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Practice paper, not an official KPM paper
50
Ujian Akhir Sesi AkademikEnd of Academic Session Test

MatematikMathematics

Tingkatan 2, 2 jam / 2 hours, 100 marks
Nama / Name
Kelas / Class
Tarikh / Date
Markah / Marks:      / 100
Instructions
  1. Kertas soalan ini mengandungi tiga bahagian: Bahagian A, Bahagian B dan Bahagian C.This question paper consists of three sections: Section A, Section B and Section C.
  2. Jawab semua soalan.Answer all questions.
  3. Tunjukkan langkah-langkah penting dalam kerja mengira anda.Show your working. It may help you to get marks.
  4. Rajah yang mengiringi soalan tidak dilukis mengikut skala kecuali dinyatakan.The diagrams in this paper are not drawn to scale unless stated.
  5. Anda dibenarkan menggunakan kalkulator saintifik.You may use a scientific calculator.

Answer schemes are in English (DLP).

Practice shows answers as you go. Exam times you and hides answers until you submit.

Bahagian ASection A

20 marks
Jawab semua soalan. Setiap soalan diikuti oleh empat pilihan jawapan, A, B, C dan D. Pilih satu jawapan yang terbaik.Answer all questions. Each question is followed by four options, A, B, C and D. Choose the best answer.
1

Question 1

Sebuah dinding batu bata disusun dalam beberapa baris. Baris pertama mempunyai 6 biji batu bata dan setiap baris seterusnya mempunyai 7 biji batu bata lebih banyak daripada baris sebelumnya. Berapakah bilangan batu bata pada baris ke-8?A brick wall is built in rows. The first row has 6 bricks and each next row has 7 more bricks than the row before it. How many bricks are in the 8th row?
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C
The numbers of bricks form the sequence 6, 13, 20, 27, … with common difference 7. T₈ = 6 + 7 × 7 = 55. (62 is the 9th row; 48 is 6 + 6 × 7.)
For the teacher: Applying, low difficulty, Chapter 1, standard 1.3.2
Textbook p. 11
2

Question 2

Kembangkan (3x − 4)(x + 5).Expand (3x − 4)(x + 5).
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A
(3x − 4)(x + 5) = 3x² + 15x − 4x − 20 = 3x² + 11x − 20.
For the teacher: Applying, low difficulty, Chapter 2, standard 2.1.2
Textbook p. 23
3

Question 3

Faktorkan 2x² + 7x − 15.Factorise 2x² + 7x − 15.
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C
Look for two numbers with product 2 × (−15) = −30 and sum 7: 10 and −3. 2x² + 10x − 3x − 15 = 2x(x + 5) − 3(x + 5) = (2x − 3)(x + 5).
For the teacher: Applying, medium difficulty, Chapter 2, standard 2.2.2
Textbook p. 30
4

Question 4

Diberi p = 2√(q + 3). Ungkapkan q dalam sebutan p.Given p = 2√(q + 3). Express q in terms of p.
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D
p = 2√(q + 3) → p/2 = √(q + 3). Square both sides: p²/4 = q + 3, so q = p²/4 − 3.
For the teacher: Applying, medium difficulty, Chapter 3, standard 3.1.2
Textbook p. 46
5

Question 5

Jumlah sudut pedalaman sebuah poligon ialah 1 440°. Namakan poligon itu.The sum of the interior angles of a polygon is 1 440°. Name the polygon.
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A
(n − 2) × 180° = 1 440° → n − 2 = 8 → n = 10, a decagon.
For the teacher: Understanding, low difficulty, Chapter 4, standard 4.2.1
Textbook p. 63
6

Question 6

Setiap sudut pedalaman sebuah poligon sekata ialah 156°. Berapakah bilangan sisi poligon itu?Each interior angle of a regular polygon is 156°. How many sides does the polygon have?
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B
Exterior angle = 180° − 156° = 24°. Number of sides = 360° ÷ 24° = 15.
For the teacher: Applying, medium difficulty, Chapter 4, standard 4.2.3
Textbook p. 65
7

