Dokumen tersebut berisi soalan-soalan matematika untuk ujian Sijil Pelajaran Malaysia (SPM). Terdapat lima bagian yang mencakup materi Aljabar, Kalkulus, Geometri, Statistik dan Trigonometri. Soalan-soalan tersebut meliputi penyelesaian persamaan, pembentukan fungsi kuadratik, bukti rumus trigonometri, pembentukan vektor, dan penyelesaian masalah geometri.
This document provides an overview of integration and how it relates to calculating areas under curves and between functions. Some key points covered include:
- Integration uses the concept of reverse differentiation to calculate the area under a function.
- The area under a function between two x-values a and b is calculated as the definite integral from a to b.
- Integrals may be used to find the area between two curves by subtracting their integrals between the intersection points.
- Integrals can represent either positive or negative areas depending on whether the area is above or below the x-axis.
Dokumen tersebut berisi soalan-soalan matematika untuk ujian Sijil Pelajaran Malaysia (SPM). Terdapat lima bagian yang mencakup materi Aljabar, Kalkulus, Geometri, Statistik dan Trigonometri. Soalan-soalan tersebut meliputi penyelesaian persamaan, pembentukan fungsi kuadratik, bukti rumus trigonometri, pembentukan vektor, dan penyelesaian masalah geometri.
This document provides an overview of integration and how it relates to calculating areas under curves and between functions. Some key points covered include:
- Integration uses the concept of reverse differentiation to calculate the area under a function.
- The area under a function between two x-values a and b is calculated as the definite integral from a to b.
- Integrals may be used to find the area between two curves by subtracting their integrals between the intersection points.
- Integrals can represent either positive or negative areas depending on whether the area is above or below the x-axis.
Dokumen tersebut merupakan spesifikasi kurikulum untuk mata pelajaran Matematik Tambahan Tingkatan 5 yang diterbitkan oleh Kementerian Pelajaran Malaysia pada tahun 2013, yang menjelaskan tujuan, objektif, organisasi kandungan dan tajuk-tajuk yang diajar dalam kurikulum tersebut."
Koleksi soalan percubaan add math kertas 1
1. peperiksaan percubaan sekolah asrama penuh dan jawapan
2. pepriksaan percubaan negeri perak dan jawapan
3. peperiksaan percubaan negeri selangor dan jawapan
4. peperiksaan percubaan negeri terengganu dan jawapan
The document discusses integration and indefinite integrals. It covers determining integrals by reversing differentiation, integrating algebraic expressions like constants, variables, and polynomials. It also discusses determining the constant of integration and using integration to find equations of curves from their gradients. Examples are provided to illustrate integrating functions and finding volumes generated by rotating an area about an axis.
This document provides guidance for mathematics teachers to improve student performance in Additional Mathematics for the SPM 2009 exam. It identifies common weaknesses and mistakes by student category (very weak to excellent). Suggestions are given to rectify issues for different topics in Paper 1 and Paper 2, such as functions, quadratic equations, vectors, and integration. For weaker students, the focus is on getting partial marks. For stronger students, emphasis is placed on careless mistakes. Teachers are advised to provide targeted practice addressing specific weaknesses.
This document provides examples of solving equations, expanding and factorizing expressions, solving simultaneous equations, working with indices and logarithms. It includes over 100 problems across these topics for students to practice. The problems range in complexity from basic single-step equations to multi-part logarithmic expressions and systems of simultaneous equations.
1. This document appears to be an answer key or marking scheme for a mathematics exam with 25 questions. It provides the answers, workings, or mark schemes for each question on the exam.
2. For each question, it lists the number of marks awarded for the full or partial answers. The total marks are tallied at the end.
3. The document contains detailed mathematical solutions and workings for the questions, evaluating answers for correctness according to set schemes.
1. Dokumen tersebut membincangkan perancangan dan pelaksanaan pengajaran pembelajaran di dalam bilik darjah.
2. Beberapa aspek utama yang dibincangkan termasuk objektif pengajaran, penggunaan sumber dan teknik pengajaran, serta kemahiran guru.
