BAHAGIAN PEPERIKSAAN DAN PENILAIAN JABATAN PENDIDIKAN POLITEKNIK KEMENTERIAN PENDIDIKAN TINGGI JABATAN MATEMATIK, SAINS & KOMPUTER

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BAHAGIAN PEPERIKSAAN DAN PENILAIAN

JABATAN PENDIDIKAN POLITEKNIK

KEMENTERIAN PENDIDIKAN TINGGI

JABATAN MATEMATIK, SAINS & KOMPUTER

PEPERIKSAAN AKHIR

SESI JUN 2017

DBM1053 : AGRICULTURAL MATHEMATICS

TARIKH : 25 OKTOBER 2017

MASA

: 8.30 PAGI - 10.30 PAGI (2 JAM)

Kertas ini mengandungi TIGA BELAS (13) halaman bercetak.

Bahagian A: Struktur (3 soalan)

Bahagian B: Struktur (3 soalan)

Dokumen sokongan yang disertakan : Kertas Graf & Formula

JANGAN BUKA KERTAS SOALAN INI SEHINGGA DIARAHKAN

(CLO yang tertera hanya sebagai rujukan)

SULIT

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2 SULIT SECTION A: 75 MARKS

BAHAGIAN A: 75 MARKAH

INSTRUCTION:

This section consists of THREE (3) structured questions. Answer ALL questions. ARAHAN:

Bahagian ini mengandungi TIGA (3) soalan berstruktur. Jawab SEMUA soalan.

QUESTION 1

SOALAN 1

Table 1: List of price for four items Jadual 1: Senarai harga bagi 4 barang Items Barang New price Harga baru Original price Harga asal P RM540 RM621 Q RM25 RM27.50 R x RM972 S RM180 RM216

(a) Table 1 above shows the original price and the new price of four items in a furniture shop. Calculate:

Jadual 1 di atas menunjukkan harga baru dan harga asal bagi empat barang di kedai perabot. Kirakan:

i. the discount for each item P, Q and S potongan bagi setiap barang P, Q dan S

[6 Marks] [6 Markah] CLO1

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3 SULIT

ii. value of x if a customer gets a 25% discount for item R.

nilai bagi x jika pelanggan mendapat potongan 25% bagi barang R. [2 Marks] [2 Markah]

ii. total amount that customer needs to pay for two items of R if the furniture shop gives 50% discount for the second item purchased.

jumlah harga yang pelanggan perlu bayar bagi dua barang R jika potongan 50% diberikan bagi barang kedua yang dibeli.

[2 marks] [2 markah]

(b) Simplify each of the following to its simplest forms: Permudahkan yang berikut kepada bentuk termudah:

i. 2 2 p q p q px py x y + _÷ − + + [2 marks] [2 markah] ii. 2 64 2 16 3 15 p p p − _÷ + [2 marks] [2 markah] iii. 2 1 5 2 2 5 x x x x − − − [3 marks] [3 markah] CLO3 C3

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4 SULIT

(c) Maria bought 4 kg of durians and 3 kg of mangoes at a total price of RM45. While Sarah bought 6 kg of durians and 4 kg of mangoes at a total price of RM65.

Maria telah membeli 4 kg durian dan 3 kg mangga dengan harga RM45. Manakala, Sarah telah membeli 6 kg durian dan 4 kg mangga dengan harga RM65.

i. Write two linear equations based on the above information. Tuliskan dua persamaan linear berdasarkan maklumat di atas.

ii. From the answer in c(i) , find the price for 1 kg of durian and 1 kg of mango by using substitution method.

Berdasarkan soalan di c(i), cari harga bagi 1 kg durian dan 1 kg mangga dengan menggunakan kaedah penggantian.

[6 marks] [6 markah] CLO3

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5 SULIT QUESTION 2

SOALAN 2

(a) Given log₂3 = 1.58 and log₂5 = 2.32, determine the value of each of the following without using a calculator.

Jika log₂3 = 1.58 dan log₂5 = 2.32, tentukan nilai bagi setiap yang berikut tanpa menggunakan kalkulator. i. log₂75 [3 marks] [3 markah] ii. log₂0.3 [4 marks] [4 markah] iii. log₂√5 [3 marks] [3 markah]

(b) The total mass of a lorry and its cargo is 4.3 tonnes. If the cargo is made up of 60 packets of soya beans and each weighing 38 kg, calculate:

Jumlah jisim sebuah lori dan muatannya ialah 4.3 tan. Jika muatan tersebut mengandungi 60 paket kacang soya dan setiap daripadanya ialah 38 kg, kira:

i. The mass of the cargo in grams (g). Jisim muatan dalam gram (g).

[4 marks] [4 markah] CLO1 C2 CLO3 C3

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6 SULIT

ii. The total mass of soya beans carried by the lorry. Jumlah jisim bagi kacang soya yang dibawa oleh lori.

