Practice paper, not an official KPM paperKertas latihan, bukan kertas rasmi KPM
50
Ujian Akhir Sesi AkademikEnd of Academic Session Test
MatematikMathematics
Tingkatan 2, 2 jam / 2 hours, 100 marksmarkah
Nama / NameNama
Kelas / ClassKelas
Tarikh / DateTarikh
Markah / marksmarkah: / 100
InstructionsArahan
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).Skema jawapan dalam Bahasa Inggeris (DLP).
Practice shows answers as you go. Exam times you and hides answers until you submit.Latihan menunjukkan jawapan semasa menjawab. Peperiksaan menetapkan masa dan menyembunyikan jawapan sehingga dihantar.
Bahagian ASection A
20 marksmarkah
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
QuestionSoalan 1
Sebuah dinding bata disusun dalam lapisan. Lapisan pertama mempunyai 40 biji bata, lapisan kedua 36 biji dan lapisan ketiga 32 biji. Bilangan bata berkurang sama banyak bagi setiap lapisan. Antara berikut, yang manakah ungkapan bagi bilangan bata dalam lapisan ke-n?A brick wall is built in layers. The first layer has 40 bricks, the second layer has 36 bricks and the third layer has 32 bricks. The number of bricks decreases by the same amount in every layer. Which of the following is the expression for the number of bricks in the nth layer?
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B
The common difference is −4, so the expression starts with −4n. For n = 1 the value must be 40, so 44 − 4(1) = 40. Check n = 3: 44 − 12 = 32. The expression 40 − 4n gives 36 for n = 1.
For the teacherUntuk guru: ApplyingMengaplikasi, mediumsederhana difficultyaras mediumsederhana, ChapterBab 1, standard 1.3.1
TextbookBuku teksp.ms. 10
2
QuestionSoalan 2
Faktorkan 18a2b + 27ab2 dengan lengkap.Factorise 18a2b + 27ab2 completely.
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C
The HCF of 18a²b and 27ab² is 9ab, so 18a²b + 27ab² = 9ab(2a + 3b). The other options take out a common factor, but not the highest one, so the factorisation is not complete.
For the teacherUntuk guru: UnderstandingMemahami, lowrendah difficultyaras lowrendah, ChapterBab 2, standard 2.2.1
TextbookBuku teksp.ms. 27
3
QuestionSoalan 3
Permudahkan x2 − 92x ÷ x + 34x2.Simplify x2 − 92x ÷ x + 34x2.
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A
Factorise: x² − 9 = (x − 3)(x + 3). Invert the second fraction and multiply: (x − 3)(x + 3)/(2x) × 4x²/(x + 3) = 4x²(x − 3)/(2x) = 2x(x − 3). Forgetting to invert gives the third option.
For the teacherUntuk guru: ApplyingMengaplikasi, hightinggi difficultyaras hightinggi, ChapterBab 2, standard 2.3.2
TextbookBuku teksp.ms. 36
4
QuestionSoalan 4
Sebuah kedai menjual buku latihan dengan harga RM5 sebuah dan mengenakan caj penghantaran RM8. Jumlah bayaran bagi x buah buku ialah RMT, dengan T = 5x + 8. Ungkapkan x dalam sebutan T.A shop sells exercise books at RM5 each and charges RM8 for delivery. The total payment for x books is RMT, where T = 5x + 8. Express x in terms of T.
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D
T = 5x + 8, so T − 8 = 5x and x = (T − 8)/5. Subtract 8 from the whole of T before dividing by 5; dividing T alone by 5 and then subtracting 8 gives a different expression.
For the teacherUntuk guru: ApplyingMengaplikasi, lowrendah difficultyaras lowrendah, ChapterBab 3, standard 3.1.2
TextbookBuku teksp.ms. 46
5
QuestionSoalan 5
Sudut pedalaman bagi sebuah poligon sekata ialah 150°. Cari bilangan sisi poligon itu.The interior angle of a regular polygon is 150°. Find the number of sides of the polygon.
