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
Bilangan hari, d, untuk memasang sebuah pagar kayu berkadar songsang dengan bilangan pekerja, w. Enam orang pekerja mengambil masa 10 hari untuk menyiapkan pagar itu. Berapakah bilangan hari yang diperlukan jika hanya 4 orang pekerja yang bekerja?The number of days, d, to put up a wooden fence varies inversely as the number of workers, w. Six workers take 10 days to finish the fence. How many days are needed if only 4 workers do the job?
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B
d = k/w, so k = dw = 6 × 10 = 60. For w = 4, d = 60 ÷ 4 = 15 days. (7 days comes from treating it as direct variation.)
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Question 2
Beban, P kN, yang boleh ditanggung oleh sebuah alang kayu berubah secara langsung dengan lebarnya, b cm, dan kuasa dua kedalamannya, d cm, dan secara songsang dengan panjangnya, L m. Diberi P = 240 apabila b = 5, d = 4 dan L = 2. Hitung nilai P apabila b = 6, d = 5 dan L = 3.The load, P kN, that a timber beam can carry varies directly as its width, b cm, and the square of its depth, d cm, and inversely as its length, L m. Given P = 240 when b = 5, d = 4 and L = 2, calculate P when b = 6, d = 5 and L = 3.
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C
P = kbd²/L. 240 = k(5)(16)/2 = 40k, so k = 6. P = 6 × 6 × 25 ÷ 3 = 300. (240 comes from forgetting to square d; 675 from multiplying by L instead of dividing.)
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Question 3
Diberi A = 3−214 dan B = 15−32. Cari 2A − B.Given A = 3−214 and B = 15−32. Find 2A − B.
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A
2A = [6 −4; 2 8]. Subtract B element by element: [6 − 1, −4 − 5; 2 − (−3), 8 − 2] = [5 −9; 5 6]. Taking 8 − (−2) or forgetting that 2 − (−3) = 5 are the common slips.
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Question 4
Cari matriks songsang bagi 5232.Find the inverse of the matrix 5232.
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D
Determinant = 5(2) − 2(3) = 4. Swap the elements of the leading diagonal and change the signs of the others: (1/4)[2 −2; −3 5]. The option with 1/16 adds the products instead of subtracting.
5
Question 5
Puan Lim, 42 tahun, membeli polisi insurans hayat dengan nilai muka RM180 000. Kadar premium bagi umurnya ialah RM4.20 bagi setiap RM1 000. Hitung premium tahunan yang perlu dibayar.Madam Lim, 42, buys a life insurance policy with a face value of RM180 000. The premium rate for her age is RM4.20 per RM1 000. Calculate the annual premium she has to pay.
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B
Premium = 180 000 ÷ 1 000 × 4.20 = 180 × 4.20 = RM756.00. Dividing by 100 gives RM7 560, the common slip.
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Question 6
Nilai boleh insurans sebuah rumah ialah RM450 000. Polisi insurans kebakaran rumah itu mempunyai syarat insurans bersama 80% dan deduktibel RM1 500. Rumah itu diinsuranskan dengan jumlah RM270 000. Berapakah pampasan yang akan diterima jika kerugian akibat kebakaran ialah RM60 000?The insurable value of a house is RM450 000. Its fire insurance policy has an 80% co-insurance clause and a RM1 500 deductible. The house is insured for RM270 000. How much compensation will be received if the loss from a fire is RM60 000?
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C
Amount required = 80% × 450 000 = RM360 000. Compensation = (270 000 ÷ 360 000) × 60 000 − 1 500 = 45 000 − 1 500 = RM43 500. RM45 000 forgets the deductible; RM58 500 ignores the co-insurance clause.
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Question 7
Antara cukai berikut, yang manakah dikutip oleh pihak berkuasa tempatan ke atas rumah, kedai dan kilang?Which of the following taxes is collected by the local authority on houses, shops and factories?
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A
Property assessment tax is charged on buildings and collected by the local authority. Quit rent is on land (State Land Office), road tax is collected by JPJ and sales tax by the Customs Department.