3. Dokumen ini memberikan panduan kepada guru dalam merancang dan melaksanakan proses pengajaran dan pembelajaran yang berkesan.
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A free trilingual eBook comprising 5 PowerPoint presentations of meaningful Buddhist stories that teach important Dhamma/Life lessons. For reflection and practice to develop the mind to grow in love, compassion and wisdom. The texts are in English, Chinese & Malay.
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1. SULIT 5 3472/1
Answer all questions.
Jawab semua soalan.
A ={ -3, -2, -1, 0, 1, 2 }
B ={ -1, 0, 1, 2, 3 }
1. Based on the above information, the relation between A and B is defined by
the set of ordered pairs
{ (-2, -1 ), (-1, 0 ), ( 0, 1 ), ( 1, 2 ), (2, 3) }.
Berdasarkan maklumat atas, hubungan antara A dan B adalah di takrifkan
oleh set pasangan bertertib
{ (-2,-1 ), (-1, 0 ), ( 0, 1 ), ( 1, 2 ), (2, 3) }.
State
Nyatakan
(a) the image of 2.
imej bagi 2.
(b) the object of 0.
objek bagi 0.
[2 marks]
[2 markah]
1
Answer : (a)…………………………………
(b)………………………………… 2
[See overleaf
3472/1 SULIT
2. SULIT 6
2. Given that f −1 : x → x − 1 and gf : x → 3 x 2 − 2 , find
Diberi fungsi f −1 : x → x − 1 dan gf : x → 3 x 2 − 2 , cari
(a) the function g (x) ,
fungsi g (x) ,
(b) the values of x if g ( x) + 3 = x
nilai-nilai x jika g ( x) + 3 = x .
[4 marks]
[4 markah]
2
Answer : (a)…………………………………
4
(b)…………………………………
3. Given the function h : x → 2 x 2 + 5 x , find
Diberi fungsi h : x → 2 x 2 + 5 x , cari
(a) h(3) ,
(b) the values of x which maps onto itself by h(x) .
nilai-nilai x yang memetakan kepada sendiri oleh h(x) .
3
[3 marks]
3 [3 markah]
Answer : (a)…………………………………
(b)…………………………………
________________________________________________________
________
3472/1 SULIT
3. SULIT 7 3472/1
4. The quadratic equation x( x + y ) + 8 = 0 does not intersects the straight line
x + 2 y = p , where p is a constant. Find the range of values of p .
Persamaan x( x + y ) + 8 = 0 tidak menyilang garis lurus x + 2 y = p , dengan
keadaan p adalah pemalar. Cari julat nilai p .
[3 marks] 4
[3 markah]
3
Answer : …………………………………
25
5. Diagram 5 shows the graph of the function y = −( x − p ) 2 + where p is a
4
constant.
25
Rajah 5 menunjukkan fungsi y = −( x − p ) 2 + , dengan keadaan p ialah
4
pemalar.
y
25
p,
4
•6
•
−2 • 3
x
Diagram 5
Find Rajah 5
Cari
5
(a) the value of p ,
nilai p , 2
(b) the equation of the axis of symmetry.
persamaan paksi simetri. [2 marks]
[2 markah]
Answer : (a)…………………………………
[See overleaf
3472/1 SULIT
4. SULIT 8
(b)…………………………………
____________________________________________________________
6. Given a quadratic function f ( x ) = 8 x + 2 x 2 = 2( x + hk ) 2 + k , where h and
k are constants.
Diberi fungsi kuadratik f ( x ) = 8 x + 2 x 2 = 2( x + hk ) 2 + k , dengan keadaan
h dan k adalah pemalar.
State the value of h and value of k ,
Nyatakan nilai h dan nilai k ,
[3 marks]
[3 markah]
Answer : …………………………………
6
3
7. Solve the equation 4 2 x −1 + 4 2 x = 4 .
Selesaikan persamaan 4 2 x −1 + 4 2 x = 4
[3 marks]
[3 markah]
7
3
Answer : …………………………………
3472/1 SULIT
5. SULIT 9 3472/1
______________________________________________________________
125m
8. Given log m 3 = p and log m 5 = r , express log m in terms of p and r .
81
125m
Diberi log m 3 = p dan log m 5 = r , ungkapkan log m dalam sebutan
81
p dan r .
