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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
  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

Sebuah kedai roti menerima tempahan kek. Bilangan hari, d, untuk menyiapkan satu tempahan berubah secara songsang dengan bilangan mesin, m, yang digunakan. Hubungan yang manakah betul?A bakery receives orders for cakes. The number of days, d, to complete one order varies inversely as the number of machines, m, used. Which relationship is correct?
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B
More machines means fewer days, so d varies inversely as m: d ∝ 1/m and dm is constant. The other options are direct variation or involve a power that the question does not mention.
For the teacher: Understanding, low difficulty, Chapter 1, standard 1.2.1
Textbook p. 22
2

Question 2

T berubah secara langsung dengan kuasa dua x dan secara songsang dengan y. Diberi T = 24 apabila x = 2 dan y = 3. Cari nilai T apabila x = 4 dan y = 6.T varies directly as the square of x and inversely as y. Given T = 24 when x = 2 and y = 3. Find the value of T when x = 4 and y = 6.
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C
T = kx²/y. 24 = k(4)/3, so k = 18. T = 18(16)/6 = 48. x is squared (×4) and y is doubled (÷2), so T doubles: 24 × 4 ÷ 2 = 48.
For the teacher: Applying, medium difficulty, Chapter 1, standard 1.3.1
Textbook p. 27
3

Question 3

Matriks K = 4−17206. Nyatakan peringkat matriks K dan unsur k32.Matrix K = 4−17206. State the order of matrix K and the element k32.
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A
K has 3 rows and 2 columns, so its order is 3 × 2. k32 is in row 3, column 2, which is 6. (0 is k31.)
For the teacher: Remembering, low difficulty, Chapter 2, standard 2.1.1
Textbook p. 39
4

Question 4

Hitung 23−104 − 123−5.Calculate 23−104 − 123−5.
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D
2A = [6 −2; 0 8]. Subtract each element: [6−1, −2−2; 0−3, 8−(−5)] = [5 −4; −3 13]. Watch the double negative in the last element.
For the teacher: Applying, low difficulty, Chapter 2, standard 2.2.1
Textbook p. 48
5

Question 5

Cari matriks songsang bagi 4−231.Find the inverse of the matrix 4−231.
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B
|M| = 4(1) − (−2)(3) = 10. Swap 4 and 1, change the signs of −2 and 3: inverse = 1/10 [1 2; −3 4]. Leaving out 1/10 (last option) does not give the inverse.
For the teacher: Applying, medium difficulty, Chapter 2, standard 2.2.4
Textbook p. 60
6

Question 6

Antara berikut, pasangan insurans dan risiko yang diliputinya yang manakah betul?Which of the following pairs of insurance and the risk it covers is correct?
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A
Fire insurance covers fire, lightning and explosion at premises. Hospital bills are medical insurance, travel insurance covers losses while travelling, and personal accident insurance covers only deaths resulting directly from an accident.
For the teacher: Understanding, low difficulty, Chapter 3, standard 3.1.1
Textbook p. 76
7

Question 7

Kadar premium bagi seorang lelaki berumur 45 tahun yang tidak merokok ialah RM3.40 bagi setiap RM1 000 nilai muka. Hitung premium tahunan bagi polisi insurans hayat dengan nilai muka RM150 000.The premium rate for a 45-year-old non-smoking male is RM3.40 per RM1 000 of face value. Calculate the annual premium for a life insurance policy with a face value of RM150 000.
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C
150 000 ÷ 1 000 × 3.40 = 150 × 3.40 = RM510.00. RM51.00 divides by 10 000 and RM5 100 is 1 500 × 3.40.
For the teacher: Applying, low difficulty, Chapter 3, standard 3.2.1
Textbook p. 81
8