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Question 8
Pendapatan bercukai Encik Rashid ialah RM58 400. Dia membayar zakat sebanyak RM350. Menggunakan jadual: RM50 001 hingga RM70 000, cukai asas RM1 800 dan 14% bagi setiap ringgit selepas RM50 000, hitung cukai pendapatan yang perlu dibayar.Encik Rashid's chargeable income is RM58 400. He paid zakat of RM350. Using the table: RM50 001 to RM70 000, base tax RM1 800 plus 14% of every ringgit above RM50 000, calculate the income tax he has to pay.
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D
Tax = 1 800 + (58 400 − 50 000) × 14% = 1 800 + 1 176 = RM2 976. Subtract zakat as a rebate: 2 976 − 350 = RM2 626. The RM400 rebate applies only when chargeable income does not exceed RM35 000.
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Question 9
Dua segi tiga, ABC dan DEF, diberikan. Antara set syarat berikut, yang manakah TIDAK mencukupi untuk membuktikan bahawa △ABC ≅ △DEF?Two triangles, ABC and DEF, are given. Which of the following sets of conditions is NOT enough to prove that △ABC ≅ △DEF?
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C
In the third set the equal angle A is not between the equal sides AB and BC, so it is the SSA pattern, which does not prove congruency. The first set is SAS, the second AAS and the fourth SSS.
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Question 10
Segi tiga P′ ialah imej bagi segi tiga P di bawah satu pembesaran dengan faktor skala −2/3. Luas P′ ialah 80 cm². Cari luas, dalam cm², segi tiga P.Triangle P′ is the image of triangle P under an enlargement with scale factor −2/3. The area of P′ is 80 cm². Find the area, in cm², of triangle P.
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B
Area of image = k² × area of object, with k² = (−2/3)² = 4/9. Area of P = 80 ÷ 4/9 = 80 × 9/4 = 180 cm². The sign of k does not affect the area.
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Question 11
Titik P(4, 2) dipetakan kepada titik P′ di bawah gabungan transformasi AB. Transformasi B ialah translasi −13 dan transformasi A ialah putaran 90° ikut arah jam pada asalan. Cari koordinat P′.Point P(4, 2) is mapped onto point P′ under the combined transformation AB. Transformation B is the translation −13 and transformation A is a rotation of 90° clockwise about the origin. Find the coordinates of P′.
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A
AB means B first, then A. B: (4, 2) → (3, 5). A: 90° clockwise about the origin takes (x, y) to (y, −x), so (3, 5) → (5, −3). (1, −1) comes from doing A first (the order BA).
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Question 12
Sebuah panel segi tiga sama kaki mempunyai luas 12 cm². Panel itu dibesarkan dengan faktor skala 3 dan kemudian imejnya dipantulkan pada satu garis lurus. Apakah luas imej akhir?An isosceles triangular panel has an area of 12 cm². It is enlarged with a scale factor of 3 and its image is then reflected in a straight line. What is the area of the final image?
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D
Enlargement multiplies the area by k² = 9, giving 12 × 9 = 108 cm². A reflection is an isometry, so it does not change the area. The final area is 108 cm².
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Question 13
Antara berikut, yang manakah sama dengan kos 140°?Which of the following is equal to cos 140°?
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B
140° is in quadrant II, where cosine is negative. The reference angle is 180° − 140° = 40°, so cos 140° = −cos 40°.
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Question 14
Diberi tan θ = −1 dengan 0° ≤ θ ≤ 360°. Cari nilai-nilai θ.Given tan θ = −1 for 0° ≤ θ ≤ 360°. Find the values of θ.
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C
Tangent is negative in quadrants II and IV. The reference angle is tan⁻¹(1) = 45°, so θ = 180° − 45° = 135° or θ = 360° − 45° = 315°.
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Question 15
Rajah 1 menunjukkan graf sebuah fungsi trigonometri bagi 0° ≤ x ≤ 360°. Antara berikut, yang manakah persamaan graf itu?Diagram 1 shows the graph of a trigonometric function for 0° ≤ x ≤ 360°. Which of the following is the equation of the graph?
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A
Maximum 3 and minimum −1: a = (3 − (−1)) ÷ 2 = 2 and c = (3 + (−1)) ÷ 2 = 1. The graph starts at its maximum, so it is a cosine graph. Three cycles in 360° means the period is 120°, so b = 360° ÷ 120° = 3. The equation is y = 2 cos 3x + 1.