[3mark
s]
[3 markah]
8
Answer ………………………………… 3
9. Given the first three terms of an arithmetic progression are 2h − 6 , h + 1 and
h − 4 , find
Diberi tiga sebutan pertama suatu janjang aritmetik ialah 2h − 6 , h + 1 dan
h − 4 , cari
(a) the value of h ,
nilai h ,
(b) the common difference of the progression.
nisbah sepunya janjang itu..
[3 marks] 9
[3 markah]
3
Answer : (a)…………………………………
(b)…………………………………
_____________________________________________________________
[See overleaf
3472/1 SULIT
6. SULIT 10
10. The first term of the geometric progression is 0.6 and the fourth term of the
progression is 9.375 , find the sum of the first three terms.
Sebutan pertama suatu janjang geometri ialah 0.6 dan sebutan keempat
janjang aritmetik ialah 9.375 , cari jumlah tiga sebutan pertama.
[3 marks]
[3 markah]
10
Answer : …………………………………
3
n +1
3
11. The n th term of a geometric progression , Tn , is given by Tn = , find
4
n +1
3
Sebutan ke- n bagi suatu janjang geometri , Tn , diberi oleh Tn = ,
4
cari
(a) the common ratio,
nisbah sepunya,
(b) the sum to infinity of the progression.
jumlah sehingga ke takterhinggaan.
11
[4 marks]
4
[4 markah]
Answer : (a)…………………………………
(b)…………………………………
_______________________________________________________________
3472/1 SULIT
7. SULIT 11 3472/1
12. Diagram 12 shows a sector AOB of a circle with center O and radius
r cm.
Rajah 12 menunjukkan sektor AOB bagi sebuah bulatan berpusat O dan
berjejari x cm.
B
θ
A O
Diagram 12
Given the length of the arc AB = 30.5 cm and the perimeter of the sector
Rajah 12
AOB is 55.5 cm.
Diberi panjang bagi lengkok AB = 30.5 cm dan perimeter sektor AOB
adalah 55.5 cm.
Find
Cari
[ Use/Guna π = 3.142 ]
(a) θ , in radians,
θ , dalam radian,
(b) the area, in cm2 , of the sector AOB .
luas , dalam cm2 , sektor AOB.
[4 marks] 12
[4 markah]
Answer : (a)………………………………… 4
(b)… ………………………………
_______________________________________________________________
13. The following information refers to the vectors p and q .
~ ~
[See overleaf
3472/1 SULIT
8. SULIT 12
Maklumat berikut adalah berkaitan dengan vektor-vektor p dan q .
~ ~
p = 5 i − 12 j
~ ~ ~
q = m i+6 j
~ ~ ~
where m is a constants.
dengan keadaan m ialah pemalar.
By using the information given, find
Dengan menggunakan maklumat di atas, cari
(a) the value of m if the vector of p and the vector of q are parallel,
~ ~
nilai m jika vektor p dan vektor q adalah selari,
~ ~
(b) the unit vector in direction of p .
~
vector unit dalam arah p .
~
[4 marks]
[4 markah]
13
4 Answer : (a)…………………………………
(b)… ………………………………
14. Diagram 14 shows a parallelogram PQRS and STQ is a straight line.
Rajah 14 menunjukkan segiempat selari PQRS dan STQ ialah garis lurus.
3472/1 SULIT
9. SULIT 13 3472/1
S R
•T
P Q
Diagram 14
Rajah 14
→ →
Given PQ = 12 a , PS = 6b and ST = 2TQ , express in terms of a and b .
~ ~
~ ~
→ →
Diberi PQ = 12 a , PS = 6b dan ST = 2TQ , ungkapkan dalam sebutan a dan b .
~ ~
~ ~
→
(a) SQ ,
→
(b) PT .