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B
Exterior angle = 180° − 150° = 30°. Number of sides = 360° ÷ 30° = 12.
For the teacherUntuk guru: ApplyingMengaplikasi, lowrendah difficultyaras lowrendah, ChapterBab 4, standard 4.2.3
TextbookBuku teksp.ms. 65
6
QuestionSoalan 6
Enam daripada tujuh sudut pedalaman sebuah heptagon ialah 120°, 135°, 140°, 128°, 150° dan 112°. Cari sudut pedalaman yang ketujuh.Six of the seven interior angles of a heptagon are 120°, 135°, 140°, 128°, 150° and 112°. Find the seventh interior angle.
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C
Sum of interior angles of a heptagon = (7 − 2) × 180° = 900°. The six given angles add up to 785°. Seventh angle = 900° − 785° = 115°.
For the teacherUntuk guru: ApplyingMengaplikasi, mediumsederhana difficultyaras mediumsederhana, ChapterBab 4, standard 4.2.1
TextbookBuku teksp.ms. 63
7
QuestionSoalan 7
Lilitan sebuah kolam ikan berbentuk bulatan ialah 88 m. Hitung jejari kolam itu. (Guna π = 227)The circumference of a circular fish pond is 88 m. Calculate the radius of the pond. (Use π = 227)
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A
C = 2πr, so r = 88 ÷ (2 × 22/7) = 14 m. 28 m is the diameter; 616 is the number you get from πr², the area in m².
For the teacherUntuk guru: ApplyingMengaplikasi, lowrendah difficultyaras lowrendah, ChapterBab 5, standard 5.3.1
TextbookBuku teksp.ms. 86
8
QuestionSoalan 8
Sebuah tingkap berbentuk kipas ialah sektor bulatan berjejari 14 cm dan bersudut 135° di pusat. Hitung luas tingkap itu. (Guna π = 227)A fan-shaped window is a sector of a circle with radius 14 cm and an angle of 135° at the centre. Calculate the area of the window. (Use π = 227)
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D
Area = 135/360 × πr² = 3/8 × 22/7 × 14 × 14 = 3/8 × 616 = 231 cm². 33 is the arc length in cm, not an area; 616 would be the whole circle.
For the teacherUntuk guru: ApplyingMengaplikasi, mediumsederhana difficultyaras mediumsederhana, ChapterBab 5, standard 5.3.4
TextbookBuku teksp.ms. 92
9
QuestionSoalan 9
Satu bentangan terdiri daripada sebuah heksagon dan enam buah segi tiga yang sama. Namakan pepejal yang dibentuk oleh bentangan itu.A net is made up of one hexagon and six identical triangles. Name the solid formed by the net.
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B
The hexagon is the base and the six triangles are the sloping faces that meet at the apex, so the solid is a hexagonal pyramid. A hexagonal prism would need two hexagons and six rectangles.
For the teacherUntuk guru: RememberingMengingat, lowrendah difficultyaras lowrendah, ChapterBab 6, standard 6.2.1
TextbookBuku teksp.ms. 103
10
QuestionSoalan 10
Sebuah tangki air berbentuk silinder berjejari 14 cm dan tinggi 20 cm. Berapa liter air yang boleh dimuatkan oleh tangki itu apabila penuh? (Guna π = 227; 1 liter = 1 000 cm3)A water tank is in the shape of a cylinder with a radius of 14 cm and a height of 20 cm. How many litres of water can the tank hold when it is full? (Use π = 227; 1 litre = 1 000 cm3)
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C
Volume = πr²h = 22/7 × 14 × 14 × 20 = 12 320 cm³. Convert: 12 320 ÷ 1 000 = 12.32 litres. 12 320 cm³ is not 12 320 litres, so the decimal point must move three places.