(c) A car with a 20 gallons gas tank can go 25 miles on 1 gallon of gas. If the tank is full at the beginning of a trip, calculate:

Sebuah kereta dengan tangki gas 20 gelen boleh bergerak sejauh 25 batu bagi 1 gelen gas. Jika tangki diisi penuh pada permulaan perjalanan, kira:

i. How much of gas (in ml) is needed for a 725 miles trip? (Given 1gallon=4.55L) Berapakah jumlah gas (dalam ml) yang diperlukan bagi perjalanan 725 batu?

(Diberi 1gelen=4.55L)

ii. How many times does driver have to refill the gas tank on a 725 miles trip? Berapa kali pemandu perlu mengisi tangki gas bagi perjalanan 725 batu?

[2 marks] [2 markah] CLO3

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SOALAN 3

(a) Figure 1 shows a pie chart of four types of vegetables produced in a greenhouse using fertigation technique. 10 kg of chillies was produced during the harvested. Calculate the weight of tomatoes, spinach and salad that was harvested.

Gambarajah 1 menunjukkan carta pai empat jenis sayur yang dihasilkan oleh sebuah rumah hijau dengan menggunakan teknik fertigasi. 10 kg cili telah diperolehi daripada hasil tuaian rumah hijau tersebut. Kira berat tomato, bayam dan salad yang telah dituai.

Figure 1 Gambarajah 1 [10 marks] [10 markah] CLO1 C2

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8 SULIT

(b) Anne bought a box of oranges which contained of 30 oranges. The weights (in gram) of the oranges are shown below. Construct a 6 classes of frequency distribution table for the following weights in gram of the 30 oranges.

Anne telah membeli sekotak buah oren yang mengandungi 30 biji buah oren. Berat (dalam gram) buah oren adalah seperti dibawah. Bina 6 kelas jadual taburan kekerapan bagi berat 30 biji buah oren dalam gram.

31 41 46 33 44 51 56 63 71 71

62 63 54 53 51 43 36 38 54 56

66 71 74 75 46 47 59 60 61 63

(c) Table 2 shows the weight of 40 patients of a clinic. Construct a histogram for the data below.

Jadual 2 menunjukkan berat 40 orang pesakit bagi sebuah klinik. Bina histogram daripada data yang diberikan.

Table 2 Jadual 2 Weight (kg) Frequency (f) 30 – 34 6 35 – 39 13 40 - 44 14 45 - 49 4 50 - 54 3 [8 marks] [8 markah] CLO3 C3 CLO3 C3

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9 SULIT SECTION B: 25 MARKS

BAHAGIAN B: 25 MARKAH

INSTRUCTION:

This section consists of THREE (3) structured questions. Answer ONE (1) question

ONLY.

ARAHAN:

Bahagian ini mengandungi TIGA (3) soalan berstruktur. Jawab SATU (1) soalan SAHAJA.

QUESTION 4

SOALAN 4

a) Mr. Lim is going to build his rectangular fish pond with an enclosed area of 500 feet2. He also decides that the length of the pond will be 5 feet longer than the width of the pond. Constructs the equation of the pond area.

En. Lim bercadang untuk membina kolam ikannya dengan keluasan sebanyak 500 kaki persegi. Beliau telah menentukan bahawa panjang kolam tersebut hendaklah 5 kaki lebih panjang daripada lebar. Bina persamaan bagi luas keseluruhan kolam tersebut.

b) Based on the answer in question 4(a), find the length and the width of the fish pond by using the formula below.

Berdasarkan jawapan di soalan 4(a), cari panjang dan lebar kolam tersebut menggunakan formula di bawah;

a ac b b x 2 4 2 − ± − = CLO1 C3 CLO2 C3 [6 marks] [6 markah] [6 marks] [6 markah] CLO2 C3

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10 SULIT

Figure 2 Gambarajah 2

c) Figure 2 above shows a 9.6 m high silo which is commonly used in agriculture to store grain in a wheat field. If the diameter of the silo is 4.5 m, determine the total surface area of the silo.

Gambarajah 2 menunjukkan sebuah silo dengan ketinggian 9.6 m yang selalu digunakan dalam pertanian untuk menyimpan bijirin di ladang gandum. Jika diameter silo ialah 4.5 m, tentukan jumlah kawasan permukaan silo tersebut.

[13 marks] [13 markah] CLO3 C4 4.5m 9.6m

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11 SULIT

QUESTION 5

SOALAN 5

a) Determine the two points of intersection for the two equations below.

Tentukan kordinat dua titik persilangan bagi dua persamaan di bawah.

y1 = x2 + x - 1

y2 = -

x

-

1

(b) Determine the intersection points at

x

– axis for equation y1 andy2 in question 5(a)

by using the formula given below;

Tentukan kordinat titik persilangan pada paksi-x untuk persamaan y1 dan y2 dalam

soalan 5(a) menggunakan formula yang diberi dibawah;

a ac b b x 2 4 2− ± − =

(c) Based on the equation from 5(a), plot the graph of the two lines on a graph paper. Berdasarkan persamaan dari soalan 5(a), plotkan kedua-dua garis tersebut dengan menggunakan kertas graf.

