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SPM 2021-2025 JAWAPAN © Pustaka Yakin Pelajar Sdn. Bhd. J1 1449 • MATEMATIK SIJIL PELAJARAN MALAYSIA 2021 KERTAS 1 1 D A: 1 050 kilometer / kilometre = 1.05 × 103 kilometer / kilometre → Salah / Incorrect B: 0.75 teraliter / teralitre = 7.5 × 10−1 teraliter / teralitre → Salah / Incorrect C: 0.089 fentometer / fentometre = 8.9 × 10−2 fentometer / fentometre → Salah / Incorrect D: 2 160 gigabait / gigabyte = 2.16 × 103 gigabait / gigabyte → Betul / Correct 2 C A, B dan D menerangkan kelebihan kad kredit. A, B and D explains the advantages of credit card. 3 D P = RM3 000 R = 5% atau 0.05 setahun 5% or 0.05 per year n = 2 t = 5 MV = P 1 + r n nt = 3000 1 + 0.05 2 2(5) = RM3 840.25 4 D Aset → Menjana pendapatan Asset → Generate income Liabiliti → Tidak menjana pendapatan Liability → Does not generate income MATEMATIK1449 • MATEMATIK J2 © Pustaka Yakin Pelajar Sdn. Bhd. 5 D A: Cukai jalan → Dikenakan cukai kepada pengguna jalan raya yang memiliki kenderaan termasuk motosikal dan kereta. Road tax → Taxed to road users who own vehicles including motorcycles and cars. B: Cukai pintu → Dikenakan cukai kepada semua pegangan atau harta tanah. Property assessment tax → Taxed to all holdings or real estate. C: Cukai pendapatan → Dikenakan cukai atas pendapatan. Income tax → Taxed on income. D: Cukai jualan dan perkhidmatan → Dikenakan cukai terhadap pengguna yang menggunakan perkhidmatan bercukai tertentu seperti perkhidmatan hotel, insurans dan takaful, penyedia makanan dan minuman, telekomunikasi, kad kredit dan sebagainya. Sale and service tax → Taxed on consumers who use certain taxable services such as hotel services, insurance and takaful, food and beverage providers, telecommunications, credit cards and etc. 6 B A: Graf berakhir bukan pada jarak 0 km seperti yang ditunjukkan dalam Jadual 1. The graph ends not at a distance of 0 km as showsn in Table 1. B: Menepati data yang ditunjukkan dalam Jadual 1. Adhere to the data shown in Table 1. C: Jarak semakin jauh (meningkat), yang mana tidak sama dengan data dalam Jadual 1 yang menunjukkan jarak semakin dekat (menurun). The distance is getting further (increasing), which is not the same as the data in Table 1 that shows the distance is getting closer (decreasing). D: Graf bermula pada jarak 0 km, yang mana tidak sama dengan data dalam Jadual 1 yang bermula pada jarak 3.2 km. The graph starts at a distance of 0 km, which is not the same as the data in Table 1 that starts at a distance of 3.2 km. 7 C Graf laju-masa / Speed-time graph: Jarak = Luas bawah graf Distance = Area under the graph (8 – 2) × u + 1 2 × (10 + u) × 2 = 220 6u + 10 + u = 220 7u = 220 – 10 u = 30 8 B R(R, 0) S(S, 0) f(x) = x2 – 7x – 8 0 = x2 – 7x – 8 0 = (x + 1)(x – 8) x + 1 = 0 x = −1 x – 8 = 0 x = 8 Titik R berada pada bahagian negatif pada paksi-x, maka: Point R is on the negative side of the x-axis, then: R(−1, 0) Titik S berada pada bahagian positif pada paksi-x, maka: Point S is on the positive side of the x-axis, then: S(8, 0)© Pustaka Yakin Pelajar Sdn. Bhd. J3 1449 • MATEMATIK 9 B p ∝ 1 √q p = k √q 4 = k √25 k = 4 × 5 = 20 p = 20 √q 10 B m = y2 – y1 x2 – x1 m = 3 – 0 0 – (–6) = 3 6 = 1 2 11 D Faktor skala / Scale factor = Imej / Image Objek / Object = 3 1 = 3 12 C Graf / Graph sin 2x: y x 1 – 1 0 45° 90° 135° 180° y = sin 2x Maka, graf y = sin 2x bagi 90° G x G 270° adalah Hence, the graph represents y = sin 2x for 90° G x G 270° is y x 1 – 1 90° 180° 270°1449 • MATEMATIK J4 © Pustaka Yakin Pelajar Sdn. Bhd. 13 B Lokus x bergerak 6 cm dari titik R = titik A dan B Locus x moves 6 cm from point R = point A and B Lokus y bergerak jarak sama dari garis PQ dan SR = titik B dan D Locus y moves such that it is equidistance from line PQ and SR = point B and D Titik yang memenuhi kedua-dua syarat ialah titik B. The point that meets both conditions is point B. 14 C VPQ = VQR = VUR = 18 US = 1 2 UR ∴k = 1 2 k2 = luas imej / area of image luas objek / area of object 1 2 2 = UST 18 UST = 4.5 Jumlah luas / Total area = 3(18) + 4.5 = 58.5 cm2 15 B PS + RQ = 100 + 150 = 250 16 B ξ = {10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20} P ∪ Q = {12, 14, 15, 16, 17, 18} (P ∪ Q)′ = {10, 11, 13, 19, 20} 17 B Hujah deduktif: Deductive argument: Premis 1: Jika P, maka Q. Premise 1: If P, then Q. Premis 2: Bukan Q adalah benar. Premise 2: Not Q is true. Kesimpulan: Bukan P adalah benar. Conclusion: Not P is true. Premis1: Jika m ÷ 8= −2, maka m = −6. Premise 1: If m ÷ 8 = −2, then m = −6. Premis 2 : m = 16 Premise 2 Kesimpulan: m ÷ 8 ≠ −2 Conclusion: m ÷ 8 ≠ −2© Pustaka Yakin Pelajar Sdn. Bhd. J5 1449 • MATEMATIK 18 C A: Julat / Range 23 hingga / to 27 = 5 kali / times B: Julat / Range 38 hingga / to 38 = 6 kali / times C: Julat / Range 41 hingga / to 49 = 8 kali / times D: Julat / Range 50 hingga / to 55 = 5 kali / times 19 B Min / Mean = ∑ fx ∑ f = (10.5 × 2) + (30.5 × 7) + (50.5 × 5) + (70.5 × 11) + (90.5 × 5) 2 + 7 + 5 + 11 + 5 = 57.17 20 B Kimia / Chemistry: Lulus / Pass = 0.4 Gagal / Fail = 0.6 Matematik / Mathematics: Lulus / Pass = 0.7 Gagal / Fail = 0.3 0.7 × 0.4 = 0.28 21 A √p–4 × q4 p × p × q × q = (p–4 × q4 ) 1 2 p2 × q2 = p–2 × q2 p2 × q2 = p–2 – 2q2 – 2 = p–4q0 = p–4 22 A √(3.36 × 103 )2 – (3.24 × 103 )2 = 889.9 cm Luas / Area = 1 2 × (3.24 ×103 ) cm × 889.9 cm = 1.44 × 106 cm2 23 D m = mencancang / vertical mengufuk / horizontal 4 3 = 2.1 x x = 1.6 Jarak PR / Distance of PR = 4.8 – 1.6 = 3.2 cm1449 • MATEMATIK J6 © Pustaka Yakin Pelajar Sdn. Bhd. 