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Question 16
Untuk 30 nilai data, Σfx = 600 dan Σfx² = 14 700. Hitung varians data itu.For 30 values of data, Σfx = 600 and Σfx² = 14 700. Calculate the variance of the data.
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D
Mean = 600 ÷ 30 = 20. Variance = Σfx² ÷ Σf − mean² = 14 700 ÷ 30 − 20² = 490 − 400 = 90. (9.49 is the standard deviation, √90.)
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Question 17
Jisim purata durian dari Ladang P ialah 1.8 kg dengan sisihan piawai 0.35 kg. Jisim purata durian dari Ladang Q ialah 1.9 kg dengan sisihan piawai 0.22 kg. Antara kesimpulan berikut, yang manakah betul?The mean mass of durians from Farm P is 1.8 kg with a standard deviation of 0.35 kg. The mean mass of durians from Farm Q is 1.9 kg with a standard deviation of 0.22 kg. Which of the following conclusions is correct?
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C
Farm Q has the greater mean (1.9 kg > 1.8 kg), so its durians are heavier on average. Farm Q also has the smaller standard deviation (0.22 < 0.35), so its masses are closer to the mean, which means more consistent.
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Question 18
Antara berikut, yang manakah ialah masalah terbuka?Which of the following is an open-ended problem?
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A
An open-ended problem has more than one acceptable answer or approach, so assumptions have to be made. The other three have one exact answer from a fixed calculation (closed problems).
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Question 19
Seorang pelajar menimbang jisim, y gram, sejenis alga di dalam sebuah akuarium pada hari ke-x. Data dalam jadual menunjukkan nilai yang dicerap. Fungsi manakah yang paling sesuai memodelkan data itu?A student weighs the mass, y grams, of a type of algae in an aquarium on day x. The data in the table are the values observed. Which function best models the data?
| x (hari / day) | 0 | 1 | 2 | 3 |
|---|---|---|---|---|
| y (g) | 6 | 12 | 24 | 48 |
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D
The values double each day: 6, 12, 24, 48. A constant ratio of 2 (not a constant difference) shows an exponential model, y = 6(2)^x. Check x = 3: 6 × 8 = 48.
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Question 20
Sebuah dewan komuniti menyimpan RM8 000 dalam akaun simpanan yang memberi faedah 4% setahun dikompaunkan setiap suku tahun. Berapakah jumlah wang dalam akaun itu selepas 3 tahun, betul kepada sen terdekat?A community hall deposits RM8 000 in a savings account that pays interest of 4% per annum compounded quarterly. How much will be in the account after 3 years, correct to the nearest sen?
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B
A = P(1 + r/n)^(nt) = 8 000(1 + 0.04/4)^(4 × 3) = 8 000(1.01)^12 = RM9 014.60. The other options use the wrong number of periods or the wrong rate per period.
Bahagian BSection B
20 marksJawab semua soalan. Setiap soalan mempunyai empat bahagian; pilih jawapan yang betul bagi setiap bahagian (1 markah setiap bahagian).Answer all questions. Each question has four parts; choose the correct answer for each part (1 mark each).
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Question 21
Kuasa, P kW, yang dijana oleh sebuah turbin angin berubah secara langsung dengan kuasa tiga halaju angin, v m/s. Kuasa yang dijana ialah 12 kW apabila halaju angin ialah 2 m/s.The power, P kW, generated by a wind turbine varies directly as the cube of the wind speed, v m/s. The power generated is 12 kW when the wind speed is 2 m/s.
[1 mark]
(a)Pilih nilai pemalar variasi, k.Choose the value of the constant of variation, k.
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1.5
P = kv³ gives 12 = k(2)³ = 8k, so k = 1.5.
[1 mark]
(b)Pilih persamaan yang menghubungkan P dan v.Choose the equation that relates P and v.
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P = 1.5v³
With k = 1.5 and P directly proportional to v³: P = 1.5v³.
[1 mark]
(c)Pilih kuasa yang dijana apabila halaju angin ialah 4 m/s.Choose the power generated when the wind speed is 4 m/s.