For the teacherUntuk guru: ApplyingMengaplikasi, mediumsederhana difficultyaras mediumsederhana, ChapterBab 6, standard 6.4.3
TextbookBuku teksp.ms. 115
11
QuestionSoalan 11
Pada sebuah peta grid, sebuah kedai roti berada di (−3, 1) dan sebuah perpustakaan berada di (9, 6). Satu unit mewakili 1 km. Hitung jarak antara kedua-dua bangunan itu.On a grid map, a bakery is at (−3, 1) and a library is at (9, 6). One unit represents 1 km. Calculate the distance between the two buildings.
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A
Horizontal difference = 9 − (−3) = 12 and vertical difference = 6 − 1 = 5. Distance = √(12² + 5²) = √169 = 13 km. 17 is 12 + 5 and 169 is the square of the distance.
For the teacherUntuk guru: ApplyingMengaplikasi, lowrendah difficultyaras lowrendah, ChapterBab 7, standard 7.1.3
TextbookBuku teksp.ms. 127
12
QuestionSoalan 12
Cari koordinat titik tengah bagi garis lurus yang menyambungkan A(−7, 4) dan B(3, −10).Find the coordinates of the midpoint of the straight line joining A(−7, 4) and B(3, −10).
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D
Midpoint = ((−7 + 3)/2, (4 + (−10))/2) = (−2, −3). (−4, −6) is the sum of the coordinates, without halving.
For the teacherUntuk guru: ApplyingMengaplikasi, lowrendah difficultyaras lowrendah, ChapterBab 7, standard 7.2.1
TextbookBuku teksp.ms. 133
13
QuestionSoalan 13
Antara hubungan berikut, yang manakah bukan satu fungsi?Which of the following relations is not a function?
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D
In a function every object has exactly one image. In {(1, 4), (1, 5), (2, 6)} the object 1 has two images, 4 and 5, so it is not a function. Different objects may share the same image, so the other three are functions.
For the teacherUntuk guru: UnderstandingMemahami, lowrendah difficultyaras lowrendah, ChapterBab 8, standard 8.1.2
TextbookBuku teksp.ms. 150
14
QuestionSoalan 14
Sebuah kereta api memecut daripada 36 km/j kepada 90 km/j dalam masa 15 saat. Hitung pecutan kereta api itu dalam m/s2.A train accelerates from 36 km/h to 90 km/h in 15 seconds. Calculate the acceleration of the train in m/s2.
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A
Change in speed = 90 − 36 = 54 km/h = 54 × 1 000 ÷ 3 600 = 15 m/s. Acceleration = 15 ÷ 15 = 1 m/s². 3.6 comes from leaving the speeds in km/h and dividing by 15.
For the teacherUntuk guru: ApplyingMengaplikasi, hightinggi difficultyaras hightinggi, ChapterBab 9, standard 9.2.2
TextbookBuku teksp.ms. 181
15
QuestionSoalan 15
Sebuah garis lurus mempunyai pintasan-x 5 dan pintasan-y −10. Cari kecerunan garis itu.A straight line has an x-intercept of 5 and a y-intercept of −10. Find the gradient of the line.
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C
Gradient = −(y-intercept) ÷ (x-intercept) = −(−10) ÷ 5 = 2. The line rises from left to right, so the gradient is positive.
For the teacherUntuk guru: ApplyingMengaplikasi, lowrendah difficultyaras lowrendah, ChapterBab 10, standard 10.1.4
TextbookBuku teksp.ms. 197
16
QuestionSoalan 16
Titik P(3, −5) dipantulkan pada paksi-y. Apakah koordinat imej titik P?The point P(3, −5) is reflected in the y-axis. What are the coordinates of the image of P?
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B
A reflection in the y-axis changes the sign of the x-coordinate and keeps the y-coordinate: (3, −5) goes to (−3, −5). (3, 5) is the reflection in the x-axis.
For the teacherUntuk guru: UnderstandingMemahami, lowrendah difficultyaras lowrendah, ChapterBab 11, standard 11.3.3
TextbookBuku teksp.ms. 220
17
QuestionSoalan 17
Satu translasi memetakan titik P(−3, 4) kepada P′(2, −1). Apakah imej bagi titik Q(0, 5) di bawah translasi yang sama?A translation maps the point P(−3, 4) onto P′(2, −1). What is the image of the point Q(0, 5) under the same translation?
