Fast Track Kertas Model SPM Matematik

JADUAL ANALISIS SOALAN MATEMATIK SPM (1449) TABLE OF ANALYSIS SPM MATHEMATICS QUESTIONS (1449) Bab/ Chapter Kertas 1 Paper 1 (1449/1) Kertas 2 Paper 2 (1449/2) Ujian Bertulis (Objektif Aneka Pilihan) Ujian Bertulis (Subjektif Respons Terhad / Subjektif Berstruktur) 2021 2022 2021 2022 Tingkatan 1/ Form 1 1 Nombor Nisbah/ Rational Numbers – – 2 Faktor dan Gandaan/ Factors and Multiples – – 3 Kuasa Dua, Punca Kuasa Dua, Kuasa Tiga dan Punca Kuasa Tiga/ Squares, Square Roots, Cubes and Cube Roots – – 4 Nisbah, Kadar dan Kadaran Ratios, Rates and Proportions – 17(a)(i) 5 Ungkapan Algebra/ Algebraic Expressions – – 6 Persamaan Linear/ Linear Equations – 17(b) 7 Ketaksamaan Linear/ Linear Inequalities – – 8 Garis dan Sudut/ Lines and Angles – – 9 Poligon Asas/ Basic Polygons – – 10 Perimeter dan Luas/ Perimeter and Area – – 11 Pengenalan Set/ Introduction to Set – – 12 Pengendalian Data/ Data Handling 1 16(b) 13 Teorem Pythagoras The Pythagoras Theorem – – Tingkatan 2/ Form 2 1 Pola dan Jujukan/ Patterns and Sequences – 2(a), (b) 2 Pemfaktoran dan Pecahan Algebra Factorisation and Algebraic Fractions – 1 3 Rumus Algebra/ Algebraic Formulae 1 – 4 Poligon/ Polygons – – 5 Bulatan/ Circles – – 6 Bentuk Geometri Tiga Dimensi Three–Dimensional Geometrical Shapes – – 7 Koordinat/ Coordinates – – 8 Graf Fungsi/ Graphs of Functions – – 9 Laju dan Pecutan/ Speed and Acceleration – – 10 Kecerunan Garis Lurus Gradient of a Straight Line 2 – 11 Transformasi Isometri Isometric Transformations – – 12 Sukatan Kecenderungan Memusat Measures of Central Tendencies – – 13 Kebarangkalian Mudah/ Simple Probability – 17(a)(ii) Tingkatan 3/ Form 3 1 Indeks/ Indices 1 – 2 Bentuk Piawai/ Standard Form 2 – 3 Matematik Pengguna: Simpanan dan Pelaburan, Kredit dan Hutang Consumer Mathematics: Savings and Investments, Credit and Debt 3 – Bab/ Chapter Kertas 1 Paper 1 (1449/1) Kertas 2 Paper 2 (1449/2) Ujian Bertulis (Objektif Aneka Pilihan) Ujian Bertulis (Subjektif Respons Terhad / Subjektif Berstruktur) 2021 2022 2021 2022 4 Lukisan Berskala/ Scale Drawings 2 – 5 Nisbah Trigonometri/ Trigonometric Ratios – 3(a), (b), 16(c) 6 Sudut dan Tangen bagi Bulatan Angles and Tangents of Circles 1 – 7 Pelan dan Dongakan/ Plans and Elevations 1 12(a), (b) 8 Lokus dalam Dua Dimensi Loci in Two Dimensions 1 – 9 Garis Lurus/ Straight Lines – 7(a), (b) Tingkatan 4/ Form 4 1 Fungsi dan Persamaan Kuadratik dalam Satu Pemboleh Ubah/ Quadratic Functions and Equations in One Variable 2 – 2 Asas Nombor/ Number Bases 1 4 3 Penaakulan Logik/ Logical Reasoning 1 – 4 Operasi Set/ Operations on Sets 2 13(a), (b) 5 Rangkaian dalam Teori Graf Network in Graph Theory 1 17(d) 6 Ketaksamaan Linear dalam Dua Pemboleh Ubah/ Linear Inequalities in Two Variables 1 15(a), (b), (c), (d) 7 Graf Gerakan/ Graphs of Motion 2 16(a), 17(c) 8 Sukatan Serakan Data Tak Terkumpul Measures of Dispersion for Ungrouped Data 1 16(d) 9 Kebarangkalian Peristiwa Bergabung Probability of Combined Events 2 8 10 Matematik Pengguna: Pengurusan Kewangan Consumer Mathematics: Financial Management 2 9(a), (b) Tingkatan 5/ Form 5 1 Ubahan/ Variation 2 5(a), (b) 2 Matriks/ Matrices 2 14(a), (b) 3 Matematik Pengguna: Insurans Consumer Mathematics: Insurance – 6(b) 4 Matematik Pengguna: Percukaian Consumer Mathematics: Taxation 1 6(a) 5 Kekongruenan, Pembesaran dan Gabungan Transformasi Congruency, Enlargement and Combined Transformations 2 11(a), (b), (c) 6 Nisbah dan Graf Fungsi Trigonometri Ratios and Graphs of Trigonometric Functions 1 – 7 Sukatan Serakan Data Terkumpul Measures of Dispersion for Grouped Data 2 10(a), (b) 8 Pemodelan Matematik Mathematical Modeling – – Jumlah/ Total 40 17 IFC_FastTrack SPM Mate.indd 2 26/07/2023 5:05 PM

