Top Class Mathematics F4

Form IC094031S


4 4
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CLASS 4 KSSM





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FORMAT 2021 Year-End Assessment

Contents






Rekod Pencapaian Pentaksiran Murid iii – vi 6.2 Systems of Linear Inequalities in Two Variables 78
Sistem Ketaksamaan Linear dalam Dua Pemboleh Ubah
SPM Practice 6 83
CHAPTER Quadratic Functions and Equations in One 1 HOTS Challenge 84
Variable
1
84
Online Quick Quiz QR code PAK-21 Corner QR code
Fungsi dan Persamaan Kuadratik dalam Satu
Pemboleh Ubah
1.1 Quadratic Functions and Equations 1 CHAPTER Graphs of Motion 85
Fungsi dan Persamaan Kuadratik 7
Graf Gerakan
SPM Practice 1 11
HOTS Challenge 12 7.1 Distance-Time Graphs 85
Online Quick Quiz QR code PAK-21 Corner QR code 12 Graf Jarak-Masa
7.2 Speed-Time Graphs 91
Graf Laju-Masa
CHAPTER Number Bases 13 SPM Practice 7 96
2
Asas Nombor
HOTS Challenge
100
Online Quick Quiz QR code PAK-21 Corner QR code 100
2.1 Number bases 13
Asas nombor
8
SPM Practice 2 31 CHAPTER Measures of Dispersion for Ungrouped Data 101
HOTS Challenge 31 Sukatan Serakan Data Tak Terkumpul
Online Quick Quiz QR code PAK-21 Corner QR code 31
8.1 Dispersion 101
Serakan
CHAPTER Logical Reasoning 32 8.2 Measures of Dispersion 104
3

Sukatan Serakan
Penaakulan Logik
SPM Practice 8 111
3.1 Statements 32 HOTS Challenge 114
Pernyataan Online Quick Quiz QR code PAK-21 Corner QR code 114
3.2 Argument 41
Hujah
9
SPM Practice 3 46 CHAPTER Probability of Combine Events 115
HOTS Challenge 49 Kebarangkalian Peristiwa Bergabung
Online Quick Quiz QR code PAK-21 Corner QR code 49
9.1 Combined Events 115
Peristiwa Bergabung
CHAPTER Operations of Sets 50 9.2 Dependent Events and Independent Events 116
4

Peristiwa Bersandar dan Peristiwa Tidak Bersandar
Operasi Set
9.3 Mutually Exclusive Events and Non-Mutually
Exclusive Events 121
4.1 Intersection of Sets 50 Peristiwa Saling Eksklusif dan Peristiwa
Persilangan Set Tidak Saling Eksklusif
4.2 Union of Sets 54 9.4 Application of Probability of Combined Events 125
Kesatuan Set Aplikasi Kebarangkalian Peristiwa Bergabung
4.3 Combined Operations on Sets 57 SPM Practice 9 129
Gabungan Operasi Set
HOTS Challenge 133
SPM Practice 4 60 Online Quick Quiz QR code PAK-21 Corner QR code 133
HOTS Challenge 63
Online Quick Quiz QR code PAK-21 Corner QR code 63
CHAPTER Consumer Mathematics: Financial 134
10
Management
CHAPTER Network in Graph Theory 64 Matematik Pengguna: Pengurusan Kewangan
5
Rangkaian dalam Teori Graf
Perancangan dan Pengurusan Kewangan
10.1 Financial Planning and Management 134
5.1 Network 64 SPM Practice 10 149
Rangkaian HOTS Challenge 152
SPM Practice 5 72 Online Quick Quiz QR code PAK-21 Corner QR code 152
HOTS Challenge 73
Online Quick Quiz QR code PAK-21 Corner QR code 73 SPM Year-End Assessment 153
CHAPTER Linear Inequalities in Two Variables 74
6
Answers
Ketaksamaan Linear dalam Dua Pemboleh Ubah
http://www.epelangi.com/TopClass/Mathematics/F4/
6.1 Linear Inequalities in Two Variables 74 FullyWorkedSolutions.pdf
Ketaksamaan Linear dalam Dua Pemboleh Ubah
© Penerbitan Pelangi Sdn. Bhd. ii