Question 8

Sebuah kereta berenjin 1 800 cc didaftarkan di Sabah dengan jumlah diinsuranskan RM28 000. Kadar polisi komprehensif bagi enjin sebesar ini ialah RM243.90 bagi RM1 000 pertama dan RM20.30 bagi setiap RM1 000 berikutnya. Hitung premium kasar polisi pihak ketiga, kebakaran dan kecurian jika diskaun tanpa tuntutan (NCD) ialah 25%.A car of 1 800 cc is registered in Sabah with a sum insured of RM28 000. The comprehensive rate for this engine size is RM243.90 for the first RM1 000 and RM20.30 for each subsequent RM1 000. Calculate the gross premium of the third party, fire and theft policy if the no claim discount (NCD) is 25%.
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D
Comprehensive basic = 243.90 + 20.30 × 27 = RM792.00. Third party, fire and theft = 75% × 792.00 = RM594.00. NCD = 25% × 594.00 = 148.50, so gross = 594.00 − 148.50 = RM445.50. RM594.00 forgets the NCD, and RM792.00 is the comprehensive basic premium.
For the teacher: Applying, high difficulty, Chapter 3, standard 3.2.2
Textbook p. 83
9

Question 9

Antara berikut, yang manakah ialah rebat cukai?Which of the following is a tax rebate?
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B
A rebate is taken off the tax itself. Zakat paid (and RM400 for a low chargeable income) is a rebate. The individual relief, EPF contributions and life insurance premiums are reliefs, which are taken off the income.
For the teacher: Understanding, low difficulty, Chapter 4, standard 4.1.3
Textbook p. 106
10

Question 10

Jumlah pendapatan tahunan Puan Hanim ialah RM96 000. Pengecualian cukai ialah RM4 000 dan jumlah pelepasan cukai ialah RM18 500. Berapakah pendapatan bercukainya?Puan Hanim's total annual income is RM96 000. The tax exemption is RM4 000 and the total tax relief is RM18 500. What is her chargeable income?
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A
Chargeable income = 96 000 − 4 000 − 18 500 = RM73 500. RM77 500 forgets the exemption; RM92 000 forgets the relief.
For the teacher: Applying, low difficulty, Chapter 4, standard 4.1.3
Textbook p. 104
11

Question 11

Pendapatan bercukai Encik Saufi ialah RM44 000. Dia membayar zakat RM350. Gunakan jadual: RM600 bagi RM35 000 pertama, kemudian 8% bagi baki hingga RM50 000. Hitung cukai pendapatan yang perlu dibayar.Encik Saufi's chargeable income is RM44 000. He paid zakat of RM350. Use the table: RM600 on the first RM35 000, then 8% on the balance up to RM50 000. Calculate the income tax payable.
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C
Tax = 600 + (44 000 − 35 000) × 8% = 600 + 720 = RM1 320. Zakat is a rebate, so tax payable = 1 320 − 350 = RM970. RM1 320 forgets the rebate.
For the teacher: Applying, low difficulty, Chapter 4, standard 4.1.3
Textbook p. 106
12

Question 12

Dalam △ABC dan △PQR, AB = PQ = 8 cm, BC = QR = 6 cm dan ∠B = ∠Q = 70°. Apakah syarat yang membuktikan bahawa kedua-dua segi tiga itu kongruen?In △ABC and △PQR, AB = PQ = 8 cm, BC = QR = 6 cm and ∠B = ∠Q = 70°. Which condition proves that the two triangles are congruent?
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D
Two pairs of sides and the angle between them are equal (B lies between AB and BC), so the rule is SAS. AAA never proves congruency.
For the teacher: Understanding, low difficulty, Chapter 5, standard 5.1.2
Textbook p. 128
13

Question 13

Satu pembesaran dengan faktor skala −3 memetakan sebuah segi empat tepat kepada imej yang berluas 135 cm². Hitung luas, dalam cm², segi empat tepat asal itu.An enlargement with a scale factor of −3 maps a rectangle to an image of area 135 cm². Calculate the area, in cm², of the original rectangle.
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B
Area of image = k² × area of object = (−3)² × area = 9 × area. Object area = 135 ÷ 9 = 15 cm². (45 divides by 3, which treats the area as if it scaled like a length.)
For the teacher: Applying, medium difficulty, Chapter 5, standard 5.2.4
Textbook p. 146
14

Question 14

Tanpa menggunakan kalkulator, cari nilai sin 240°.Without using a calculator, find the value of sin 240°.
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A
240° is in quadrant III where sin is negative. The reference angle is 240° − 180° = 60°, so sin 240° = −sin 60° = −√3/2.
For the teacher: Applying, low difficulty, Chapter 6, standard 6.1.2
Textbook p. 180
15