KERTAS MODEL SPM SPM MODEL PAPER Matematik/Mathematics Kertas 1/Paper 1 1449/1 1 jam 30 minit/1 hour 30 minutes 1 Jawab semua soalan. Answer all questions. 1. Luas permukaan lautan pada bumi ialah 361.1 juta km2 . Ungkapkan luas permukaan lautan tersebut dalam bentuk piawai. The surface area of the sea on the earth is 361.1 million km2 . Express the surface area of the sea in a standard form. A 3.611 × 105 B 3.611 × 106 C 3.611 × 107 D 3.611 × 108 2. ——————— 0.082 × 7 000 0.22 = A 1.435 × 104 B 1.435 × 105 C 2.87 × 102 D 2.87 × 103 3. Bundarkan 52.10528 betul kepada empat angka bererti. Round off 52.10528 correct to four significant figures. A 52.1 B 52.11 C 52.105 D 52.1053 4. Ungkapkan 3(54 ) + 52 + 19 sebagai suatu nombor dalam asas lapan. Express 3(54 ) + 52 + 19 as a number in base eight. A 32778 B 35778 C 42778 D 45778 5. Diberi 11100112 – 10010112 = 1510 + a510, cari nilai a. Given 11100112 – 10010112 = 1510 + a510, find the value of a. A 1 B 2 C 3 D 4 6. Dalam Rajah 1, AF ialah sisi sepunya bagi heksagon sekata ABCDEF dan poligon P. In Diagram 1, AF is the common side of the regular hexagon ABCDEF and polygon P. B A C D E F P Rajah 1 Diagram 1 Cari bilangan sisi bagi poligon P. Find the number of sides of polygon P. A 8 B 10 C 12 D 14 7. Dalam Rajah 2, PQR ialah tangen kepada bulatan di Q. In Diagram 2, PQR is a tangent to the circle at Q. 75° S P Q R y Rajah 2 Diagram 2 Cari nilai y. Find the value of y. A 30° B 45° C 55° D 75° KM1 K1 – 1 © Pan Asia Publications Sdn. Bhd. KM1_K1&2 Fast track Mate SPM.indd 1 21/07/2023 9:11 AM

28. Rajah 9 menunjukkan graf laju-masa bagi pergerakan suatu zarah dalam tempoh t saat. Diagram 9 shows the speed-time graph for the movement of a particle for a period of t seconds. 4 4 7 Laju (m s–1) Speed (m s–1) Masa (s) Time (s) O t Rajah 9 Diagram 9 Diberi jumlah jarak yang dilalui oleh zarah itu dalam tempoh t saat ialah 50 m, hitung nilai t. Given the total distance travelled by the particle in a period of t seconds is 50 m, calculate the value of t. A 8 B 9 C 10 D 11 29. Dalam Rajah 10, segi tiga L ialah imej bagi segi tiga K di bawah suatu putaran 90° lawan arah jam. In Diagram 10, triangle L is the image of triangle K under an anticlockwise rotation of 90°. A B C D L K Rajah 10 Diagram 10 Antara titik A, B, C dan D, yang manakah pusat putaran itu? Which of the points A, B, C and D is the centre of the rotation? 30. Rajah 11 menunjukkan skor yang diperoleh sekumpulan murid dalam suatu kuiz. Diagram 11 shows the scores obtained by a group of pupils in a quiz. 37 49 44 40 95 82 39 47 52 50 48 Rajah 11 Diagram 11 Hitung julat antara kuartil bagi set data itu. Calculate the interquartile range of the data set. A 12 C 14 B 13 D 15 31. Rajah 12 ialah plot batang-dan-daun yang menunjukkan tinggi, dalam cm, bagi sekumpulan murid. Diagram 12 is a stem-and-leaf plot that shows the height, in cm, of a group of pupils. Batang Stem Daun Leaf 15 16 17 18 0 4 5 6 8 2 2 4 5 6 7 9 3 5 6 7 8 9 0 1 Kekunci: 15 | 0 bermakna 150 cm Key: 15 | 0 means 150 cm Rajah 12 Diagram 12 Tentukan sisihan piawai bagi data itu. Determine the standard deviation of the data. A 9.43 C 9.33 B 9.44 D 9.34 32. Rajah 13 menunjukkan suatu graf mudah. Diagram 13 shows a simple graph. A E B C D Rajah 13 Diagram 13 Cari bilangan bucu bagi graf mudah itu. Find the number of vertices of the simple graph. A 5 C 7 B 6 D 14 © Pan Asia Publications Sdn. Bhd. KM1 K1 – 6 KM1_K1&2 Fast track Mate SPM.indd 6 21/07/2023 9:11 AM

KERTAS MODEL SPM SPM MODEL PAPER Matematik/Mathematics Kertas 2/Paper 2 1449/2 2 jam 30 minit/2 hours 30 minutes 1 Bahagian A Section A [40 markah] [40 marks] Jawab semua soalan. Answer all questions. 1. Diberi bahawa set semesta, ξ = {x : 20 < x < 30, x ialah suatu integer}, set A = {21, 23, 25, 27, 29} dan set B = {20, 25, 30}. Given that the universal set, ξ = {x : 20 < x < 30, x is an integer}, set A = {21, 23, 25, 27, 29} and set B = {20, 25, 30}. (a) Lengkapkan gambar rajah Venn di ruang jawapan untuk menunjukkan hubungan antara set ξ, set A dan set B. [1 markah] Complete the Venn diagram in the answer space to show the relationship among sets ξ, A and B. [1 mark] (b) Cari Aʹ  B. [2 markah] Find Aʹ  B. [2 marks] Jawapan/ Answer: (a) ξ (b) KM1 K2 – 1 © Pan Asia Publications Sdn. Bhd. KM1_K1&2 Fast track Mate SPM.indd 1 21/07/2023 9:11 AM

