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This document is a mark scheme for an Additional Math exam containing 25 questions. It provides the answers and working for each question worth 1-3 marks. The questions cover topics such as algebra, calculus, probability, and statistics. In general, the mark scheme aims to show the steps required to earn marks for solving problems that are typical exam questions in Additional Mathematics.
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The document discusses the benefits of exercise for mental health. Regular physical activity can help reduce anxiety and depression and improve mood and cognitive functioning. Exercise causes chemical changes in the brain that may help protect against mental illness and improve symptoms.
This document is a marking scheme for an Additional Mathematics exam paper. It provides the solutions to questions 1 through 15 on the paper and assigns marks to each part of each question's solution. For multiple part questions, each part is assigned marks. The highest number of marks given for a single part is 7. Overall, this marking scheme evaluates students' work on an Additional Mathematics exam and is used to determine marks and grades for their performance.
This document is a past year exam paper for Additional Mathematics. It consists of 3 sections - Section A with 6 multiple choice questions worth a total of 40 marks, Section B with 4 structured questions worth a total of 40 marks, and Section C with 2 essay questions worth a total of 20 marks. The document provides relevant formulae, instructions for candidates, diagrams, questions, and spaces for working. It tests students' knowledge and skills in algebra, calculus, geometry, trigonometry and statistics.
This document contains a marking scheme for an Additional Mathematics Paper 1 exam with 25 questions. It provides the solutions, workings, and marks allocated for each question. The marking scheme is intended to guide teachers in accurately and consistently marking student exam papers based on the model answers and steps provided.
Dokumen tersebut memberikan peraturan pemarkahan untuk soal tambahan matematika Sijil Pelajaran Malaysia tahun 2014. Dokumen tersebut merupakan dokumen rahasia dan meliputi 16 halaman tentang pedoman penilaian soal-soal ujian.
Dokumen tersebut memberikan informasi tentang peraturan pemarkahan untuk soal tambahan matematika Sijil Pelajaran Malaysia tahun 2013. Dokumen tersebut merupakan dokumen rahasia dan meliputi 14 halaman tentang pedoman penilaian soal-soal.
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Dokumen tersebut berisi petunjuk pemarkahan untuk soal tambahan matematika dalam ujian Sijil Pelajaran Malaysia. Dokumen tersebut merupakan dokumen rahasia dan hak ciptanya dimiliki oleh JUJ Pahang.
Spm 2014 add math modul sbp super score [lemah] k2 set 3 dan skema
1. MODUL SUPER SCORE SBP 2014
KERTAS 2
SET 3
NAMA : MARKAH
TARIKH :
Answer all questions.
Jawab semua soalan.
1. Solve the following simultaneous equations k – h = 2 and k 2 + 2h 2 = 9.
Give the answers correct to three decimal places. [5 marks]
Selesaikan persamaan serentak k – h = 2 dan k 2 + 2h 2 = 9.
Beri jawapan betul kepada tiga tempat perpuluhan. [5 markah]
2. (a) Sketch the graph of y = 1 - cos 2x for 0 x 2π. [4 marks]
Lakar graf bagi y = 1 - kos 2x untuk 0 x 2π. [4 markah]
(b) Hence, using the same axes, sketch a suitable straight line to find the number of solutions for
x
cos x for 0 x 2π. State the number of solutions. [3 marks]
the equation 1 2
1
2
Seterusnya, dengan menggunakan paksi yang sama, lakar satu garis lurus yang sesuai untuk
mencari bilangan penyelesaian bagi persamaan x
1 2
1
2
cos x
untuk 0 x 2π.
Nyatakan bilangan penyelesaian ini. [3 markah]
3. The table shows the values of two variables, x and y, obtained from an experiment. Variables x
a b
y x
and y are related by the equation 3
, where a and b are constants.
Jadual menunjukkan nilai-nilai bagi dua pembolehubah, x dan y, yang diperoleh daripada satu
a b
y x
eksperimen . Pembolehubah x dan y dihubungkan oleh persamaan 3
, dengan keadaan a
dan b ialah pemalar.
x 1.5 2 2.5 3 5 8
y 2.503 0.741 0.556 0.476 0.351 0.312
(a) Based on the above table, construct a table for the values of
1
x
and
1
y
. [2 marks]
Berdasarkan jadual di atas, bina satu jadual bagi nilai-nilai
1
x
dan
1
y
. [2 markah]
(b) Plot
1
y
against
1
x
, using a scale of 2 cm to 0.1 unit on the
1
x
-axis and 2 cm to 0.5 unit on the
1
y
-axis. Hence, draw the line of best fit. [3 marks]
Plot
1
y
melawan
1
x
, dengan menggunakan skala 2 cm kepada 0.1 unit pada paksi-
1
x
dan
2 cm kepada 0.5 unit pada paksi-
1
y
. Seterusnya, lukis garis lurus penyuaian terbaik.
[3 markah]
2. MODUL SUPER SCORE SBP 2014
(c) Use the graph in (b) to find the value of
Gunakan graf di (b) untuk mencari nilai
(i) a
(ii) b
[5 marks]
[5 markah]
4. Diagram 4 shows a trapezium OPQR where OQ and PR intersect at T. OR is paralles to PQ such
that PQ OR 2 . Given that x OR 6 and y OQ 3 .
Rajah 4 menunjukkan trapezium OPQR dengan keadaan OQ dan PR bersilang di T. OR adalah
selari dengan PQ supaya PQOR2 . Diberi bahawa x OR 6 dan y OQ3 .