Question 15

Graf bagi y = 3 sin 2x + 1 dilukis untuk 0° ≤ x ≤ 360°. Apakah nilai maksimum dan kala graf itu?The graph of y = 3 sin 2x + 1 is drawn for 0° ≤ x ≤ 360°. What are the maximum value and the period of the graph?
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D
Maximum = c + a = 1 + 3 = 4. Period = 360° ÷ b = 360° ÷ 2 = 180°. A maximum of 3 is the amplitude, not the maximum; 720° multiplies by 2 instead of dividing.
For the teacher: Analysing, high difficulty, Chapter 6, standard 6.2.2
Textbook p. 189
16

Question 16

Satu jadual kekerapan menunjukkan masa menunggu (minit) dalam kelas 110 – 119, 120 – 129 dan seterusnya. Apakah sempadan bawah kelas 110 – 119?A frequency table shows waiting times (minutes) in the classes 110 – 119, 120 – 129 and so on. What is the lower boundary of the class 110 – 119?
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C
The class before is 100 – 109. Lower boundary = (109 + 110) ÷ 2 = 109.5. (114.5 is the midpoint of the class and 110.5 is wrong because boundaries lie halfway between classes.)
For the teacher: Remembering, low difficulty, Chapter 7, standard 7.1.1
Textbook p. 199
17

Question 17

Bagi 40 nilai data, Σfx = 1 200 dan Σfx² = 40 000. Hitung sisihan piawai bagi data itu.For 40 values of data, Σfx = 1 200 and Σfx² = 40 000. Calculate the standard deviation of the data.
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A
Mean = 1 200 ÷ 40 = 30. Variance = 40 000 ÷ 40 − 30² = 1 000 − 900 = 100. Standard deviation = √100 = 10. (100 is the variance; 31.62 forgets to subtract the mean squared.)
For the teacher: Applying, high difficulty, Chapter 7, standard 7.2.2
Textbook p. 212
18

Question 18

Min markah ujian Matematik bagi Kelas P dan Kelas Q ialah sama, iaitu 62. Sisihan piawai Kelas P ialah 4.5 dan sisihan piawai Kelas Q ialah 9.8. Pernyataan yang manakah benar?The mean marks in a Mathematics test for Class P and Class Q are the same, 62. The standard deviation of Class P is 4.5 and the standard deviation of Class Q is 9.8. Which statement is true?
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D
The means are equal, so neither class scored higher on average. The smaller standard deviation (4.5) means the marks of Class P are closer to the mean, that is more consistent.
For the teacher: Analysing, low difficulty, Chapter 7, standard 7.2.4
Textbook p. 215
19

Question 19

Sekumpulan murid membina model untuk meramalkan keuntungan jualan kantin. Mereka membandingkan jawapan model dengan jualan sebenar untuk menyemak sama ada jawapan itu munasabah. Komponen manakah dalam proses pemodelan yang sedang dilakukan?A group of pupils builds a model to predict the profit from canteen sales. They compare the answer of the model with the actual sales to check whether the answer is reasonable. Which component of the modeling process are they doing?
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C
Checking whether the answer solves the problem and is sensible in the real world is the component 'verify and interpret'.
For the teacher: Understanding, low difficulty, Chapter 8, standard 8.1.1
Textbook p. 230
20

Question 20

Rahimah melabur RM12 000 dalam satu akaun yang membayar faedah 5% setahun, dikompaun setiap setengah tahun. Hitung jumlah wang dalam akaun itu selepas 3 tahun.Rahimah invests RM12 000 in an account that pays interest of 5% per annum, compounded half-yearly. Calculate the amount in the account after 3 years.
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B
Rate per period = 5% ÷ 2 = 2.5% and the number of periods = 2 × 3 = 6. A = 12 000(1.025)⁶ = RM13 916.32. RM13 891.50 compounds only once a year; RM13 800 is simple interest; RM16 081.15 uses 5% for each half-year.
For the teacher: Applying, high difficulty, Chapter 8, standard 8.1.3
Textbook p. 240