Question 7

Sebuah tingkap kaca berwarna berbentuk sektor bulatan yang berjejari 21 cm dan bersudut 120° di pusat. Hitung panjang lengkok, dalam cm, tingkap itu. (Guna π = 227)A stained-glass window is the shape of a sector of a circle with radius 21 cm and angle 120° at the centre. Calculate the arc length, in cm, of the window. (Use π = 227)
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B
Arc length = (120/360) × 2 × (22/7) × 21 = (1/3) × 132 = 44 cm. (132 cm is the whole circumference.)
For the teacher: Applying, medium difficulty, Chapter 5, standard 5.3.3
Textbook p. 89
8

Question 8

Diameter sebuah meja bulat ialah 1.4 m. Hitung lilitan, dalam m, meja itu. (Guna π = 227)The diameter of a round table is 1.4 m. Calculate the circumference, in m, of the table. (Use π = 227)
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C
C = πd = (22/7) × 1.4 = 4.4 m. (1.54 is the area πr², 2.2 is πr.)
For the teacher: Applying, low difficulty, Chapter 5, standard 5.3.1
Textbook p. 86
9

Question 9

Sebuah bentangan (jaring) terdiri daripada satu bulatan dan satu sektor bagi bulatan yang lebih besar. Pepejal manakah yang dibentuk oleh jaring itu?A net consists of one circle and one sector of a larger circle. Which solid is formed by the net?
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B
The circle is the base and the sector curls round to form the curved surface of a cone. A cylinder needs two circles and a rectangle.
For the teacher: Remembering, low difficulty, Chapter 6, standard 6.2.1
Textbook p. 103
10

Question 10

Sebuah corong berbentuk kon mempunyai jejari tapak 7 cm dan tinggi 12 cm. Hitung isi padu, dalam cm³, corong itu. (Guna π = 227)A funnel in the shape of a cone has a base radius of 7 cm and a height of 12 cm. Calculate the volume, in cm³, of the funnel. (Use π = 227)
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C
V = (1/3)πr²h = (1/3) × (22/7) × 7² × 12 = 616 cm³. (1 848 cm³ is a cylinder with the same radius and height.)
For the teacher: Applying, medium difficulty, Chapter 6, standard 6.4.2
Textbook p. 113
11

Question 11

Titik P(−2, 3) dan titik Q(4, 11) terletak pada satah Cartes. Hitung jarak, dalam unit, antara P dengan Q.Point P(−2, 3) and point Q(4, 11) lie on a Cartesian plane. Calculate the distance, in units, between P and Q.
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B
PQ = √[(4 − (−2))² + (11 − 3)²] = √(36 + 64) = √100 = 10. (100 forgets the square root; 14 is 6 + 8.)
For the teacher: Applying, low difficulty, Chapter 7, standard 7.1.3
Textbook p. 128
12

Question 12

Titik tengah bagi garis lurus AB ialah M(2, 5). Diberi A(−3, 8), cari koordinat titik B.The midpoint of the straight line AB is M(2, 5). Given A(−3, 8), find the coordinates of point B.
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D
M is the midpoint, so (−3 + x)/2 = 2 and (8 + y)/2 = 5. x = 7, y = 2. B is (7, 2).
For the teacher: Analysing, high difficulty, Chapter 7, standard 7.2.4
Textbook p. 137
13

Question 13

Antara lakaran graf berikut, yang manakah mewakili fungsi y = 3x?Which of the following graph sketches represents the function y = 3x?
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C
The graph of y = 3/x has two separate branches, one in the first and one in the third quadrant, and never touches the axes. y = x² is U-shaped, y = x³ is S-shaped and y = 2x + 1 is a straight line.
For the teacher: Understanding, low difficulty, Chapter 8, standard 8.2.1
Textbook p. 154
14