[4 marks]
[4 markah]
14
4
Answer : (a)…………………………………
(b)… ………………………………
m
15. Given that x and y are related by the equation x + = ny , where m and n are
x
[See overleaf
3472/1 SULIT
10. SULIT 14
constants. A straight line is obtained by plotting xy against x2, as shown in
Diagram 15.
m
Diberi x dan y dihubungkan oleh persamaan x + = ny , dengan keadaan m
x
dan n adalah pemalar. Suatu graf garis lurus diperolehi apabila memplotkan xy
melawan x2, seperti dalam Rajah 15.
xy
(12, 2 )
( 6, 0) x2
Diagram 15
Rajah 15
Calculate the value of m and of n.
Cari nilai m dan nilai n.
[4 marks]
[4 markah]
15
4
Answer : m=…………………………………
n=…………………………………
_______________________________________________________________
16. A point P (8, t ) divides the line joining M (4, 1) and N ( r , 7 ) such that
3472/1 SULIT
11. SULIT 15 3472/1
2MP = 3PN.
Titik P (8, t ) membahagi garis yang menyambung M (4,1) dan N ( r , 7 )
dengan keadaan 2MP = 3PN.
Find the value of
Cari nilai bagi
(a) r
(b) t
[3 marks]
[3 markah]
16
3
Answer : (a)…………………………………
(b)…………………………………
______________________________________________________________
17. Solve the equation 3 sin 2 x = 4 cos x such that .
Selesaikan persamaan untuk
[4 marks]
[4 markah]
17
4
Answer : …………………………………
18. Find f ,, ( x ) for the function f ( x) = ( x 2 + 3)3
[See overleaf
3472/1 SULIT
12. SULIT 16
Cari f ,, ( x ) bagi fungsi f ( x ) = ( x 2 + 3)3 .
[3 marks]
[3 markah]
18
2
Jawapan : ……………………………………
________________________________________________________________
19. The curve y = 2 x 2 + hx + 3 has a gradient of at the point where , x = −1
find the value of h.
Persamaan lengkung , mempunyai kecerunan pada
x = −1 , cari nilai bagi h.
[3 marks]
[3 markah]
19
2
Answer : …………………………………
3472/1 SULIT
13. SULIT 17 3472/1
5 5
20. Given that ∫ g ( x)dx = 5
1
, find the value of m if ∫[mx − 2 g ( x)] dx = −3m .
1
5 5
Diberi ∫ g ( x)dx = 5 , cari nilai bagi m jika ∫[mx − 2 g ( x)] dx = −3m .
1 1
[3 marks] 20
[3 markah]
3
Answer : …………………………………
21. Table 21 shows the frequency distribution of ages of workers.
Jadual 21 menunjukkan taburan frekuensi bagi umur pekerja.
Age/Umur
28-32 33-37 38-42 43-47 48-52
( years/tahun )
Number of
workers/ 16 38 26 11 9
Bilangan pekerja
Table 21
Jadual 21
75 − F
Given the third quartile of ages of workers is K = L + 5 ,
G
find the values of K K , L , G and F.
75 − F
Diberi kuartil ketiga bagi umur pekerja-pekerja adalah K = L + 5 ,
G
cari nilai-nilai bagi K , L , G dan F.
[ 4 marks ]
21
Answer : K =………………………….
L = ....................................
4
G =…………………………
F=……….......……………
_______________________________________________________________
22. A debating team consists of 5 students. These 5 students are chosen from
[See overleaf
3472/1 SULIT
14. SULIT 18
4 monitors, 2 assistant monitors and 6 prefects. Calculate the number of
different ways the team can be formed if
Suatu pasukan bahas terdiri dari 5 orang pelajar. Pelajar-pelajar ini akan
dipilih dari 4 orang ketua kelas, 2 orang penolong ketua kelas dan 6 orang
pengawas sekolah. Kira bilangan cara pasukan ini boleh dibentuk jika
(a) there is no restriction
tiada syarat dikenakan
(b) the team contains only one monitor and exactly 3 prefects
pasukan ini terdiri dari hanya seorang ketua kelas dan tepat 3 orang
pengawas.