00 CONTENT Top Class MATH F4.indd 2 05/12/2020 4:56 PM

CHAPTER Quadratic Functions and Equations in One Variable

1 1

Fungsi dan Persamaan Kuadratik dalam Satu Pemboleh Ubah






1.1 Quadratic Functions and Equations Textbook
Fungsi dan Persamaan Kuadratik
pg. 1 – 31

SMART Notes


1. Quadratic expression: 4. Shapes of quadratic function graph:
Ungkapan kuadratik: Bentuk-bentuk graf bagi fungsi kuadratik:
a, b and c are constants, a ≠ 0 (a) a  0
a, b dan c ialah pemalar, a ≠ 0 y
x is a variable
ax + bx + c x ialah pemboleh ubah
2
The highest power of variable x is 2
Kuasa tertinggi bagi pemboleh ubah x c
ialah 2 O x Minimum point
Titik minimum
Example / Contoh:
(a) 6x 2 Axis of symmetri
Paksi simetri
2
(b) 6x + 7 (b) a  0
(c) 3x + 5x + 4 y
2
Maximum point
7 Titik maksimum
(d) – x + 8x + 9 x
2
9 O
c
2. Quadratic function:
Fungsi kuadratik:
f(x) = ax + bx + c
2

Example / Contoh: 5. Quadratic equation:
(a) f(x) = 16x + 4x Persamaan kuadratik:
2
2
(b) f(x) = 2x – 5 ax + bx + c = 0
2
(c) f(x) = 6x + 5x + 12 Example / Contoh:
2
(d) f(x) = –7x + 6x – 11
2
(a) 2x – 4x + 5 = 0
2
(b) x – 3x + 7 = 0
2
3. Characteristics of quadratic functions:
2
Ciri-ciri fungsi kuadratik: (c) x – 6x = 0
2
• curved shape of the graph (d) 3x + 4x – 8 = 0
graf berbentuk melengkung 6. A root of quadratic equation is the value of variable x,
• has minimum point or maximum point which satisfies the quadratic equation.
mempunyai titik minimum atau titik maksimum Punca bagi persamaan kuadratik merupakan nilai pemboleh
• the axis of symmetry of the graph is parallel to ubah, x, yang memuaskan persamaan kuadratik tersebut.
the y-axis and passes through minimum point or
maximum point
paksi simetri graf adalah selari dengan paksi-y dan melalui
titik minimum atau titik maksimum The relation of a quadratic function is many-to-one
relation.
Hubungan bagi suatu fungsi kuadratik ialah hubungan NOTES
banyak-kepada-satu






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01 Top Class Math F4.indd 1 05/12/2020 5:00 PM

Mathematics Form 4 Chapter 1 Quadratic Functions and Equations in One Variable

1. Mark (✓) for the quadratic expression in one variable and (✗) if not. Hence, give your reason. PL 1
Tandakan (✓) bagi ungkapan kuadratik dalam satu pemboleh ubah dan (✗) jika bukan. Kemudian, berikan sebab anda.
Expression / Ungkapan (✓) / (✗) Reason / Sebab