Question 14

Sebuah kereta api memperlahankan lajunya daripada 90 km/j kepada 36 km/j dalam masa 12 s. Hitung nyahpecutan, dalam m/s², kereta api itu.A train slows down from 90 km/h to 36 km/h in 12 s. Calculate the deceleration, in m/s², of the train.
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A
90 km/h = 25 m/s and 36 km/h = 10 m/s. Deceleration = (25 − 10) ÷ 12 = 1.25 m/s². (4.5 divides 54 km/h by 12 without changing the units.)
For the teacher: Analysing, high difficulty, Chapter 9, standard 9.2.2
Textbook p. 181
15

Question 15

Satu garis lurus melalui titik (−2, 7) dan (4, −5). Hitung kecerunan garis lurus itu.A straight line passes through the points (−2, 7) and (4, −5). Calculate the gradient of the straight line.
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A
m = (−5 − 7) ÷ (4 − (−2)) = −12 ÷ 6 = −2. The line slopes downwards, so the gradient is negative.
For the teacher: Applying, medium difficulty, Chapter 10, standard 10.1.4
Textbook p. 197
16

Question 16

Titik P(−3, 4) dipetakan kepada P'(2, −1) di bawah suatu translasi. Nyatakan vektor translasi itu.The point P(−3, 4) is mapped onto P'(2, −1) under a translation. State the translation vector.
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D
Move right 2 − (−3) = 5 and up −1 − 4 = −5 (that is, 5 units down). The vector is (5, −5).
For the teacher: Understanding, low difficulty, Chapter 11, standard 11.2.3
Textbook p. 217
17

Question 17

Titik (4, −1) diputarkan 90° lawan arah jam pada asalan. Apakah koordinat imej titik itu?The point (4, −1) is rotated 90° anticlockwise about the origin. What are the coordinates of its image?
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C
A 90° anticlockwise rotation about the origin takes (x, y) to (−y, x): (4, −1) → (1, 4). (−1, −4) is the clockwise rotation and (−4, 1) is a 180° rotation.
For the teacher: Analysing, high difficulty, Chapter 11, standard 11.4.3
Textbook p. 225
18

Question 18

Min bagi lima nombor ialah 12. Apabila nombor keenam ditambah, min enam nombor itu menjadi 14. Cari nombor keenam itu.The mean of five numbers is 12. When a sixth number is added, the mean of the six numbers becomes 14. Find the sixth number.
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B
Total of five numbers = 5 × 12 = 60. Total of six numbers = 6 × 14 = 84. Sixth number = 84 − 60 = 24.
For the teacher: Analysing, high difficulty, Chapter 12, standard 12.1.2
Textbook p. 255
19

Question 19

Sebuah beg mengandungi 5 biji bola merah, 7 biji bola biru dan 8 biji bola hijau. Sebiji bola dipilih secara rawak. Hitung kebarangkalian bahawa bola itu bukan berwarna biru.A bag contains 5 red balls, 7 blue balls and 8 green balls. A ball is chosen at random. Calculate the probability that the ball is not blue.
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D
n(S) = 5 + 7 + 8 = 20. P(blue) = 7/20, so P(not blue) = 1 − 7/20 = 13/20. (Or 5 + 8 = 13 balls are not blue.)
For the teacher: Understanding, low difficulty, Chapter 13, standard 13.3.2
Textbook p. 288
20

Question 20

Sepucuk huruf dipilih secara rawak daripada perkataan CONSTRUCTION. Cari kebarangkalian bahawa huruf itu ialah huruf vokal.A letter is chosen at random from the word CONSTRUCTION. Find the probability that the letter is a vowel.
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A
CONSTRUCTION has 12 letters, so n(S) = 12. The vowels are O, U, I, O, so there are 4. P(vowel) = 4/12 = 1/3. (2/3 is the probability of a consonant.)
For the teacher: Understanding, low difficulty, Chapter 13, standard 13.2.1
Textbook p. 283