R
Q
T
Express in terms of x and y
Ungkapkan dalam sebutan x dan y
(a) QR
(b) RP
(c) OP
Diagram / Rajah 4
[4 marks / markah]
O
P
5. (a) In an examination, 65% of the candidates passed the examination. If a sample of 8 candidates
is chosen randomly, find the probability that exactly 5 of them passed the examination.
[2 marks]
Dalam satu peperiksaan, 65% daripada calon yang menduduki peperiksaan itu lulus. Jika
sampel 8 orang calon dipilih secara rawak, cari kebarangkalian bahawa tepat 5 orang calon
lulus peperiksaan itu. [2 markah]
(b) The height, in cm, of the students in a certain school is found to be normally distributed with
mean 160 cm and variance 144 cm2. Find the probability that the height of the students
chosen randomly is less than 155 cm. [2 marks]
Tinggi, dalam cm, bagi pelajar di sebuah sekolah didapati bertabur secara normal dengan
min 160 cm dan varians 144cm2. Cari kebarangkalian bahawa tinggi pelajar yang dipilih
secara rawak adalah kurang daripada 155 cm. [2 markah]
6. Table shows the price indices for three items D, E and F, used in the production of a type of shoe.
Jadual menunjukkan indeks harga bagi tiga bahan D, E dan F, digunakan dalam pengeluaran
sejenis kasut.
3. MODUL SUPER SCORE SBP 2014
Item
Bahan
Price index in the year 2006
based on the year 2004
Indeks harga pada tahun 2006
berasaskan tahun 2004
Price index in the year 2008
based on the year 2004
Indeks harga pada tahun 2008
berasaskan tahun 2004
D 121 130
E 114 x
F y 150
(a) Find the price index of item D in the year 2008 based on the year 2006. [2 marks]
Cari indeks harga bagi bahan D pada tahun 2008 berasaskan tahun 2006. [2 markah]
(b) The price of item E in the year 2004 is RM 7.50 and its price in the year 2008 is RM10.50.
Find
Harga bagi bahan E pada tahun 2004 ialah RM7.50 dan harganya pada tahun 2008 ialah
RM10.50. Cari
(i) the value of x,
nilai x,
(ii) the price of item E in the year 2006.
Harga bahan E pada tahun 2006.
[3 marks]
[3 markah]
(c) The composite index for the production cost of the shoe in the year 2006 based on the year
2004 is 115.7. The cost of the item D, E and F are in ratio of 5 : 2 : 3. Find the value of y.
[3 marks]
Indeks gubahan bagi kos pengeluaran kasut tersebut pada tahun 2006 berasaskan tahun 2004
ialah 115.7. Kos bagi bahan D, E dan F adalah dalam nisbah 5 : 2 : 3. Cari nilai y.
[3 markah]
(d) Given the price of the shoe in the year 2006 is RM147.40. Find the corresponding price of the
shoe in the year 2004. [2 marks]
Diberi harga kasut tersebut pada tahun 2006 ialah RM147.40. Cari harga yang sepadan bagi
kasut tersebut pada tahun 2004. [2 markah]
7. Diagram shows a triangle PQR. QRS = 30° and QSR is an obtuse angle.
Rajah menunjukkan sebuah segi tiga PQR. QRS = 30° dan QSR adalah sudut cakah.
(a) Calculate,
10 cm
8 cm
P
Q
R
S
4. MODUL SUPER SCORE SBP 2014
Hitungkan,
(i) QSR,
(ii) the length, in cm, of PR,
panjang, dalam cm, bagi PR,
(iii) the area, in cm2, of the QSR .
luas, dalam cm2, bagi QSR .
(b) Point R’ lies on the line QR such that RS = R’S.
Titik R’ berada di atas garis QR supaya RS = R’S.
(i) Sketch the triangle QR’S,
Lak arkan segi tiga QR’S,
(ii) State QR’S.
Nyatakan QR’S.
[10 marks]
[10 markah]
5. MODUL SUPER SCORE SBP 2014
Jawapan/Answer :
No Answer
1
x = h = 0.786, 2.120; k = 2.786, 0.120
2
4
a ) QR 3 y
6
x
b ) RP 3 y
9
x
c ) OP 3 y
3
x
5
2786. 0 ) a
3 384 . 0 ) b
6
a) 107.44
b) (i) 140 (ii) RM8.55
c) y = 108
d) RM 127.40
7
x
(a) (i) 141.318° (ii) 14.905 (iii) 6.038
(b) (i) (ii) 150°
S R
R’
Q
Answer 3:
(a)
1
x
0.67 0.50 0.40 0.33 0.20 0.13
1
y
0.40 1.35 1.80 2.10 2.85 3.21
Y =
1
, X =
y
1
x
a
y
=
b
x
+ 3
1
2
y
y 1 cos2x
x
y
2
1
0
π 2π
Number of solution is 4
6. MODUL SUPER SCORE SBP 2014
a(
1
) = b(
y
1
) + 3
x
1
y
b
= ) (
a
1
x
+
3
a
Y = mX + c m =
b
, c =
a
3
a
(b)
1
y
(c)(i) y – intercept =
3
a
3.85 =
3
a
, a = 0.7792
(c)(ii) gradient =
b
a
–5.2037 =
b
0.7792
b = –4.0547
4.50
4.00
3.50
3.00
2.50
2.00
1.50
1.00
0.50
0.00
21. 3 40. 0
0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00
1
x
y-intercept, c = 3.85 Gradient, m =
13. 0 67. 0
= –5.2037