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96 kW
P = 1.5 × 4³ = 1.5 × 64 = 96 kW.
[1 mark]
(d)Tandakan BENAR atau PALSU: Jika halaju angin digandakan, kuasa yang dijana menjadi 8 kali ganda.Mark TRUE or FALSE: If the wind speed is doubled, the power generated becomes 8 times as large.
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True
Doubling v multiplies v³ by 2³ = 8, so P is multiplied by 8.
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Question 22
Sebuah kedai kraf menjual kotak burung dan pasu hiasan. Matriks A = 20153010 menunjukkan bilangan kotak burung dan pasu hiasan yang dijual, masing-masing pada hari Sabtu (baris pertama) dan Ahad (baris kedua). Matriks B = 1812 menunjukkan harga seunit, dalam RM, kotak burung (baris pertama) dan pasu hiasan (baris kedua).A craft shop sells bird boxes and decorative pots. Matrix A = 20153010 shows the number of bird boxes and decorative pots sold on Saturday (first row) and Sunday (second row), with bird boxes in the first column. Matrix B = 1812 shows the price of one bird box (first row) and one decorative pot (second row), in RM.
[1 mark]
(a)Pilih peringkat bagi matriks AB.Choose the order of matrix AB.
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2 × 1
A is 2 × 2 and B is 2 × 1. The inner numbers match (2 and 2), so AB has order 2 × 1 (the outer numbers).
[1 mark]
(b)Pilih jumlah jualan pada hari Sabtu.Choose the total sales on Saturday.
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RM540
Row 1 of AB: 20 × 18 + 15 × 12 = 360 + 180 = RM540.
[1 mark]
(c)Pilih jumlah jualan bagi kedua-dua hari.Choose the total sales for the two days.
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RM1 200
Row 2 of AB: 30 × 18 + 10 × 12 = 540 + 120 = RM660. Total = 540 + 660 = RM1 200.
[1 mark]
(d)Tandakan BENAR atau PALSU: Hasil darab BA boleh ditentukan.Mark TRUE or FALSE: The product BA can be determined.
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False
B is 2 × 1 and A is 2 × 2. The number of columns of B (1) is not equal to the number of rows of A (2), so BA is not defined.
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Question 23
Encik Faizal mempunyai polisi insurans kesihatan dengan penyertaan bersama 80/20 dan deduktibel RM800. Bil hospitalnya ialah RM12 800 dan semua perbelanjaan itu dilindungi.Encik Faizal has a health insurance policy with 80/20 co-insurance participation and a deductible of RM800. His hospital bill is RM12 800 and all of the expenses are covered.
[1 mark]
(a)Pilih jumlah selepas deduktibel ditolak.Choose the amount after the deductible is subtracted.
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RM12 000
12 800 − 800 = RM12 000.
[1 mark]
(b)Pilih jumlah yang dibayar oleh syarikat insurans.Choose the amount paid by the insurance company.
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RM9 600
80% × 12 000 = RM9 600. (RM10 240 is 80% of the full bill, which ignores the deductible.)
[1 mark]
(c)Pilih jumlah yang perlu dibayar oleh Encik Faizal.Choose the amount Encik Faizal has to pay.
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RM3 200
20% × 12 000 + 800 = 2 400 + 800 = RM3 200. Check: 9 600 + 3 200 = 12 800.
[1 mark]
(d)Tandakan BENAR atau PALSU: Deduktibel dikenakan apabila tuntutan dibuat di bawah polisi insurans hayat.Mark TRUE or FALSE: A deductible applies when a claim is made under a life insurance policy.
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False
Deductibles are found in property, medical and motor insurance, but not in life insurance.
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Question 24
Diberi sin θ = −7/25 dan 180° < θ < 270°.Given sin θ = −7/25 and 180° < θ < 270°.
[1 mark]
(a)Pilih sukuan tempat θ berada.Choose the quadrant in which θ lies.
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Quadrant III
180° < θ < 270° is quadrant III (sin and cos negative, tan positive).
[1 mark]
(b)Pilih nilai kos θ.Choose the value of cos θ.
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−24/25
The triangle is 7, 24, 25. In quadrant III, cosine is negative: cos θ = −24/25.