Bahagian BSection B

20 marks
Jawab semua soalan.Answer all questions.
21

Question 21

Seorang tukang kayu menulis beberapa ungkapan algebra untuk mengira panjang papan yang diperlukan.A carpenter writes some algebraic expressions to work out the lengths of the planks needed.
[1 mark] (a)Lengkapkan pemfaktoran 6ab − 15a = 3a( ____ ).Complete the factorisation 6ab − 15a = 3a( ____ ).
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2b − 5
6ab ÷ 3a = 2b and 15a ÷ 3a = 5, so 6ab − 15a = 3a(2b − 5).
[1 mark] (b)Faktorkan sepenuhnya m² − 49.Factorise m² − 49 completely.
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(m + 7)(m − 7)
Difference of two squares: m² − 7² = (m + 7)(m − 7).
[2 marks] (c)Ungkapkan 32p + 53p sebagai satu pecahan tunggal dalam bentuk termudah.Express 32p + 53p as a single fraction in its simplest form.
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For the teacher: Applying, low difficulty, Chapter 2, standard 2.2.2
Textbook p. 29
22

Question 22

Rajah 1 menunjukkan sebuah kolam bulat berjejari 14 m di sebuah taman. Sebuah laluan selebar 7 m dibina mengelilingi kolam itu. (Guna π = 227)Diagram 1 shows a circular pond of radius 14 m in a garden. A path 7 m wide is built around the pond. (Use π = 227)
Circular pond of radius 14 m surrounded by a path 7 m wide
Rajah 1Diagram 1
[2 marks] (a)Hitung luas, dalam m², kolam itu.Calculate the area, in m², of the pond.
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[2 marks] (b)Hitung luas, dalam m², laluan itu.Calculate the area, in m², of the path.
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For the teacher: Applying, medium difficulty, Chapter 5, standard 5.3.4
Textbook p. 92
23

Question 23

Rajah 2 menunjukkan satu hubungan daripada set A = {−2, −1, 1, 2} kepada set B = {1, 4, 9} dengan petua “kuasa dua bagi”.Diagram 2 shows a relation from set A = {−2, −1, 1, 2} to set B = {1, 4, 9} with the rule “the square of”.
Arrow diagram: -2 and 2 map to 4, -1 and 1 map to 1, nothing maps to 9
Rajah 2Diagram 2
[1 mark] (a)Nyatakan jenis hubungan daripada set A kepada set B.State the type of relation from set A to set B.
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Many-to-one
Both −2 and 2 have the image 4, and both −1 and 1 have the image 1: more than one object maps to the same image, so the relation is many-to-one.
[1 mark] (b)Nyatakan julat hubungan itu.State the range of the relation.
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The range is the set of images that are actually reached. 9 is in set B but no object maps to it.
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[2 marks] (c)Diberi fungsi f(x) = 3x − 7, cari
(i) f(4),
(ii) nilai x apabila f(x) = 8.Given the function f(x) = 3x − 7, find
(i) f(4),
(ii) the value of x when f(x) = 8.
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For the teacher: Understanding, low difficulty, Chapter 8, standard 8.1.2
Textbook p. 150
24

Question 24

Rajah 3 menunjukkan segi tiga P dan imejnya, segi tiga Q, pada suatu grid.Diagram 3 shows triangle P and its image, triangle Q, on a grid.
Triangle P with vertices (1,1), (1,4), (3,1) and triangle Q with vertices (9,1), (9,4), (7,1) on a grid
Rajah 3Diagram 3
[2 marks] (a)Huraikan selengkapnya penjelmaan yang memetakan segi tiga P kepada segi tiga Q.Describe in full the transformation that maps triangle P onto triangle Q.
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[1 mark] (b)Tandakan BENAR atau PALSU: Segi tiga Q kongruen dengan segi tiga P.Mark TRUE or FALSE: Triangle Q is congruent to triangle P.
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True
A reflection is an isometry: the image has the same size and shape as the object, so it is congruent.
[1 mark] (c)Sebuah papan tanda berbentuk segi tiga sama sisi. Nyatakan peringkat simetri putaran bagi papan tanda itu.A signboard is in the shape of an equilateral triangle. State the order of rotational symmetry of the signboard.
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3
An equilateral triangle fits onto itself 3 times in one complete turn (at 120°, 240° and 360°).
For the teacher: Applying, medium difficulty, Chapter 11, standard 11.3.3
Textbook p. 220
25