[3 marks]
[3 markah]
Answer : (a)…………………………………
22
(b)… ………………………………
3
23. Four girls and three boys are to be seated in a row. Calculate the number
of possible arrangements if
Empat orang perempuan dan tiga orang lelaki akan duduk dalam satu
barisan. Cari bilangan susunan jika
(a) all the three boys have to be seated together
23 semua lelaki akan duduk bersebelahan antara satu sama lain.
(b) a boy has to be seated at the centre
3
seorang lelaki akan duduk di tengah barisan itu.
[3 marks]
[3 markah]
Answer : (a)…………………………………
(b)… ………………………………
_________________________________________________________
24. In a box of oranges, 15% of the fruits are rotten. If 10 oranges are chosen
at random from the box, find the probability that
3472/1 SULIT
15. SULIT 19 3472/1
Dalam suatu kotak yang mengandungi buah oren, 15% daripada buah
tersebut adalah busuk . Jika 10 biji oren dipilih secara rawak dari kotak
itu, cari kebarangkalian
(a) exactly 5 rotten oranges are chosen,
tepat 5 biji oren dipilih adalah busuk,
(b) not more than 2 rotten oranges are chosen.
tidak lebih daripada 2 biji oren yang dipilih adalah busuk.
[4 marks]
[4 markah]
24
Answer : (a)………………………………… 3
(b)… ………………………………
_________________________________________________________
25.Diagram 25 shows a standard normal distribution graph.
[See overleaf
3472/1 SULIT
16. SULIT 20
Rajah 25 menunjukkan suatu graf taburan normal piawai.
f(z))
0.8858
-k k z
Diagram 25
Rajah 25
The probability represented by the area of the shaded region is 0.8858.
Kebarangkalian yang diwakili sebagai luas kawasan berlorek ialah
0.8858.
(a) Find the value of P( Z > k )
Cari nilai bagi P( Z > k )
(b) X is a continuous random variable which is normally distributed with
a mean of µ and a variance of 4.
If the value of X is 85 when the Z-score is k, find the value of µ .
X adalah pembolehubah rawak selanjar yang bertabur secara
normal mempunyai min, µ dan varians, 4, cari nilai bagi µ .
25 [3 marks]
3
Answer : (a)…………………………………
(b)… ………………………………
______________________________________________________________
END OF QUESTION PAPER
INFORMATION FOR CANDIDATES
3472/1 SULIT
17. SULIT 21 3472/1
1. This question paper consists of 25 questions.
2. Answer all questions.
3. Give only one answer for each question.
4. Write your answers in the spaces provided in this question paper.
5. Show your working. It may help you to get marks.
6. If you wish to change your answer, cross out the answer that you have done. Then write
down the new answer.
7. The diagrams in the questions provided are not drawn to scale unless stated.
8. The marks allocated for each question are shown in brackets.
9. A list of formulae is provided on pages 2 to 4.
10. Four-figure mathematical tables are allowed.
11. You may use a non-programmable scientific calculator.
12. Hand in this question paper to the invigilator at the end of the examination.
MAKLUMAT UNTUK CALON
1. Kertas soalan ini mengandungi 25 soalan.
2. Jawab semua soalan.
3. Bagi setiap soalan beri satu jawapan sahaja.
4. Jawapan anda hendaklah ditulis pada ruang yang disediakan dalam kertas soalan ini.
5. Tunjukkan langkah-langkah penting dalam kerja mengira anda. Ini boleh membantu anda
untuk mendapatkan markah.
6. Jika anda hendak menukar jawapan, batalkan dengan kemas jawapan yang telah dibuat.
Kemudian tulis jawapan yang baharu.
7. Rajah yang mengiringi soalan tidak dilukis mengikut skala kecuali dinyatakan.
8. Markah yang diperuntukkan bagi setiap soalan ditunjukkan dalam kurungan.
9. Satu senarai rumus disediakan di halaman 2 hingga 4.
10. Buku sifir matematik empat angka dibenarkan.
11. Anda dibenarkan menggunakan kalkulator saintifik yang tidak boleh diprogram.
12. Serahkan kertas soalan ini kepada pengawas peperiksaan pada akhir peperiksaan.
[See overleaf
3472/1 SULIT