[1 mark]
(c)Pilih nilai tan θ.Choose the value of tan θ.
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7/24
tan θ = sin θ ÷ cos θ = (−7/25) ÷ (−24/25) = 7/24, positive in quadrant III.
[1 mark]
(d)Pilih nilai θ, betul kepada satu tempat perpuluhan.Choose the value of θ, correct to one decimal place.
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196.3°
Reference angle α = sin⁻¹(7/25) = 16.26°. In quadrant III, θ = 180° + 16.26° = 196.3°.
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Question 25
Lengkung sebuah jambatan pejalan kaki dimodelkan oleh fungsi y = ax² + bx, dengan y m ialah tinggi lengkung pada jarak mengufuk x m dari satu hujungnya. Lengkung itu melalui titik (6, 4.5) dan (12, 0).The arch of a footbridge is modelled by the function y = ax² + bx, where y m is the height of the arch at a horizontal distance x m from one end. The arch passes through the points (6, 4.5) and (12, 0).
[1 mark]
(a)Pilih persamaan yang diperoleh apabila titik (12, 0) digantikan.Choose the equation obtained when the point (12, 0) is substituted.
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144a + 12b = 0
Put x = 12 and y = 0 into y = ax² + bx: 0 = a(144) + b(12).
[1 mark]
(b)Pilih nilai a dan nilai b.Choose the values of a and b.
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a = −0.125, b = 1.5
From (12, 0): b = −12a. From (6, 4.5): 36a + 6b = 4.5, so 36a − 72a = 4.5 and a = −0.125. Then b = 1.5.
[1 mark]
(c)Pilih tinggi lengkung pada x = 3.Choose the height of the arch at x = 3.
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3.375 m
y = −0.125(9) + 1.5(3) = −1.125 + 4.5 = 3.375 m.
[1 mark]
(d)Tandakan BENAR atau PALSU: Model ini boleh digunakan untuk mencari tinggi lengkung pada x = 15 m.Mark TRUE or FALSE: The model can be used to find the height of the arch at x = 15 m.
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False
The arch only exists for 0 ≤ x ≤ 12. Using the model at x = 15 goes outside the range it was built for (it would give a negative height).
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
Encik Danish ialah seorang arkitek landskap. Jumlah pendapatan tahunannya ialah RM96 500. Dia menderma RM1 500 kepada sebuah pertubuhan yang diluluskan (pengecualian cukai). Jumlah pelepasan cukai ialah RM21 000. Dia membayar zakat RM600. Sebahagian daripada jadual kadar cukai pendapatan ditunjukkan dalam Jadual 1.Encik Danish is a landscape architect. His total annual income is RM96 500. He donates RM1 500 to an approved organisation (a tax exemption). His total tax relief is RM21 000. He pays zakat of RM600. Part of the income tax rate table is shown in Table 1.
| Pendapatan bercukai (RM) Chargeable income (RM) | Cukai asas (RM) Base tax (RM) | Kadar bagi baki Rate on the balance |
|---|---|---|
| 50 001 – 70 000 | 1 800 | 14% |
| 70 001 – 100 000 | 4 600 | 21% |
[2 marks]
(a)Hitung pendapatan bercukai Encik Danish.Calculate Encik Danish's chargeable income.
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Tick each point you got.
[3 marks]
(b)Hitung cukai pendapatan yang perlu dibayar oleh Encik Danish, selepas rebat zakat.Calculate the income tax Encik Danish has to pay, after the zakat rebate.
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Tick each point you got.
[2 marks]
(c)Potongan cukai bulanan (PCB) ialah RM380 sebulan selama 12 bulan. Nyatakan sama ada PCB mencukupi, dan hitung jumlah yang perlu dibayar atau dituntut balik.The monthly tax deduction (PCB) is RM380 a month for 12 months. State whether the PCB is enough, and calculate the amount to be paid or refunded.
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Tick each point you got.
[1 mark]
(d)Encik Danish memandu sebuah kereta 1 998 cc. Cukai jalan ialah RM280 bagi 1 800 cc pertama dan RM0.50 bagi setiap cc selebihnya. Hitung cukai jalan kereta itu.Encik Danish drives a 1 998 cc car. The road tax is RM280 for the first 1 800 cc and RM0.50 for each extra cc. Calculate the road tax of the car.