Question 25

Bilangan pengunjung ke sebuah gerai kraf tangan sempena karnival sekolah pada tujuh hari berturut-turut ialah
36, 40, 38, 40, 35, 42, 84The numbers of visitors to a handicraft stall at a school carnival on seven consecutive days are
36, 40, 38, 40, 35, 42, 84
[1 mark] (a)Hitung min bilangan pengunjung sehari.Calculate the mean number of visitors per day.
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[1 mark] (b)Cari median bagi data itu.Find the median of the data.
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[2 marks] (c)Penganjur ingin melaporkan bilangan pengunjung yang biasa pada satu hari. Antara min dengan median, yang manakah lebih sesuai? Berikan satu sebab.The organiser wants to report the usual number of visitors on a day. Which is more suitable, the mean or the median? Give one reason.
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For the teacher: Evaluating, high difficulty, Chapter 12, standard 12.1.5
Textbook p. 262

Bahagian CSection C

60 marks
Jawab semua soalan. Tunjukkan langkah-langkah penting dalam kerja mengira anda.Answer all questions. Show the important steps in your working.
26

Question 26

Rajah 4 menunjukkan tiga corak jubin yang mengelilingi sebuah kolam persegi di sebuah taman. Corak n mempunyai kolam berukuran n × n petak yang dikelilingi oleh jubin perang.Diagram 4 shows three patterns of tiles around a square pond in a garden. Pattern n has a pond of n × n squares surrounded by brown tiles.
Pattern 1: 1 by 1 pond with 8 tiles; Pattern 2: 2 by 2 pond with 12 tiles; Pattern 3: 3 by 3 pond with 16 tiles
Rajah 4Diagram 4
[2 marks] (a)Nyatakan bilangan jubin keliling dalam Corak 4 dan dalam Corak 5.State the number of border tiles in Pattern 4 and in Pattern 5.
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[3 marks] (b)Tulis satu ungkapan algebra bagi bilangan jubin keliling dalam Corak n.Write an algebraic expression for the number of border tiles in Pattern n.
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[2 marks] (c)Corak yang manakah menggunakan 100 jubin keliling?Which pattern uses 100 border tiles?
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[3 marks] (d)Jujukan 87, 80, 73, … menurun dengan beza yang sama. Cari sebutan pertama yang negatif.The sequence 87, 80, 73, … decreases by the same amount each time. Find the first term that is negative.
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For the teacher: Applying, low difficulty, Chapter 1, standard 1.3.3
Textbook p. 12
27

Question 27

Pentagon ABCDE with angles 108 degrees, 2x, (x + 24), (3x - 6) and 90 degrees
Rajah 5Diagram 5
Regular hexagon above side AB and regular pentagon below it; angle x at B between the two polygons
Rajah 6Diagram 6
[3 marks] (a)(i) Hitung jumlah sudut pedalaman sebuah oktagon.
(ii) Sebuah papan tanda berhenti berbentuk oktagon sekata. Hitung sudut pedalaman papan tanda itu.(i) Calculate the sum of the interior angles of an octagon.
(ii) A stop sign is in the shape of a regular octagon. Calculate the interior angle of the sign.
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[3 marks] (b)Rajah 5 menunjukkan pelan sebuah plot tanah berbentuk pentagon ABCDE. Cari nilai x.Diagram 5 shows the plan of a plot of land in the shape of pentagon ABCDE. Find the value of x.
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[2 marks] (c)Rajah 6 menunjukkan corak jubin lantai yang terdiri daripada sebuah heksagon sekata dan sebuah pentagon sekata yang berkongsi sisi AB. Hitung nilai x.Diagram 6 shows a floor tile design made of a regular hexagon and a regular pentagon that share side AB. Calculate the value of x.
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[2 marks] (d)Sudut pedalaman sebuah poligon sekata ialah 160°. Cari bilangan sisi poligon itu.The interior angle of a regular polygon is 160°. Find the number of sides of the polygon.
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For the teacher: Applying, low difficulty, Chapter 4, standard 4.2.3
Textbook p. 66
28