Example
(i) x – x + 3 ✓ Has one variable, x and the highest power of x is 2.
2
Mempunyai satu pemboleh ubah, x dan kuasa tertinggi bagi x ialah 2.
(ii) 4x – y Has two variables, x and y.
2
✗
Mempunyai dua pemboleh ubah, x dan y.
2
2x – 3 + 9 Not in the form of quadratic expression.
(iii) ✗
x Bukan dalam bentuk ungkapan kuadratik.
(a) (y + 4)(y – 3) ✓ Has one variable, y and the highest power of y is 2.
= y – y – 12 Mempunyai satu pemboleh ubah, y dan kuasa tertinggi bagi y ialah 2.
2
(b) ab – b + 9 Has two variables, a and b.
2
✗
Mempunyai dua pemboleh ubah, a dan b.
(c) 6x – 6x + 4 The highest power of x is 3.
2
3
✗
Kuasa tertinggi bagi x ialah 3.
2
g + 2 1 2 Has one variable, g and the highest power of g is 2.
(d) =  g + ✓
2
3 3 3 Mempunyai satu pemboleh ubah, g dan kuasa tertinggi bagi g ialah 2.
(e) –9b 2 Has one variable, b and the highest power of b is 2.
✓
Mempunyai satu pemboleh ubah, b dan kuasa tertinggi bagi b ialah 2.
2
w + 6w Not in the form of quadratic expression.
(f) ✗
w – 1 Bukan dalam bentuk ungkapan kuadratik.
2. Match the following relations of each of the following functions, f that mapped set P to set Q. Hence, identify
the relation of the function. PL 1
Padankan hubungan berikut bagi setiap fungsi, f yang memetakan set P kepada set Q. Kemudian, kenal pasti hubungan fungsi tersebut.

Function f(x) = x 2 f(x) = x + 4
Fungsi

P Q P Q
f f
–4 –2 2
Arrow diagram –2 0 –1 3
Rajah anak panah 0 4 0 4
2 16 1 5
4 2 6


Relation Many-to-one One-to-one
Hubungan Banyak kepada satu Satu kepada satu


3. Complete the following table below for each of the following quadratic functions. PL 1
Lengkapkan jadual di bawah bagi setiap fungsi kuadratik berikut.
Quadratic function a b c Shape of the graph Maximum point / Minimum point
Fungsi kuadratik Bentuk graf Titik maksimum / Titik minimum
Example
f(x) = 2x + 6x – 5 2 6 –5 Minimum point
2
Titik minimum
2
(a) f(x) = 3x + 6x + 7 3 6 7 Minimum point
Titik minimum



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01 Top Class Math F4.indd 2 05/12/2020 5:00 PM

Mathematics Form 4 Chapter 1 Quadratic Functions and Equations in One Variable

(b) f(x) = –6x + 5x – 4 –6 5 – 4 Maximum point
2
Titik maksimum

2
(c) f(x) = 5x – 10 5 0 –10 Minimum point
Titik minimum


(d) f(x) = –x – x –1 –1 0 Maximum point
2
Titik maksimum

2
(e) f(x) = x + 10x – 4 1 10 – 4 Minimum point
Titik minimum



4. Draw the axis of symmetry and state equation of axis of symmetry of each of the following quadratic functions.
Lukis paksi simetri dan nyatakan persamaan paksi simetri bagi setiap fungsi kuadratik yang berikut. PL 2
Example (a) (b)

f(x) f(x) f(x)
6 3 15

4 2 10

2 1 5
x x x
–2 –1 O 1 2 –10 –8 –6 –4 –2 O –1 O 1 2 3
–1 –1



Equation of axis of symmetry: Equation of axis of symmetry: Equation of axis of symmetry:
Persamaan paksi simetri: Persamaan paksi simetri: Persamaan paksi simetri:
x = –1 x = –5 x = 2





(c) (d) (e)

f(x) f(x) f(x)



(0, 2) (20, 2)
(1, 2) (4, 2)

(–1, 0) (2, 0)
x x
O O
x
O



Equation of axis of symmetry: Equation of axis of symmetry: Equation of axis of symmetry:
Persamaan paksi simetri: Persamaan paksi simetri: Persamaan paksi simetri:
x = 10 1 x = 2.5
x =
2




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01 Top Class Math F4.indd 3 05/12/2020 5:00 PM

Mathematics Form 4 Chapter 1 Quadratic Functions and Equations in One Variable

(c) The diagram below shows the positions of two divers, A and B on different height.
Rajah di bawah menunjukkan kedudukan dua penerjun A dan B pada ketinggian berbeza.