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Tick each point you got.
27
Question 27
Jadual 2 menunjukkan jisim 40 biji manggis yang dituai dari Kebun A.Table 2 shows the masses of 40 mangosteens harvested from Orchard A.
| Jisim (g) / Mass (g) | 60–69 | 70–79 | 80–89 | 90–99 | 100–109 |
|---|---|---|---|---|---|
| Bilangan / Number | 4 | 9 | 15 | 8 | 4 |
[2 marks]
(a)Hitung min jisim manggis itu, dalam g.Calculate the mean mass of the mangosteens, in g.
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Tick each point you got.
[3 marks]
(b)Hitung varians dan sisihan piawai jisim itu, betul kepada dua tempat perpuluhan.Calculate the variance and the standard deviation of the masses, correct to two decimal places.
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[3 marks]
(c)Kebun B menghasilkan manggis dengan min jisim 86.0 g dan sisihan piawai 8.6 g. Bandingkan kedua-dua kebun dan nyatakan kesimpulan anda.Orchard B produces mangosteens with a mean mass of 86.0 g and a standard deviation of 8.6 g. Compare the two orchards and state your conclusion.
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Tick each point you got.
28
Question 28
Sebuah studio reka bentuk membeli dua jenis pasu tanaman untuk sebuah taman. Tiga pasu besar dan dua pasu kecil berharga RM191. Dua pasu besar dan lima pasu kecil berharga RM230. Harga sebuah pasu besar ialah RMp dan harga sebuah pasu kecil ialah RMq.A design studio buys two types of plant pots for a garden. Three large pots and two small pots cost RM191. Two large pots and five small pots cost RM230. The price of a large pot is RMp and the price of a small pot is RMq.
[2 marks]
(a)Tulis maklumat di atas dalam bentuk persamaan matriks.Write the information above as a matrix equation.
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Tick each point you got.
[2 marks]
(b)Cari matriks songsang bagi matriks pekali dalam (a).Find the inverse of the coefficient matrix in (a).
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Tick each point you got.
[4 marks]
(c)Dengan menggunakan kaedah matriks, hitung nilai p dan nilai q.By using the matrix method, calculate the value of p and the value of q.
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Tick each point you got.
[2 marks]
(d)Studio itu mempunyai RM350. Adakah wang itu cukup untuk membeli 5 pasu besar dan 4 pasu kecil? Tunjukkan pengiraan anda.The studio has RM350. Is that enough to buy 5 large pots and 4 small pots? Show your calculation.
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Tick each point you got.
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Question 29
Rajah 2 menunjukkan segi tiga PQR dan imejnya, P′Q′R′, di bawah satu pembesaran pada satah Cartes. Rajah itu ialah pelan sebuah bed bunga dan 1 unit pada grid mewakili 0.5 m.Diagram 2 shows triangle PQR and its image, P′Q′R′, under an enlargement on a Cartesian plane. The diagram is the plan of a flower bed and 1 unit on the grid represents 0.5 m.
[3 marks]
(a)Huraikan selengkapnya pembesaran itu.Describe in full the enlargement.
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Tick each point you got.
[3 marks]
(b)Hitung luas, dalam unit persegi, bagi (i) segi tiga PQR, (ii) segi tiga P′Q′R′.Calculate the area, in square units, of (i) triangle PQR, (ii) triangle P′Q′R′.
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Tick each point you got.
[2 marks]
(c)Di bawah pembesaran lain dengan pusat yang sama dan faktor skala −1.5, R dipetakan kepada R″. Cari koordinat R″.Under another enlargement with the same centre and scale factor −1.5, R is mapped onto R″. Find the coordinates of R″.
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Tick each point you got.
[2 marks]
(d)Hitung luas sebenar, dalam m², bed bunga yang diwakili oleh P′Q′R′.Calculate the actual area, in m², of the flower bed represented by P′Q′R′.
