayar oleh Encik Faizal.Calculate Encik Faizal's annual premium.
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[1 mark]
(c)Tandakan BENAR atau PALSU: Kadar premium bagi perokok biasanya lebih tinggi daripada kadar bagi bukan perokok yang sama umur.Mark TRUE or FALSE: The premium rate for a smoker is usually higher than the rate for a non-smoker of the same age.
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True
A smoker has a higher chance of illness, so the rate is higher.
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Question 23
Jumlah pendapatan tahunan Cikgu Nora, seorang guru, ialah RM58 400. Dia menderma RM600 kepada sebuah rumah anak yatim yang diluluskan (pengecualian cukai) dan menuntut jumlah pelepasan cukai RM15 000.The total annual income of Cikgu Nora, a teacher, is RM58 400. She donates RM600 to an approved orphanage (tax exemption) and claims a total tax relief of RM15 000.
[1 mark]
(a)Derma kepada pertubuhan yang diluluskan ialahA donation to an approved organisation is a
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tax exemption
Gifts and donations to approved organisations are tax exemptions; they are taken off the total income.
[2 marks]
(b)Hitung pendapatan bercukai Cikgu Nora.Calculate Cikgu Nora's chargeable income.
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[1 mark]
(c)Tandakan BENAR atau PALSU: Rebat cukai ditolak daripada pendapatan bercukai sebelum cukai dikira.Mark TRUE or FALSE: A tax rebate is deducted from the chargeable income before the tax is calculated.
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False
A rebate is deducted from the tax payable. A relief is deducted from the income.
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Question 24
Sebuah logo sekolah dilukis pada bulatan unit berpusat di asalan O. Titik P(−0.6, 0.8) terletak pada bulatan itu dan θ ialah sudut yang diukur lawan arah jam dari paksi-x positif ke OP.A school logo is drawn on a unit circle with centre at the origin O. The point P(−0.6, 0.8) lies on the circle and θ is the angle measured anticlockwise from the positive x-axis to OP.
[1 mark]
(a)Pilih sukuan tempat P berada.Choose the quadrant in which P lies.
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II
x is negative and y is positive, so P is in quadrant II.
[1 mark]
(b)Pilih nilai tan θ.Choose the value of tan θ.
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−4/3
tan θ = y ÷ x = 0.8 ÷ (−0.6) = −4/3.
[2 marks]
(c)Cari nilai θ, betul kepada 0.1° terdekat.Find the value of θ, correct to the nearest 0.1°.
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25
Question 25
Jadual kekerapan merekodkan jisim, dalam kg, surat khabar lama yang dikumpulkan oleh 40 murid dalam kempen kitar semula. Kelas pertama ialah 20 – 29 dan kelas seterusnya ialah 30 – 39.A frequency table records the mass, in kg, of old newspapers collected by 40 pupils in a recycling campaign. The first class is 20 – 29 and the next class is 30 – 39.
[1 mark]
(a)Pilih sempadan bawah bagi selang kelas 30 – 39.Choose the lower boundary of the class interval 30 – 39.
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29.5
The class before it ends at 29: (29 + 30) ÷ 2 = 29.5.
[1 mark]
(b)Pilih titik tengah bagi selang kelas 30 – 39.Choose the midpoint of the class interval 30 – 39.
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34.5
(30 + 39) ÷ 2 = 34.5.
[2 marks]
(c)Diberi Σf = 40, Σfx = 1 440 dan Σfx² = 55 600. Hitung varians dan sisihan piawai.Given Σf = 40, Σfx = 1 440 and Σfx² = 55 600. Calculate the variance and the standard deviation.
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Bahagian CSection C
60 marksJawab semua soalan. Tunjukkan langkah-langkah penting dalam kerja mengira anda.Answer all questions. Show the important steps in your working.
26
Question 26
[2 marks]
(a)Diberi P = 3−124 dan Q = 150−2. Cari 2P − Q.Given P = 3−124 and Q = 150−2. Find 2P − Q.
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[2 marks]
(b)Cari matriks songsang bagi M = 3245.Find the inverse matrix of M = 3245.
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[4 marks]
(c)Sebuah kelab membeli 3 pen penanda dan 2 buku nota dengan harga RM19. Kemudian kelab itu membeli 4 pen penanda dan 5 buku nota dengan harga RM37. Harga sebatang pen penanda ialah RMx dan harga sebuah buku nota ialah RMy.
Tulis dua persamaan linear itu sebagai satu persamaan matriks. Seterusnya, dengan kaedah matriks, cari nilai x dan nilai y.A club buys 3 marker pens and 2 notebooks for RM19. Later the club buys 4 marker pens and 5 notebooks for RM37. The price of a marker pen is RMx and the price of a notebook is RMy.
Write the two linear equations as one matrix equation. Hence, using the matrix method, find the value of x and of y.