B
7.5 m
A
5 m





(i) Based on the graphs of height-time below, (ii) Calculate the time taken, in second, by both
determine which graph represents each of divers to reach water.
the following divers? Then, state the value Hitung masa yang diambil, dalam saat, oleh kedua-
of p and of q. dua penerjun mencecah air.
Berdasarkan graf tinggi-masa di bawah, tentukan Equation for diver A: h = –14t + 5
2
graf yang manakah mewakili setiap penerjun itu? Persamaan bagi penerjun A: h = –14t + 5
2
Kemudian, nyatakan nilai p dan nilai q.
–14t + 5 = 0
2
Height, h(m) Height, h(m) t = –5
2
Tinggi, h(m) Tinggi, h(m) –14
p t = 0.60
q Equation for diver B: h = –14t + 7.5
2
2
2
h(t) = –14t + p h(t) = –14t + q
Persamaan bagi penerjun B: h = –14t + 7.5
2
–14t + 7.5 = 0
2
–7.5
Time, t(s) Time, t(s) t =
2
O O
Masa, t(s) Masa, t(s) –14
t = 0.73
Diver Diver
A
Penerjun B Penerjun
p = 7.5 q = 5
(d) An entrepreneur of rental car has the total hours of 180 hours per week when a car is rented for RM10
per hour. The entrepreneur will receive an additional of 12 hours for every decrease RM1 in rental rate.
Seorang pengusaha sewa kereta mempunyai jumlah masa sebanyak 180 jam setiap minggu apabila sebuah kereta disewa dengan
harga RM10 per jam. Penyusaha itu akan menerima tambahan 12 jam bagi setiap pengurangan RM1 pada kadar sewaan.
(i) Form a quadratic equation for the weekly (ii) If the entrepreneur obtained the weekly
total rental, in RM, obtained if he reduces total rental of RM1 200 after reducing the
the rental rate. rental rate, find the rental rate of a car per
Bentukkan satu persamaan kuadratik bagi jumlah hour that week.
sewaan mingguan, dalam RM, yang diperoleh jika dia Jika pengusaha itu memperoleh jumlah sewaan
mengurangkan kadar sewa. mingguan sebanyak RM1 200 selepas mengurangkan
kadar sewa, cari kadar sewa sebuah kereta per jam
Let x be the reduce of every RM1 for the pada minggu itu.
rental rate per hour and S(x) is the total S(x) = 1 200
2
rental rate weekly. –12x – 60x + 1 800 = 1 200
2
Katakan x ialah pengurangan setiap RM1 bagi kadar 12x + 60x – 1 800 = –1 200
sewa per jam dan S(x) ialah jumlah sewaan mingguan. 12x + 60x – 600 = 0
2
(x – 5)(x + 10) = 0
Total of rental rate weekly
Jumlah sewaan mingguan x – 5 = 0 or x + 10 = 0
= Rental rate per hour × Number of hours x = 5 atau x = –10
Kadar sewa per jam × Bilangan jam Reduced rental rate per hour = RM5
= (10 – x) × (180 + 12x) Pengurangan kadar sewa per jam
= 1 800 + 120x – 180x – 12x 2
= –12x – 60x + 1 800 Thus, rental rate of a car per hour
2
Maka, kadar sewa sebuah kereta per jam
= RM10 – RM5
= RM5

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01 Top Class Math F4.indd 10 05/12/2020 5:00 PM