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30
Question 30
Jawatankuasa sebuah taman komuniti mempunyai 40 m pagar untuk mengelilingi sebuah kebun herba berbentuk segi empat tepat. Satu sisi kebun itu bersebelahan dengan dinding sedia ada dan tidak perlu dipagar, seperti dalam Rajah 3. Lebar kebun itu ialah x m dan luasnya ialah A m².The committee of a community garden has 40 m of fencing to enclose a rectangular herb garden. One side of the garden is next to an existing wall and needs no fence, as shown in Diagram 3. The width of the garden is x m and its area is A m².
[2 marks]
(a)Tunjukkan bahawa A = 40x − 2x².Show that A = 40x − 2x².
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[2 marks]
(b)Nyatakan jenis fungsi yang memodelkan A dan satu andaian yang dibuat.State the type of function that models A and one assumption that is made.
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[3 marks]
(c)Lengkapkan jadual nilai A bagi x = 0, 5, 10, 15 dan 20, dan nyatakan nilai x yang memberikan luas maksimum.Complete a table of values of A for x = 0, 5, 10, 15 and 20, and state the value of x that gives the maximum area.
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[3 marks]
(d)Jawatankuasa memerlukan kebun dengan luas tepat 150 m². Cari dua pasang ukuran lebar dan panjang yang mungkin.The committee needs a garden with an area of exactly 150 m². Find the two possible pairs of width and length.
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[2 marks]
(e)Seorang ahli jawatankuasa berkata, "Kebun berbentuk segi empat sama akan memberikan luas yang paling besar." Adakah dia betul? Berikan justifikasi anda.A committee member says, "A square garden gives the largest area." Is she correct? Justify your answer.
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31
Question 31
Rajah 4 menunjukkan segi tiga ABC, PQR dan DEF pada satah Cartes untuk sebuah reka bentuk corak lantai. Segi tiga PQR ialah imej bagi ABC di bawah transformasi M. Segi tiga DEF ialah imej bagi PQR di bawah transformasi N.Diagram 4 shows triangles ABC, PQR and DEF on a Cartesian plane for a floor pattern design. Triangle PQR is the image of ABC under transformation M. Triangle DEF is the image of PQR under transformation N.
[2 marks]
(a)Huraikan selengkapnya transformasi M.Describe in full the transformation M.
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[3 marks]
(b)Huraikan selengkapnya transformasi N.Describe in full the transformation N.
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[2 marks]
(c)Hitung luas, dalam unit persegi, segi tiga DEF.Calculate the area, in square units, of triangle DEF.
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[3 marks]
(d)Cari koordinat imej bagi titik C di bawah (i) gabungan transformasi NM, (ii) gabungan transformasi MN.Find the coordinates of the image of point C under (i) the combined transformation NM, (ii) the combined transformation MN.
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[2 marks]
(e)Amin berkata bahawa mengubah tertib transformasi M dan N tidak mengubah imej akhir. Adakah Amin betul? Berikan alasan anda.Amin says that changing the order of transformations M and N does not change the final image. Is Amin correct? Give your reason.
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Test specification (JSU)
| Chapter | Remembering | Understanding | Applying | Analysing | Evaluating | Creating | Items | marks |
|---|---|---|---|---|---|---|---|---|
| 1. Variation | – | – | 3 (6) | – | – | – | 3 | 6 |
| 2. Matrices | – | – | 4 (16) | – | – | – | 4 | 16 |
| 3. Consumer Mathematics: Insurance | – | – | 3 (6) | – | – | – | 3 | 6 |
| 4. Consumer Mathematics: Taxation | 1 (1) | – | 2 (9) | – | – | – | 3 | 10 |
| 5. Congruency, Enlargement and Combined Transformations | – | 1 (1) | 3 (12) | 1 (1) | 1 (12) | – | 6 | 26 |
| 6. Ratios and Graphs of Trigonometric Functions | – | 1 (1) | 2 (5) | 1 (1) | – | – | 4 | 7 |
| 7. Measures of Dispersion for Grouped Data | – | – | 1 (1) | – | 2 (9) | – | 3 | 10 |
| 8. Mathematical Modeling | – | 1 (1) | 1 (1) | 2 (5) | 1 (12) | – | 5 | 19 |
| Total | 1 (1) | 3 (3) | 19 (56) | 4 (7) | 4 (33) | 0 (0) | 31 | 100 |
Each cell shows items (marks).