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D
The translation vector is (2 − (−3), −1 − 4) = (5, −5). Q(0, 5) goes to (0 + 5, 5 − 5) = (5, 0). (−5, 10) comes from subtracting the vector.
For the teacherUntuk guru: AnalysingMenganalisis, hightinggi difficultyaras hightinggi, ChapterBab 11, standard 11.2.3
TextbookBuku teksp.ms. 217
18
QuestionSoalan 18
Cari median bagi data 12, 7, 15, 9, 4, 11.Find the median of the data 12, 7, 15, 9, 4, 11.
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A
Arrange in order: 4, 7, 9, 11, 12, 15. There are six values, so the median is the mean of the 3rd and 4th: (9 + 11) ÷ 2 = 10. 9.67 is the mean, not the median.
For the teacherUntuk guru: ApplyingMengaplikasi, mediumsederhana difficultyaras mediumsederhana, ChapterBab 12, standard 12.1.1
TextbookBuku teksp.ms. 254
19
QuestionSoalan 19
Sebuah kotak mengandungi 20 keping kupon yang dinomborkan 1 hingga 20. Sekeping kupon dipilih secara rawak. Cari kebarangkalian bahawa nombor pada kupon itu ialah nombor perdana.A box contains 20 coupons numbered 1 to 20. One coupon is chosen at random. Find the probability that the number on the coupon is a prime number.
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C
The prime numbers from 1 to 20 are 2, 3, 5, 7, 11, 13, 17 and 19, which is 8 numbers. P = 8/20 = 2/5. The number 1 is not a prime number, so 9/20 is wrong.
For the teacherUntuk guru: ApplyingMengaplikasi, mediumsederhana difficultyaras mediumsederhana, ChapterBab 13, standard 13.2.1
TextbookBuku teksp.ms. 280
20
QuestionSoalan 20
Sebuah beg mengandungi 24 biji guli berwarna merah, biru dan hijau. Kebarangkalian memilih sebiji guli merah ialah 13 dan kebarangkalian memilih sebiji guli biru ialah 14. Cari bilangan guli hijau dalam beg itu.A bag contains 24 marbles which are red, blue or green. The probability of choosing a red marble is 13 and the probability of choosing a blue marble is 14. Find the number of green marbles in the bag.
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B
Red = 24 × 1/3 = 8 and blue = 24 × 1/4 = 6. Green = 24 − 8 − 6 = 10. (Or P(green) = 1 − 1/3 − 1/4 = 5/12, and 5/12 × 24 = 10.)
For the teacherUntuk guru: AnalysingMenganalisis, hightinggi difficultyaras hightinggi, ChapterBab 13, standard 13.4.1
TextbookBuku teksp.ms. 291
Bahagian BSection B
20 marksmarkah
Jawab semua soalan. Tunjukkan langkah-langkah penting dalam kerja mengira anda.Answer all questions. Show the important steps in your working.
21
QuestionSoalan 21
Sebuah lantai mozek dipasang dalam gelang-gelang jubin. Bilangan jubin dalam empat gelang pertama ialah 7, 12, 17, 22, … dan corak itu diteruskan dengan cara yang sama.A mosaic floor is laid in rings of tiles. The numbers of tiles in the first four rings are 7, 12, 17, 22, … and the pattern continues in the same way.
[1 markmarkah](a)Tulis dua sebutan seterusnya dalam pola itu.Write the next two terms of the pattern.
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[1 markmarkah](b)Tulis satu ungkapan bagi bilangan jubin dalam gelang ke-n.Write an expression for the number of tiles in the nth ring.
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[2 marksmarkah](c)Gelang yang manakah mempunyai 152 biji jubin?Which ring has 152 tiles?