Mathematics Form 4 Chapter 1 Quadratic Functions and Equations in One Variable

SPM Practice 1





Paper 1 Paper 2

1. 6 – 3(4 – y) = 1. A toy rocket is fired into the air from a point O on the
2
2
2
SPM A y + 3 C –y + 3y – 6 SPM top of a barn. The distance between the toy rocket
2016 2014
2
2
B –2y + 16 D –3y + 24y – 42 and the ground at t seconds after thrown is given by
2
s = −5t + 10t + 20. Find the time when the toy rocket
2. Which of the following represents the change of graph of hit the ground.
function y = 2x to y = 2x – 6x? Sebuah roket mainan dilancarkan ke udara dari suatu titik O
2
2
Antara berikut, graf yang manakah mewakili perubahan graf dia atas sebuah bangsal. Jarak antara roket mainan itu dengan
2
bagi fungsi y = 2x kepada y = 2x – 6x? tanah selepas t saat dilancarkan diberi oleh s = −5t + 10t + 20.
2
2
A
f(x) Cari masa apabila roket mainan itu tiba di permukaan tanah.
f(x) = 2x 2
Answer / Jawapan:
When the toy rocket hit the ground, s = 0.
Apabila roket mainan itu tiba di permukaan tanah, s = 0.
x
O Thus/ Maka,
2
f(x) = 2x – 6x 2
−5t + 10t + 20 = 0
B f(x) 5t – 10t – 20 = 0
2
f(x) = 2x 2 (5t + 2)(t – 5) = 0
5t + 2 = 0 , t – 5 = 0
2
t = – , t = 5
5
x Because of t  0, thus the toy rocket hits the ground at
O t = 5.
2
f(x) = 2x – 6x
Oleh sebab t  0, roket mainan itu tiba di permukaan tanah
C f(x) pada t = 5.
2
f(x) = 2x – 6x
x
O
f(x) = 2x 2
2. Solve the following quadratic equation:
D
f(x) Selesaikan persamaan kuadratik yang berikut:
2
f(x) = 2x – 6x –6y – 2 = 7
y 1 – y
x
Answer / Jawapan:
–6y – 2 7
O y = 1 – y
f(x) = 2x 2 (−6y − 2)(1 − y) = 7y
−6y + 6y – 2 + 2y − 7y = 0
2
3. The diagram below shows the graphs of two quadratic 6y − 11y −2 = 0
2
functions. (6y + 1)(y − 2) = 0
Rajah di bawah menunjukkan graf bagi dua fungsi kuadratik.
6y + 1 = 0 or y – 2 = 0
f(x) 1
y = – atau y = 2
2
f(x) = –2x + 2 6
x
O
2
f(x) = ax + c
What are the possible values of a and c?
Apakan nilai yang mungkin bagi a dan c?
A a = –1, c = 1 C a = –3, c = 2
B a = – 4, c = 0 D a = 2, c = 3

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01 Top Class Math F4.indd 11 05/12/2020 5:00 PM

Mathematics Form 4 Chapter 1 Quadratic Functions and Equations in One Variable

2
3. It is given a quadratic function f(x) = 2x + 3x – 9. 4. An aquarium has a length of (x + 5) cm, a width of x cm
Diberi fungsi kuadratik f(x) = 2x + 3x – 9. SPM and a height of 40 cm. The total volume of the aquarium
2
2017 3
(a) Calculate the roots of the quadratic function. is 30 000 cm . The aquarium will be filled fully with water.
Hitung punca-punca bagi fungsi kuadratik itu. Calculate the value of x.
(b) Then, sketch the graph of the function. Sebuah akuarium mempunyai panjang (x + 5) cm, lebar
Kemudian, lakarkan graf bagi fungsi itu. x cm dan tinggi 40 cm. Jumlah isi padu akuarium itu ialah
3
30 000 cm . Akuarium itu akan diisi penuh dengan air. Hitung
Answer / Jawapan: nilai x.
2
(a) 2x + 3x – 9 = 0
(2x – 3)(x + 3) = 0 Answer / Jawapan:
(x + 5)(x)(40) = 30 000
2x – 3 = 0 or / atau x + 3 = 0 (x + 5)(40x) = 30 000
x = 3 x = –3 2
2 40x + 200x = 30 000
2
40x + 200x – 30 000 = 0
(b) a = 2  0, thus the graph shape is . x + 5x – 750 = 0
2
a = 2  0, maka graf berbentuk . (x – 25)(x + 30) = 0
When x = 0, x – 25 = 0 or / atau x + 30 = 0
Apabila x = 0, x = 25 x = –30
2
f(0) = 2(0) + 3(0) – 9 Thus/ Maka, x = 25 cm
= –9
f(x)



x
–3 O –
3
2
–9

HOTS Challenge


The diagram below shows four circles in a rectangle.
Rajah di bawah menunjukkan empat bulatan dalam sebuah segi empat tepat.