Bahagian B Section B [45 markah] [45 marks] Jawab semua soalan. Answer all questions. 11. Rajah 7 menunjukkan duit saku mingguan, dalam RM, yang diterima oleh 40 orang murid di sebuah sekolah. Diagram 7 shows the weekly pocket-money, in RM, received by 40 pupils in a school. 24 28 34 10 17 10 25 28 20 22 12 36 40 11 17 15 25 27 43 27 23 32 36 19 23 28 14 12 28 28 34 18 33 30 24 18 18 22 33 22 Rajah 7 Diagram 7 (a) Berdasarkan data dalam Rajah 7, lengkapkan Jadual 2 di ruang jawapan. [4 markah] Based on the data in Diagram 7, complete Table 2 in the answer space. [4 marks] (b) Berdasarkan Jadual 2, tentukan kelas mod dan julat bagi duit saku mingguan. [2 markah] Based on Table 2, determine the modal class and range for the weekly pocket-money. [2 marks] (c) Untuk ceraian soalan ini, gunakan kertas graf yang disediakan di halaman KM1K2-10. Menggunakan skala 2 cm kepada RM5 pada paksi mengufuk dan 2 cm kepada 5 orang murid pada paksi mencancang, lukis satu ogif bagi data tersebut. Seterusnya, tentukan median bagi data tersebut. [4 markah] For this part of the question, use the graph paper provided on page KM1K2-10. Using a scale of 2 cm to RM5 on the horizontal axis and 2 cm to 5 pupils on the vertical axis, draw an ogive for the data. Hence, determine the median of the data. [4 marks] Jawapan/ Answer: (a) Selang kelas Class interval Sempadan atas Upper boundary Kekerapan Frequency Kekerapan longgokan Cumulative frequency 1 – 5 6 – 10 11 – 15 16 – 20 21 – 25 26 – 30 31 – 35 36 – 40 41 – 45 Jadual 2 Table 2 (b) (c) Median/ Median = KM1 K2 – 9 © Pan Asia Publications Sdn. Bhd. KM1_K1&2 Fast track Mate SPM.indd 9 21/07/2023 9:11 AM

Graf untuk Soalan 11 Graph for Question 11 © Pan Asia Publications Sdn. Bhd. KM1 K2 – 10 KM1_K1&2 Fast track Mate SPM.indd 10 21/07/2023 9:11 AM

Bahagian C Section C [15 markah] [15 marks] Bahagian ini mengandungi dua soalan. Jawab satu soalan. This section consists of two questions. Answer one question. 16. (a) Encik Azizul mempunyai polisi insurans perubatan dengan deduktibel sebanyak RM20 000 setahun dan had tahunan bernilai RM200 000. Pada tahun pertama dalam tempoh insuransnya, Encik Azizul telah dimasukkan ke hospital swasta untuk pembedahan kaki akibat kemalangan jalan raya. Dia dikenakan kos rawatan sebanyak RM15 000. Pada tahun kedua dalam tempoh insuransnya, Encik Azizul telah menjalani rawatan kanser dengan kos sebanyak RM150 000. Hitung jumlah kos rawatan yang perlu ditanggung oleh Encik Azizul dan jumlah kos rawatan yang dibayar oleh syarikat insurans bagi tahun pertama dan tahun kedua polisi insuransnya. [5 markah] Mr Azizul has a medical insurance policy with a deductible of RM20 000 per annum and an annual limit of RM200 000. In the first year of his insurance period, Mr Azizul was admitted to a private hospital for foot surgery as a result of road accident. He was charged a treatment cost of RM15 000. In the second year of his insurance period, Mr Azizul underwent cancer treatment with a cost of RM150 000. Calculate the total treatment cost to be borne by Mr Azizul and the total treatment cost paid by the insurance company for the first and second year of his insurance policy. [5 marks] Jawapan/ Answer: (a) (b) Encik James dan isterinya memperoleh gaji tahunan masing-masing sebanyak RM74 000 dan RM58 000 pada tahun 2020. Pada tahun tersebut, Encik James dan isteri masing-masing telah menderma sebanyak RM600 kepada tabung pandemik Covid-19 dan RM450 kepada sebuah badan kebajikan yang diluluskan oleh kerajaan. Jadual 4 menunjukkan jadual pelepasan cukai yang ingin dituntut oleh Encik James dan isterinya manakala Jadual 5 menunjukkan sebahagian daripada kadar cukai pendapatan individu pada tahun 2020. Mr James and his wife earn an annual salaries of RM74 000 and RM58 000 respectively in 2020. In that year, Mr James and his wife each donated RM600 to the Covid-19 pandemic fund and RM450 to a charity certified by the government. Table 4 shows the tax relief schedule to be claimed by Mr James and his wife whereas Table 5 shows part of the individual income tax rates in the year 2020. Pelepasan cukai Tax relief Encik James (RM) Mr James (RM) Isteri (RM) Wife (RM) Individu Individual 9 000 9 000 Gaya hidup (terhad RM2 500) Lifestyle (limited to RM2 500) 3 000 3 300 Insurans hayat dan KWSP (terhad RM7 000) Life insurance and EPF (limited to RM7 000) 8 900 7 200 Insurans perubatan (terhad RM3 000) Medical insurance (limited to RM3 000) 2 600 2 100 Yuran pengajian sendiri (terhad RM7 000) Self-study fees (limited to RM7 000) 4 300 3 700 Jadual 4 Table 4 KM1 K2 – 17 © Pan Asia Publications Sdn. Bhd. KM1_K1&2 Fast track Mate SPM.indd 17 21/07/2023 9:11 AM