Bahagian BSection B

20 marks
Jawab semua soalan.Answer all questions.
21

Question 21

Dua gerai di pasar malam mencatat bilangan pesanan dalam bentuk matriks.Two stalls at a night market record the numbers of orders in the form of matrices.
[2 marks] (a)Diberi matriks M = 5−2810−4. Nyatakan (i) peringkat M, (ii) unsur m23.Given matrix M = 5−2810−4. State (i) the order of M, (ii) the element m23.
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[2 marks] (b)Diberi 2p5−13 + 4q3−2 = 10921. Cari nilai p dan nilai q.Given 2p5−13 + 4q3−2 = 10921. Find the value of p and the value of q.
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For the teacher: Applying, low difficulty, Chapter 2, standard 2.2.2
Textbook p. 43
22

Question 22

Jumlah pendapatan tahunan Encik Zaki ialah RM85 000. Pengecualian cukainya ialah RM1 200 dan jumlah pelepasan cukainya ialah RM19 800. Dia membayar zakat RM260.Encik Zaki's total annual income is RM85 000. His tax exemption is RM1 200 and his total tax relief is RM19 800. He paid zakat of RM260.
[1 mark] (a)Hitung pendapatan bercukai Encik Zaki.Calculate Encik Zaki's chargeable income.
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[3 marks] (b)Jadual menunjukkan bahawa cukai bagi pendapatan bercukai RM50 001 hingga RM70 000 ialah RM1 800 bagi RM50 000 pertama dan 14% bagi setiap ringgit selebihnya. Hitung cukai pendapatan yang perlu dibayar oleh Encik Zaki.The table shows that the tax on a chargeable income of RM50 001 to RM70 000 is RM1 800 on the first RM50 000 and 14% on every ringgit after that. Calculate the income tax Encik Zaki must pay.
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For the teacher: Applying, low difficulty, Chapter 4, standard 4.1.3
Textbook p. 105
23

Question 23

Rajah 1 menunjukkan segi tiga ABC dan imejnya ADE di bawah suatu pembesaran dengan pusat A. ABD dan ACE ialah garis lurus. AB = 5 cm, BD = 3 cm dan luas segi tiga ABC ialah 25 cm². Kawasan BDEC berlorek.Diagram 1 shows triangle ABC and its image ADE under an enlargement with centre A. ABD and ACE are straight lines. AB = 5 cm, BD = 3 cm and the area of triangle ABC is 25 cm². The region BDEC is shaded.
Triangle ABC inside triangle ADE with common vertex A; AB 5 cm, BD 3 cm, area of ABC 25 square centimetres, region BDEC shaded
Rajah 1Diagram 1
[2 marks] (a)Nyatakan faktor skala pembesaran itu.State the scale factor of the enlargement.
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[2 marks] (b)Hitung luas, dalam cm², kawasan berlorek BDEC.Calculate the area, in cm², of the shaded region BDEC.
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For the teacher: Applying, low difficulty, Chapter 5, standard 5.2.4
Textbook p. 146
24

Question 24

Rajah 2 ialah satu ogif yang menunjukkan bil air bulanan, dalam RM, bagi 80 buah rumah di sebuah taman perumahan.Diagram 2 is an ogive showing the monthly water bills, in RM, of 80 houses in a housing estate.
Ogive of monthly water bills of 80 houses: cumulative frequency 0, 5, 20, 40, 60, 74, 80 at boundaries 19.5, 29.5 to 79.5
Rajah 2Diagram 2
[2 marks] (a)Berdasarkan ogif itu, nyatakan kuartil pertama dan kuartil ketiga bagi bil air itu.Based on the ogive, state the first quartile and the third quartile of the water bills.
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[2 marks] (b)Cari julat antara kuartil. Nyatakan maksud nilai itu.Find the interquartile range. State what the value means.
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For the teacher: Analysing, medium difficulty, Chapter 7, standard 7.1.4
Textbook p. 207
25

Question 25

Pancutan air di sebuah pusat membeli-belah membentuk lengkung kuadratik y = ax² + bx, dengan y ialah tinggi, dalam m, dan x ialah jarak mengufuk, dalam m, dari muncung. Pancutan itu melalui titik (10, 6) dan (20, 8).A water jet at a shopping centre forms a quadratic curve y = ax² + bx, where y is the height, in m, and x is the horizontal distance, in m, from the nozzle. The jet passes through the points (10, 6) and (20, 8).
[2 marks] (a)Bentuk dua persamaan serentak dalam a dan b.Form two simultaneous equations in a and b.
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[2 marks] (b)Selesaikan persamaan itu dan tulis model bagi pancutan itu.Solve the equations and write the model of the jet.
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For the teacher: Applying, high difficulty, Chapter 8, standard 8.1.2
Textbook p. 238