Tulis dua persamaan linear itu sebagai satu persamaan matriks. Seterusnya, dengan kaedah matriks, cari nilai x dan nilai y.A club buys 3 marker pens and 2 notebooks for RM19. Later the club buys 4 marker pens and 5 notebooks for RM37. The price of a marker pen is RMx and the price of a notebook is RMy.
Write the two linear equations as one matrix equation. Hence, using the matrix method, find the value of x and of y.
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27
Question 27
Jadual menunjukkan masa menunggu 40 penduduk di sebuah klinik kesihatan percuma yang dianjurkan oleh sekolah.
The table shows the waiting time of 40 residents at a free health clinic organised by a school.
| Masa menunggu (minit) | 10 – 14 | 15 – 19 | 20 – 24 | 25 – 29 | 30 – 34 |
|---|---|---|---|---|---|
| Bilangan penduduk | 3 | 6 | 16 | 10 | 5 |
| Waiting time (minutes) | 10 – 14 | 15 – 19 | 20 – 24 | 25 – 29 | 30 – 34 |
|---|---|---|---|---|---|
| Number of residents | 3 | 6 | 16 | 10 | 5 |
[2 marks]
(a)Hitung min masa menunggu.Calculate the mean waiting time.
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[3 marks]
(b)Hitung varians dan sisihan piawai masa menunggu itu.Calculate the variance and the standard deviation of the waiting time.
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[3 marks]
(c)Di sebuah klinik lain, min masa menunggu ialah 21.5 minit dan sisihan piawainya ialah 7.2 minit. Bandingkan masa menunggu di kedua-dua klinik dan nyatakan klinik yang lebih baik. Beri satu sebab.At another clinic, the mean waiting time is 21.5 minutes and the standard deviation is 7.2 minutes. Compare the waiting times at the two clinics and state which clinic is better. Give one reason.
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28
Question 28
Rajah 1 menunjukkan segi tiga ABC dan imejnya A′B′C′ di bawah suatu pembesaran pada pusat P bagi reka bentuk sebuah mural komuniti.Diagram 1 shows triangle ABC and its image A′B′C′ under an enlargement at centre P for the design of a community mural.
[3 marks]
(a)Huraikan selengkapnya pembesaran yang memetakan segi tiga ABC kepada segi tiga A′B′C′.Describe in full the enlargement that maps triangle ABC onto triangle A′B′C′.
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[2 marks]
(b)Luas segi tiga ABC ialah 1 unit². Hitung luas segi tiga A′B′C′, dalam unit².The area of triangle ABC is 1 unit². Calculate the area of triangle A′B′C′, in unit².
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[3 marks]
(c)T ialah translasi −4−2 dan E ialah pembesaran dalam (a). Tulis koordinat imej bagi titik A, B dan C di bawah penjelmaan gabungan TE.T is the translation −4−2 and E is the enlargement in (a). Write the coordinates of the images of the points A, B and C under the combined transformation TE.
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[2 marks]
(d)Dalam segi tiga PQR dan segi tiga STU, PQ = ST, ∠PQR = ∠STU dan ∠QPR = ∠TSU. (i) Nyatakan syarat kekongruenan yang digunakan. (ii) Jika TU = 7.4 cm, nyatakan panjang QR.In triangle PQR and triangle STU, PQ = ST, ∠PQR = ∠STU and ∠QPR = ∠TSU. (i) State the congruency condition used. (ii) If TU = 7.4 cm, state the length of QR.
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29
Question 29
Rajah 2 menunjukkan graf bagi fungsi y = a sin bx + c untuk 0° ≤ x ≤ 360°, dengan a, b dan c ialah pemalar dan a > 0. Graf itu memodelkan ketinggian lampu hiasan sebuah gerai pada pesta komuniti.Diagram 2 shows the graph of the function y = a sin bx + c for 0° ≤ x ≤ 360°, where a, b and c are constants and a > 0. The graph models the height of a decorative light at a stall at a community festival.
[2 marks]
(a)Daripada graf itu, nyatakan nilai maksimum dan nilai minimum bagi y.From the graph, state the maximum value and the minimum value of y.
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[3 marks]
(b)Cari nilai a, b dan c.Find the values of a, b and c.
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[2 marks]
(c)Hitung nilai y apabila x = 20°.Calculate the value of y when x = 20°.
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[3 marks]
(d)Cari nilai-nilai x, bagi 0° ≤ x ≤ 120°, apabila y = 0.5.Find the values of x, for 0° ≤ x ≤ 120°, when y = 0.5.
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Question 30
Masa, T jam, yang diambil oleh sekumpulan sukarelawan untuk mengecat pagar sebuah sekolah berubah secara langsung dengan panjang pagar, L m, dan secara songsang dengan bilangan sukarelawan, n. Seramai 6 orang sukarelawan mengambil masa 4 jam untuk mengecat pagar sepanjang 60 m.The time, T hours, taken by a group of volunteers to paint the fence of a school varies directly as the length of the fence, L m, and inversely as the number of volunteers, n. 6 volunteers take 4 hours to paint a fence of length 60 m.