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For the teacherUntuk guru: ApplyingMengaplikasi, lowrendah difficultyaras lowrendah, ChapterBab 1, standard 1.3.2
TextbookBuku teksp.ms. 11
22
QuestionSoalan 22
Luas, A cm2, sebuah tingkap berbentuk trapezium diberi oleh rumus A = ½(a + b)h, dengan a cm dan b cm ialah panjang dua sisi selari dan h cm ialah jarak antara kedua-duanya.The area, A cm2, of a trapezium-shaped window is given by the formula A = ½(a + b)h, where a cm and b cm are the lengths of the two parallel sides and h cm is the distance between them.
[1 markmarkah](a)Hitung A apabila a = 12, b = 8 dan h = 5.Calculate A when a = 12, b = 8 and h = 5.
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[1 markmarkah](b)Ungkapkan h sebagai perkara rumus.Express h as the subject of the formula.
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[2 marksmarkah](c)Diberi A = 240, b = 18 dan h = 12. Cari nilai a.Given A = 240, b = 18 and h = 12. Find the value of a.
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For the teacherUntuk guru: ApplyingMengaplikasi, lowrendah difficultyaras lowrendah, ChapterBab 3, standard 3.1.2
TextbookBuku teksp.ms. 46
23
QuestionSoalan 23
Rajah 1 menunjukkan corak bulatan berpusat O pada sebuah tingkap kaca. AB ialah satu perentas dan M ialah titik tengah AB. OM dipanjangkan supaya bertemu bulatan di Q.Diagram 1 shows a circular pattern with centre O on a glass window. AB is a chord and M is the midpoint of AB. OM is extended to meet the circle at Q.
Rajah 1Diagram 1
[1 markmarkah](a)Nyatakan panjang AM.State the length of AM.
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[2 marksmarkah](b)Hitung panjang OM.Calculate the length of OM.
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[1 markmarkah](c)Cari panjang MQ.Find the length of MQ.
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For the teacherUntuk guru: ApplyingMengaplikasi, mediumsederhana difficultyaras mediumsederhana, ChapterBab 5, standard 5.2.3
TextbookBuku teksp.ms. 85
24
QuestionSoalan 24
Rajah 2 ialah grid peta yang menunjukkan stesen bas A dan sekolah B. Satu unit pada grid mewakili 100 m.Diagram 2 is a map grid that shows the bus station A and the school B. One unit on the grid represents 100 m.
Rajah 2Diagram 2
[1 markmarkah](a)Cari koordinat titik tengah AB.Find the coordinates of the midpoint of AB.
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[2 marksmarkah](b)Hitung jarak sebenar, dalam m, antara A dan B.Calculate the actual distance, in m, between A and B.
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[1 markmarkah](c)Sebuah kedai C terletak supaya B ialah titik tengah AC. Cari koordinat C.A shop C is placed so that B is the midpoint of AC. Find the coordinates of C.
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For the teacherUntuk guru: ApplyingMengaplikasi, mediumsederhana difficultyaras mediumsederhana, ChapterBab 7, standard 7.1.3
TextbookBuku teksp.ms. 127
25
QuestionSoalan 25
Rajah 3 menunjukkan segi tiga ABC dan imejnya A′B′C′ pada satah Cartes. Seorang pereka jubin menjalankan satu transformasi ke atas ABC untuk memperoleh A′B′C′.Diagram 3 shows triangle ABC and its image A′B′C′ on a Cartesian plane. A tile designer carries out one transformation on ABC to obtain A′B′C′.
Rajah 3Diagram 3
[2 marksmarkah](a)Huraikan transformasi itu dengan lengkap.Describe the transformation completely.
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[2 marksmarkah](b)Hana berkata, "A′B′C′ juga boleh diperoleh daripada ABC melalui satu translasi kerana A dan C dipetakan tepat kepada A′ dan C′." Adakah Hana betul? Berikan justifikasi anda.Hana says, "A′B′C′ can also be obtained from ABC by a translation because A and C map exactly onto A′ and C′." Is Hana correct? Justify your answer.