(x + 20) cm

(5x – 40) cm

2
Given that the area of the rectangle is 7.84 m . Find the diameter, in cm, of a circle.
2
DIberi luas bagi segi empat tepat tersebut ialah 7.84 m . Cari radius, dalam cm, bagi satu bulatan.
Answer / Jawapan:
(5x – 40)(x + 20) = 78 400
5x + 100x – 40x – 800 = 78 400
2
5x + 60x – 800 – 78 400 = 0
2
2
5x + 60x – 79 200 = 0
2
x + 12x – 15 840 = 0
(x – 120)(x + 132) = 0
x = 120, x = –132 (not valid/ tidak diterima)
Diameter of a circle/ Diameter bagi satu bulatan
= x + 20
= 120 + 20 HOTS
= 140 cm


Quiz 1
21
PAK-





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01 Top Class Math F4.indd 12 05/12/2020 5:00 PM

Questions based on new SPM 2021
format (following the instrument sample)



SPM Year-End Assessment SAMPLE





Paper 1
Kertas 1
1 hour 30 minutes
1 jam 30 minit

Instructions: This question paper consists of 40 questions. Answer all questions. For each question, choose only
one answer. The diagrams given in the questions are not drawn to scale unless stated. The use of
a non-programmable scientific calculator is allowed.
Arahan: Kertas soalan ini mengandungi 40 soalan. Jawab semua soalan. Pilih satu jawapan sahaja untuk setiap soalan. Rajah yang diberikan
dalam soalan tidak dilukis mengikut skala kecuali dinyatakan. Penggunaan kalkulator saintifik yang tidak boleh diprogramkan
adalah dibenarkan.

1. Express 0.008257 in standard form. S
Ungkapkan 0.008257 dalam bentuk piawai.
A 8.257 × 10 C 8.257 × 10 3 R T
–4
B 8.257 × 10 D 8.257 × 10 4
–3
0.0853 y
2. =
(4 × 10 ) V U
2 3
Diagram 1
A 1.33 × 10 C 2.13 × 10 8 Rajah 1
–9
B 2.13 × 10 D 1.33 × 10
–8
9
Find the value of y.
3. The thickness of a sheet of paper is approximately Cari nilai y.
–3
8.5 × 10 mm. The height of a stack of this type of A 54° C 78°
paper is 510 mm. Estimate the number of sheets B 72° D 84°
of paper in the stack.
Ketebalan bagi sehelai kertas dianggarkan 8.5 × 10 mm. 9. Diagram 2 shows a regular hexagon ABCDEG, AFG
–3
Ketebalan bagi timbunan kertas jenis ini ialah 510 mm. is a triangle and AEF is a straight line.
Anggarkan bilangan helai kertas dalam timbunan tersebut. Rajah 2 menunjukkan sebuah heksagon sekata ABCDEG, AFG
A 6 × 10 C 6 × 10 4 ialah sebuah segi tiga dan AEF ialah garis lurus.
2
B 6 × 10 D 6 × 10 A G
5
3
4. Which of the following has the largest value?
Antara yang berikut, yang manakah mempunyai nilai paling B
besar? E x
A 23 4 C 31 10 F
B 15 6 D 10110 2 C D
Diagram 2
5. State the digit value of 3 in the number 2312 4, in Rajah 2
base ten.
Nyatakan nilai digit bagi 3 dalam nombor 2312 4, dalam Given that ∠AGF = 130°. Find the value of x.
asas sepuluh. Diberi bahawa ∠AGF = 130°. Cari nilai x.
A 3 C 48 A 10° C 18°
B 12 D 192 B 15° D 20°
3
4
6. Express 9 + 9 + 9 + 7 as a number in base nine. 10. In Diagram 3, PQR is a tangent to the circle QST
4
Ungkapkan 9 + 9 + 9 + 7 sebagai nombor dalam asas with centre O at Q.
3
sembilan. Dalam Rajah 3, PQR ialah tangen kepada bulatan QST yang
A 1117 9 C 11107 9 berpusat O pada Q.
B 11017 9 D 11170 9 P Q R
36°
7. 100110 2 – 1101 2 = 70°
A 10111 2 C 11011 2
B 11001 2 D 11010 2 O
x
8. Diagram 1 shows a regular pentagon RSTUV. SU
is a straight line. T S
Rajah 1 menunjukkan sebuah pentagon sekata RSTUV. SU Diagram 3
ialah garis lurus. Rajah 3