Question 28

Rajah 7 menunjukkan jaring sebuah prisma yang dibuat daripada kadbod untuk model bumbung sebuah rumah.Diagram 7 shows the net of a prism made of cardboard for the model of a roof of a house.
Net: three rectangles 6 cm, 8 cm and 10 cm wide and 12 cm long, with a right-angled triangle of sides 6, 8 and 10 cm above and below the middle rectangle
Rajah 7Diagram 7
[1 mark] (a)Namakan pepejal yang dibentuk oleh jaring itu.Name the solid formed by the net.
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[3 marks] (b)Hitung jumlah luas permukaan, dalam cm², prisma itu.Calculate the total surface area, in cm², of the prism.
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[2 marks] (c)Hitung isi padu, dalam cm³, prisma itu.Calculate the volume, in cm³, of the prism.
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[4 marks] (d)Dua jenis tin silinder yang berisi serbuk koko dijual di sebuah kedai. Tin P berjejari 7 cm dan tinggi 18 cm, berharga RM13.86. Tin Q berjejari 5 cm dan tinggi 21 cm, berharga RM9.90. Tin yang manakah lebih berbaloi dari segi harga bagi setiap cm³ isi padu? Tunjukkan pengiraan anda. (Guna π = 227)Two types of cylindrical tins of cocoa powder are sold in a shop. Tin P has radius 7 cm and height 18 cm and costs RM13.86. Tin Q has radius 5 cm and height 21 cm and costs RM9.90. Which tin is better value in terms of price per cm³ of volume? Show your calculations. (Use π = 227)
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For the teacher: Evaluating, medium difficulty, Chapter 6, standard 6.4.3
Textbook p. 115
29

Question 29

Rajah 8 menunjukkan graf jarak-masa bagi perjalanan sebuah lori yang membawa bahan binaan dari sebuah kilang ke tapak pembinaan.Diagram 8 shows the distance-time graph of the journey of a lorry carrying building materials from a factory to a construction site.
Distance-time graph: (0,0) to (30,40), flat to (45,40), then to (120,100); time in minutes, distance in km
Rajah 8Diagram 8
[2 marks] (a)Hitung laju, dalam km/j, lori itu dalam 30 minit yang pertama.Calculate the speed, in km/h, of the lorry in the first 30 minutes.
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[2 marks] (b)Berapa lamakah, dalam minit, lori itu berhenti?For how long, in minutes, did the lorry stop?
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[3 marks] (c)Hitung laju purata, dalam km/j, lori itu bagi seluruh perjalanan, termasuk masa berhenti.Calculate the average speed, in km/h, of the lorry for the whole journey, including the time it stopped.
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[3 marks] (d)Sebuah van bergerak daripada keadaan rehat dan mencapai laju 72 km/j dalam masa 10 s. Hitung pecutan, dalam m/s², van itu.A van starts from rest and reaches a speed of 72 km/h in 10 s. Calculate the acceleration, in m/s², of the van.
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For the teacher: Applying, medium difficulty, Chapter 9, standard 9.1.4
Textbook p. 177
30

Question 30

Rajah 9 menunjukkan sebuah tanjakan kerusi roda di sebuah bangunan. Rajah 10 menunjukkan satu garis lurus yang memotong paksi-x dan paksi-y pada satah Cartes.Diagram 9 shows a wheelchair ramp at a building. Diagram 10 shows a straight line that cuts the x-axis and the y-axis on a Cartesian plane.
Ramp rising 0.9 m over a horizontal distance of 3.6 m
Rajah 9Diagram 9
Straight line through (-4, 0) and (0, 6)
Rajah 10Diagram 10
[2 marks] (a)Hitung kecerunan tanjakan dalam Rajah 9.Calculate the gradient of the ramp in Diagram 9.
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[3 marks] (b)Berdasarkan Rajah 10, cari kecerunan garis lurus itu.Based on Diagram 10, find the gradient of the straight line.
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[3 marks] (c)Titik A(−1, 7) dan titik B(5, k) terletak pada satu garis lurus yang berkecerunan −32. Cari nilai k.Point A(−1, 7) and point B(5, k) lie on a straight line with gradient −32. Find the value of k.
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[2 marks] (d)Sebuah tanjakan lain, Q, naik 0.8 m bagi setiap 2.5 m jarak mengufuk. Antara tanjakan dalam Rajah 9 dengan tanjakan Q, yang manakah lebih curam? Tunjukkan pengiraan anda.Another ramp, Q, rises 0.8 m for every 2.5 m of horizontal distance. Which is steeper, the ramp in Diagram 9 or ramp Q? Show your calculation.
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For the teacher: Applying, low difficulty, Chapter 10, standard 10.1.5
Textbook p. 199
31