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For the teacherUntuk guru: EvaluatingMenilai, hightinggi difficultyaras hightinggi, ChapterBab 11, standard 11.3.3
TextbookBuku teksp.ms. 220
Bahagian CSection C
60 marksmarkah
Jawab semua soalan. Tunjukkan langkah-langkah penting dalam kerja mengira anda.Answer all questions. Show the important steps in your working.
26
QuestionSoalan 26
Selesaikan soalan-soalan berikut.Answer the following questions.
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[3 marksmarkah](d)Ungkapkan 3p − 2 − 2p + 2 sebagai satu pecahan tunggal dalam bentuk termudah.Express 3p − 2 − 2p + 2 as a single fraction in its simplest form.
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For the teacherUntuk guru: ApplyingMengaplikasi, lowrendah difficultyaras lowrendah, ChapterBab 2, standard 2.2.2
TextbookBuku teksp.ms. 29
27
QuestionSoalan 27
Selesaikan soalan-soalan berikut tentang poligon.Answer the following questions about polygons.
[2 marksmarkah](a)Lantai sebuah gazebo berbentuk oktagon sekata. Hitung (i) sudut peluaran, (ii) sudut pedalaman, oktagon itu.The floor of a gazebo is a regular octagon. Calculate (i) the exterior angle, (ii) the interior angle, of the octagon.
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[3 marksmarkah](b)Lima sudut pedalaman sebuah pentagon ialah 100°, 120°, 110°, x dan 2x. Cari nilai x.The five interior angles of a pentagon are 100°, 120°, 110°, x and 2x. Find the value of x.
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[5 marksmarkah](c)Rajah 4 menunjukkan sebuah heksagon sekata dan sebuah oktagon sekata yang berkongsi sisi PQ pada pelan sebuah laman. (i) Cari nilai p. (ii) Seorang tukang jubin ingin mengisi sudut kosong itu dengan satu poligon sekata supaya tiada ruang kosong di sekeliling titik P. Adakah ini boleh dilakukan? Jelaskan.Diagram 4 shows a regular hexagon and a regular octagon that share the side PQ on the plan of a garden. (i) Find the value of p. (ii) A tiler wants to fill the gap with one regular polygon so that there is no space left around the point P. Is this possible? Explain.Rajah 4Diagram 4
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For the teacherUntuk guru: AnalysingMenganalisis, mediumsederhana difficultyaras mediumsederhana, ChapterBab 4, standard 4.2.4
TextbookBuku teksp.ms. 67
28
QuestionSoalan 28
Rajah 5 menunjukkan reka bentuk P bagi sebuah dewan komuniti. Dewan itu terdiri daripada sebuah kuboid dan sebuah bumbung berbentuk prisma segi tiga. Lebar dewan ialah 8 m, panjangnya 12 m dan tinggi dindingnya 5 m. Bumbung itu menambah 3 m tinggi di atas dinding. (Guna π = 227)Diagram 5 shows design P for a community hall. The hall is made up of a cuboid and a roof in the shape of a triangular prism. The width of the hall is 8 m, its length is 12 m and its walls are 5 m high. The roof adds 3 m of height above the walls. (Use π = 227)
Rajah 5Diagram 5
[3 marksmarkah](a)Hitung jumlah isi padu, dalam m3, dewan itu.Calculate the total volume, in m3, of the hall.
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[3 marksmarkah](b)Setiap tiang silinder dalam dewan itu berjejari 0.35 m dan tinggi 5 m. Hitung luas permukaan melengkung satu tiang dan kos mengecat 6 batang tiang pada kadar RM12 bagi setiap m2.Each cylindrical pillar in the hall has a radius of 0.35 m and a height of 5 m. Calculate the curved surface area of one pillar and the cost of painting 6 pillars at RM12 per m2.