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

[3 marks] (a)Harga, P (RM), sebuah kotak kek cawan berubah secara langsung dengan bilangan kek cawan, n. Diberi P = 36 apabila n = 12. Cari hubungan antara P dengan n dan hitung harga bagi 30 biji kek cawan.The price, P (RM), of a box of cupcakes varies directly as the number of cupcakes, n. Given P = 36 when n = 12. Find the relationship between P and n and calculate the price of 30 cupcakes.
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[2 marks] (b)Masa, t jam, untuk mencetak sejumlah poster berubah secara songsang dengan bilangan pencetak, n. Empat pencetak mengambil masa 6 jam. Hitung masa yang diambil oleh 8 pencetak.The time, t hours, to print a number of posters varies inversely as the number of printers, n. Four printers take 6 hours. Calculate the time taken by 8 printers.
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[3 marks] (c)y berubah secara langsung dengan kuasa dua x dan secara songsang dengan punca kuasa dua z. Diberi y = 12 apabila x = 2 dan z = 16. Cari nilai y apabila x = 5 dan z = 25.y varies directly as the square of x and inversely as the square root of z. Given y = 12 when x = 2 and z = 16. Find the value of y when x = 5 and z = 25.
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For the teacher: Applying, low difficulty, Chapter 1, standard 1.1.2
Textbook p. 8
27

Question 27

[3 marks] (a)Encik Kamal, 42 tahun dan tidak merokok, membeli polisi insurans hayat dengan nilai muka RM200 000. Kadar premiumnya ialah RM4.22 bagi setiap RM1 000. Dia menambah perlindungan penyakit kritikal sebanyak 25% daripada nilai muka dengan kadar RM2.10 bagi setiap RM1 000. Hitung jumlah premium tahunan Encik Kamal.Encik Kamal, 42 years old and a non-smoker, buys a life insurance policy with a face value of RM200 000. The premium rate is RM4.22 per RM1 000. He adds critical illness cover of 25% of the face value at a rate of RM2.10 per RM1 000. Calculate Encik Kamal's total annual premium.
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[3 marks] (b)Cik Liyana tinggal di Semenanjung Malaysia. Kereta berenjin 1 500 cc miliknya diinsuranskan dengan polisi komprehensif, jumlah diinsuranskan RM52 000. Kadar bagi enjin sehingga 1 650 cc ialah RM305.50 bagi RM1 000 pertama dan RM26 bagi setiap RM1 000 berikutnya. NCD ialah 40%. Hitung premium kasar yang perlu dibayar.Cik Liyana lives in Peninsular Malaysia. Her car of 1 500 cc is insured with a comprehensive policy, sum insured RM52 000. The rate for engines up to 1 650 cc is RM305.50 for the first RM1 000 and RM26 for each subsequent RM1 000. The NCD is 40%. Calculate the gross premium she must pay.
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[2 marks] (c)Nilai insurans sebuah rumah ialah RM300 000 dan polisi kebakarannya mengandungi klausa ko-insurans 80% dan tolakan RM1 500. Rumah itu diinsuranskan dengan RM180 000. Jika berlaku kerugian separa RM60 000, hitung pampasan yang dibayar.The insurable value of a house is RM300 000 and its fire policy contains an 80% co-insurance clause and a deductible of RM1 500. The house is insured for RM180 000. If a partial loss of RM60 000 occurs, calculate the compensation paid.
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For the teacher: Applying, low difficulty, Chapter 3, standard 3.2.1
Textbook p. 81
28