KERTAS MODEL SPM SPM MODEL PAPER Matematik/Mathematics Kertas 1/Paper 1 1449/1 4 1 jam 30 minit/1 hour 30 minutes KM4 K1 – 1 © Pan Asia Publications Sdn. Bhd. Jawab semua soalan. Answer all questions. 1. Yang manakah bukan ciri sistem perbankan Islam? Which of the following is not the characteristic of Islamic banking system? A Kadar pulangan ditentukan pada peringkat awal penyimpanan. The rate of return is determined on the early stage of savings. B Berdasarkan hukum Islam (syarak). Based on the Islamic law (syarak). C Risiko diuruskan mengikut penjanjian. Risk is managed according to the agreement. D Berdasarkan prinsip keadilan, halal dan perkongsian keuntungan tanpa riba. Based on the principle of justice, halal and profitsharing without usury. 2. Apakah yang dimaksudkan dengan ko-insurans? What is the meaning of co-insurance? A Suatu jumlah yang perlu ditanggung oleh pemegang polisi sebelum layak membuat tuntutan daripada syarikat insurans. An amount that must be borne by the policyholder before they can make a claim from the insurance company. B Perkongsian bersama kerugian antara syarikat insurans dengan pemegang polisi. Cost sharing of the loss between the insurance company and the policyholder. C Perlindungan yang diberikan jika pemegang polisi mengalami kecederaan anggota badan, kecacatan, hilang upaya ataupun meninggal dunia berpunca secara langsung daripada kemalangan. Coverage given if the policyholder suffers a bodily injury, disability or death resulting directly from accident. D Perlindungan terhadap kerugian akibat kebakaran, kilat dan letupan yang berlaku pada rumah kediaman atau bangunan perniagaan. Coverage against damage caused by fire, lightning and explosion that occur at home or business premise. 3. Rajah 1 menunjukkan sebuah bulatan unit yang dilukis pada satah Cartes dengan O sebagai asalan. Diagram 1 shows a unit circle drawn on a Cartesian plane with O as the origin. A(0.40, 0.91) B(–0.82, –0.57) y x β α O Rajah 1 Diagram 1 Cari nilai sin a – cos b. Find the value of sin a – cos b. A 0.09 C 1.73 B 0.42 D 2.70 4. Rajah 2 menunjukkan heksagon PʹQʹRʹSʹTʹUʹ ialah imej bagi heksagon PQRSTU di bawah suatu pembesaran dengan faktor skala 2k – 1. Diagram 2 shows hexagon PʹQʹRʹSʹTʹUʹ is an image of hexagon PQRSTU under an enlargement with a scale factor of 2k – 1. Q' R' S' T' U' P' Q P R S T U Rajah 2 Diagram 2 Nyatakan nilai k. State the value of k. A 2 C 4 B 3 D 5 KM4_K1&2 Fast track Mate SPM.indd 1 21/07/2023 9:13 AM

KM4 K1 – 3 © Pan Asia Publications Sdn. Bhd. 11. Antara graf laju-masa berikut, yang manakah mempunyai pecutan melebihi 5 m s–2? Which of the following speed-time graphs has the acceleration greater than 5 m s–2? A 0 8 18 15 Masa (s) Time (s) Laju (m s–1) Speed (m s–1) B 0 6 22 18 Masa (s) Time (s) Laju (m s–1) Speed (m s–1) C 0 2 25 12 Masa (s) Time (s) Laju (m s–1) Speed (m s–1) D 0 5 12 9 Masa (s) Time (s) Laju (m s–1) Speed (m s–1) 12. Diberi bahawa P = {Nombor perdana kurang daripada 100} dan Q = {2, h, k, l, 97}. Jika Q ⊂ P, tentukan nilai h, k dan l yang mungkin. Given that P = {Prime number less than 100} and Q = {2, h, k, l, 97}. If Q ⊂ P, determine the possible values of h, k and l. A h = 3, k = 53 dan/ and l = 67 B h = 4, k = 15 dan/ and l = 88 C h = 19, k = 73 dan/ and l = 87 D h = 17, k = 73 dan/ and l = 81 13. Rajah 5 menunjukkan sebuah trapezium ABCD. Diagram 5 shows a trapezium ABCD. 58° 62° A h° k° B D P C Rajah 5 Diagram 5 Jika AB = AP, cari nilai h + k. If AB = AP, find the value of h + k. A 94 C 112 B 108 D 156 14. Dalam Rajah 6, PQR dan QST ialah garis lurus. In Diagram 6, PQR and QST are straight lines. 122 cm P Q R S T y x Rajah 6 Diagram 6 Diberi bahawa sin x = 60 61, QR = TQ dan TS : SQ = 1 : 3, cari nilai tan y. Given that sin x = 60 61, QR = TQ and TS : SQ = 1 : 3, find the value of tan y. A 3 5 C 3 2 B 4 5 D 4 3 15. Diberi bahawa 3(2k + hk) – 2k(h – 1) = 5, ungkapkan k dalam sebutan h. Given that 3(2k + hk) – 2k(h – 1) = 5, express k in terms of h. A k = h 5 + 8 B k = 5 h + 8 C k = 15 h – 8 D k = 8 h + 5 16. ( q3 p2 ) 2 × p4 q6 = A p4 q9 C p–4q–6 B p2 q–6 D p–2q9 KM4_K1&2 Fast track Mate SPM.indd 3 21/07/2023 9:13 AM