Question 31

Rajah 11 menunjukkan sebuah pemutar adil yang mempunyai lapan sektor sama saiz bernombor 1 hingga 8, yang digunakan dalam satu permainan di karnival sekolah.Diagram 11 shows a fair spinner with eight equal sectors numbered 1 to 8, used in a game at a school carnival.
Spinner with eight equal sectors numbered 1 to 8
Rajah 11Diagram 11
[3 marks] (a)Pemutar itu diputar sekali. A ialah peristiwa mendapat nombor yang lebih besar daripada 5.
(i) Senaraikan semua unsur peristiwa A.
(ii) Cari P(A).
(iii) Cari P(A′).The spinner is spun once. A is the event of getting a number greater than 5.
(i) List all the elements of event A.
(ii) Find P(A).
(iii) Find P(A′).
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[3 marks] (b)Sebuah beg mengandungi 12 biji guli merah, 8 biji guli hijau dan beberapa biji guli kuning. Kebarangkalian memilih sebiji guli hijau secara rawak ialah 15.
(i) Cari jumlah bilangan guli dalam beg itu.
(ii) Cari kebarangkalian bahawa guli yang dipilih bukan berwarna merah.A bag contains 12 red marbles, 8 green marbles and some yellow marbles. The probability of choosing a green marble at random is 15.
(i) Find the total number of marbles in the bag.
(ii) Find the probability that the marble chosen is not red.
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[4 marks] (c)Di sebuah gerai undian, Kotak A mengandungi 3 biji bola merah daripada 12 biji bola, dan Kotak B mengandungi 4 biji bola merah daripada 18 biji bola. Murid yang memilih sebiji bola merah secara rawak akan memenangi hadiah.
(i) Kotak yang manakah memberi peluang menang yang lebih besar? Tunjukkan pengiraan anda.
(ii) Jika 2 biji bola merah ditambah ke dalam Kotak B, adakah jawapan anda dalam (i) berubah? Jelaskan.At a lucky-draw stall, Box A contains 3 red balls out of 12 balls, and Box B contains 4 red balls out of 18 balls. A pupil who chooses a red ball at random wins a prize.
(i) Which box gives the greater chance of winning? Show your calculations.
(ii) If 2 more red balls are added to Box B, does your answer in (i) change? Explain.
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For the teacher: Evaluating, high difficulty, Chapter 13, standard 13.4.1
Textbook p. 291
Test specification (JSU)
ChapterRememberingUnderstandingApplyingAnalysingEvaluatingCreatingItemsmarks
1. Patterns and Sequences––2 (11)–––211
2. Factorisation and Algebraic Fractions––3 (6)–––36
3. Algebraic Formulae––1 (1)–––11
4. Polygon–1 (1)2 (11)–––312
5. Circles––3 (6)–––36
6. Three-Dimensional Geometrical Shapes1 (1)–1 (1)–1 (10)–312
7. Coordinates––1 (1)1 (1)––22
8. Graphs of Functions–2 (5)––––25
9. Speed and Acceleration––1 (10)1 (1)––211
10. Gradient of a Straight Line––2 (11)–––211
11. Isometric Transformations–1 (1)1 (4)1 (1)––36
12. Measures of Central Tendencies–––1 (1)1 (4)–25
13. Simple Probability–2 (2)––1 (10)–312
Total1 (1)6 (9)17 (62)4 (4)3 (24)0 (0)31100
Each cell shows items (marks).