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[4 marksmarkah](c)Jawatankuasa komuniti membandingkan reka bentuk P dengan reka bentuk Q, iaitu dewan berbentuk silinder berjejari 7 m dan tinggi 4 m. Jawatankuasa mahu dewan yang mempunyai luas lantai sekurang-kurangnya 150 m2 dan isi padu tidak melebihi 620 m3. Reka bentuk yang manakah memenuhi kedua-dua syarat? Tunjukkan pengiraan anda.The community committee compares design P with design Q, a cylindrical hall with a radius of 7 m and a height of 4 m. The committee wants a hall with a floor area of at least 150 m2 and a volume of not more than 620 m3. Which design meets both conditions? Show your calculations.
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For the teacherUntuk guru: EvaluatingMenilai, mediumsederhana difficultyaras mediumsederhana, ChapterBab 6, standard 6.4.3
TextbookBuku teksp.ms. 115
29
QuestionSoalan 29
Selesaikan soalan-soalan berikut tentang kecerunan.Answer the following questions about gradient.
[2 marksmarkah](a)Peraturan bangunan menetapkan bahawa kecerunan maksimum sebuah tanjakan kerusi roda ialah 112. Sebuah tanjakan perlu menaikkan pengguna setinggi 0.9 m. Hitung panjang mengufuk minimum tanjakan itu.A building regulation states that the maximum gradient of a wheelchair ramp is 112. A ramp must raise the user by 0.9 m. Calculate the minimum horizontal length of the ramp.
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[2 marksmarkah](b)Rajah 6 menunjukkan garis lurus AB pada satah Cartes. Cari kecerunan AB.Diagram 6 shows the straight line AB on a Cartesian plane. Find the gradient of AB.Rajah 6Diagram 6
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[3 marksmarkah](c)Garis lurus ST mempunyai kecerunan −34 dan pintasan-x 8. Cari pintasan-y bagi ST.The straight line ST has a gradient of −34 and an x-intercept of 8. Find the y-intercept of ST.
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[3 marksmarkah](d)Titik P(−2, h), Q(4, 7), R(1, −5) dan S(5, 3) ialah bucu sebuah sisi empat. PQ selari dengan RS. Cari nilai h.The points P(−2, h), Q(4, 7), R(1, −5) and S(5, 3) are vertices of a quadrilateral. PQ is parallel to RS. Find the value of h.
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For the teacherUntuk guru: ApplyingMengaplikasi, lowrendah difficultyaras lowrendah, ChapterBab 10, standard 10.1.5
TextbookBuku teksp.ms. 198
30
QuestionSoalan 30
Rajah 7 ialah piktograf yang menunjukkan bilangan pengunjung ke sebuah perpustakaan komuniti dari Isnin hingga Sabtu.Diagram 7 is a pictograph that shows the number of visitors to a community library from Monday to Saturday.
Rajah 7Diagram 7
[1 markmarkah](a)Nyatakan bilangan pengunjung pada hari Rabu.State the number of visitors on Wednesday.
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[1 markmarkah](b)Nyatakan mod bagi data itu.State the mode of the data.
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[2 marksmarkah](c)Hitung min bilangan pengunjung sehari.Calculate the mean number of visitors per day.
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[2 marksmarkah](d)Cari median bagi data itu.Find the median of the data.
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[4 marksmarkah](e)Pada hari Ahad, sebuah pameran buku menarik 90 orang pengunjung. Data Ahad ditambah kepada data enam hari itu. (i) Hitung min baharu bagi tujuh hari itu. (ii) Min atau median baharu, yang manakah lebih sesuai untuk menggambarkan bilangan pengunjung pada hari biasa? Berikan alasan anda.On Sunday, a book fair attracted 90 visitors. The Sunday figure is added to the data of the six days. (i) Calculate the new mean for the seven days. (ii) Which is more suitable to describe the number of visitors on a typical day, the new mean or the new median? Give a reason.
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For the teacherUntuk guru: ApplyingMengaplikasi, lowrendah difficultyaras lowrendah, ChapterBab 12, standard 12.1.6
TextbookBuku teksp.ms. 265
31
QuestionSoalan 31
Jadual 1 menunjukkan tempat 120 orang penduduk sebuah taman perumahan lazimnya membeli barang dapur dalam satu tinjauan komuniti.