24 C x2 – 4x = 4 3 2 – x 2 3x2 – 12x = 8 – 2x 3x2 – 12x + 2x – 8 = 0 3x2 – 10x – 8 = 0 (3x + 2)(x − 4) = 0 x = – 2 3 , x = 4 25 B Graf menunjukkan hubungan H. Maka, B dan D diambil kira. The graph shows the relationship of H. Then, B and D are taken into account. P(−3, −1) Q(3, 8) B: 2y ≥ 3x + 7 Gantikan koordinat titik P / Substitute the coordinates of P: 2(−1) ≥ 3(−3) + 7 −2 ≥ –2(Benar / True) Gantikan koordinat titik Q / Substitute the coordinates of Q: 2(8) ≥ 3(3) + 7 16 ≥ 16(Benar / True) 26 C pq + 1 = q2 + p pq − p = q2 − 1 p(q − 1) = q2 − 1 p = q2 – 1 q – 1 p = (q – 1)(q + 1) q – 1 = q + 1 27 B h ∝ 1 t t = 40 h = 1 250 h = k t 1 250 = k 40 k = 50 000 h = 50 000 t h = 50 000 100 = 500 cm© Pustaka Yakin Pelajar Sdn. Bhd. J7 1449 • MATEMATIK 28 D 3 –5 2 4 1 –x = –x –17 (3)(1) + 2(–x) = –x 3 – 2x + x = 0 –x = −3 x = 3 (−5)(1) + (4)(–x) = −17 –5 – 4x = −17 x = –17 + 5 –4 x = 3 29 D x = 180° – 70° 2 = 55° y = 180° − 65° − 55° = 60° 30 C 1 : m P = 1 386 Q = 154 P: 22 7 × r2 = 1 386 r = 21 Q: 22 7 × r2 = 154 r = 7 Imej / Image : Objek / Object = 7 : 21 = 7 7 : 21 7 = 1 : 3 ∴m = 3 31 D A:1449 • MATEMATIK J8 © Pustaka Yakin Pelajar Sdn. Bhd. B: C: D: 32 D 24 – 5 – 7 – 3 = 9 26 – 5 – 7 – 9 = 5 48 – 5 – 9 – 7 – 3 – 9 − 5 = 10 3 2 9 R B H 5 ξ 7© Pustaka Yakin Pelajar Sdn. Bhd. J9 1449 • MATEMATIK 33 A MM : MT = 2 : 1 60 – 8 – 11 – 10 – 10 = 21 3 bahagian / parts = 21 1 bahagian / part = 21 3 = 7 MM = 2 × 7 = 14 orang murid / students MT = 1 × 7 = 7 orang murid / students Jumlah kutipan yuran / Total fee collection = (8 × 3) + (11 × 5) + (10 × 5) + (10 × 5) + (14 × 4) + (7 × 6) = 277 34 C {GE, GT, EG, ET, TE, TG} 35 A Harga jualan / Selling price = RM550 000 t = 5 Wang pendahuluan / Deposit = 10 100 × 550 000 = 55 000 Jumlah pendapatan / Total income = RM7 200 Perbelanjaan / Expenses = RM4 000 7 200 – 4 000 − 55 000 5 × 12 = RM2 283.33 36 (Tidak ada dalam pilihan jawapan / None in the answer choices) (17 × 100) × (4 × 100) = 680 000 680 000 – 2(200 × 200) – (100 × 300) = 570 000 570 000 28 000 = 20.36 ∴ 21 tin cat / can of paint1449 • MATEMATIK J10 © Pustaka Yakin Pelajar Sdn. Bhd. 37 B 5 –7 –2 3 2 3 = 1 2x 16 –20 5(2) + (−2)(3) = 16 2x 10 – 6 = 16 2x 2x = 4 x = 2 38 C 25 100 × x =15 x = 60 1 2 × 60 = 30 Kekerapan longgokan Cumulative frequency Panjang (cm) Length (cm) 15 14.5 19.5 24.5 29.5 34.5 39.5 44.5 Median panjang / Median of length = 29.5 39 D Isnin / Monday : 1001102 = (1 × 25 ) + (1 × 22 ) + (1 × 2) = 38 pengunjung / visitors Selasa / Tuesday: 55 pengunjung / visitors Rabu / Wednesday: 22013 = (2 × 33 ) + (2 × 32 ) + (1 × 30 ) = 73 pengunjung / visitors Khamis / Thursday: 1248 = (1 × 82 ) + (2 × 81 ) + (4 × 80 ) = 84 pengunjung / visitors Purata / Mean = 38 + 55 + 73 + 84 4 = 62.5 pengunjung / visitors