Question 28

[3 marks] (a)Tanpa menggunakan kalkulator, cari nilai bagi (i) sin 135°, (ii) kos 330°, (iii) tan 240°. Beri jawapan dalam bentuk surd jika perlu.Without using a calculator, find the value of (i) sin 135°, (ii) cos 330°, (iii) tan 240°. Give answers in surd form where needed.
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[3 marks] (b)Diberi sin θ = −5/13 dengan 180° < θ < 270°. Cari nilai kos θ dan tan θ.Given sin θ = −5/13 with 180° < θ < 270°. Find the value of cos θ and of tan θ.
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[4 marks] (c)Rajah 3 menunjukkan graf bagi y = a kos bx + c untuk 0° ≤ x ≤ 360°, dengan a, b dan c ialah pemalar positif. Nyatakan (i) amplitud, (ii) kala graf itu. Seterusnya, tulis nilai a, b dan c.Diagram 3 shows the graph of y = a cos bx + c for 0° ≤ x ≤ 360°, where a, b and c are positive constants. State (i) the amplitude, (ii) the period of the graph. Hence write the values of a, b and c.
Cosine curve for x from 0 to 360 degrees with maximum value 3 and minimum value negative 1; three complete waves
Rajah 3Diagram 3
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For the teacher: Applying, low difficulty, Chapter 6, standard 6.1.2
Textbook p. 180
29

Question 29

Encik Hairi dan isterinya, Puan Salwa, bekerja sepenuh masa. Jumlah pendapatan tahunan Encik Hairi ialah RM74 000, jumlah pelepasan cukainya ialah RM16 500 dan dia membayar zakat RM500. Jumlah pendapatan tahunan Puan Salwa ialah RM38 000 dan jumlah pelepasan cukainya ialah RM12 000. Mereka tiada pengecualian cukai.
Jadual cukai (Tahun Taksiran 2020):
RM20 001 – RM35 000: RM150 bagi RM20 000 pertama + 3% bagi baki
RM35 001 – RM50 000: RM600 bagi RM35 000 pertama + 8% bagi baki
RM50 001 – RM70 000: RM1 800 bagi RM50 000 pertama + 14% bagi baki
RM70 001 – RM100 000: RM4 600 bagi RM70 000 pertama + 21% bagi baki
Rebat RM400 diberikan jika pendapatan bercukai tidak melebihi RM35 000.Encik Hairi and his wife, Puan Salwa, work full time. Encik Hairi's total annual income is RM74 000, his total tax relief is RM16 500 and he paid zakat of RM500. Puan Salwa's total annual income is RM38 000 and her total tax relief is RM12 000. They have no tax exemption.
Tax table (Assessment Year 2020):
RM20 001 – RM35 000: RM150 on the first RM20 000 + 3% on the balance
RM35 001 – RM50 000: RM600 on the first RM35 000 + 8% on the balance
RM50 001 – RM70 000: RM1 800 on the first RM50 000 + 14% on the balance
RM70 001 – RM100 000: RM4 600 on the first RM70 000 + 21% on the balance
A rebate of RM400 is given if the chargeable income does not exceed RM35 000.
[3 marks] (a)Hitung cukai pendapatan yang perlu dibayar oleh Encik Hairi dengan penilaian berasingan.Calculate the income tax payable by Encik Hairi under separate assessment.
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[2 marks] (b)Hitung cukai pendapatan yang perlu dibayar oleh Puan Salwa dengan penilaian berasingan.Calculate the income tax payable by Puan Salwa under separate assessment.
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[3 marks] (c)Jika mereka memilih penilaian bersama, jumlah pelepasan cukai yang boleh dituntut oleh pasangan itu ialah RM19 500 dan zakat RM500 ditolak daripada cukai. Hitung cukai pendapatan yang perlu dibayar.If they choose joint assessment, the total tax relief the couple can claim is RM19 500 and the zakat of RM500 is deducted from the tax. Calculate the income tax payable.
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[2 marks] (d)Pasangan itu ingin membayar cukai yang paling sedikit. Pilih jenis penilaian yang lebih berpatutan dan nyatakan jumlah yang dijimatkan.The couple wants to pay the least tax. Choose the assessment that is more economical and state the amount saved.
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For the teacher: Analysing, medium difficulty, Chapter 4, standard 4.1.3
Textbook p. 109
30