[2 marks]
(a)Tulis hubungan antara T, L dan n, dan cari pemalar variasi, k.Write the relation between T, L and n, and find the constant of variation, k.
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[2 marks]
(b)Hitung masa untuk 8 orang sukarelawan mengecat pagar sepanjang 150 m.Calculate the time for 8 volunteers to paint a fence of length 150 m.
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[3 marks]
(c)Berapakah bilangan sukarelawan yang diperlukan untuk mengecat pagar sepanjang 120 m dalam masa 3 jam?How many volunteers are needed to paint a fence of length 120 m in 3 hours?
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[3 marks]
(d)Sebuah jawatankuasa mempunyai 12 orang sukarelawan dan perlu mengecat pagar sepanjang 180 m dalam masa 5 jam. Adakah mereka dapat menyiapkannya tepat pada masanya? Tunjukkan kerja anda dan cadangkan bilangan sukarelawan minimum yang diperlukan.A committee has 12 volunteers and must paint a fence of length 180 m within 5 hours. Can they finish on time? Show your working and suggest the minimum number of volunteers needed.
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[2 marks]
(e)Jika bilangan sukarelawan digandakan dan panjang pagar dikurangkan separuh, apakah yang berlaku kepada masa T? Terangkan.If the number of volunteers is doubled and the length of the fence is halved, what happens to the time T? Explain.
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31
Question 31
Sebuah kelas mengumpulkan RM5 000 untuk membeli buku bagi perpustakaan komuniti. Wang itu akan disimpan dalam salah satu daripada dua pelan.
Pelan A: faedah kompaun 4% setahun, dikompaunkan setiap setengah tahun.
Pelan B: faedah mudah 4.4% setahun.A class collects RM5 000 to buy books for a community library. The money will be saved in one of two plans.
Plan A: compound interest of 4% per annum, compounded semi-annually.
Plan B: simple interest of 4.4% per annum.
Pelan A: faedah kompaun 4% setahun, dikompaunkan setiap setengah tahun.
Pelan B: faedah mudah 4.4% setahun.A class collects RM5 000 to buy books for a community library. The money will be saved in one of two plans.
Plan A: compound interest of 4% per annum, compounded semi-annually.
Plan B: simple interest of 4.4% per annum.
[2 marks]
(a)Tulis model bagi jumlah wang, RMA dan RMB, selepas t tahun bagi Pelan A dan Pelan B.Write the models for the amount of money, RMA and RMB, after t years for Plan A and Plan B.
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[2 marks]
(b)Hitung jumlah wang bagi setiap pelan selepas 5 tahun.Calculate the amount of money for each plan after 5 years.
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[3 marks]
(c)Cari bilangan tahun penuh yang paling kecil apabila Pelan A memberi jumlah yang lebih besar daripada Pelan B. Tunjukkan pengiraan anda.Find the smallest whole number of years after which Plan A gives a larger amount than Plan B. Show your calculations.
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[3 marks]
(d)Perpustakaan komuniti memerlukan sekurang-kurangnya RM6 800 secepat mungkin. Pelan manakah yang patut dipilih oleh kelas itu? Terangkan dengan menggunakan pengiraan.The community library needs at least RM6 800 as early as possible. Which plan should the class choose? Explain using calculations.
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[2 marks]
(e)Nyatakan satu andaian yang dibuat dalam model itu dan satu cara untuk memperbaiki model tersebut.State one assumption made in the model and one way to refine the model.
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Test specification (JSU)
| Chapter | Remembering | Understanding | Applying | Analysing | Evaluating | Creating | Items | marks |
|---|---|---|---|---|---|---|---|---|
| 1. Variation | – | 1 (1) | 2 (5) | 1 (1) | 1 (12) | – | 5 | 19 |
| 2. Matrices | – | – | 3 (10) | 1 (1) | – | – | 4 | 11 |
| 3. Consumer Mathematics: Insurance | – | – | 3 (6) | – | – | – | 3 | 6 |
| 4. Consumer Mathematics: Taxation | – | – | 3 (6) | – | – | – | 3 | 6 |
| 5. Congruency, Enlargement and Combined Transformations | 1 (1) | – | 3 (12) | – | – | – | 4 | 13 |
| 6. Ratios and Graphs of Trigonometric Functions | – | 1 (1) | 2 (5) | 2 (11) | – | – | 5 | 17 |
| 7. Measures of Dispersion for Grouped Data | 1 (1) | 1 (4) | 2 (9) | – | – | – | 4 | 14 |
| 8. Mathematical Modeling | – | 1 (1) | 1 (1) | – | 1 (12) | – | 3 | 14 |
| Total | 2 (2) | 4 (7) | 19 (54) | 4 (13) | 2 (24) | 0 (0) | 31 | 100 |
Each cell shows items (marks).