KERTAS MODEL SPM SPM MODEL PAPER Matematik/Mathematics Kertas 2/Paper 2 1449/2 4 2 jam 30 minit/2 hours 30 minutes Bahagian A Section A [40 markah] [40 marks] Jawab semua soalan. Answer all questions. KM4 K2 – 1 © Pan Asia Publications Sdn. Bhd. 1. Rajah 1 menunjukkan tiga susunan mancis yang pertama mengikut suatu jujukan. Diagram 1 shows the first three arrangement of matchsticks according to a sequence. Rajah 1 Diagram 1 (a) Nyatakan pola bagi jujukan itu. [1 markah] State the pattern of the sequence. [1 mark] (b) Hitung jumlah bilangan mancis dari susunan ke-8 hingga susunan ke-12 bagi jujukan itu. [1 markah] Calculate the total number of matchsticks from the 8th to the 12th arrangement of the sequence. [1 mark] Jawapan/ Answer: (a) (b) 2. Lydia akan pergi berjoging di taman yang berdekatan dengan rumahnya jika dia tidak bekerja pada hari tersebut. Diberi bahawa dia tidak bekerja sebanyak dua hari dalam seminggu dan kebarangkalian Lydia akan pergi berjoging di taman ialah 3 5, hitung kebarangkalian dia tidak pergi berjoging di taman pada suatu hari tertentu. [2 markah] Lydia will go jogging at a park near her house if she does not work on that particular day. Given that she does not work two days a week and the probability that Lydia will go jogging at the park is 3 5, calculate the probability that she will not go jogging at the park on a particular day. [2 marks] Jawapan/ Answer: KM4_K1&2 Fast track Mate SPM.indd 1 21/07/2023 9:13 AM

© Pan Asia Publications Sdn. Bhd. KM4 K2 – 10 13. Rajah 9 menunjukkan gabungan pepejal dua buah prisma tegak masing-masing dengan tapak segi empat tepat AGVHBU dan BPSH yang terletak pada satah mengufuk. Sebuah semi silinder dikeluarkan daripada salah satu prisma tersebut. AUBPQRCDEF ialah keratan rentas seragam bagi kedua-dua buah prisma tegak tersebut. Diberi bahawa tepi AF, GL, BC, HI, PQ dan ST adalah tegak dan diameter bagi semi silinder ialah 2 cm. Diagram 9 shows the composite solid of two right prisms with the rectangular bases AGVHBU and BPSH respectively which lie on a horizontal plane. A semi-cylinder is taken out from one of the prisms. AUBPQRCDEF is the uniform cross-section of both right prisms. Given that the edges AF, GL, BC, HI, PQ and ST are vertical and the diameter of the semi-cylinder is 2 cm. A G Y X L F E U B P Q R C D T S V H K J I W 3 cm 6 cm 3 cm 2 cm 1 cm 1 cm 1 cm 4 cm 3 cm Rajah 9 Diagram 9 Lukis dengan skala penuh, Draw to full scale, (a) dongakan gabungan pepejal itu pada satah mencancang yang selari dengan AU dan BP sebagaimana dilihat dari arah X, [4 markah] the elevation of the composite solid on a vertical plane parallel to AU and BP as viewed from X, [4 marks] (b) dongakan gabungan pepejal itu pada satah mencancang yang selari dengan AG sebagaimana dilihat dari arah Y. [5 markah] the elevation of the composite solid on a vertical plane parallel to AG as viewed from Y. [5 marks] KM4_K1&2 Fast track Mate SPM.indd 10 21/07/2023 9:13 AM

© Pan Asia Publications Sdn. Bhd. KM4 K2 – 16 16. Encik Ahmad bekerja sebagai seorang guru sukan di sebuah sekolah menengah di negeri Selangor. Mr Ahmad works as a sport teacher in a secondary school in Selangor. (a) Pada hari persekolahan, Encik Ahmad akan memandu dari rumahnya ke sekolah. Beliau akan berhenti di sebuah kedai makan yang berada di perjalanan antara rumah dan sekolah untuk sarapan pagi. Rajah 10 menunjukkan graf jarak-masa bagi kereta Encik Ahmad pada hari persekolahan tertentu. On schooling day, Mr Ahmad will drive from his house to the school. He will stop at an eatery shop which is located on the route between his house and the school for breakfast. Diagram 10 shows the distance-time graph for Mr Ahmad’s car on a certain schooling day. Jarak (km) Distance (km) Masa (minit) Time (minute) 15 50 15 8 0 28 Rajah 10 Diagram 10 (i) Nyatakan masa yang paling lewat Encik Ahmad perlu bertolak dari rumahnya jika beliau perlu tiba di sekolah sebelum atau pada 6.55 a.m.. State the latest time Mr Ahmad must leave from his house if he has to reach the school not later than 6.55 a.m.. (ii) Hitung laju purata, dalam km min–1, bagi kereta beliau. Calculate the average speed, in km min–1, of his car. [3 markah] [3 marks] Jawapan/ Answer: (a) (i) (ii) (b) Rajah 11 menunjukkan carta pai bagi pembahagian gaji bulanan Encik Ahmad. Diagram 11 shows the pie chart of the division of the monthly salary of Mr Ahmad. Pelaburan Investment Simpanan Savings Hiburan Entertainment Pengangkutan Transportation Makanan Foods 110° Rajah 11 Diagram 11 Bahagian C Section C [15 markah] [15 marks] Bahagian ini mengandungi dua soalan. Jawab satu soalan. This section consists of two questions. Answer one question. KM4_K1&2 Fast track Mate SPM.indd 16 21/07/2023 9:13 AM