153 © Penerbitan Pelangi Sdn. Bhd.






11 Ass Top Class Math F4.indd 153 05/12/2020 5:21 PM

Questions based on new SPM 2021
format (following the instrument sample)
Mathematics Form 4 Year-End Assessment

Paper 2
Kertas 2
2 hours 30 minutes
2 jam 30 minit

Section A
Bahagian A
[40 marks]
[40 markah]
Answer all questions in this section.
Jawab semua soalan dalam bahagian ini.



1. The Venn diagram in the answer space shows universal set j, set P, set Q and set R. On the diagram given,
shade the set
Gambar rajah Venn di ruang jawapan menunjukkan set semesta j, set P, set Q dan set R. Pada rajah yang diberi, lorekkan set
[3 marks / 3 markah]

Answer / Jawapan:
(a) P > Q (b) P > (Q9 < R)

P Q P Q

R R









2. Solve the following quadratic equation.
Selesaikan persamaan kuadratik yang berikut.
4x + 3
5x =
x – 2
[4 marks / 4 markah]
Answer / Jawapan:
4x + 3
5x =
x – 2
5x(x – 2) = 4x + 3
5x – 10x = 4x + 3
2
5x – 10x – 4x – 3 = 0
2
5x – 14x – 3 = 0
2
(x – 3)(5x + 1) = 0
1
x = 3 or / atau x = –
5


3. (a) For each of the following statement, state whether the statement is true or false.
Bagi setiap pernyataan yang berikut, nyatakan sama ada pernyataan tersebut adalah benar atau palsu.
8
2
(i) 8 = 16 or / atau = 4
2
(ii) (–6)(–3) = 18 and / dan –6  –3
(b) Write down the contrapositive of the following implication:
Tulis kontrapositif bagi implikasi yang berikut:
If 10 is an even number, then 10 is divisible by 2.
Jika 10 ialah nombor genap, maka 10 boleh dibahagi tepat dengan 2.




© Penerbitan Pelangi Sdn. Bhd. 158






11 Ass Top Class Math F4.indd 158 05/12/2020 5:21 PM

Questions based on new SPM 2021
format (following the instrument sample)
Mathematics Form 4 Year-End Assessment

Section B
Bahagian B
[45 marks]
[45 markah]
Answer all questions in this section.
Jawab semua soalan di bahagian ini.


11. (a) Determine whether the following sentence is a statement or not. Give your justification.
Tentukan sama ada ayat yang berikut merupakan pernyataan atau tidak. Berikan justifikasi anda.

n – 1 = 5

(b) Write down two implications based on the following compound statement.
Tulis dua implikasi berdasarkan pernyataan majmuk yang berikut.
Set M is an empty set if and only if set M does not have elements.
Set M ialah set kosong jika dan hanya jika set M tidak mempunyai unsur.
(c) Write down the conclusion to complete the following argument.
Tulis kesimpulan untuk melengkapkan hujah berikut.
Premise 1: All even numbers are divisible by 2.
Premis 1 : Semua nombor genap boleh dibahagi tepat dengan 2.
Premise 2: 54 is an even number.
Premis 2 : 54 ialah nombor genap.
Conclusion / Kesimpulan:

(d) (i) Make a general conclusion by induction for the sequence of numbers –3, 12, 37, 72, …, which follows
the following pattern:
Buat satu kesimpulan umum secara induktif bagi urutan nombor –3, 12, 37, 72, …, yang mengikut pola berikut:
2
–3 = 5(1) – 8
2
12 = 5(2) – 8
2
37 = 5(3) – 8
2
72 = 5(4) – 8
….…………….
(ii) Find the 9 term in the sequence shown above.
th
Cari sebutan ke-9 dalam senarai nombor berpola di atas.
[9 marks / 9 markah]
Answer / Jawapan:
(a) Not a statement. Because the truth value of the mathematical sentence cannot be determined.
Bukan pernyataan. Kerana nilai kebenaran bagi ayat matematik itu tidak dapat ditentukan.




(b) Implication 1 / Implikasi 1: If set M is an empty set, then set M does not have elements.
Jika set M ialah set kosong, maka set M tidak mempunyai unsur.
Implication 2 / Implikasi 2: If set M does not have elements, then set M is an empty set.
Jika set M tidak mempunyai unsur, maka set M ialah set kosong.




(c) Conclusion / Kesimpulan: 54 is divisible by 2. / 54 boleh dibahagi tepat dengan 2.



(d) (i) 5n – 8, where / di mana n = 1, 2, 3, 4, …
2
(ii) 5(9) – 8 = 397
2




163 © Penerbitan Pelangi Sdn. Bhd.






11 Ass Top Class Math F4.indd 163 05/12/2020 5:21 PM

Questions based on new SPM 2021
format (following the instrument sample)
Mathematics Form 4 Year-End Assessment

Section C
Bahagian C
[15 marks]
[15 markah]
Answer one question in this section.
Jawab satu soalan dalam bahagian ini.

16. Diagram 7 shows the marks obtained by 30 students in a Mathematics test.
Rajah 7 menunjukkan markah yang diperoleh oleh 30 orang pelajar dalam suatu ujian Matematik.

26 48 66 34 55 29
90 57 18 50 67 46
40 92 64 86 70 59
84 31 53 62 78 72
52 68 60 75 38 95
Diagram 7
Rajah 7
(a) Draw a stem-and-leaf plot to represent the information above.
Lukis plot batang-dan-daun untuk mewakili maklumat di atas.
[4 marks / 4 markah]
(b) Based on the given information, calculate
Berdasarkan maklumat yang diberikan, hitung
(i) range / julat [1 mark / 1 markah]
(ii) interquartil range / julat antara kuartil [2 marks / 2 markah]
(iii) mean / min [3 marks / 3 markah]
(iv) variance / varians [4 marks / 4 markah]
(v) standard deviation / sisihan piawai [1 mark / 1 markah]
Answer / Jawapan:

(a) Stem Leaf
Batang Daun
1 8
2 6 9
3 1 4 8
4 0 6 8
5 0 2 3 5 7 9
6 0 2 4 6 7 8
7 0 2 5 8
8 4 6
9 0 2 5

Key: 3 1 means 31 marks.
Kekunci: 3 1 bermakna 31 markah.



(b) n = 30
Σx = 26 + 48 + 66 + 34 + 55 + 29 + 90 + 57 + 18 + 50 + 67 + 46 + 40 + 92 + 64 + 86 + 70 + 59 + 84
+ 31 + 53 + 62 + 78 + 72 + 52 + 68 + 60 + 75 + 38 + 95
= 1 765
Σx = 26 + 48 + 66 + 34 + 55 + 29 + 90 + 57 + 18 + 50 + 67 + 46 + 40 + 92 + 64 + 86
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
+ 70 + 59 + 84 + 31 + 53 + 62 + 78 + 72 + 52 + 68 + 60 + 75 + 38 + 95 2
2
2
2
2
2
2
2
2
2
2
2
2
2
= 116 033
(i) Range / Julat = 95 – 18
= 77
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11 Ass Top Class Math F4.indd 168 05/12/2020 5:21 PM

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