Tempat membeli
Pasar raya
Pasar basah
Kedai runcit
Dalam talian
Bilangan penduduk
45
30
25
20
Table 1 shows where 120 residents of a housing estate usually buy their groceries in a community survey.
Place of purchase
Supermarket
Wet market
Mini-market
Online
Number of residents
45
30
25
20
[1 markmarkah](a)Seorang penduduk dipilih secara rawak. Cari kebarangkalian bahawa dia lazimnya membeli barang dapur dalam talian.A resident is chosen at random. Find the probability that the resident usually buys groceries online.
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[2 marksmarkah](b)Cari kebarangkalian bahawa penduduk itu tidak lazimnya membeli di pasar raya.Find the probability that the resident does not usually buy at the supermarket.
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[3 marksmarkah](c)Taman perumahan itu mempunyai 2 400 orang penduduk. Anggarkan bilangan penduduk yang lazimnya membeli di pasar basah atau dalam talian.The housing estate has 2 400 residents. Estimate the number of residents who usually buy at the wet market or online.
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[4 marksmarkah](d)Sebuah gerai karnival taman itu mempunyai dua permainan. Permainan P: Lambung sekeping syiling dan baling sebiji dadu adil sekali. Pemain menang jika mendapat gambar dan nombor genap. Permainan Q: Satu kad dipilih secara rawak daripada sebuah kotak yang mengandungi 5 keping kad merah dan 7 keping kad biru. Pemain menang jika kad itu merah. Pemilik gerai berkata, "Peluang menang dalam Permainan P ialah ½ kerana hasilnya sama ada menang atau kalah." Adakah pemilik gerai itu betul? Permainan yang manakah memberi peluang menang yang lebih baik? Tunjukkan pengiraan anda.A stall at the estate's carnival has two games. Game P: Toss a coin and roll a fair die once. A player wins by getting a head and an even number. Game Q: One card is chosen at random from a box that contains 5 red cards and 7 blue cards. A player wins if the card is red. The stall owner says, "The chance of winning Game P is ½ because the result is either a win or a loss." Is the stall owner correct? Which game gives the better chance of winning? Show your calculations.
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For the teacherUntuk guru: EvaluatingMenilai, hightinggi difficultyaras hightinggi, ChapterBab 13, standard 13.3.2
TextbookBuku teksp.ms. 288
Test specification (JSU)Jadual Spesifikasi Ujian (JSU)
ChapterBab
RememberingMengingat
UnderstandingMemahami
ApplyingMengaplikasi
AnalysingMenganalisis
EvaluatingMenilai
CreatingMencipta
Items
marksmarkah
1. Patterns and Sequences
–
–
2 (5)
–
–
–
2
5
2. Factorisation and Algebraic Fractions
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1 (1)
2 (11)
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–
–
3
12
3. Algebraic Formulae
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–
2 (5)
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–
–
2
5
4. Polygon
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–
2 (2)
1 (10)
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–
3
12
5. Circles
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–
3 (6)
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–
–
3
6
6. Three-Dimensional Geometrical Shapes
1 (1)
–
1 (1)
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1 (10)
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3
12
7. Coordinates
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–
3 (6)
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–
–
3
6
8. Graphs of Functions
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1 (1)
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–
–
–
1
1
9. Speed and Acceleration
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–
1 (1)
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–
–
1
1
10. Gradient of a Straight Line
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–
2 (11)
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–
–
2
11
11. Isometric Transformations
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1 (1)
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1 (1)
1 (4)
–
3
6
12. Measures of Central Tendencies
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–
2 (11)
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–
–
2
11
13. Simple Probability
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–
1 (1)
1 (1)
1 (10)
–
3
12
TotalJumlah
1 (1)
3 (3)
21 (60)
3 (12)
3 (24)
0 (0)
31
100
Each cell shows items (marks).Setiap petak menunjukkan item (markah).