Question 30

[4 marks] (a)Diberi A = 2314 dan B = 5−102. Hitung (i) 2A − B, (ii) AB.Given A = 2314 and B = 5−102. Calculate (i) 2A − B, (ii) AB.
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[2 marks] (b)Cari matriks songsang bagi 3254.Find the inverse of the matrix 3254.
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[3 marks] (c)Seorang penjual buah menjual 3 kg rambutan dan 2 kg manggis dengan harga RM38. Dia menjual 5 kg rambutan dan 4 kg manggis dengan harga RM70. Tulis persamaan serentak itu dalam bentuk persamaan matriks, dan seterusnya cari harga, dalam RM, bagi 1 kg setiap jenis buah dengan kaedah matriks.A fruit seller sells 3 kg of rambutans and 2 kg of mangosteens for RM38. He sells 5 kg of rambutans and 4 kg of mangosteens for RM70. Write the simultaneous equations in the form of a matrix equation and hence find the price, in RM, of 1 kg of each fruit by the matrix method.
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[3 marks] (d)Kos membeli ialah RM4.50 sekilogram bagi rambutan dan RM7.20 sekilogram bagi manggis. Pada hari Sabtu, dia menjual 12 kg rambutan dan 7 kg manggis. Dengan menggunakan pendaraban matriks, hitung keuntungan hari itu. Dia menyasarkan keuntungan sekurang-kurangnya RM40. Adakah sasarannya tercapai? Beri alasan.The cost price is RM4.50 per kg for rambutans and RM7.20 per kg for mangosteens. On Saturday he sold 12 kg of rambutans and 7 kg of mangosteens. Using matrix multiplication, calculate the profit that day. He aims for a profit of at least RM40. Is his target achieved? Give a reason.
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For the teacher: Evaluating, medium difficulty, Chapter 2, standard 2.2.5
Textbook p. 63
31

Question 31

Jadual menunjukkan bilangan bungkus nasi lemak yang dijual setiap hari oleh Gerai A dalam tempoh 40 hari.
Jualan / Sales20 – 2930 – 3940 – 4950 – 5960 – 69
Bilangan hari / Number of days3815104

Bagi Gerai B, min jualan harian ialah 47.2 bungkus dan sisihan piawainya ialah 6.4 bungkus.The table above shows the number of packets of nasi lemak sold each day by Stall A over 40 days.
For Stall B, the mean daily sales is 47.2 packets and the standard deviation is 6.4 packets.
[3 marks] (a)Hitung min bilangan bungkus yang dijual sehari oleh Gerai A.Calculate the mean number of packets sold per day by Stall A.
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[3 marks] (b)Hitung varians dan sisihan piawai jualan Gerai A. Beri jawapan betul kepada dua tempat perpuluhan.Calculate the variance and standard deviation of the sales of Stall A. Give the answers correct to two decimal places.
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[2 marks] (c)Cari julat jualan Gerai A. Nyatakan kelas yang mengandungi median.Find the range of the sales of Stall A. State the class that contains the median.
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[2 marks] (d)Gerai manakah yang jualannya lebih konsisten? Pemilik pasar ingin memilih satu gerai untuk menyediakan bekalan tetap bagi sebuah kantin. Gerai manakah patut dipilih? Beri alasan anda.Which stall has more consistent sales? The market owner wants to choose one stall to give a steady supply to a canteen. Which stall should be chosen? Give your reason.
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[2 marks] (e)Selepas satu promosi, jualan Gerai A bertambah 5 bungkus setiap hari. Nyatakan min dan sisihan piawai yang baharu. Terangkan jawapan anda.After a promotion, the sales of Stall A increase by 5 packets every day. State the new mean and standard deviation. Explain your answer.
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For the teacher: Evaluating, high difficulty, Chapter 7, standard 7.2.3
Textbook p. 213
Test specification (JSU)
ChapterRememberingUnderstandingApplyingAnalysingEvaluatingCreatingItemsmarks
1. Variation–1 (1)2 (9)–––310
2. Matrices1 (1)–3 (6)–1 (12)–519
3. Consumer Mathematics: Insurance–1 (1)3 (10)–––411
4. Consumer Mathematics: Taxation–1 (1)3 (6)1 (10)––517
5. Congruency, Enlargement and Combined Transformations–1 (1)2 (5)–––36
6. Ratios and Graphs of Trigonometric Functions––2 (11)1 (1)––312
7. Measures of Dispersion for Grouped Data1 (1)–1 (1)2 (5)1 (12)–519
8. Mathematical Modeling–1 (1)2 (5)–––36
Total2 (2)5 (5)18 (53)4 (16)2 (24)0 (0)31100
Each cell shows items (marks).