J1 © Pan Asia Publications Sdn. Bhd. JAWAPAN/ ANSWERS Kertas Model 1/ Model Paper 1 Kertas 1/ Paper 1 1. D 2. A 3. B 4. B 5. B 6. C 7. B 8. D 9. C 10. C 11. D 12. B 13. A 14. A 15. C 16. C 17. A 18. A 19. C 20. A 21. C 22. B 23. C 24. C 25. B 26. B 27. C 28. A 29. B 30. A 31. B 32. A 33. B 34. C 35. B 36. D 37. D 38. C 39. D 40. C Kertas 2/ Paper 2 Bahagian A/ Section A 1. (a) A B • 21 • 23 • 27 • 29 • 20 • 30 • 25 • 22 • 24 • 26 • 28 ξ (b) Aʹ = {20, 22, 24, 26, 28, 30} Aʹ  B = {20, 22, 24, 26, 28, 30}  {20, 25, 30} = {20, 30} 2. —1 2 × —4 3 × —– 22 7 × 1—– 21 2 2 3 + —– 22 7 × 1—– 14 2 2 2 × h = 5 412 2 425.5 + 154h = 5 412 154h = 2 986.5 h = 19.39 ∴ Tinggi silinder/ Height of cylinder = 19.39 cm 3. (a) mAB = mCD mAB = —–—– 0 – 5 2 – 0 = – —5 2 5 = – —5 2 (3) + c c = —– 25 2 ∴ Persamaan garis lurus AB ialah y = – — 5 2 x + —– 25 2 . The equation of the straight line AB is y = – —5 2 x + —– 25 2 . (b) 0 = – —5 2 x + —– 25 2 x = 5 ∴ Pintasan-x/ x-intercept = 5 4. (a) Perimeter kawasan berlorek Perimeter of the shaded region = 14 + —––– 180° 360° × 2 × —– 22 7 × 7 + 2 × —– 22 7 × 3.5 = 14 + 22 + 22 = 58 cm (b) Luas kawasan berlorek Area of the shaded region = —––– 180° 360° × —– 22 7 × 72 – —– 22 7 × 3.52 = 77 – 38.5 = 38.5 cm2 5. (a) 100 80 60 40 20 O 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Laju (km j–1) Speed (km h–1) Masa (j) Time (h) (b) Kadar perubahan laju Rate of change of speed = (0 – 80) km j–1/ km h–1 —–—————————– (0.7 – 0.5) j/ h = –400 km j–2/ km h–2 (c) Jarak/ Distance = 80 × 0.5 + — 1 2 × 80 × 0.2 = 40 + 8 = 48 km 6. (a) 1 bahagian/ part = 4 keping/ pieces 2 bahagian/ parts = 7 keping/ pieces 3 bahagian/ parts = 10 keping/ pieces Jadi/ So, n = 3n + 1 Bilangan kepingan kayu untuk 30 bahagian Number of pieces of wood for 30 parts = 3(30) + 1 = 91 keping/ pieces (b) 127 = 3(n) + 1 n = 42 bahagian/ parts Jawapan Lengkap (Kertas 1) Complete Answers (Paper 1) https://bit.ly/442S71e Jaw_Fast Track SPM Matematik.indd 1 14/07/2023 12:35 PM

© Pan Asia Publications Sdn. Bhd. J2 7. Andaikan umur Fatin ialah x tahun. Let the age of Fatin is x years. Jadi, umur adik Fatin ialah (x – 4) tahun. So, the age of Fatin’s sister is (x – 4) years. x(x – 4) = 96 x2 – 4x – 96 = 0 (x – 12)(x + 8) = 0 x = 12 atau/ or x = –8 Oleh sebab umur tidak boleh negatif, maka umur Fatin ialah 12 tahun. Since age cannot be negative, thus the age of Fatin is 12 years. 8. (a) V = {A, B, C, D, E, F) n(V) = 6 (b) E = {(A, B), (A, F), (A, A), (B, C), (B, B), (C, D), (C, F), (C, F), (D, E), (E, F)} n(E) = 10 9. (a) (i) atau/ or (ii) dan/ and (b) (i) PQ dan RS adalah garis selari. PQ and RS are parallel lines. (ii) 1 + 4n2 , n = 1, 2, 3, 4, … 10. (a) Kebarangkalian bahawa kedua-dua murid itu memilih persatuan Matematik Probability that both pupils choose mathematics association = —5 7 × —4 6 = —– 10 21 (b) Kebarangkalian bahawa kedua-dua murid itu mempunyai jantina yang sama Probability that both pupils have the same gender = —2 8 × —1 7 + —6 8 × —5 7 = —– 1 28 + —– 15 28 = —4 7 Bahagian B/ Section B 11. (a) Selang kelas Class interval Sempadan atas Upper boundary Kekerapan Frequency Kekerapan longgokan Cumulative frequency 1 – 5 5.5 0 0 6 – 10 10.5 2 2 11 – 15 15.5 5 7 16 – 20 20.5 7 14 21 – 25 25.5 9 23 26 – 30 30.5 8 31 31 – 35 35.5 5 36 36 – 40 40.5 3 39 41 – 45 45.5 1 40 (b) Kelas mod/ Modal class = 21 – 25 Julat/ Range = Titik tengah kelas tertinggi – Titik tengah kelas terendah Midpoint of the highest class – Midpoint of the lowest class = 43 – 8 = 35 (c) 40 35 30 25 20 15 10 5 0 5.5 10.5 15.5 20.5 25.5 30.5 35.5 40.5 45.5 Median/ Median = 24 Duit saku (RM) Pocket-money (RM) Kekerapan longgokan Cumulative frequency Median/ Median = 24 12. (a) H / D G / L / C O / J N / I K / H P M E / A F / B 3 cm 6 cm 1 cm 2 cm 1 cm (b) 2 cm 2 cm 1 cm 3 cm 3 cm 6 cm 5 cm F / E G / H B / A I / H J / C / D N / M O / P K L 13. (a) x = –12, y = 8 x = –8, y = 9.5 Jaw_Fast Track SPM Matematik.indd 2 14/07/2023 12:35 PM