[10 marks] [10 markah] [7 marks] [7 markah] CLO 2 C2 CLO2 C3 CLO2 C3

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SOALAN 6

Figure 3 Gambarajah 3

(a) By referring to Figure 3 above, if AD=2 cm, calculate: Berdasarkan Gambarajah 3 di atas, jika AD=2 cm, kira:

i.

∡CAB

ii. CD

iii.

∡CBA

[7 marks] [7 markah]

(b) Determine the values of θ below if: Tentukan nilai bagi θ dibawah jika:

i. sin θ = 0.9063, where 0° ≤ θ ≤ 180°

ii. tan θ = -0.4663, where 0° ≤ θ ≤ 360° [8 marks] [8 markah] CLO 2 C3 CLO 2 C3 A D C 10cm 4cm B

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13 SULIT

Figure 3 Gambarajah 3 (c) From the Figure 3 above, calculate:

Berdasarkan Gambarajah 3 di atas, cari:

i. the angle between the ladder and horizontal ground. sudut di antara tangga dan tanah mendatar.

ii. the highest floor the ladder can reach from the ground if the height of each floor is 3 m.

tingkat tertinggi tangga tersebut boleh capai dari tanah jika ketinggian setiap tingkat adalah 3 meter.

iii. the highest floor that can be reached by a kite if the maximum elevation angle of the kite from the ground is 80 degrees.

tingkat tertinggi yang boleh dicapai dengan layang-layang jika sudut ketinggian maksimum layang-layang dari tanah adalah 80 darjah.

[5 marks] [5 markah] SOALAN TAMAT CLO 2 C4 75m 16m 9m

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Formula Page 1 of 5

Algebraic

completing the square

2 2 2 2 1 2 1                   bx b c b ax quadratic formula a ac b b x 2 4 2 _    Laws of indices a. aman amn b.   _a  , _a 0 a a a a m n n m n m c.

   

_am n _ _an m __amn d. _an__bn _

 

_ab n e.  , 0       b b a b a n n n Laws of logarithms

a. log_bMNlog_bMlog_bN

b. M N N M b b b log log log   c. M N bM N b log log 

Changes of bases of logarithms

a. b N N a a b log log log  b. b N n b _log 1 log 

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Formula Page 2 of 5 Basic Identities sin2 __{+ cos}2__{= 1} 1 + tan2__{= sec}2_ 1 + cot2 __{= cosec}2_ Compound Angle

sin (+) = sin  cos  + cos  sin  cos ( + ) = cos cos  - sin sin  tan ( + ) = tan  + tan 

1 – tan tan  Double Angle

sin (2) = 2 sin  cos  cos (2) = cos2_{- sin}2 = 2cos2_{- 1} = 1 – 2sin2 tan (2) = 2tan 1 – tan2_ Law of Sine a = b = c

sin A sin B sin C Law of Cosine

a2_{= b}2_{+ c}2_{– 2bc cos A} b2_{= a}2_{+ c}2_{– 2ac cos B} c2 = a2 + b2 – 2ab cos C

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Formula Page 3 of 5 Radian to degree Length of arc Area of Sector 5.1 Solid Formulae 5) Cone V = 1/3 π2h A = πrs + πr2 6) Pyramid V = 1/3 x base area x height 7) Sphere V = 4/3πr3 A = 4πr2 8) Trapezium A = ½ t (a+b) Solid Formulae 1) Cube V = x3 2) Cuboid V = l x b x h 3) Prism V = area of cross section x length 4) Cylinder V = πr2h A = 2πr2 + 2πrh s = r θ  2 2 1 r A    180  radian

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Formula Page 4 of 5 1 2 1 2 x x y y m   

Distance between two points

   2 2 1 2 2 1 x y y x AB   

Division of line segment         2 , 2 2 1 2 1 x y y x           n m ny ny n m nx nx₁ ₂ ₁ ₂ , Statistics Mean 1. Ungrouped data : n x x 



2. Ungrouped data (in Frequency Table) :



 f fx x 3. Grouped data :



 f fx x Median 1. Ungrouped data : 2 1  T_n m

2 1  T_n m 3. Grouped data : c f F n L m m _              2

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Formula Page 5 of 5 1. Ungrouped data :

 

2 2 2 _x n x  





 

2 2 2 _x f fx  



 3. Grouped data :

 

2 2 2 _x f fx  



 Standard Deviation 1. Ungrouped data :

 

2 2 x n x  





 

2 2 x f fx  



 3. Grouped data :

 

2 2 x f fx  