J7 © Pan Asia Publications Sdn. Bhd. (c) Andaian: Pemanjangan spring adalah berkadar malar dengan pertambahan berat beban yang sepadan. Assumption: The extensions of the spring is constantly proportional with the increment of the corresponding weight of load. Pemboleh ubah yang terlibat ialah pemanjangan spring, x cm, dan berat beban, w N. The variables involved are the extensions of the spring, x cm, and the weight of load, w N. 14. (a) (i) H ialah translasi 1 6 2 –2 . H is a translation 1 6 2 –2 . (ii) K ialah pembesaran dengan faktor skala 3 pada pusat P. K is an enlargement about the centre P with a scale factor of 3. (b) Pembesaran dengan faktor skala 3 pada pusat (–12, 6). Enlargement about the centre (–12, 6) with a scale factor of 3. (c) Katakan A ialah luas suku bulatan ABC. Let A be the area of the quadrant ABC. Luas kawasan berlorek = 18π Area of the shaded region A × 32 – A = 18π 9A – A = 18π 8A = 18π A = —– 18 8 π A = —9 4 π πr2 —–– 4 = —9 4 π r2 = 9 r = 3 cm 15. (a) Bilangan ahli isi rumah Number of household members 1 2 3 4 5 6 7 Bilangan rumah (unit) Number of houses (unit) 6 9 9 8 5 2 1 (b) Kuartil pertama/ First quartile = 1—– 40 4 2th + 1—– 40 4 + 12th ————————— 2 = —————– 10th + 11th 2 = ——–– 2 + 2 2 = 2 Median/ Median = 1—– 40 2 2th + 1—– 40 2 + 12th ————————— 2 = —————– 20th + 21th 2 = ——–– 3 + 3 2 = 3 Kuartil ketiga/ Third quartile = 1——–– 3(40) 4 2th + 1——–– 3(40) 4 + 12th ———————————– 2 = —————– 30th + 31th 2 = ——–– 4 + 4 2 = 4 (c) x f fx fx2 1 6 6 6 2 9 18 36 3 9 27 81 4 8 32 128 5 5 25 125 6 2 12 72 7 1 7 49 Σf = 40 Σfx = 127 Σfx2 = 497 Varians/ Variance = Σfx2 ——Σf – 1 Σfx ——Σf 2 2 = —–– 497 40 – 1—–– 127 40 2 2 = 2.3444 Sisihan piawai/ Standard deviation =  2.3444 = 1.5311 Bahagian C/ Section C 16. (a) Jumlah bilangan jam kerja lebih masa Total number of hours of overtime work = 3 + 2 + 3 + 5 + 5 + 3 + 1 + 2 + 2 + 4 + 4 + 5 + 3 + 2 + 1 + 1 + 4 + 2 + 2 + 4 + 5 + 2 + 2 + 3 + 4 + 3 + 2 + 2 = 81 Jumlah bayaran gaji pada Januari 2020 Total salary payment in January 2020 = 2 998 2 350 + 81 × x = 2 998 81x = 2 998 – 2 350 x = 8 Jumlah bayaran gaji pada Februari 2020 Total salary payment in February 2020 = 2 350 + 58 × 8 = RM2 814 (b) (i) Encik Sim (RM) Mr Sim (RM) Isteri (RM) Wife (RM) Jumlah pendapatan Total income RM28 200 + RM7 592 = RM35 792 RM54 000 Jumlah pengecualian Total exemption –RM1 350 –RM1 100 Individu Individual –RM9 000 –RM9 000 Gaya hidup Lifestyle –RM2 500 –RM2 100 KWSP dan insurans hayat EPF and life insurance –RM5 800 –RM4 500 Jaw_Fast Track SPM Matematik.indd 7 14/07/2023 12:35 PM

J – 1 © Pan Asia Publications Sdn. Bhd. JAWAPAN/ANSWERS Kertas Model 1/ Model Paper 1 Kertas 1/ Paper 1 1. D Luas permukaan lautan Surface area of the sea = 361.1 × 1 000 000 = 361 100 000 = 3.611 × 108 2. A ———––——–– 0.082 × 7 000 0.22 = ——– 574 0.04 = 14 350 = 1.435 × 104 3. B 52.10528 Tambah 1 kepada digit 0 kerana digit seterusnya, 5, adalah sama dengan 5. Add 1 to the digit 0 since the next digit, 5, is equal to 5. = 52.11 (4 angka bererti/ significant figures) 4. B 3(54 ) + 52 + 19 = 3(625) + 25 + 19 = 191910 8 1919 Baki/ Remainder 8 239 ... 7 8 29 ... 7 8 3 ... 5 0 ... 3 ∴ 3(54 ) + 52 + 19 = 35778 5. B 11100112 – 10010112 = 1510 + a510 1010002 = 1510 + a510 25 + 23 = 1510 + a510 4010 = 1510 + a510 a510 = 4010 – 1510 a510 = 2510 ∴ a = 2 6. C Sudut pedalaman bagi heksagon sekata Interior angle of regular hexagon = (6 – 2) × 180° —–—————– 6 = —––– 720° 6 = 120° Sudut pedalaman bagi poligon P Interior angle of polygon P = 360° – 120° – 90° = 150° Bilangan sisi bagi poligon P Number of sides for polygon P = 360° —–————– 180° – 150° = 12 7. B y = 180° – 105° – 30° = 45° 8. D kos ∠ACD/ cos ∠ACD = – 12 52 + 122  = – —– 12 13 9. C Daripada graf/ From the graph, –kos 180°/ –cos 180°= 1 2α = 1 α = —1 2 –kos x/ –cos x = – —1 2 = –0.5 x = 60° Koordinat bagi titik A ialah (60°, –0.5). The coordinates of point A is (60°, –0.5). 10. C ——– h h – 3 = — 3 k hk = 3(h – 3) hk – 3h = –9 h(k – 3) = –9 h = ——– –9 k – 3 h = ——– 9 3 – k 11. D 11 – 4(2 – 2k) = 23 11 – 8 + 8k = 23 8k = 20 k = —– 20 8 k = 2— 1 2 12. B 32x = ——256 8x 32x × 8x= 256 256x = 256 x = 1 JawLengkap_Fast Track SPM Mate.indd 1 18/07/2023 11:35 AM

J – 9 © Pan Asia Publications Sdn. Bhd. Jumlah jarak yang dilalui, S (m) Total distance travelled, S (m) O Masa, t (s) Time, t (s) Kecerunan/ Gradient = ———– 40 – 0 25 – 0 = —8 5 Maka, model matematik yang mewakili maklumat dalam Jadual 3 ialah S = —8 5 t. Thus, the mathematical model that represents the information in Table 3 is S = —8 5 t. 31. C Jumlah jarak yang dilalui oleh zarah Total distance travelled by the particle = —1 2 × 5 × (10 + 3) + 3 × 3 + —1 2 × 4 × 3 = 47.5 m 32. B Jumlah insurans yang harus dibeli oleh Encik Ngu Amount of insurance that Mr Ngu should buy = RM600 000 × 75% = RM450 000 33. A Pokok ialah graf terkait yang tidak mempunyai kitar, gelung atau berbilang tepi. Tree is a connected graph that has no cycle, loop or multiple edges. 34. C Daripada plot kotak/ From the box plot, Kuartil pertama/ First quartile = 40 Kuartil ketiga/ Third quartile = 95 Julat antara kuartil/ Interquartile range = 95 – 40 = 55 35. D 45° 3.3 m 1.75 m 7 m h tan 45° = —h 7 h = 7 tan 45° h = 7 m Ketinggian tegak belon udara panas dari permukaan tanah Vertical height of the hot air balloon from the ground surface = 1.75 + 7 + 3.3 = 12.05 m 36. B P ξ R Q 7 4 9 3 5 12 Kebarangkalian bahawa murid tidak terlibat dalam manamana tiga kelab Probability that the pupil does not involved in any of the three clubs = —– 12 40 = —– 3 10 37. D Perbelanjaan tetap Fixed expenses = (RM8 800 – RM3 100) × —2 3 = RM3 800 38. B VU 1 —3 = k V = k ——– 3U V ∝ 1 ——– 3U ∴ V berubah secara songsang dengan punca kuasa tiga U. V varies inversely as the cube root of U. 39. B [3 2 5] + 3[–1 3 1] – 2[–3 4 –2] = [3 2 5] + [–3 9 3] – [–6 8 –4] = [3 – 3 – (–6) 2 + 9 – 8 5 + 3 – (–4)] = [6 3 12] 40. A [2 1]3 2p 4 –p = [2p + 3] [2(2p) + 1(–p)] = [2p + 3] 4p – p = 2p + 3 3p – 2p = 3 p = 3 Kertas Model 4/ Model Paper 4 Kertas 1/ Paper 1 1. A Kadar pulangan yang sebenar ditentukan selepas tempoh matang. The actual rate of return is determined upon maturity. 2. B Ko-insurans merupakan perkongsian bersama kerugian antara syarikat insurans dengan pemegang polisi. Co-insurance is the cost sharing of the loss between the insurance company and the policyholder. JawLengkap_Fast Track SPM Mate.indd 9 18/07/2023 11:35 AM

My progress in FAST TRACK SPM Model Paper Sila isikan markah anda dalam ruang yang disediakan untuk menilai prestasi anda. Please fill your marks in the space provided to track your progress. Prestasi saya dalam FAST TRACK Kertas Model SPM Kertas Model SPM SPM Model Paper 1 Kertas / Bahagian Paper / Section Markah penuh Full marks Markah diperoleh Marks obtained Kertas 1 Paper 1 40 Jumlah Total Kertas 2 Paper 2 Bahagian A Section A 40 Bahagian B Section B 45 Bahagian C Section C 15 Jumlah Total Kertas Model SPM SPM Model Paper 3 Kertas / Bahagian Paper / Section Markah penuh Full marks Markah diperoleh Marks obtained Kertas 1 Paper 1 40 Jumlah Total Kertas 2 Paper 2 Bahagian A Section A 40 Bahagian B Section B 45 Bahagian C Section C 15 Jumlah Total Kertas Model SPM SPM Model Paper 2 Kertas / Bahagian Paper / Section Markah penuh Full marks Markah diperoleh Marks obtained Kertas 1 Paper 1 40 Jumlah Total Kertas 2 Paper 2 Bahagian A Section A 40 Bahagian B Section B 45 Bahagian C Section C 15 Jumlah Total Kertas Model SPM SPM Model Paper 4 Kertas / Bahagian Paper / Section Markah penuh Full marks Markah diperoleh Marks obtained Kertas 1 Paper 1 40 Jumlah Total Kertas 2 Paper 2 Bahagian A Section A 40 Bahagian B Section B 45 Bahagian C Section C 15 Jumlah Total IBC_FastTrack SPM Mate 1 24/07/2023 9:39 AM